TY - JOUR TI - Nonnegative matrix factorization and applications AU - Chu, Moody T. AU - Plemmons, R. T2 - IMAGE DA - 2005/// PY - 2005/// VL - 34 SP - 1–5 ER - TY - RPRT TI - Optimality, Computation and Interpretation of nonnegative matrix factorizations AU - Chu, Moody T. AU - Diele, F. AU - Plemmons, R. AU - Ragni, S. DA - 2005/// PY - 2005/// M3 - Preprint ER - TY - JOUR TI - Nonnegative matrix factorization and applications T2 - IMAGE DA - 2005/// PY - 2005/// UR - https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=73a543613d5eee22fd0172f5c1397ac23d8c09c0 ER - TY - JOUR TI - Nonnegative Matrix Factorization And Applications AU - Chu, Moody AU - Plemmons, Robert DA - 2005/// PY - 2005/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.7507 ER - TY - JOUR TI - Immersed finite element for elasticity system with discontinuities AU - Li, Zhilin AU - Yang, X. T2 - AMS Contemporary Mathematics DA - 2005/// PY - 2005/// VL - 383 SP - 285–298 ER - TY - CHAP TI - Explicit construction of the hilbert class fields of imaginary quadratic fields with class numbers 7 and 11 AU - Kaltofen, Erich AU - Yui, Noriko T2 - EUROSAM 84 PY - 2005/12/1/ DO - 10.1007/bfb0032853 SP - 310-320 OP - PB - Springer-Verlag SN - 354013350X UR - http://dx.doi.org/10.1007/bfb0032853 DB - Crossref ER - TY - CHAP TI - Discretize then Optimize AU - Betts, J.T. AU - Campbell, S.L. T2 - Mathematics for industry : challenges and frontiers : a process view: practice and theory A2 - Ferguson, D.R. A2 - Peters, T.J. PY - 2005/// PB - SIAM Publications SN - 9780898715989 ER - TY - CONF TI - The role of model formulation in DAE integration: Experience gained in developing Scicos AU - Najafi, M. AU - Nikoukhah, R. AU - Campbell, S.L. T2 - IMACS World congress A2 - Dangoumau, N. A2 - Benrejeb, M. A2 - Borne, P. C2 - 2005/// C3 - 17th IMACS world congress on scientific computation, applied mathematics and simulation: Paris, France, July 11-15, 2005 CY - Paris, France DA - 2005/// PY - 2005/7/11/ PB - École centrale de Lille ER - TY - CONF TI - Direct Transcription Solution of Higher-Index Optimal Control Problems AU - Engelsone, A. AU - Campbell, S.L. AU - Betts, J.T. T2 - IMACS World congress A2 - Dangoumau, Nathalie A2 - Benrejeb, Mohamed A2 - Borne, Pierre C2 - 2005/// C3 - 17th IMACS world congress on scientific computation, applied mathematics and simulation: Paris, France, July 11-15, 2005 CY - Paris, France DA - 2005/// PY - 2005/7/11/ PB - École centrale de Lille ER - TY - BOOK TI - Numerical Analysis and Its Applications T2 - Lecture Notes in Computer Science A3 - Li, Zhilin A3 - Vulkov, Lubin A3 - Waśniewski, Jerzy DA - 2005/// PY - 2005/// DO - 10.1007/b106395 M1 - 3401 PB - Springer SN - 9783540249375 9783540318521 UR - http://dx.doi.org/10.1007/b106395 ER - TY - MGZN TI - Why aren’t SIAM conferences cheaper? AU - Ipsen, I.C.F. T2 - SIAM News DA - 2005/1// PY - 2005/1// VL - 38 SP - 1 M1 - 1 ER - TY - JOUR TI - Basic Polyhedra in Knot Theory T2 - Kragujevac Journal of Mathematics DA - 2005/// PY - 2005/// VL - 28 SP - 155–164 ER - TY - JOUR TI - The Fourth World Congress of Nonlinear Analysts: Modelling, control and analysis of coupled problems, processes and phenomena AU - V.N. Melnik, Roderick AU - Smith, Ralph AU - Shillor, Meir T2 - Nonlinear Analysis: Theory, Methods & Applications DA - 2005/11// PY - 2005/11// DO - 10.1016/j.na.2005.01.041 VL - 63 IS - 5-7 SP - e1421-e1423 J2 - Nonlinear Analysis: Theory, Methods & Applications LA - en OP - SN - 0362-546X UR - http://dx.doi.org/10.1016/j.na.2005.01.041 DB - Crossref ER - TY - CONF TI - A new generation of iterative transform algorithms for phase contrast tomography AU - Bauschke, H.H. AU - Combettes, P.L. AU - Luke, D.R. T2 - Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing AB - Improvements in electromagnetic sources, detectors, optical components, and computational imaging have made it possible to achieve three-dimensional atomic-scale resolution using tomographic phase-contrast imaging techniques. These greater capabilities have placed a premium on improving the efficiency and stability of phase retrieval algorithms for recovering the missing phase information in diffraction observations. In some cases, so called direct methods suffice, but, for large macromolecules and nonperiodic structures, one must rely on numerical techniques for reconstructing the missing phase. This is the principal motivation of our work. We report on recent progress in algorithms for iterative phase retrieval. The theory of convex optimisation is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged alternating reflectors and determine the fundamental mathematical properties of the related operator in the convex case. Numerical studies support our theoretical observations and demonstrate the effectiveness of the newer generation of algorithms compared to the current state of the art. C2 - 2005/// C3 - Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing CY - Philadelphia, PA DA - 2005/// PY - 2005/3/19/ DO - 10.1109/ICASSP.2005.1415952 VL - 4 SP - 89–92 ER - TY - CONF TI - Éclatement des contraintes en reconstruction tomographique AU - Capricelli, T.D. AU - Combettes, P.L. T2 - Actes du Vingtième Colloque GRETSI sur le Traitement du Signal et des Images C2 - 2005/9/6/ CY - Louvain-la-Neuve, Belgium DA - 2005/9/6/ PY - 2005/9/6/ ER - TY - CONF TI - A forward-backward algorithm for image restoration with sparse representations AU - Chaux, C. AU - Combettes, P.L. AU - Pesquet, J.-C. AU - Wajs, V.R. T2 - Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations C2 - 2005/// C3 - Proceedings of the International Conference on Signal Processing with Adaptative Sparse Structured Representations CY - Rennes, France DA - 2005/// PY - 2005/11/16/ SP - 49–52 ER - TY - JOUR TI - The asymptotic behavior of the composition of two resolvents AU - Bauschke, H AU - Combettes, P AU - Reich, S T2 - Nonlinear Analysis AB - The asymptotic behavior of the composition of two resolvents in a Hilbert space is investigated. Connections are made between the solutions of associated monotone inclusion problems and their dual versions. The applications provided include a study of an alternating minimization procedure and a new proof of von Neumann's classical result on the method of alternating projections. DA - 2005/1// PY - 2005/1// DO - 10.1016/S0362-546X(04)00344-X VL - 60 IS - 2 SP - 283-301 J2 - Nonlinear Analysis LA - en OP - SN - 0362-546X UR - http://dx.doi.org/10.1016/S0362-546X(04)00344-X DB - Crossref ER - TY - JOUR TI - Quantifying Vasculature: New Measures Applied to Arterial Trees in the Quail Chorioallantoic Membrane AU - Lubkin, Sharon R. AU - Funk, Sarah E. AU - Sage, E. Helene T2 - Journal of Theoretical Medicine AB - A wide variety of measures is currently in use in the morphometry of vascular systems. We introduce two additional classes of measures based on erosions and dilations of the image. Each measure has a clear biological interpretation in terms of the measured structures and their function. The measures are illustrated on images of the arterial tree of the quail chorioallantoic membrane (CAM). The new measures are correlated with widely-used measures, such as fractal dimension, but allow a clearer biological interpretation. To distinguish one CAM arterial tree from another, we propose reporting just three independent, uncorrelated numbers: (i) the fraction of tissue which is vascular ( VF 0 , a pure ratio), (ii) a measure of the typical distance of the vascularized tissue to its vessels ( CL , a length), and (iii) the flow capacity of the tissue ( P , an area). An unusually large CL would indicate the presence of large avascular areas, a characteristic feature of tumor tissue. CL is inversely highly correlated with fractal dimension of the skeletonized image, but has a more direct biological interpretation. DA - 2005/// PY - 2005/// DO - 10.1080/10273660500264684 VL - 6 IS - 3 SP - 173-180 J2 - Journal of Theoretical Medicine LA - en OP - SN - 1027-3662 1607-8578 UR - http://dx.doi.org/10.1080/10273660500264684 DB - Crossref ER - TY - CONF TI - Generic matrix multiplication and memory management in linBox AU - Kaltofen, Erich AU - Morozov, Dmitriy AU - Yuhasz, George T2 - the 2005 international symposium AB - We describe the design and implementation of two components in the LinBox library. The first is an implementation of black box matrix multiplication as a lazy matrix-times-matrix product. The implementation uses template meta-programming to set the intermediate vector type used during application of the matrix product. We also describe an interface mechanism that allows incorporation of external components with native memory management such as garbage collection into LinBox. An implementation of the interface based on SACLIB's field arithmetic procedures is presented. C2 - 2005/// C3 - Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05 DA - 2005/// DO - 10.1145/1073884.1073915 PB - ACM Press SN - 1595930957 UR - http://dx.doi.org/10.1145/1073884.1073915 DB - Crossref ER - TY - CONF TI - On the complexity of factoring bivariate supersparse (Lacunary) polynomials AU - Kaltofen, Erich AU - Koiran, Pascal T2 - the 2005 international symposium AB - We present algorithms that compute the linear and quadratic factors of supersparse (lacunary) bivariate polynomials over the rational numbers in polynomial-time in the input size. In supersparse polynomials, the term degrees can have hundreds of digits as binary numbers. Our algorithms are Monte Carlo randomized for quadratic factors and deterministic for linear factors. Our approach relies on the results by H. W. Lenstra, Jr., on computing factors of univariate supersparse polynomials over the rational numbers. Furthermore, we show that the problem of determining the irreducibility of a supersparse bivariate polynomial over a large finite field of any characteristic is co-NP-hard via randomized reductions. C2 - 2005/// C3 - Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05 DA - 2005/// DO - 10.1145/1073884.1073914 PB - ACM Press SN - 1595930957 UR - http://dx.doi.org/10.1145/1073884.1073914 DB - Crossref ER - TY - CONF TI - Computation of consistent initial conditions for multi-mode DAEs: application to Scicos AU - Najafi, M. AU - Nikoukhah, R. AU - Campbell, S.L. T2 - 2004 IEEE International Symposium on Computer Aided Control Systems Design AB - Scicos, which can simulate hybrid systems, has been extended to include some types of implicit models. This results in multi-mode DAEs. Switching from one model to another requires robust and efficient reinitialization. This paper discusses some of the special problems faced in the simulation of multi-model DAEs and proposes two solutions for finding consistent initial conditions. These methods are designed to take advantage of the data and algorithms available in Scicos C2 - 2005/3/21/ C3 - 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) DA - 2005/3/21/ DO - 10.1109/cacsd.2004.1393863 PB - IEEE SN - 0780386361 UR - http://dx.doi.org/10.1109/cacsd.2004.1393863 DB - Crossref ER - TY - CONF TI - A comparison of optimal and suboptimal auxiliary signal design approaches for robust failure detection AU - Choe, D. AU - Campbell, Stephen L. AU - Nikoukhah, R. T2 - 2005 IEEE Conference on Control Applications, 2005. CCA 2005. AB - Recently a new approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals was introduced. This approach involved offline computation of an auxiliary signal and online application of the detection and identification test. The theory and algorithms include optimization over a parameter beta. By considering a modification of the original problem it is possible to avoid this parameter and solve a related but different problem which is more of a standard robust control problem. This modification provides a suboptimal solution of the original problem and would appear to greatly speed up the algorithms. This paper provides the first examination of the effect of ignoring the parameter beta. We provide examples showing that the more usual robust control approach cannot solve some problems that the new approach can. We also provide insight into when the simpler algorithm can be used and what is the cost in doing so C2 - 2005/9/12/ C3 - Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005. DA - 2005/9/12/ DO - 10.1109/cca.2005.1507340 PB - IEEE SN - 0780393546 UR - http://dx.doi.org/10.1109/cca.2005.1507340 DB - Crossref ER - TY - JOUR TI - Problems and techniques AU - Ipsen, I. T2 - SIAM Review DA - 2005/// PY - 2005/// VL - 47 IS - 4 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-28244444106&partnerID=MN8TOARS ER - TY - CONF TI - Auxiliary Signal Design for Robust Failure Detection: A Case Study AU - Choe, D. AU - Campbell, S.L. AU - Nikoukhah, R. T2 - 2005 International Conference on Control and Automation AB - Recently an approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals was introduced. This approach involved offline computation of an auxiliary signal and online application of the detection and identification test software has been developed to carry out this approach. This paper provides the first careful case study investigating a number of issues related to use of this software. Guidelines for users and suggestions for improvement are presented. C2 - 2005/11/15/ C3 - 2005 International Conference on Control and Automation DA - 2005/11/15/ DO - 10.1109/icca.2005.1528269 PB - IEEE SN - 0780391373 UR - http://dx.doi.org/10.1109/icca.2005.1528269 DB - Crossref ER - TY - JOUR TI - Generalized cluster complexes and Coxeter combinatorics AU - Fomin, Sergey AU - Reading, Nathan T2 - International Mathematics Research Notices AB - We introduce and study a family of simplicial complexes associated to an arbitrary finite root system and a nonnegative integer parameter m. For m = 1, our construction specializes to the (simplicial) generalized associahedra or, equivalently, to the cluster complexes for the cluster algebras of finite type. Our computation of the face numbers and h-vectors of these complexes produces the enumerative invariants defined in other contexts by C. A. Athanasiadis, suggesting links to a host of well-studied problems in algebraic combinatorics of finite Coxeter groups, root systems, and hyperplane arrangements. Recurrences satisfied by the face numbers of our complexes lead to combinatorial algorithms for determining Coxeter-theoretic invariants. That is, starting with a Coxeter diagram of a finite Coxeter group, one can compute the Coxeter number, the exponents, and other classical invariants by a recursive procedure that only uses most basic graph-theoretic concepts applied to the input diagram. DA - 2005/// PY - 2005/// DO - 10.1155/IMRN.2005.2709 VL - 2005 IS - 44 SP - 2709–2757 UR - https://doi.org/10.1155/IMRN.2005.2709 ER - TY - CONF TI - Estimating first-order finite-difference information in image restoration problems AU - Combettes, P.L. AU - Pesquet, J. T2 - 2004 International Conference on Image Processing, 2004. ICIP '04. AB - First-order finite-difference information has been exploited in a variety of image and signal restoration settings. These approaches typically require - implicitly or explicitly - that certain attributes of the finite-difference images be known a priori. We propose a new statistical framework in which such attributes are estimated a posteriori from the observed data under the assumption that the noise is additive and Gaussian. Our analysis can be directly applied to the construction of property sets in set theoretic estimation methods. The proposed framework is illustrated through an application to image denoising. C2 - 2005/4/19/ C3 - 2004 International Conference on Image Processing, 2004. ICIP '04. CY - Singapore DA - 2005/4/19/ PY - 2004/10/24/ DO - 10.1109/icip.2004.1418755 PB - IEEE SN - 0780385543 UR - http://dx.doi.org/10.1109/icip.2004.1418755 ER - TY - CONF TI - Theoretical analysis of some regularized image denoising methods AU - Combettes, P.L. AU - Wajs, V.R. T2 - 2004 International Conference on Image Processing, 2004. ICIP '04. AB - Regularization techniques have been in use in signal recovery for over four decades. In this paper, we propose a new synthetic approach to the study of regularization methods in image denoising problems based on Moreau's proximity operators. We exploit the remarkable properties enjoyed by these operators to establish in a systematic fashion a variety of properties of regularized denoising problems and to propose new numerical schemes to solve them. C2 - 2005/4/19/ C3 - 2004 International Conference on Image Processing, 2004. ICIP '04. CY - Singapore DA - 2005/4/19/ PY - 2004/10/24/ DO - 10.1109/icip.2004.1419462 PB - IEEE SN - 0780385543 UR - http://dx.doi.org/10.1109/icip.2004.1419462 ER - TY - JOUR TI - Parallel Block-Iterative Reconstruction Algorithms for Binary Tomography AU - Capricelli, Thomas D. AU - Combettes, Patrick L. T2 - Electronic Notes in Discrete Mathematics AB - A convex programming approach to binary tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with new constraints on the sinogram. A convex objective is then minimized over the resulting feasibility set via a parallel block-iterative method. The new constraints involve noise-based confidence regions and a binarity-promoting total variation constraint. DA - 2005/7// PY - 2005/7// DO - 10.1016/j.endm.2005.05.068 VL - 20 SP - 263-280 J2 - Electronic Notes in Discrete Mathematics LA - en OP - SN - 1571-0653 UR - http://dx.doi.org/10.1016/j.endm.2005.05.068 DB - Crossref ER - TY - JOUR TI - Equilibrium programming in Hilbert spaces AU - Combettes, P.L. AU - Hirstoaga, S.A. T2 - Journal of Nonlinear and Convex Analysis DA - 2005/4// PY - 2005/4// VL - 6 IS - 1 SP - 117–136 ER - TY - CONF TI - Numerical Solution of the Nonlinear Helmholtz Equation Using Nonorthogonal Expansions AU - Fibich, G. AU - Tsynkov, S. V. C2 - 2005/// C3 - Proceedings of the 7th International Conference on Mathematical and Numerical Aspects of Wave Propagation, WAVES 2005, Brown University, Providence, RI, June 20 -- 24, 2005 DA - 2005/// SP - 379-381 ER - TY - CONF TI - Terahertz-Frequency Quantum Oscillator Operating in the Positive Differential Resistance Region AU - Zhao, P AU - Woolard, D L AU - Lasater, M S AU - Kelley, C T T2 - North Carolina State University, Center for Research in Scientific Computation C2 - 2005/// C3 - Proceedings of SPIE Defense and Security Symposium 2005: Terahertz for Military & Security Application III, paper number 5790-34 DA - 2005/// VL - 5790 SP - 289-300 ER - TY - RPRT TI - Multilevel wavelet solver for the Ornstein-Zernike equation AU - Federov, M V AU - Chuev, G N AU - Kelley, C T AU - Pettitt, B Montgomery A3 - North Carolina State University, Center for Research in Scientific Computation DA - 2005/1// PY - 2005/1// M1 - CRSC-TR05-07 PB - North Carolina State University, Center for Research in Scientific Computation SN - CRSC-TR05-07 ER - TY - JOUR TI - Problems and Techniques AU - Ipsen, Ilse T2 - SIAM Review AB - Suppose you are a bicycle messenger in the busy business district of a large city. Here is what your day looks like: You are to deliver incoming mail to building i, and you are to pick up outgoing mail destined only for building i + 1. All in all you are responsible for m buildings. Your bike, however, is not of the highest quality: It can accommodate only mail for a single delivery. Riding from building i to building j requires tij minutes. Once you arrive at a building, you need d minutes to get off your bike, run into the building, and get onto your bike again. Moreover, once incoming mail has arrived at building i, it takes pi minutes for the outgoing mail to be ready (if this is too long, you may want to make another delivery and pickup in the meantime). You are to visit each building k times. Question: In which order should you visit the buildings so that you finish your work as fast as possible? The above description is a simplified version of the problem discussed in the paper by Milind W. Dawande, H. Neil Geismar, and Suresh P. Sethi. There the messenger is a robot, the buildings are machines, and the mail represents parts to be processed by the machines. The authors show that there exists a cyclic schedule that maximizes long-term throughput. Cyclic schedules are preferred in industrial environments, because they are easy to implement and control. Since the literature on robotic cell scheduling is full of different models for different kinds of industrial applications, it is important to know that all optimal schedules can be reduced to cyclic schedules. The authors end their paper by describing several challenging open problems. The paper by Miguel Torres-Torriti and Hannah Michalska describes a software package (LTP), implemented in Maple, for the symbolic manipulation of expressions that occur in the context of Lie algebra theory. This theory has found applications in classical and quantum mechanics, analysis of dynamical systems, construction of nonlinear filters, and the design of feedback control laws for nonlinear systems. Since the symbolic computations are often complex and tedious, the development of software for applications of Lie algebra theory is crucial. The LTP software package is targeted at applications such as solution of differential equations evolving on Lie groups, and structure analysis of general dynamical systems. DA - 2005/1// PY - 2005/1// DO - 10.1137/siread000047000004000707000001 VL - 47 IS - 4 SP - 707-707 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-28244444106&partnerID=MN8TOARS ER - TY - CHAP TI - Gröbner basis degree bounds on Tor•^K[Λ](k, k)• and discrete Morse theory for posets AU - Hersh, Patricia AU - Welker, Volkmar T2 - Integer Points in Polyhedra-geometry, number theory, algebra, optimization A2 - Barvinok, Alexander A2 - Beck, Matthias A2 - Haase, Christian A2 - Reznick, Bruce A2 - Welker, Volkmar T3 - Contemporary Mathematics PY - 2005/// DO - 10.1090/conm/374/06902 SP - 101-138 PB - American Mathematical Society SN - 9780821834596 9780821879641 SV - 374 ER - TY - JOUR TI - The asymptotic behavior of the composition of two resolvents AU - Bauschke, Heinz H. AU - Combettes, Patrick L. AU - Reich, Simeon T2 - Nonlinear Analysis: Theory, Methods & Applications AB - The asymptotic behavior of the composition of two resolvents in a Hilbert space is investigated. Connections are made between the solutions of associated monotone inclusion problems and their dual versions. The applications provided include a study of an alternating minimization procedure and a new proof of von Neumann's classical result on the method of alternating projections. DA - 2005/1// PY - 2005/1// DO - 10.1016/j.na.2004.07.054 VL - 60 IS - 2 SP - 283-301 J2 - Nonlinear Analysis: Theory, Methods & Applications LA - en OP - SN - 0362-546X UR - http://dx.doi.org/10.1016/j.na.2004.07.054 DB - Crossref KW - duality KW - firmly nonexpansive operator KW - gradient projection method KW - Hilbert space KW - monotone inclusion KW - monotone operator KW - proximal iteration KW - resolvent ER - TY - JOUR TI - Signal Recovery by Proximal Forward-Backward Splitting AU - Combettes, Patrick L. AU - Wajs, Valérie R. T2 - Multiscale Modeling & Simulation AB - We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s. DA - 2005/1// PY - 2005/1// DO - 10.1137/050626090 VL - 4 IS - 4 SP - 1168-1200 J2 - Multiscale Model. Simul. LA - en OP - SN - 1540-3459 1540-3467 UR - http://dx.doi.org/10.1137/050626090 DB - Crossref ER - TY - JOUR TI - Extrapolation algorithm for affine-convex feasibility problems AU - Bauschke, Heinz H. AU - Combettes, Patrick L. AU - Kruk, Serge G. T2 - Numerical Algorithms AB - The convex feasibility problem under consideration is to find a common point of a countable family of closed affine subspaces and convex sets in a Hilbert space. To solve such problems, we propose a general parallel block-iterative algorithmic framework in which the affine subspaces are exploited to introduce extrapolated over-relaxations. This framework encompasses a wide range of projection, subgradient projection, proximal, and fixed point methods encountered in various branches of applied mathematics. The asymptotic behavior of the method is investigated and numerical experiments are provided to illustrate the benefits of the extrapolations. DA - 2005/12/30/ PY - 2005/12/30/ DO - 10.1007/s11075-005-9010-6 VL - 41 IS - 3 SP - 239-274 J2 - Numer Algor LA - en OP - SN - 1017-1398 1572-9265 UR - http://dx.doi.org/10.1007/s11075-005-9010-6 DB - Crossref KW - affinite sets KW - convex feasibility problem KW - convex sets KW - extrapolation KW - Hilbert space KW - projection method ER - TY - CHAP TI - Fast explicit operator splitting method. Application to the polymer system AU - Chertock, A. AU - Kurganov, A. AU - Petrova, G. T2 - Finite Volumes for Complex Applications IV PY - 2005/// VL - IV SP - 63–72 PB - ISTE, London ER - TY - CHAP TI - Conservative locally moving mesh method for multifluid flows AU - Chertock, A. AU - Kurganov, A. T2 - Finite Volumes for Complex Applications IV PY - 2005/// SP - 273–284 PB - ISTE, London ER - TY - BOOK TI - Smart Material Systems: Model Development AU - Smith, R.C. DA - 2005/// PY - 2005/// PB - SIAM ER - TY - JOUR TI - Effective solution of linear Diophantine equation systems with an application in chemistry AU - Papp, Dávid AU - Vizvári, Béla T2 - Journal of Mathematical Chemistry DA - 2005/11/23/ PY - 2005/11/23/ DO - 10.1007/s10910-005-9001-9 VL - 39 IS - 1 SP - 15-31 J2 - J Math Chem LA - en OP - SN - 0259-9791 1572-8897 UR - http://dx.doi.org/10.1007/s10910-005-9001-9 DB - Crossref KW - decomposition of overall reaction KW - linear Diophantine equations KW - linear programming ER - TY - CONF TI - Rotation invariant topology coding of 2D and 3D objects using Morse theory AU - Baloch, S. AU - Krim, H. AU - Kogan, I. AU - Zenkov, D. T2 - rnational Conference on Image Processing AB - In this paper, we propose a numerical algorithm for extracting the topology of a three-dimensional object (2 dimensional surface) embedded in a three-dimensional space /spl Ropf//sup 3/. The method is based on capturing the topology of a modified Reeb graph by tracking the critical points of a distance function. As such, the approach employs Morse theory in the study of translation, rotation, and scale invariant skeletal graphs. The latter are useful in the representation and classification of objects in /spl Ropf//sup 3/. C2 - 2005/// C3 - IEEE International Conference on Image Processing 2005 DA - 2005/// DO - 10.1109/icip.2005.1530512 VL - 3 SP - 796-799 PB - IEEE SN - 0780391349 UR - http://dx.doi.org/10.1109/icip.2005.1530512 DB - Crossref ER - TY - JOUR TI - How to get SIAM cooperation for your meeting AU - Ipsen, I.C.F. T2 - SIAM News DA - 2005/3// PY - 2005/3// VL - 38 IS - 2 ER - TY - CONF TI - 3D object representation with topo-geometric shape models AU - Baloch, S. AU - Krim, H. AU - Kogan, I.A. AU - Zenkov, D.V. C2 - 2005/// C3 - Proceedings of European Signal Processing Conference (EUSIPCO) DA - 2005/// SP - 2386-2389 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84863687976&partnerID=MN8TOARS ER - TY - JOUR TI - The order dimension of Bruhat order on infinite Coxeter groups AU - Reading, Nathan AU - Waugh, Debra J. T2 - The Electronic Journal of Combinatorics DA - 2005/// PY - 2005/// VL - 11 IS - 2 SP - Research Paper 13, 26 UR - http://www.combinatorics.org/Volume_11/Abstracts/v11i2r13.html ER - TY - JOUR TI - Lattice congruences, fans and Hopf algebras AU - Reading, Nathan T2 - Journal of Combinatorial Theory, Series A AB - We give a unified explanation of the geometric and algebraic properties of two well-known maps, one from permutations to triangulations, and another from permutations to subsets. Furthermore we give a broad generalization of the maps. Specifically, for any lattice congruence of the weak order on a Coxeter group we construct a complete fan of convex cones with strong properties relative to the corresponding lattice quotient of the weak order. We show that if a family of lattice congruences on the symmetric groups satisfies certain compatibility conditions then the family defines a sub Hopf algebra of the Malvenuto–Reutenauer Hopf algebra of permutations. Such a sub Hopf algebra has a basis which is described by a type of pattern avoidance. Applying these results, we build the Malvenuto–Reutenauer algebra as the limit of an infinite sequence of smaller algebras, where the second algebra in the sequence is the Hopf algebra of non-commutative symmetric functions. We also associate both a fan and a Hopf algebra to a set of permutations which appears to be equinumerous with the Baxter permutations. DA - 2005/5// PY - 2005/5// DO - 10.1016/j.jcta.2004.11.001 VL - 110 IS - 2 SP - 237-273 J2 - Journal of Combinatorial Theory, Series A LA - en OP - SN - 0097-3165 UR - http://dx.doi.org/10.1016/j.jcta.2004.11.001 DB - Crossref KW - Coexter group KW - fan poset KW - hyperplane arrangement KW - Malvenuto-Reutenauer Hopf algebra KW - pattern avoidance KW - permutohedron KW - poset of regions KW - weak order ER - TY - JOUR TI - On optimizing discrete Morse functions AU - Hersh, Patricia T2 - Advances in Applied Mathematics AB - In 1998, Forman introduced discrete Morse theory as a tool for studying CW complexes by producing smaller, simpler-to-understand complexes of critical cells with the same homotopy types as the original complexes. This paper addresses two questions: (1) under what conditions may several gradient paths in a discrete Morse function simultaneously be reversed to cancel several pairs of critical cells, to further collapse the complex, and (2) which gradient paths are individually reversible in lexicographic discrete Morse functions on poset order complexes. The latter follows from a correspondence between gradient paths and lexicographically first reduced expressions for permutations. As an application, a new partial order on the symmetric group recently introduced by Remmel is proven to be Cohen–Macaulay. DA - 2005/9// PY - 2005/9// DO - 10.1016/j.aam.2005.04.001 VL - 35 IS - 3 SP - 294-322 J2 - Advances in Applied Mathematics LA - en OP - SN - 0196-8858 UR - http://dx.doi.org/10.1016/j.aam.2005.04.001 DB - Crossref ER - TY - JOUR TI - AU - Babson, Eric AU - Hersh, Patricia T2 - Transactions of the American Mathematical Society AB - This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with 0 ^ \hat {0} and 1 ^ \hat {1} from any lexicographic order on its maximal chains. Specifically, if we attach facets according to the lexicographic order on maximal chains, then each facet contributes at most one new face which is critical, and at most one Betti number changes; facets which do not change the homotopy type also do not contribute any critical faces. Dimensions of critical faces as well as a description of which facet attachments change the homotopy type are provided in terms of interval systems associated to the facets. As one application, the Möbius function may be computed as the alternating sum of Morse numbers. The above construction enables us to prove that the poset Π n / S λ \Pi _n/S_{\lambda } of partitions of a set { 1 λ 1 , , k λ k } \{ 1^{\lambda _1 },\dots ,k^{\lambda _k }\} with repetition is homotopy equivalent to a wedge of spheres of top dimension when λ \lambda is a hook-shaped partition; it is likely that the proof may be extended to a larger class of λ \lambda and perhaps to all λ \lambda , despite a result of Ziegler (1986) which shows that Π n / S λ \Pi _n/S_{\lambda } is not always Cohen-Macaulay. DA - 2005/2/1/ PY - 2005/2/1/ DO - 10.1090/s0002-9947-04-03495-6 VL - 357 IS - 02 SP - 509-535 J2 - Trans. Amer. Math. Soc. OP - SN - 0002-9947 UR - http://dx.doi.org/10.1090/s0002-9947-04-03495-6 DB - Crossref ER - TY - JOUR TI - Toric Ideals of Phylogenetic Invariants AU - Sturmfels, Bernd AU - Sullivant, Seth T2 - Journal of Computational Biology AB - Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety. Several widely used models for biological sequences have transition matrices that can be diagonalized by means of the Fourier transform of an abelian group. Their phylogenetic invariants form a toric ideal in the Fourier coordinates. We determine generators and Gröbner bases for these toric ideals. For the Jukes–Cantor and Kimura models on a binary tree, our Gröbner bases consist of certain explicitly constructed polynomials of degree at most four. DA - 2005/3// PY - 2005/3// DO - 10.1089/cmb.2005.12.204 VL - 12 IS - 2 SP - 204-228 J2 - Journal of Computational Biology LA - en OP - SN - 1066-5277 1557-8666 UR - http://dx.doi.org/10.1089/cmb.2005.12.204 DB - Crossref ER - TY - JOUR TI - Small Contingency Tables with Large Gaps AU - Sullivant, Seth T2 - SIAM Journal on Discrete Mathematics AB - We construct examples of contingency tables on n binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide evidence that linear programming may not be an effective heuristic for detecting disclosures when releasing margins of multiway tables. DA - 2005/1// PY - 2005/1// DO - 10.1137/s0895480104444090 VL - 18 IS - 4 SP - 787-793 J2 - SIAM J. Discrete Math. LA - en OP - SN - 0895-4801 1095-7146 UR - http://dx.doi.org/10.1137/s0895480104444090 DB - Crossref KW - disclosure limitation KW - integer programming KW - Grobner basis KW - contingency table ER - TY - JOUR TI - A level-set method for interfacial flows with surfactant AU - Xu, J. J. AU - Li, Zhilin AU - Lowengrub, J. AU - Zhao, H. K. T2 - Journal of Computational Physics AB - A level-set method for the simulation of fluid interfaces with insoluble surfactant is presented in two-dimensions. The method can be straightforwardly extended to three-dimensions and to soluble surfactants. The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao [J. Xu, H. Zhao. An Eulerian formulation for solving partial differential equations along a moving interface, J. Sci. Comput. 19 (2003) 573–594] with the immersed interface method originally developed by LeVeque and Li and [R. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (1994) 1019–1044] for solving the fluid flow equations and the Laplace–Young boundary conditions across the interfaces. Novel techniques are developed to accurately conserve component mass and surfactant mass during the evolution. Convergence of the method is demonstrated numerically. The method is applied to study the effects of surfactant on single drops, drop–drop interactions and interactions among multiple drops in Stokes flow under a steady applied shear. Due to Marangoni forces and to non-uniform Capillary forces, the presence of surfactant results in larger drop deformations and more complex drop–drop interactions compared to the analogous cases for clean drops. The effects of surfactant are found to be most significant in flows with multiple drops. To our knowledge, this is the first time that the level-set method has been used to simulate fluid interfaces with surfactant. DA - 2005/// PY - 2005/// DO - 10.1016/j.jcp.2005.07.016 VL - 212 IS - 2 SP - 590–616 KW - incompressible stokes flow KW - interfaces KW - insoluble surfactant KW - Marangoni force KW - capillary force KW - level set method KW - immersed interface method ER - TY - CONF TI - Sparse multidimensional representation using shearlets AU - Labate, D. AU - Lim, W. AU - Kutyniok, G. AU - Weiss, G. A2 - M. Papadakis, A. F. Laine A2 - Unser, M. A. AB - In this paper we describe a new class of multidimensional representation systems, called shearlets. They are obtained by applying the actions of dilation, shear transformation and translation to a fixed function, and exhibit the geometric and mathematical properties, e.g., directionality, elongated shapes, scales, oscillations, recently advocated by many authors for sparse image processing applications. These systems can be studied within the framework of a generalized multiresolution analysis. This approach leads to a recursive algorithm for the implementation of these systems, that generalizes the classical cascade algorithm. C2 - 2005/// C3 - Wavelets XI: 31 July-3 August, 2005, San Diego, California, USA DA - 2005/// DO - 10.1117/12.613494 SP - 254-262 PB - Bellingham, Wash. : SPIE SN - 0819459194 ER - TY - JOUR TI - Representations for the Drazin inverse of a 2 x 2 block matrix AU - Hartwig, R AU - Li, XZ AU - Wei, YM T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - Two representations for the Drazin inverse of a $2\times2$ block matrix $M=[{A \atop C}\;{B \atop D}]$, where A and D are square matrices, in terms of the Drazin inverses of A and D have been recently developed under the assumptions that $C(I-AA^{D})=0$ and $(I-AA^{D})B=0$, and that the generalized Schur complement $D-CA^{D}B$ is either nonsingular or zero. These two representations of $M^{D}$ are extended to the case where $C(I-AA^{D})=0$ and $(I-AA^{D})B=0$ are substituted with $C(I-AA^{D})B=0$ and $A(I-AA^{D})B=0$. Moreover, upper bounds for the index of M are studied. Numerical examples are given to illustrate the new results. DA - 2005/// PY - 2005/// DO - 10.1137/040606685 VL - 27 IS - 3 SP - 757-771 SN - 1095-7162 KW - index KW - Drazin inverse KW - generalized Schur complement KW - weighted Drazin inverse ER - TY - JOUR TI - A finite dimensional L-infinity algebra example in gauge theory AU - Daily, Marilyn AU - Lada, Tom T2 - HOMOLOGY HOMOTOPY AND APPLICATIONS AB - We construct an example of a finite dimensional $L_{\infty}$ algebra which is generated by a Lie algebra together with a non-Lie action on another vector space. We then show how this example fits into the gauge transformation theory of Berends, Burgers and Van Dam. DA - 2005/// PY - 2005/// DO - 10.4310/HHA.2005.v7.n2.a4 VL - 7 IS - 2 SP - 87-93 SN - 1532-0081 KW - finite dimensional L-infinity algebra KW - gauge algebras ER - TY - JOUR TI - Periodic solutions of nonlinear second-order difference equations AU - Rodriguez, Jesus AU - Etheridge, Debra Lynn T2 - ADVANCES IN DIFFERENCE EQUATIONS AB - We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by (t + 1) + cy(t) = f (y(t)), where f: ℝ → ℝ and β > 0 is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant uf (u) > 0 such that |u| ≥ β whenever c = 1. For such an equation we prove that if N is an odd integer larger than one, then there exists at least one N-periodic solution unless all of the following conditions are simultaneously satisfied: |b| < 2, N across-1(-b/2), and π is an even multiple of c ≠ 0. DA - 2005/// PY - 2005/// DO - 10.1155/ade.2005.173 IS - 2 SP - 173-192 SN - 1687-1839 ER - TY - JOUR TI - Global attractor of coupled difference equations and applications to Lotka-Volterra systems AU - Pao, C. V. T2 - ADVANCES IN DIFFERENCE EQUATIONS AB - This paper is concerned with a coupled system of nonlinear difference equations which is a discrete approximation of a class of nonlinear differential systems with time delays. The aim of the paper is to show the existence and uniqueness of a positive solution and to investigate the asymptotic behavior of the positive solution. Sufficient conditions are given to ensure that a unique positive equilibrium solution exists and is a global attractor of the difference system. Applications are given to three basic types of Lotka-Volterra systems with time delays where some easily verifiable conditions on the reaction rate constants are obtained for ensuring the global attraction of a positive equilibrium solution. DA - 2005/// PY - 2005/// DO - 10.1155/ade.2005.57 IS - 1 SP - 57-79 SN - 1687-1847 ER - TY - JOUR TI - L-2 semigroup and linear stability for Riemann solutions of conservation laws AU - Lin, X. B. T2 - Dynamics of Partial Differential Equations AB - Riemann solutions for the systems of conservation laws u +f(u) = 0 are self-similar solutions of the form u = u( = ). Using the change of vari- ables x = = ; t = ln( ), Riemann solutions become stationary to the system ut + (Df(u) xI)ux = 0. For the linear variational system around the Rie- mann solution with n-Lax shocks, we introduce a semigroup in the Hilbert space with weighted L 2 norm. We show that (A) the region consists of normal points only. (B) Eigenvalues of the linear system correspond to zeros of the determinant of a transcendental matrix. They lie on vertical lines in the complex plane. There can be resonance values where the response of the system to forcing terms can be arbitrarily large, see Denition 6.2. Resonance values also lie on vertical lines in the complex plane. (C) Solutions of the linear system are O(e t) for any constant that is greater than the largest real parts of the eigenvalues and the coordinates of resonance lines. This work can be applied to the linear and nonlinear stability of Riemann solutions of conserva- tion laws and the stability of nearby solutions of the Dafermos regularizations ut + (Df(u) xI)ux = u xx. DA - 2005/// PY - 2005/// DO - 10.4310/dpde.2005.v2.n4.a2 VL - 2 IS - 4 SP - 301-333 ER - TY - JOUR TI - Focal power AU - Hartwig, R. E. AU - Maroulas, J. T2 - Electronic Journal of Linear Algebra AB - The properties of a 2 × 2 blockmatrix M over a field for which (Mk)11 = (M)k11 are examined. This “fire-wall” property will be characterized by the vanishing of the sequence of moments Fi = CDiB. DA - 2005/// PY - 2005/// DO - 10.13001/1081-3810.1150 VL - 13 SP - 56-71 ER - TY - JOUR TI - Well-posedness in Maxwell systems with distributions of polarization relaxation parameters AU - Banks, HT AU - Gibson, NL T2 - APPLIED MATHEMATICS LETTERS AB - We present existence, uniqueness and continuous dependence (with respect to probability distributions on polarization parameters) of solutions in Maxwell systems. This provides a theoretical and computational foundation for associated inverse problems. DA - 2005/4// PY - 2005/4// DO - 10.1016/j.aml.2004.02.008 VL - 18 IS - 4 SP - 423-430 SN - 0893-9659 KW - well-posedness KW - Maxwell's equations with polarization KW - relaxation parameters ER - TY - JOUR TI - Parameter estimation techniques for a class of nonlinear hysteresis models AU - Smith, RC AU - Hatch, AG T2 - INVERSE PROBLEMS AB - This paper addresses the development of parameter estimation techniques for a class of models used to characterize hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials employed in a wide range of actuators and sensors. These models are formulated as integral equations with known kernels and unknown densities to be identified through least-squares techniques. Due to the compactness of the integral operators, the resulting discretized models inherit ill-posedness which must be accommodated through regularization. The accuracy of regularized finite-dimensional models is illustrated through comparison with experimental data. DA - 2005/8// PY - 2005/8// DO - 10.1088/0266-5611/21/4/011 VL - 21 IS - 4 SP - 1363-1377 SN - 1361-6420 ER - TY - JOUR TI - Equivalence of low-frequency stability conditions for multidimensional detonations in three models of combustion AU - Jenssen, HK AU - Lyng, G AU - Williams, M T2 - INDIANA UNIVERSITY MATHEMATICS JOURNAL AB - We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-Stokes (RNS) model, and the simpler Zeldovich-von Neumann-Doring (ZND) and Chapman-Jouguet (CJ) models. The determinants are functions of frequencies (‚;·), where ‚ is a complex variable dual to the time variable, and · 2 R di1 is dual to the transverse spatial variables. The zeros of these determinants in 0 correspond to perturbations that grow exponentially with time. The CJ determinant, ¢CJ(‚;·), turns out to be explicitly computable. The RNS and ZND determinants are impossible to compute explicitly, but we are able to compute their first-order low-frequency expansions with an error term that is uniformly small with re- spect to all possible (‚;·) directions. Somewhat surprisingly, this computation yields an Equivalence Theorem: the leading coecient in the expansions of both the RNS and ZND determinants is a constant multiple of ¢CJ! In this sense the low-frequency stability condi- tions for strong detonations in all three models are equivalent. By computing ¢CJ we are able to give low-frequency stability criteria valid for all three models in terms of the physical quantities: Mach number, Gruneisen coecient, compression ratio, and heat release. The Equivalence Theorem and its surrounding analysis is a step toward the rigorous theoretical justification of the CJ and ZND models as approximations to the full RNS model. DA - 2005/// PY - 2005/// DO - 10.1512/iumj.2005.54.2685 VL - 54 IS - 1 SP - 1-64 SN - 1943-5258 KW - multidimensional detonations KW - stability KW - Evans function ER - TY - JOUR TI - A homogenized energy model for hysteresis in ferroelectric materials: General density formulation AU - Smith, RC AU - Hatch, AG AU - Mukherjee, B AU - Liu, SF T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - In this article, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations that can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data. DA - 2005/9// PY - 2005/9// DO - 10.1177/1045389X05054789 VL - 16 IS - 9 SP - 713-732 SN - 1045-389X KW - hysteresis KW - ferroelectric materials KW - nonlinear constitutive relations ER - TY - JOUR TI - The McCormack model for gas mixtures: The temperature-jump problem AU - Siewert, CE T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK DA - 2005/3// PY - 2005/3// DO - 10.1007/s00033-004-3116-x VL - 56 IS - 2 SP - 273-292 SN - 0044-2275 KW - rarefied gas dynamics KW - temperature jump coefficient KW - binary gas mixture KW - discrete ordinates ER - TY - JOUR TI - Symmetric brace algebras AU - Lada, T AU - Markl, M T2 - APPLIED CATEGORICAL STRUCTURES AB - We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to examine the L∞-algebras that result from a particular gauge theory for massless particles of high spin. DA - 2005/8// PY - 2005/8// DO - 10.1007/s10485-005-0911-2 VL - 13 IS - 4 SP - 351-370 SN - 1572-9095 KW - brace algebra KW - strongly homotopy structure KW - gauge algebra ER - TY - JOUR TI - Sustainable global economic growth AU - Chukwu, EN T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS AB - This survey highlights some recent advances on modeling the economic state of some nations of the world which are linked up in solidarity and competition or which are isolated. The problem of controllability, convergence, and permanence are explored. Some practical recent policy implications are deduced. Earth revolves around the sun in approximately circular orbit with radius r=a, completing a revolution in the time T=2π(a3/GM)1/2 which is one earth year; here M is the mass of the sun and G is the universal gravitational constant. The gravitational force of the sun on the earth is given by GMm/r2 where m is the mass of the earth. Therefore, if the earth “stood still” losing its orbital velocity, it will fall straight on a line into the sun in accordance with Newton's second law.Md2rdt2=-GMMr2. If this calamity occurred what fraction of the normal year T will it take for the earth to splash into the sun?” (Nagle, Saff, Snider) “Why did the earth stand still?” (Ndu Udo) “The symbol of Love and the earth's lover is the moon. With joy it dances around the earth in a circular orbit. When the inhabitants of the earth prefer hate and revenge to love, the moon stops to love, and stands still, losing its orbital velocity. It falls straight on a line into the earth in accordance with Newton's second law. The crash makes the earth stand still precipitating the Armageddon.” (Wisdom Goodness) DA - 2005/11/30/ PY - 2005/11/30/ DO - 10.1016/j.na.2004.09.021 VL - 63 IS - 5-7 SP - 785-798 SN - 0362-546X KW - global economic growth KW - economic state KW - MATLAB KW - private and government strategies KW - interaction term KW - solidarity KW - competition matrix KW - controllability KW - omega problem ER - TY - JOUR TI - Stability and attractivity of periodic solutions of parabolic systems with time delays AU - Pao, CV T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS AB - This paper is concerned with the existence, stability, and global attractivity of time-periodic solutions for a class of coupled parabolic equations in a bounded domain. The problem under consideration includes coupled system of parabolic and ordinary differential equations, and time delays may appear in the nonlinear reaction functions. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. The existence of time-periodic solutions is for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement using Schauder fixed point theorem, while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme. The results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system. Applications are also given to three Lotka–Volterra reaction diffusion model problems, and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions. DA - 2005/4/15/ PY - 2005/4/15/ DO - 10.1016/j.jmaa.2004.09.014 VL - 304 IS - 2 SP - 423-450 SN - 1096-0813 KW - periodic solution KW - parabolic boundary problem KW - upper and lower solutions KW - quasimonotone function KW - asymptotic stability KW - global attractivity KW - time delays KW - Lotka-Volterra diffusion models ER - TY - JOUR TI - Resolving tylenchid evolutionary relationships through multiple gene analysis derived from EST data AU - Scholl, EH AU - Bird, DM T2 - MOLECULAR PHYLOGENETICS AND EVOLUTION AB - Sequence-based phylogenetic analyses typically are based on a small number of character sets and report gene trees which may not reflect the true species tree. We employed an EST mining strategy to suppress such incongruencies, and recovered the most robust phylogeny for five species of plant-parasitic nematode (Meloidogyne arenaria, M. chitwoodi, M. hapla, M. incognita, and M. javanica), three closely related tylenchid taxa (Heterodera glycines, Globodera pallida, and G. rostochiensis) and a distant taxon, Caenorhabditis elegans. Our multiple-gene approach is based on sampling more than 80,000 publicly available tylenchid EST sequences to identify phylum-wide orthologues. Bayesian inference, minimum evolution, maximum likelihood and protein distance methods were employed for phylogenetic reconstruction and hypothesis tests were constructed to elucidate differential selective pressures across the phylogeny for each gene. Our results place M. incognita and M. javanica as sister taxa, with M. arenaria as the next closely related nematode. Significant differences in selective pressure were revealed for some genes under some hypotheses, though all but one gene are exclusively under purifying selection, indicating conservation across the orthologous groups. This EST-based multi-gene analysis is a first step towards accomplishing genome-wide coverage for tylenchid evolutionary analyses. DA - 2005/9// PY - 2005/9// DO - 10.1016/j.ympev.2005.03.016 VL - 36 IS - 3 SP - 536-545 SN - 1095-9513 KW - Bayesian KW - Caenorhabditis elegans KW - COG KW - cyst nematode KW - orthologues KW - root-knot nematode ER - TY - JOUR TI - Periodic dynamical systems in unidirectional metapopulation models AU - Franke, JE AU - Yakubu, AA T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - In periodically varying environments, population models generate periodic dynamical systems. To understand the effects of unidirectional dispersal on local patch dynamics in fluctuating environments, dynamical systems theory is used to study the resulting periodic dynamical systems. In particular, a unidirectional dispersal linked two patch nonautonomous metapopulation model is constructed and used to explain the qualitative dynamics of linked versus unlinked independent patches. As in single-patch, single-species population models, unidirectional nonautonomous models support multiple attractors where local population models support single attractors. DA - 2005/6// PY - 2005/6// DO - 10.1080/10236190412331334563 VL - 11 IS - 7 SP - 687-700 SN - 1563-5120 KW - metapopulation KW - multiple attractors KW - nonautonomous models KW - periodic dynamical systems KW - unidirectional dispersal ER - TY - JOUR TI - On the accuracy of semi-Lagrangian numerical simulation of internal gravity wave motion in the atmosphere AU - Semazzi, FHM AU - Scroggs, JS AU - Pouliot, GA AU - McKee-Burrows, AL AU - Norman, M AU - Poojary, V AU - Tsai, YM T2 - JOURNAL OF THE METEOROLOGICAL SOCIETY OF JAPAN AB - We have investigated the accuracy ofthe semi-implicit semi-Lagrangian (SISL) method in simulating internal gravity wave (IGW) motion. We have focused on the relative accuracy of the hydrostatic, and nonhydrostatic IGW solutions. The analysis is based on a linearized model and a Global Circulation Model-Dynamic Core (GCM-DC) with a stretched grid.The nonhydrostatic version of the GCM-DC model produces the familiar IGW train disturbance anchored to an isolated hypothetical mountain. The wave has a distinct tilt away from the vertical direction, which is consistent with classical theory. For the hydrostatic version of the model, the axis of the resulting IGW train rests nearly perpendicular to the mountain top, thus again consistent with classical theory. Increasing the time step from 10 s; Courant number (Cn) = 0.5; to 60 s (Cn = 3.0), results in stable solutions for both the hydrostatic and nonhydrostatic versions of the model. The nonhydrostatic solution is in close agreement with the control run however, the hydrostatic solution exhibits large phase truncation errors.The solutions for the one-dimensional linearized SISL model confirm the GCM-DC results that the nonhydrostatic IGW train is less damped and shifted by the SISL scheme than the corresponding hydrostatic IGW motion. The linear solutions indicate very high accuracy of the physical mode of the solution, but it rapidly deteriorates when Cn exceeds unity. As Δt → 0 the amplitude of the computational mode tends to zero and its frequency to infinity. However, as Δt → ∞, the frequency of the computational SISL mode asymptotically approaches the value of the frequency of the corresponding SISL physical mode. Furthermore, the amplitude of the SISL computational mode is directly proportional to the size of the time step. Therefore, at large time steps, the amplification of the computational mode could offset some of the numerical damping of the physical mode by the SISL scheme. DA - 2005/10// PY - 2005/10// DO - 10.2151/jmsj.83.851 VL - 83 IS - 5 SP - 851-869 SN - 2186-9057 ER - TY - JOUR TI - Human T cells armed with Her2/neu bispecific antibodies divide, are cytotoxic, and secrete cytokines with repeated stimulation AU - Grabert, R. C. AU - Cousens, L. P. AU - Smith, J. A. AU - Olson, S. AU - Gall, J. AU - Young, W. B. AU - Davol, P. A. AU - Lum, L. G. T2 - Clinical Cancer Research DA - 2005/// PY - 2005/// VL - 12 IS - 2 SP - 569-576 ER - TY - JOUR TI - Heterogeneity influence on electric field induced piezoelectric microfracture AU - Oates, WS T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - Spatial variations in piezoelectric material properties can influence localized residual stresses under electro-mechanical loading, which has been shown to contribute to microfractures (Jiang, Q., Subbarao, E.C. and Cross, L.E. 1994. ''Grain Size Dependence of Electric Fatigue Behavior of Hot Pressed PLZT Ferroelectric Ceramics,'' Acta Metall. Mater., 42(11):3687–3694; Lynch, C.S. 1998. ''Fracture of Ferroelectric and Relaxor Electro-ceramics: Influences of Electric Field,'' Acta Mater., 46(2):599–608; Wang, Z., Jiang, Q., White, G.S. and Richardson, A.K. 1998. ''Processing Flaws in PZT Transducer Rings,'' Smart Mater. Struct., 7:867–873). The effect of residual stress on piezoelectric microfracture has been modeled by introducing a crack at the edge of a piezoelectric elliptic inclusion with dissimilar piezoelectric matrix material properties. Piezoelectric weight functions were used to assess changes in intensity factors and energy release rates when an inclusion is present. The shape of the elliptic inclusion is shown to have an effect on local driving forces. Additionally, comparison of impermeable and permeable crack face boundary conditions illustrate the importance of applying the more 'physical' permeable conditions to achieve positive flaw-localized driving forces under electrical loading. DA - 2005/9// PY - 2005/9// DO - 10.1177/1045389X05054850 VL - 16 IS - 9 SP - 733-741 SN - 1530-8138 KW - piezoelectric KW - microfracture KW - heterogeneity KW - weight function ER - TY - JOUR TI - HIV dynamics: Modeling, data analysis, and optimal treatment protocols AU - Adams, BM AU - Banks, HT AU - Davidian, M AU - Kwon, HD AU - Tran, HT AU - Wynne, SN AU - Rosenberg, ES T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented. DA - 2005/12/1/ PY - 2005/12/1/ DO - 10.1016/j.cam.2005.02.004 VL - 184 IS - 1 SP - 10-49 SN - 1879-1778 KW - HIV models KW - parameter estimation KW - data and model reduction KW - structured treatment interruptions KW - optimal control ER - TY - JOUR TI - Application of rotational isomeric state theory to ionic polymer stiffness predictions AU - Weiland, LM AU - Lada, EK AU - Smith, RC AU - Leo, DJ T2 - JOURNAL OF MATERIALS RESEARCH AB - Presently, rotational isomeric state (RIS) theory directly addresses polymer chain conformation as it relates to mechanical response trends. The primary goal of this work is to explore the adaptation of this methodology to the prediction of material stiffness. This multiscale modeling approach relies on ionomer chain conformation and polymer morphology and thus has potential as both a predictive modeling tool and a synthesis guide. The Mark–Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for four solvated Nafion® cases. For each case, a probability density function for chain length is estimated using various statistical techniques, including the classically applied cubic spline approach. It is found that the stiffness prediction is sensitive to the fitting strategy. The significance of various fitting strategies, as they relate to the physical structure of the polymer, are explored so that a method suitable for stiffness prediction may be identified. DA - 2005/9// PY - 2005/9// DO - 10.1557/JMR.2005.0292 VL - 20 IS - 9 SP - 2443-2455 SN - 0884-2914 ER - TY - JOUR TI - A hierarchical Bayesian approach for parameter estimation in HIV models AU - Banks, HT AU - Grove, S AU - Hu, S AU - Ma, YY T2 - INVERSE PROBLEMS AB - A hierarchical Bayesian approach is developed to estimate parameters at both the individual and the population levels in a HIV model, with the implementation carried out by Markov Chain Monte Carlo (MCMC) techniques. Sample numerical simulations and statistical results are provided to demonstrate the feasibility of this approach. DA - 2005/12// PY - 2005/12// DO - 10.1088/0266-5611/21/6/001 VL - 21 IS - 6 SP - 1803-1822 SN - 1361-6420 ER - TY - JOUR TI - Zonal uniformity in mechanical properties of the chondrocyte pericellular matrix: Micropipette aspiration of canine chondrons isolated by cartilage homogenization AU - Guilak, F AU - Alexopoulos, LG AU - Haider, MA AU - Ting-Beall, HP AU - Setton, LA T2 - ANNALS OF BIOMEDICAL ENGINEERING DA - 2005/10// PY - 2005/10// DO - 10.1007/s10439-005-4479-7 VL - 33 IS - 10 SP - 1312-1318 SN - 0090-6964 KW - cartilage KW - cell KW - mechanics KW - mechanical properties KW - osteoarthritis KW - pericellular KW - collagen KW - micropipette aspiration KW - biomechanics KW - chondron KW - collagen type VI ER - TY - JOUR TI - Population models with periodic recruitment functions and survival rates AU - Franke, JE AU - Yakubu, AA T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - We study the combined effects of periodically varying carrying capacity and survival rate on populations. We show that our populations with constant recruitment functions do not experience either resonance or attenuance when either only the carrying capacity or the survival rate is fluctuating. However, when both carrying capacity and survival rate are fluctuating the populations experience either attenuance or resonance, depending on parameter regimes. In addition, we show that our populations with Beverton–Holt recruitment functions experience attenuance when only the carrying capacity is fluctuating. DA - 2005/12/1/ PY - 2005/12/1/ DO - 10.1080/10236190500386275 VL - 11 IS - 14 SP - 1169-1184 SN - 1563-5120 KW - attenuance KW - periodic carrying capacity KW - periodic survival rate KW - resonance ER - TY - JOUR TI - Parameter estimation in a coupled system of nonlinear size-structured populations AU - Ackleh, A. S. AU - Banks, H. T. AU - Deng, K. AU - Hu, S. H. T2 - Mathematical Biosciences and Engineering AB - A least squares technique is developed for identifying unknown parameters in a coupled system of nonlinear size-structured populations. Convergence results for the parameter estimation technique are established. Ample numerical simulations and statistical evidence are provided to demonstrate the feasibility of this approach. DA - 2005/// PY - 2005/// DO - 10.3934/mbe.2005.2.289 VL - 2 IS - 2 SP - 289-315 ER - TY - JOUR TI - On the constructive inverse problem in differential Galois theory AU - Cook, WJ AU - Mitschi, C AU - Singer, MF T2 - COMMUNICATIONS IN ALGEBRA AB - We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G 1 · ··· · G r , where each G i is a simple group of type Aℓ, Cℓ, Dℓ, E6, or E7, we construct a differential equation over C(x) having Galois group G. DA - 2005/// PY - 2005/// DO - 10.1080/00927870500243304 VL - 33 IS - 10 SP - 3639-3665 SN - 1532-4125 KW - Galois theory KW - inverse problem KW - linear differential equations KW - Picard-Vessiot ER - TY - JOUR TI - On minimizing sequences for an optimization problem governed by an integral equation AU - Medhin, N. G. AU - Sambandham, M. T2 - Dynamic Systems and Applications DA - 2005/// PY - 2005/// VL - 14 IS - 04-Mar SP - 607-614 ER - TY - BOOK TI - Inverse Eigenvalue problems: Theory, algorithms, and applications AU - Chu, M. T.-C. AU - Golub, G. H. AB - The basic goal of an inverse eigenvalue problem is to reconstruct the physical parameters of a certain system from the knowledge or desire of its dynamical behavior. Depending on the application, inverse eigenvalue problems appear in many different forms. This book discusses the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems. CN - QA193 .C48 2005 DA - 2005/// PY - 2005/// DO - 10.1093/acprof:oso/9780198566649.001.0001 PB - Oxford: Oxford University Press SN - 0198566646 ER - TY - JOUR TI - Adaptive optimization of least-squares tracking algorithms: With applications to adaptive antenna arrays for randomly time-varying mobile communications systems AU - Buche, R AU - Kushner, HJ T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL AB - Adaptive antenna arrays are used for reducing the effects of interference and increasing capacity in mobile communications systems. Typical algorithms recursively compute the antenna weights that minimize the weighted error function (at discrete times kh, k=1,2,..., for a sampling interval h) /spl sigma//sub l=1//sup k//spl alpha//sup k-l/[e/sub l/(W)]/sup 2/, where e/sub l/(W) is a measure of the reception error at time lh with antenna weight vector W, and /spl alpha/<1. The forgetting factor /spl alpha/<1 allows tracking as conditions change and the minimization is used only to get the weights. The average detection error rate depends heavily on the chosen value of /spl alpha/, whose optimal value can change rapidly in time, perhaps significantly in seconds. We add another adaptive loop that tracks the optimal value of /spl alpha/ and greatly improves the operation when the environment is randomly time-varying. The additional adaptive loop is based on an approximation to a natural "gradient descent" method. The algorithm is practical and can improve the performance considerably. In terms of average detection error rates and for all of the scenarios tested, the new system tracks the optimal value of /spl alpha/ well, and always performs better (sometimes much better) than the original algorithm that uses any fixed value of /spl alpha/. Although the initial motivation arises in adaptive antennas, the method can be used to improve algorithms for tracking parameters of time-varying nonlinear systems, where similar issues are involved. DA - 2005/11// PY - 2005/11// DO - 10.1109/TAC.2005.858682 VL - 50 IS - 11 SP - 1749-1760 SN - 1558-2523 KW - adaptive antennas KW - mobile communications KW - randomly time-varying channels KW - stochastic approximation KW - tracking time-varying parameters ER - TY - JOUR TI - A rate-dependent two-dimensional free energy model for ferroelectric single crystals AU - Seelecke, S AU - Kim, SJ AU - Ball, BL AU - Smith, RC T2 - CONTINUUM MECHANICS AND THERMODYNAMICS AB - The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [29–31] is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90°-switching processes, and a local maximum, across which 180°-switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO3 single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90°- and 180°-switching processes are discussed in detail. DA - 2005/12// PY - 2005/12// DO - 10.1007/s00161-005-0207-7 VL - 17 IS - 4 SP - 337-350 SN - 1432-0959 KW - ferroelectric materials KW - 2-D free energy model KW - hysteresis KW - rate-dependent effects ER - TY - JOUR TI - A multi-model approach to failure detection in uncertain sampled-data systems AU - Nikoukhah, R AU - Campbell, SL T2 - EUROPEAN JOURNAL OF CONTROL AB - In this paper we propose a methodology for active failure detection for sampled-data systems in the presence of model uncertainty. Active failure detection consists of injecting a signal (called an auxiliary signal) into the system. Using a multi-model framework to represent normal and failed behaviors of the system,we develop algorithms for the design of optimal auxiliary signals and online detection tests. The tests give guaranteed detection. Any conservatism inherited from the multi-model framework increases the size of the test signal and is not reflected in missed failures or false alarms as with several other approaches. DA - 2005/// PY - 2005/// DO - 10.3166/ejc.11.255-265 VL - 11 IS - 3 SP - 255-265 SN - 0947-3580 KW - active failure detection KW - auxiliary signal design KW - multi-model identification KW - sampled-data systems ER - TY - JOUR TI - The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas AU - Garcia, RDM AU - Siewert, CE T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK DA - 2005/11// PY - 2005/11// DO - 10.1007/s00033-005-0007-8 VL - 57 IS - 1 SP - 94-122 SN - 0044-2275 KW - rarefied gas dynamics KW - sound-wave propagation KW - discrete ordinates ER - TY - JOUR TI - Results on asymptotic behaviour for discrete, two-patch metapopulations with density-dependent selection AU - Selgrade, JF AU - Roberds, JH T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - A 4-dimensional system of nonlinear difference equations tracking allele frequencies and population sizes for a two-patch metapopulation model is studied. This system describes intergenerational changes brought about by density-dependent selection within patches and moderated by the effects of migration between patches. To determine conditions which result in similar behaviour at the level of local populations, we introduce the concept of symmetric equilibrium and relate it to properties of allelic and genotypic fitness. We present examples of metapopulation stability, instability and bistability, as well as an example showing that differentially greater migration into a stable patch results in metapopulation stability. Finally, we illustrate a Naimark-Sacker bifurcation giving a globally asymptotically stable invariant curve for the 4-dimensional model. DA - 2005/4// PY - 2005/4// DO - 10.1080/10236190412331335508 VL - 11 IS - 4-5 SP - 459-476 SN - 1563-5120 KW - metapopulation KW - equilibrium KW - attractor KW - discrete population model ER - TY - JOUR TI - Pseudo-transient Continuation for Nonsmooth Nonlinear Equations AU - Fowler, K R AU - Kelley, C T T2 - SIAM J. Numer. Anal. AB - Pseudo-transient continuation is a Newton-like iterative method for computing steady-state solutions of differential equations in cases where the initial data are far from a steady state. The iteration mimics a temporal integration scheme, with the time step being increased as steady state is approached. The iteration is an inexact Newton iteration in the terminal phase. In this paper we show how steady-state solutions to certain ordinary and differential algebraic equations with nonsmooth dynamics can be computed with the method of pseudo-transient continuation. An example of such a case is a discretized PDE with a Lipschitz continuous, but nondifferentiable, constitutive relation as part of the nonlinearity. In this case we can approximate a generalized derivative with a difference quotient. The existing theory for pseudo-transient continuation requires Lipschitz continuity of the Jacobian. Newton-like methods for nonsmooth equations have been globalized by trust-region methods, smooth approximations, and splitting methods in the past, but these approaches are not designed to find steady-state solutions of time-dependent problems. The method in this paper synthesizes the ideas from nonsmooth calculus and the method of pseudo-transient continuation. DA - 2005/// PY - 2005/// DO - 10.1137/s0036142903431298 VL - 43 IS - 4 SP - 1385-1406 ER - TY - JOUR TI - Nonlinear discrete Sturm-Liouville problems AU - Rodriguez, J T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS AB - In this paper we study nonlinear boundary value problems of the form Δ[p(t−1)Δy(t−1)]+q(t)y(t)+λy(t)=f(y(t));t=a+1,…,b+1, subject to a11y(a)+a12Δy(a)=0anda21y(b+1)+a22Δy(b+1)=0. The parameter λ is an eigenvalue of the associated linear problem; that is, there is a nontrivial function u that satisfies the boundary conditions and also Δ[p(t−1)Δu(t−1)]+q(t)u(t)+λu(t)=0 for t in {a+1,a+2,…,b+1}. We establish sufficient conditions for the solvability of such problems. In addition, in those cases where the nonlinearity is “small,” we provide a qualitative analysis of the relation between solutions of the nonlinear problem and eigenfunctions of the linear one. DA - 2005/8/1/ PY - 2005/8/1/ DO - 10.1016/j.jmaa.2005.01.032 VL - 308 IS - 1 SP - 380-391 SN - 0022-247X KW - boundary value problems KW - Brower Fixed Point Theorem KW - Implicit Function Theorem ER - TY - JOUR TI - Multiple attractors via CUSP bifurcation in periodically varying environments AU - Franke, JE AU - Yakubu, AZ T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - Abstract Periodically forced (non-autonomous) single species population models support multiple attractors via tangent bifurcations, where the corresponding autonomous models support single attractors. Elaydi and Sacker obtained conditions for the existence of single attractors in periodically forced discrete-time models. In this paper, the Cusp Bifurcation Theorem is used to provide a general framework for the occurrence of multiple attractors in such periodic dynamical systems. Keywords: Periodic dynamical systemsSemi-conjugacyTangent bifurcationMultiple attractors DA - 2005/4// PY - 2005/4// DO - 10.1080/10236190412331335436 VL - 11 IS - 4-5 SP - 365-377 SN - 1023-6198 KW - periodic dynamical systems KW - semi-conjugacy KW - tangent bifurcation KW - multiple attractors ER - TY - JOUR TI - Functionals and the quantum master equation AU - Fulp, RO T2 - INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS AB - The quantum master equation is usually formulated in terms of functionals of the components of mappings from a space-time manifold M into a finite-dimensional vector space. The master equation is the sum of two terms one of which is the anti-bracket (odd Poisson bracket) of functionals and the other is the Laplacian of a functional. Both of these terms seem to depend on the fact that the mappings on which the functionals act are vector-valued. It turns out that neither this Laplacian nor the anti-bracket is well-defined for sections of an arbitrary vector bundle. We show that if the functionals are permitted to have their values in an appropriate graded tensor algebra whose factors are the dual of the space of smooth functions on M, then both the anti-bracket and the Laplace operator can be invariantly defined. Additionally, one obtains a new anti-bracket for ordinary functionals. DA - 2005/9// PY - 2005/9// DO - 10.1007/s10773-005-4832-5 VL - 44 IS - 9 SP - 1599-1616 SN - 0020-7748 KW - quantum master equation KW - functionals KW - antibracket KW - Laplacian KW - Batalin-Vilkovisky ER - TY - CHAP TI - Augmented Strategies for Interface and Irregular Domain Problems AU - Li, Zhilin T2 - Numerical Analysis and Its Applications A2 - Li, Z. A2 - Vulkov, L. A2 - Wasniewski, J. T3 - Lecture Notes in Computer Science AB - The augmented strategies for interface problems and problems defined on irregular domains are reviewed in this paper. There are at least two reasons to use augmented strategies. The first one is to get faster algorithms, particularly, to take advantages of existing fast solvers. The second reason is that, for some interface problems, an augmented approach may be the only way to derive an accurate algorithm. Using an augmented approach, one or several quantities of co-dimension one are introduced. The GMRES iterative method is often used to solve the augmented variable(s) that are only defined along the interface or the irregular boundary. Several examples of augmented methods are provided in this paper. CN - QA297 .N8415 2004 PY - 2005/// DO - 10.1007/978-3-540-31852-1_7 VL - 3401 SP - 66–79 PB - Springer SN - 9783540249375 9783540318521 SV - 3401 UR - http://dx.doi.org/10.1007/978-3-540-31852-1_7 ER - TY - JOUR TI - Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion AU - Pao, CV T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS AB - The aim of this paper is to investigate the existence and method of construction of solutions for a general class of strongly coupled elliptic systems by the method of upper and lower solutions and its associated monotone iterations. The existence problem is for nonquasimonotone functions arising in the system, while the monotone iterations require some mixed monotone property of these functions. Applications are given to three Lotka–Volterra model problems with cross-diffusion and self-diffusion which are some extensions of the classical competition, prey–predator, and cooperating ecological systems. The monotone iterative schemes lead to some true positive solutions of the competition system, and to quasisolutions of the prey–predator and cooperating systems. Also given are some sufficient conditions for the existence of a unique positive solution to each of the three model problems. DA - 2005/3/15/ PY - 2005/3/15/ DO - 10.1016/j.na.2004.10.008 VL - 60 IS - 7 SP - 1197-1217 SN - 0362-546X KW - elliptic systems KW - reaction-diffusion equations KW - cross-diffusion KW - Lotka -Volterra systems KW - upper and lower solutions KW - monotone iterations ER - TY - JOUR TI - On the low-rank approximation of data on the unit sphere AU - Chu, M AU - Del Buono, N AU - Lopez, L AU - Politi, T T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - In various applications, data in multidimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the m-dimensional unit sphere Sm-1 by k-dimensional great circles with k much less than m. The task is cast as an algebraically constrained low-rank matrix approximation problem. Using the fidelity of the low-rank approximation to the original data as the cost function, this paper offers an analytic expression of the projected gradient which, on one hand, furnishes the first order optimality condition and, on the other hand, can be used as a numerical means for solving this problem. DA - 2005/// PY - 2005/// DO - 10.1137/S0895479803433295 VL - 27 IS - 1 SP - 46-60 SN - 1095-7162 KW - standardized data KW - linear model KW - factor analysis KW - low-rank approximation KW - latent semantic indexing KW - projected gradient ER - TY - JOUR TI - Numerical issues in plasticity models for granular materials AU - Gremaud, PA T2 - JOURNAL OF VOLCANOLOGY AND GEOTHERMAL RESEARCH AB - Friction plays a fundamental role in the mechanics of granular materials. Two problems are considered: (i) heap formation and (ii) granular flow. Both problems admit closely related mathematical models. In each case, analytical and numerical difficulties are discussed. Efficient and reliable numerical methods are proposed and implemented. The results are illustrated by several computational experiments. DA - 2005/1/1/ PY - 2005/1/1/ DO - 10.1016/j.jvolgeores.2004.06.018 VL - 139 IS - 1-2 SP - 23-31 SN - 0377-0273 KW - granular material KW - plasticity KW - heap formation KW - granular flow KW - numerical methods ER - TY - JOUR TI - Investigation of laser beam-induced current techniques for heterojunction photodiode characterization AU - Redfern, DA AU - Fang, W AU - Ito, K AU - Bahir, G AU - Musca, CA AU - Dell, JM AU - Faraone, L T2 - JOURNAL OF APPLIED PHYSICS AB - A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P-n HgCdTe heterojunction photodiode structures. In particular, the question of correctly identifying erroneous device structures formed during the fabrication process is addressed, and experimental measurements are presented to support the simulation results. DA - 2005/8/1/ PY - 2005/8/1/ DO - 10.1063/1.1993754 VL - 98 IS - 3 SP - SN - 1089-7550 ER - TY - JOUR TI - Inclined-plane model of the 2004 Tour de France AU - Hannas, BL AU - Goff, JE T2 - EUROPEAN JOURNAL OF PHYSICS AB - We make modifications to a model we created to predict the stage-winning times of the 2003 Tour de France. With the modifications in place, we model the 2004 Tour de France. We demonstrate here the utility of our 2003 model with its successful application to the 2004 race; our total of all stage-winning times is just 0.05% different from the actual total. We also apply our 2004 model to the 2003 Tour de France and compare our results with our 2003 model. Our 2004 model misses the actual sum of stage-winning times in the 2003 race by just 1.77%. DA - 2005/3// PY - 2005/3// DO - 10.1088/0143-0807/26/2/004 VL - 26 IS - 2 SP - 251-259 SN - 1361-6404 ER - TY - JOUR TI - Green challenges: student perspectives from the 2004 ACS-PRF Summer School on Green Chemistry AU - Bektesevic, S AU - Beier, JC AU - Chen, L AU - Eghbali, N AU - King, S AU - Levitin, G AU - Mehta, G AU - Mullins, RJ AU - Reiner, JL AU - Weikel, R AU - Xie, SW AU - Gunn, E T2 - GREEN CHEMISTRY AB - Participants in the American Chemical Society-Petroleum Research Fund (ACS-PRF) Summer School on Green Chemistry discuss the topics covered and lessons learned during the week-long summer school held July 31 through August 7, 2004, at Carnegie Mellon University. An outline of the program is accompanied by a discussion of the challenges and needs of the field of green chemistry as seen by the participants. These include further education of the public as well as members of the scientific community, thorough research and rigorous publication standards, and the formation of a cooperative and collaborative group of researchers. DA - 2005/// PY - 2005/// DO - 10.1039/b501692b VL - 7 IS - 6 SP - 403-407 SN - 1463-9270 ER - TY - JOUR TI - Discrete nonholonomic LL systems on Lie groups AU - Fedorov, YN AU - Zenkov, DV T2 - NONLINEARITY AB - This paper studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G. Assuming that the discrete Lagrangian and constraints are left-invariant, the discrete Euler–Lagrange equations are reduced to the discrete Euler–Poincaré–Suslov equations. The dynamics associated with the discrete Euler–Poincaré–Suslov equations is shown to evolve on a subvariety of the Lie group G. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and discrete momentum conservation is discussed. DA - 2005/9// PY - 2005/9// DO - 10.1088/0951-7715/18/5/017 VL - 18 IS - 5 SP - 2211-2241 SN - 1361-6544 ER - TY - JOUR TI - Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation AU - Olufsen, MS AU - Ottesen, JT AU - Tran, HT AU - Ellwein, LM AU - Lipsitz, LA AU - Novak, V T2 - JOURNAL OF APPLIED PHYSIOLOGY AB - Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO(2) concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing. DA - 2005/10// PY - 2005/10// DO - 10.1152/japplphysiol.00177.2005 VL - 99 IS - 4 SP - 1523-1537 SN - 1522-1601 KW - cardiovascular system KW - mathematical modeling KW - cerebral blood flow KW - gravitational effect KW - autonomic regulation KW - cerebral autoregulation ER - TY - JOUR TI - An operator splitting scheme with a distributed Lagrange multiplier based fictitious domain method for wave propagation problems AU - Bokil, VA AU - Glowinski, R T2 - JOURNAL OF COMPUTATIONAL PHYSICS AB - We propose a novel fictitious domain method based on a distributed Lagrange multiplier technique for the solution of the time-dependent problem of scattering by an obstacle. We study discretizations that include a fully conforming approach as well as mixed finite element formulations utilizing the lowest order Nedelec edge elements (in 2D) on rectangular grids. We also present a symmetrized operator splitting scheme for the scattering problem, which decouples the operator that propagates the wave from the operator that enforces the Dirichlet condition on the boundary of an obstacle. A new perfectly matched layer (PML) model is developed to model the unbounded problem of interest. This model is based on a formulation of the wave equation as a system of first-order equations and uses a change of variables approach that has been developed to construct PML's for Maxwell's equations. We present an analysis of our fictitious domain approach for a one-dimensional wave problem. Based on calculations of reflection coefficients, we demonstrate the advantages of our fictitious domain approach over the staircase approximation of the finite difference method. We also demonstrate some important properties of the distributed multiplier approach that are not shared by a boundary multiplier fictitious domain approach for the same problem. Numerical results for two-dimensional wave problems that validate the effectiveness of the different methods are presented. DA - 2005/5/1/ PY - 2005/5/1/ DO - 10.1016/j.jcp.2004.10.040 VL - 205 IS - 1 SP - 242-268 SN - 1090-2716 KW - fictitious domains KW - perfectly matched layer KW - mixed finite element methods KW - operator splitting ER - TY - JOUR TI - A survey of eigenvector methods for Web information retrieval AU - Langville, AN AU - Meyer, CD T2 - SIAM REVIEW AB - Web information retrieval is significantly more challenging than traditional well-controlled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Web's hyperlink structure. This structure has been exploited by several of today's leading Web search engines, particularly Google and Teoma. In this survey paper, we focus on Web information retrieval methods that use eigenvector computations, presenting the three popular methods of HITS, PageRank, and SALSA. DA - 2005/3// PY - 2005/3// DO - 10.1137/S0036144503424786 VL - 47 IS - 1 SP - 135-161 SN - 1095-7200 KW - eigenvector KW - Markov chain KW - information retrieval KW - HITS KW - PageRank KW - SALSA ER - TY - JOUR TI - Time-reversal refocusing for point source in randomly layered media AU - Fouque, JP AU - Garnier, J AU - Nachbin, A AU - Solna, K T2 - WAVE MOTION AB - This paper demonstrates the interest of a time-reversal method for the identification of source in a randomly layered medium. An active source located inside the medium emits a pulse that is recorded on a small time-reversal mirror. The wave is sent back into the medium, either numerically in a computer with the knowledge of the medium, or physically into the real medium. Our goal is to give a precise description of the refocusing of the pulse. We identify and analyze a regime where the pulse refocuses on a ring at the depth of the source and at a critical time. Our objective is to find the location of the source and we show that the time-reversal refocusing contains information which can be used to this effect and which cannot be obtained by a direct arrival-time analysis. The time-reversal technique gives a robust procedure to locate and characterize the source also in the case with ambient noise created by other sources located at the surface. DA - 2005/9// PY - 2005/9// DO - 10.1016/j.wavemoti.2005.03.001 VL - 42 IS - 3 SP - 238-260 SN - 1878-433X KW - acoustic waves KW - random media KW - asymptotic theory KW - time reversal ER - TY - JOUR TI - Non-linear dynamics of thin films and fluid interfaces - Preface AU - Behringer, RP AU - Shearer, M T2 - PHYSICA D-NONLINEAR PHENOMENA DA - 2005/9/15/ PY - 2005/9/15/ DO - 10.1016/j.physd.2005.08.003 VL - 209 IS - 1-4 SP - VII-VIII SN - 1872-8022 ER - TY - JOUR TI - Kinetics and nucleation for driven thin film flow AU - Levy, R AU - Shearer, M T2 - PHYSICA D-NONLINEAR PHENOMENA AB - The lubrication theory of thin liquid films, driven by a constant surface stress opposing gravity, is described by a scalar fourth order PDE for the film height h:ht+(h2−h3)x=−γ(h3hxxx)x, in which γ is a positive constant related to surface tension. In this paper, the wave structure of solutions observed in numerical simulations with γ>0 is related to the recent hyperbolic theory of the underlying scalar conservation law, in which γ=0. This theory involves a kinetic relation, describing possible undercompressive shocks, and a nucleation condition, governing the transition from classical to non-classical solution of the Riemann problem. The kinetic relation and nucleation condition are derived from consideration of traveling wave solutions (with γ>0). The kinetic relation is identified with a codimension-one bifurcation of the corresponding vector field, for which there is a traveling wave approximating an undercompressive shock. The nucleation condition is identified as a transition in the vector field at which there is no traveling wave connecting upstream and downstream heights. The thresholds defined by these conditions are incorporated into a Riemann solver map, which is tested for initial value problems for the full PDE. It is found that the parameter γ determines a limit to the applicability of the hyperbolic theory, in which the fourth order diffusion can dominate short-time transients, resulting in long-time convergence to the classical solution when the hyperbolic theory would predict a non-classical solution. DA - 2005/9/15/ PY - 2005/9/15/ DO - 10.1016/j.physd.2005.07.003 VL - 209 IS - 1-4 SP - 145-163 SN - 0167-2789 KW - kinetics KW - nucleation KW - Marangoni KW - Riemann solver KW - thin films KW - hyperbolic conservation laws KW - traveling waves ER - TY - JOUR TI - A method for determination of optimal gaits with application to a snake-like serial-link structure AU - Hicks, G AU - Ito, K T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL AB - In this paper, we present a method of determining optimal gaits for shape actuated locomotion systems. This method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy. Symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic-like coupling between group, shape, and momenta coordinates. This form allows one to focus on designing gaits, abandoning concern over shape dynamics. Using this vantage point we indicate how a numerical optimal control method based on Gaussian quadrature may be acclimatized to periodicity, thus providing optimal gaits. The method is demonstrated by means of its application to a snake-like serial-link structure or snake robot. This application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms. DA - 2005/9// PY - 2005/9// DO - 10.1109/tac.2005.854583 VL - 50 IS - 9 SP - 1291-1306 SN - 1558-2523 KW - locomotion KW - optimal gaits KW - numerical optimal control KW - reduction ER - TY - JOUR TI - Population dynamics models in plant-insect herbivore-pesticide interactions AU - Adams, BM AU - Banks, HT AU - Banks, JE AU - Stark, JD T2 - MATHEMATICAL BIOSCIENCES AB - We consider several population dynamics models in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). We carry out parameter estimation computations along with statistical analysis to compare autonomous versus non-autonomous model dynamics. We conclude with a brief discussion of some not-so-subtle pitfalls that can arise when using quantitative measures of model fit-to-data to make biological inferences as well as offer a positive example of how one might combine a priori biological hypothesis and intuition with rather sophisticated (from a field biology viewpoint) mathematical methodologies to suggest synergisms. DA - 2005/7// PY - 2005/7// DO - 10.1016/j.mbs.2004.09.001 VL - 196 IS - 1 SP - 39-64 SN - 1879-3134 KW - plant-insect interactions KW - inverse problems KW - hypothesis testing KW - standard errors in dynamical models ER - TY - JOUR TI - Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions AU - Fibich, G. AU - Tsynkov, S. T2 - Journal of Computational Physics AB - In [J. Comput. Phys. 171 (2001) 632–677] we developed a fourth-order numerical method for solving the nonlinear Helmholtz equation which governs the propagation of time-harmonic laser beams in media with a Kerr-type nonlinearity. A key element of the algorithm was a new nonlocal two-way artificial boundary condition (ABC), set in the direction of beam propagation. This two-way ABC provided for reflectionless propagation of the outgoing waves while also fully transmitting the given incoming beam at the boundaries of the computational domain. Altogether, the algorithm of [J. Comput. Phys. 171 (2001) 632–677] has allowed for a direct simulation of nonlinear self-focusing without neglecting nonparaxial effects and backscattering. To the best of our knowledge, this capacity has never been achieved previously in nonlinear optics. In the current paper, we propose an improved version of the algorithm. The principal innovation is that instead of using the Dirichlet boundary conditions in the direction orthogonal to that of the laser beam propagation, we now introduce Sommerfeld-type local radiation boundary conditions, which are constructed directly in the discrete framework. Numerically, implementation of the Sommerfeld conditions requires evaluation of eigenvalues and eigenvectors for a non-Hermitian matrix. Subsequently, the separation of variables, which is a key building block of the aforementioned nonlocal ABC, is implemented through an expansion with respect to the nonorthogonal basis of the eigenvectors. Numerical simulations show that the new algorithm offers a considerable improvement in its numerical performance, as well as in the range of physical phenomena that it is capable of simulating. DA - 2005/11// PY - 2005/11// DO - 10.1016/j.jcp.2005.04.015 VL - 210 IS - 1 SP - 183-224 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1016/j.jcp.2005.04.015 DB - Crossref KW - Kerr media KW - intense laser light KW - diffraction KW - nonparaxiality KW - nonlinear self-focusing KW - backscattering KW - critical and subcritical nonlinearity KW - solitary waves KW - counter-propagation KW - fourth-order approximation KW - iterative solution KW - separation of variables KW - nonlocal artificial boundary conditions (ABCs) KW - Sommerfeld radiation boundary conditions ER - TY - JOUR TI - Instability of travelling wave profiles for the Lax-Friedrichs scheme AU - Baiti, P. AU - Bressan, A. AU - Jenssen, H. K. T2 - Discrete and Continuous Dynamical Systems DA - 2005/// PY - 2005/// VL - 13 IS - 4 SP - 877-899 ER - TY - JOUR TI - Cooperation and competition in modeling the dynamics of gross-domestic products of nations AU - Chukwu, EN T2 - APPLIED MATHEMATICS AND COMPUTATION AB - In this paper two major models of the gross-domestic product of four interacting nations are derived. One is an ordinary differential game of pursuit. The other is a hereditary one which utilizes the principle of rational expectations. A theory of interactions via net export is postulated. The UN and IMF data for a group of nations are used to validate it, and test for competition and cooperation MATLAB and MAPLE programs are used. The consequences of cooperation and competition are studied. DA - 2005/4/15/ PY - 2005/4/15/ DO - 10.1016/j.amc.2003.12.141 VL - 163 IS - 2 SP - 991-1021 SN - 0096-3003 ER - TY - JOUR TI - Canonical transformations of local functionals and sh-Lie structures AU - Al-Ashhab, S AU - Fulp, R T2 - JOURNAL OF GEOMETRY AND PHYSICS AB - In many Lagrangian field theories, there is a Poisson bracket on the space of local functionals. One may identify the fields of such theories as sections of a vector bundle. It is known that the Poisson bracket induces an sh-Lie structure on the graded space of horizontal forms on the jet bundle of the relevant vector bundle. We consider those automorphisms of the vector bundle which induce mappings on the space of functionals preserving the Poisson bracket and refer to such automorphisms as canonical automorphisms. We determine how such automorphisms relate to the corresponding sh-Lie structure. If a Lie group acts on the bundle via canonical automorphisms, there are induced actions on the space of local functionals and consequently on the corresponding sh-Lie algebra. We determine conditions under which the sh-Lie structure induces an sh-Lie structure on a corresponding reduced space where the reduction is determined by the action of the group. These results are not directly a consequence of the corresponding theorems on Poisson manifolds as none of the algebraic structures are Poisson algebras. DA - 2005/4/1/ PY - 2005/4/1/ DO - 10.1016/j.geomphys.2004.07.005 VL - 53 IS - 4 SP - 365-391 SN - 1879-1662 KW - Poisson geometry KW - de Rham complex KW - local functional KW - sh-Lie algebra KW - jet bundle ER - TY - JOUR TI - A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue AU - Banks, HT AU - Pinter, GA T2 - MULTISCALE MODELING & SIMULATION AB - Motivated by a problem involving wave propagation through viscoelastic biotissue, we present a theoretical framework for treating hysteresis as multiscale phenomena which must be averaged across distributions of internal variables. The resulting systems entail probability measure-dependent partial differential equations for which we establish well-posedness in a framework that leads readily to computationally useful approximations. DA - 2005/// PY - 2005/// DO - 10.1137/040603693 VL - 3 IS - 2 SP - 395-412 SN - 1540-3467 KW - multiscale modeling KW - hysteresis KW - wave propagation KW - biotissues KW - probability measures KW - Prohorov metric ER - TY - JOUR TI - On computing minimal realizable spectral radii of non-negative matrices AU - Chu, MT AU - Xu, SF T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS AB - For decades considerable efforts have been exerted to resolve the inverse eigenvalue problem for non-negative matrices. Yet fundamental issues such as the theory of existence and the practice of computation remain open. Recently, it has been proved that, given an arbitrary (n–1)-tuple ℒ︁ = (λ2,…,λn) ∈ ℂn–1 whose components are closed under complex conjugation, there exists a unique positive real number ℛ(ℒ︁), called the minimal realizable spectral radius of ℒ︁, such that the set {λ1,…,λn} is precisely the spectrum of a certain n × n non-negative matrix with λ1 as its spectral radius if and only if λ1 ⩾ ℛ(ℒ︁). Employing any existing necessary conditions as a mode of checking criteria, this paper proposes a simple bisection procedure to approximate the location of ℛ(ℒ︁). As an immediate application, it offers a quick numerical way to check whether a given n-tuple could be the spectrum of a certain non-negative matrix. Copyright © 2004 John Wiley & Sons, Ltd. DA - 2005/2// PY - 2005/2// DO - 10.1002/nla.395 VL - 12 IS - 1 SP - 77-86 SN - 1099-1506 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-20744446749&partnerID=MN8TOARS KW - non-negative matrices KW - Perron-Frobenius theorem KW - inverse eigenvalue problem KW - minimal realizable spectral radius KW - bisection method ER - TY - JOUR TI - Multiplicity one for representations corresponding to spherical distribution vectors of class rho AU - Helminck, AG AU - Helminck, GF T2 - ACTA APPLICANDAE MATHEMATICAE AB - In this paper one considers a unimodular second countable locally compact group G and the homogeneous space X:=H\G, where H is a closed unimodular subgroup of G. Over X complex vector bundles are considered such that H acts on the fibers by a unitary representation ρ with closed image. The natural action of G on the space of square integrable sections is unitary and possesses an integral decomposition in so-called spherical distributions of class ρ. The uniqueness of this decomposition can be characterized by a number of equivalent properties. Uniqueness is shown to hold for a class of semidirect products. In the case that H is compact, the multiplicity free decomposition is shown to be equivalent with the commutativity of a suitable convolution algebra. As an example, one takes for X a symmetric k-variety $\mathcal{H}_{k}\backslash \mathcal{G}_{k}$ , with k a locally compact field of characteristic not equal to two, and for ρ a character of ℋk, whose square is trivial. Here $\mathcal{G}$ is a reductive algebraic group defined over k and ℋ is the fixed point group of an involution σ of $\mathcal{G}$ defined over k. It is shown then that the natural representation ℒ of G k on the Hilbert space $L^{2}(\mathcal{H}_{k}\backslash \mathcal{G}_{k})$ is multiplicity free if ℋ is anisotropic. Next a criterion is derived that leads to multiplicity one also in the noncompact situation. Finally, in the non-Archimedean case, a general procedure is given that might lead to showing that a pair $(\mathcal{G}_{k},\mathcal{H}_{k})$ is a generalized Gelfand pair. Here $\mathcal{G}$ and ℋ are suitable algebraic groups defined over k. DA - 2005/3// PY - 2005/3// DO - 10.1007/s10440-005-0461-5 VL - 86 IS - 1-2 SP - 21-48 SN - 1572-9036 KW - Hilbert subspace KW - distribution vector KW - spherical distribution KW - Plancherel formula ER - TY - JOUR TI - Equivalence of quantum states under local unitary transformations AU - Fei, SM AU - Jing, NH T2 - PHYSICS LETTERS A AB - In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented. DA - 2005/7/4/ PY - 2005/7/4/ DO - 10.1016/j.physleta.2005.05.050 VL - 342 IS - 1-2 SP - 77-81 SN - 1873-2429 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-20444462791&partnerID=MN8TOARS KW - local unitary transformation KW - quantum states KW - tensor decomposable ER - TY - JOUR TI - Connectivity in the set of Gabor frames AU - Labate, D AU - Wilson, E T2 - APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS AB - In this paper we present a constructive proof that the set of Gabor frames is path-connected in the L 2 ( R n ) -norm. In particular, this result holds for the set of Gabor–Parseval frames as well as for the set of Gabor orthonormal bases. In order to prove this result, we introduce a construction which shows exactly how to modify a Gabor frame or Parseval frame to obtain a new one with the same property. Our technique is a modification of a method used in [Glas. Mat. 38 (58) (2003) 75–98] to study the connectivity of affine Parseval frames. DA - 2005/1// PY - 2005/1// DO - 10.1016/j.acha.2004.09.003 VL - 18 IS - 1 SP - 123-136 SN - 1096-603X KW - connectivity KW - frames KW - Gabor systems ER - TY - JOUR TI - Conjugacy decomposition of reductive monoids AU - Putcha, MS T2 - MATHEMATISCHE ZEITSCHRIFT DA - 2005/8// PY - 2005/8// DO - 10.1007/s00209-005-0779-8 VL - 250 IS - 4 SP - 841-853 SN - 0025-5874 ER - TY - JOUR TI - A computational and statistical framework for multidimensional domain acoustooptic material interrogation AU - Banks, HT AU - Bokil, VA T2 - QUARTERLY OF APPLIED MATHEMATICS AB - We consider an electromagnetic interrogation technique in two and three dimensions for identifying the dielectric parameters (including the permittivity, the conductivity and the relaxation time) of a Debye medium. In this technique, a travelling acoustic pressure wave in the Debye medium is used as a virtual reflector for an interrogating microwave electromagnetic pulse that is generated in free space. The reflections of the microwave pulse from the air-Debye interface and from the acoustic pressure wave are recorded at a remote antenna. The data is used in an inverse problem to estimate the locally pressure dependent dielectric parameters of the Debye medium. We present a time domain formulation that is solved using finite differences (FDTD) in time and in space. Perfectly matched layer (PML) absorbing boundary conditions are used to absorb outgoing waves at the finite boundaries of the computational domain, preventing spurious reflections from reentering the domain. Using the method of least squares for the parameter identification problem, we compare two different algorithms (the gradient based Levenberg-Marquardt method and the gradient free, simplex based Nelder-Mead method) in solving an inverse problem to calculate estimates for two or more dielectric parameters. Finally we use statistical error analysis to construct confidence intervals for all the presented estimates, thereby providing a probabilistic statement about the computational procedure with uncertainty aspects of estimates. DA - 2005/3// PY - 2005/3// DO - 10.1090/S0033-569X-05-00949-0 VL - 63 IS - 1 SP - 156-200 SN - 0033-569X KW - electromagnetic-acoustic interaction KW - Debye dielectric materials KW - pulsed antenna source microwaves KW - inverse problems KW - FDTD KW - statistical inference ER - TY - JOUR TI - On wavelet-based numerical homogenization AU - Chertock, A AU - Levy, D T2 - MULTISCALE MODELING & SIMULATION AB - Recently, a wavelet-based method was introduced for the systematic derivation of subgrid scale models in the numerical solution of partial differential equations. Starting from a discretization of the multiscale differential operator, the discrete operator is represented in a wavelet space and projected onto a coarser subspace. The coarse (homogenized) operator is then replaced by a sparse approximation to increase the efficiency of the resulting algorithm. In this work we show how to improve the efficiency of this numerical homogenization method by choosing a different compact representation of the homogenized operator. In two dimensions our approach for obtaining a sparse representation is significantly simpler than the alternative sparse representations. $L^{\infty}$ error estimates are derived for a sample elliptic problem. An additional improvement we propose is a natural fine-scales correction that can be implemented in the final homogenization step. This modification of the scheme improves the resolution of the approximation without any significant increase in the computational cost. We apply our method to a variety of test problems including one- and two-dimensional elliptic models as well as wave propagation problems in materials with subgrid inhomogeneities. DA - 2005/// PY - 2005/// DO - 10.1137/030600783 VL - 3 IS - 1 SP - 65-88 SN - 1540-3459 KW - numerical homogenization KW - wavelets KW - Helmholtz equation ER - TY - JOUR TI - On the complexity of computing determinants AU - Kaltofen, E AU - Villard, G T2 - COMPUTATIONAL COMPLEXITY AB - We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n × n matrix A with integer entries in $$\left( {n^{3.2} \log \left\| A \right\|} \right)^{1 + o(1)} $$ and $$\left( {n^{2.697263} \log \left\| A \right\|} \right)^{1 + o(1)} $$ bit operations; here $$\left\| A \right\|$$ denotes the largest entry in absolute value and the exponent adjustment by “+o(1)” captures additional factors $$C_1 (\log n)^{C_2 } \left( {\log \log \left\| A \right\|} \right)^{C_3 } $$ for positive real constants C1, C2, C3. The bit complexity $$\left( {n^{3.2} \log \left\| A \right\|} \right)^{1 + o(1)} $$ results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications. DA - 2005/2// PY - 2005/2// DO - 10.1007/s00037-004-0185-3 VL - 13 IS - 3-4 SP - 91-130 SN - 1420-8954 KW - integer matrix KW - matrix determinant KW - characteristic polynomial KW - Smith normal form KW - bit complexity KW - division-free complexity KW - randomized algorithm KW - multivariable control theory KW - realization KW - matrix sequence KW - block Wiedemann algorithm KW - block Lanczos algorithm ER - TY - JOUR TI - Quadratic optimization in the problems of active control of sound AU - Lončarić, J. AU - Tsynkov, S.V. T2 - Applied Numerical Mathematics AB - We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulation of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources, which is equivalent to minimization in the sense of L1. By contrast, in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L2 norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L2 minimization is an easy problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we can compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L2 differ drastically from those obtained in the sense of L1. DA - 2005/3// PY - 2005/3// DO - 10.1016/j.apnum.2004.08.041 VL - 52 IS - 4 SP - 381-400 J2 - Applied Numerical Mathematics LA - en OP - SN - 0168-9274 UR - http://dx.doi.org/10.1016/j.apnum.2004.08.041 DB - Crossref KW - noise cancellation KW - active control sources KW - volumetric and surface controls KW - general solution KW - monopoles and dipoles KW - radiation of waves KW - complex-valued quantities KW - L-2-minimization KW - overdetermined systems KW - least squares KW - unconstrained minimization KW - constrained minimization ER - TY - JOUR TI - Gap detection with electromagnetic terahertz signals AU - Banks, HT AU - Gibson, NL AU - Winfree, WP T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS AB - We apply an inverse problem formulation to determine characteristics of a defect from a perturbed electromagnetic interrogating signal. A defect (gap) inside of a dielectric material causes a disruption, via reflections and refractions at the material interfaces, of the windowed interrogating signal. We model the electromagnetic waves inside the material with Maxwell's equations. This leads to a non-standard, nonlinear optimization problem for the dimensions and location of the defect. Using simulations as forward solves, we employ a Newton-based, iterative optimization scheme to a novel modified least-squares objective function. Numerical results are given in tables and plots, standard errors are calculated, and computational issues are addressed. DA - 2005/4// PY - 2005/4// DO - 10.1016/j.nonrwa.2004.09.004 VL - 6 IS - 2 SP - 381-416 SN - 1468-1218 KW - electromagnetic interrogation KW - dielectrics KW - terahertz KW - nonlinear optimization ER - TY - JOUR TI - Reduced-order-based feedback control of the Kuramoto–Sivashinsky equation AU - Lee, C.H. AU - Tran, H.T. T2 - Journal of Computational and Applied Mathematics AB - In this paper, we consider the Kuramoto–Sivashinsky equation (KSE), which describes the long-wave motions of a thin film over a vertical plane. Solution procedures for the KSE often yield a large or infinite-dimensional nonlinear system. We first discuss two reduced-order methods, the approximate inertial manifold and the proper orthogonal decomposition, and show that these methods can be used to obtain a reduced-order system that can accurately describe the dynamics of the KSE. Moreover, from this resulting reduced-order system, the feedback controller can readily be designed and synthesized. For our control techniques, we use the linear and nonlinear quadratic regulator methods, which are the first- and second-order approximated solutions of the Hamilton–Jacobi–Bellman equation, respectively. Numerical simulations comparing the performance of the reduced-order-based linear and nonlinear controllers are presented. DA - 2005/1// PY - 2005/1// DO - 10.1016/j.cam.2004.02.021 VL - 173 IS - 1 SP - 1-19 J2 - Journal of Computational and Applied Mathematics LA - en OP - SN - 0377-0427 UR - http://dx.doi.org/10.1016/j.cam.2004.02.021 DB - Crossref KW - viscous film flows KW - Kuramoto-Sivashinsky equation KW - nonlinear feedback control KW - approximate inertial manifold KW - proper orthogonal decomposition ER - TY - JOUR TI - k-alternating knots AU - Hackney, P AU - Van Wyk, L AU - Walters, N T2 - TOPOLOGY AND ITS APPLICATIONS AB - A projection of a knot is k - alternating if its overcrossings and undercrossings alternate in groups of k as one reads around the projection (an obvious generalization of the notion of an alternating projection). We prove that every knot admits a 2-alternating projection, which partitions nontrivial knots into two classes: alternating and 2-alternating. DA - 2005/5/14/ PY - 2005/5/14/ DO - 10.1016/j.topol.2004.11.007 VL - 150 IS - 1-3 SP - 125-131 SN - 1879-3207 KW - knots KW - alternating knots KW - almost-alternating knots ER - TY - JOUR TI - Well-posedness results for a class of toxicokinetic models AU - Banks, H. T. AU - Potter, L. K. T2 - Dynamic Systems and Applications DA - 2005/// PY - 2005/// VL - 14 IS - 2 SP - 297-322 ER - TY - JOUR TI - The semi-iterative method applied to the hyper-power iteration AU - Chen, XZ AU - Hartwig, RE T2 - NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS AB - The semi-iterative method (SIM) is applied to the hyper-power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi-iterative–hyper-power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd. DA - 2005/11// PY - 2005/11// DO - 10.1002/nla.429 VL - 12 IS - 9 SP - 895-910 SN - 1070-5325 KW - hyper-power iteration KW - semi-iterative method KW - asymptotic convergence rate KW - quotient convergence rate KW - root-convergence rate ER - TY - JOUR TI - On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from their three largest eigenvalues AU - Chu, MT AU - Diele, F AU - Ragni, S T2 - INVERSE PROBLEMS AB - The inverse problem of constructing a symmetric Toeplitz matrix with prescribed eigenvalues has been a challenge both theoretically and computationally in the literature. It is now known in theory that symmetric Toeplitz matrices can have arbitrary real spectra. This paper addresses a similar problem—can the three largest eigenvalues of symmetric pentadiagonal Toeplitz matrices be arbitrary? Given three real numbers ν ⩽ µ ⩽ λ, this paper finds that the ratio , including infinity if µ = ν, determines whether there is a symmetric pentadiagonal Toeplitz matrix with ν, µ and λ as its three largest eigenvalues. It is shown that such a matrix of size n × n does not exist if n is even and α is too large or if n is odd and α is too close to 1. When such a matrix does exist, a numerical method is proposed for the construction. DA - 2005/12// PY - 2005/12// DO - 10.1088/0266-5611/21/6/005 VL - 21 IS - 6 SP - 1879-1894 SN - 1361-6420 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-28544445478&partnerID=MN8TOARS ER - TY - JOUR TI - Measure-valued solutions for a hierarchically size-structured population AU - Ackleh, AS AU - Ito, K T2 - JOURNAL OF DIFFERENTIAL EQUATIONS AB - We present a hierarchically size-structured population model with growth, mortality and reproduction rates which depend on a function of the population density (environment). We present an example to show that if the growth rate is not always a decreasing function of the environment (e.g., a growth which exhibits the Allee effect) the emergence of a singular solution which contains a Dirac delta mass component is possible, even if the vital rates of the individual and the initial data are smooth functions. Therefore, we study the existence of measure-valued solutions. Our approach is based on the vanishing viscosity method. DA - 2005/10/15/ PY - 2005/10/15/ DO - 10.1016/j.jde.2004.12.013 VL - 217 IS - 2 SP - 431-455 SN - 0022-0396 KW - hierarchical size-structured population model KW - measure-valued solutions KW - viscosity method KW - growth rate with an Allee effect ER - TY - JOUR TI - Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains AU - Ito, K AU - Li, ZL AU - Kyei, Y T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING AB - Second and fourth order Cartesian grid based finite difference methods are proposed for elliptic and parabolic partial differential equations, and associated eigenvalue problems on irregular domains with general boundary conditions. Our methods are based on the continuation of a solution idea using multivariable Taylor's expansion of the solution about selected boundary points, and the core ideas of the immersed interface method. The methods offer systematic treatment of the general boundary conditions in two- and three-dimensional domains and are directly applied to semi-discretize heat equations on irregular domains. Convergence analysis and numerical examples are presented. The validity and effectiveness of the proposed methods are demonstrated through our numerical results including computations of the eigenvalues of the associated eigenvalue problem. DA - 2005/// PY - 2005/// DO - 10.1137/03060120X VL - 27 IS - 1 SP - 346-367 SN - 1095-7197 KW - fourth order finite difference schemes KW - elliptic and parabolic equations on irregular domains KW - immersed interface method ER - TY - JOUR TI - A temperature-dependent constitutive model for relaxor ferroelectrics AU - Smith, RC AU - Hom, CL T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - This paper addresses the development of a temperature-dependent constitutive model for relaxor ferroelectric materials. These compounds exhibit a diffuse transition region between the paraelectric and ferroelectric phases due to the chemical heterogeneity of the materials. At low temperatures, the materials exhibit significant dielectric hysteresis in the relation between the applied field E and the macroscopic polarization P, with the degree of hysteresis decreasing as the temperature increases to freezing temperature T f . Above the freezing temperature, the relation is single-valued, but nonlinear. These phenomena are modeled by assuming that the material is comprised of an aggregate of micropolar regions having a range of Curie temperatures. Thermodynamic principles are employed to obtain a micropolar model, which predicts the saturation polarization and distribution of regions as a function of temperature. A corresponding macroscopic model is then constructed to predict the dielectric behavior of the material above the freezing temperature. Hysteresis below the freezing point is incorporated through the quantification of energy required to bend and translate domain walls pinned at sites, including inclusions, point defects, and local fields, inherent to the material. The resulting ordinary differential equation (ODE) model quantifies the constitutive nonlinearities and hysteresis exhibited by the materials through a wide range of temperatures and input drive levels. The predictive capabilities of the model are illustrated through a comparison with PMN (lead magnesium niobate) and PMN-PT-BT (PT: lead titanate; BT: barium titanate) data collected at temperatures ranging from 133 to 313 K. DA - 2005/5// PY - 2005/5// DO - 10.1177/1045389x05051699 VL - 16 IS - 5 SP - 433-448 SN - 1045-389X KW - hysteresis KW - relaxor ferroelectrics KW - nonlinear constitutive relations ER - TY - JOUR TI - A homogenized free energy model for hysteresis in thin-film shape memory alloys AU - Massad, JE AU - Smith, RC T2 - THIN SOLID FILMS AB - Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in microelectromechanical systems due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteretic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent to the constituent materials. We develop a model that quantifies the nonlinearities and hysteresis inherent to SMAs. The fully thermomechanical model is based on free energy principles combined with stochastic homogenization techniques. It predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. The main advantages of this model are that it admits a simple, low-order formulation suitable for implementation and subsequent control design, and that most of the model parameters are identifiable directly from standard measurements. We illustrate aspects of the model through comparison with thin-film SMA superelastic and shape memory effect hysteresis data. DA - 2005/10/1/ PY - 2005/10/1/ DO - 10.1016/j.tsf.2005.04.079 VL - 489 IS - 1-2 SP - 266-290 SN - 1879-2731 KW - shape memory alloy KW - hysteresis model KW - thin film KW - polycrystals ER - TY - JOUR TI - A formula for N-Row Macdonald polynomials AU - Williams, EA T2 - JOURNAL OF ALGEBRAIC COMBINATORICS AB - We derive a formula for the n-row Macdonald polynomials with the coefficients presented both combinatorically and in terms of very-well-poised hypergeometric series. DA - 2005/3// PY - 2005/3// DO - 10.1007/s10801-005-6902-4 VL - 21 IS - 2 SP - 111-130 SN - 1572-9192 KW - Macdonald polynomials KW - symmetric functions KW - hypergeometric series ER - TY - JOUR TI - Time domain electromagnetic scattering using finite elements and perfectly matched layers AU - Banks, HT AU - Browning, BL T2 - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING AB - We consider a model for the interrogation of a planar Debye medium by a non-harmonic microwave pulse from an antenna source in free space, and we compute the reflected solution using finite elements in the spatial variables and finite differences in the time variable. Perfectly matched layers (PMLs) and an absorbing boundary condition are used to damp waves interacting with artificial boundaries imposed to allow finite computational domains. We present simulation results showing that numerical reflections from interfaces at PML boundaries can be controlled. DA - 2005/// PY - 2005/// DO - 10.1016/j.cma.2004.06.013 VL - 194 IS - 2-5 SP - 149-168 SN - 0045-7825 KW - scattering KW - Debye KW - perfectly matched layers KW - absorbing boundary condition ER - TY - JOUR TI - The McCormack model for gas mixtures: Plane Couette flow AU - Garcia, RDM AU - Siewert, CE T2 - PHYSICS OF FLUIDS AB - An analytical version of the discrete-ordinates method is used to establish a concise and particularly accurate solution to the problem of plane Couette flow for a binary gas mixture described by the McCormack kinetic model. The solution yields, for the general (specular-diffuse) case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species of gas particles. Highly accurate numerical results are reported for the case of a helium–argon mixture confined between molybdenum and tantalum plates. The algorithm is considered especially easy to use, and the developed (FORTRAN) code requires typically less than a second on a 2.2GHz Pentium 4 machine to compute all quantities of interest with at least five figures of accuracy. DA - 2005/3// PY - 2005/3// DO - 10.1063/1.1845911 VL - 17 IS - 3 SP - SN - 1070-6631 ER - TY - JOUR TI - The Maurer-Cartan structure of BRST differentials AU - Gao, J. N. T2 - Journal of Mathematical Physics DA - 2005/// PY - 2005/// VL - 46 IS - 6 ER - TY - JOUR TI - Positively selected sites in the Arabidopsis receptor-like kinase gene family AU - Strain, E AU - Muse, SV T2 - JOURNAL OF MOLECULAR EVOLUTION DA - 2005/9// PY - 2005/9// DO - 10.1007/s00239-004-0308-0 VL - 61 IS - 3 SP - 325-332 SN - 1432-1432 KW - receptor-like kinase KW - positive selection KW - gene family KW - leucine-rich repeat ER - TY - JOUR TI - On degenerate saturated-diffusion equations with convection AU - Chertock, A AU - Kurganov, A AU - Rosenau, P T2 - NONLINEARITY AB - We study a class of degenerate parabolic convection–diffusion equations, endowed with a mechanism for saturation of the diffusion flux, which corrects the unphysical gradient-flux relations at high gradients. This paper extends our previous works on the effects of diffusion with saturation on convection and the impact of saturation on porous media-type diffusion, where it has been demonstrated that a nonlinear saturating diffusion is susceptible to a self-induced formation of discontinuities. In this work we demonstrate that nonlinear convection enhances the breakdown effect. We carry both analytical and numerical studies of the model equation, ut + f(u)x = [φ(u)Q(ux, u)]x, where Q is a bounded increasing function, φ(0) = 0 and φ(u) ∼ un, n > 0 for u ∼ 0. Depending on a choice of n, we obtain two distinctive processes. If 0 ≤ n ≤ 1, a discontinuity forms only when the upstream–downstream disparity exceeds a critical threshold, but if n > 1, all travelling waves are found to have a sharp discontinuous front. In fact, given a compact or a semi-compact initial datum, the front will not start to move until such a discontinuity forms. DA - 2005/3// PY - 2005/3// DO - 10.1088/0951-7715/18/2/009 VL - 18 IS - 2 SP - 609-630 SN - 1361-6544 UR - https://doi-org.prox.lib.ncsu.edu/10.1088/0951-7715/18/2/009 ER - TY - JOUR TI - On a system of rational difference equations AU - Clark, CA AU - Kulenovic, MRS AU - Selgrade, JF T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS AB - We investigate the global character of solutions of the system of difference equations with positive parameters and non-negative initial conditions. DA - 2005/6// PY - 2005/6// DO - 10.1080/10236190412331334464 VL - 11 IS - 7 SP - 565-580 SN - 1563-5120 KW - difference equation KW - global asymptotic stability KW - invariant set KW - monotone map KW - stable manifold ER - TY - JOUR TI - Diagonalizing triangular matrices via orthogonal Pierce decompositions AU - Hartwig, RE AU - Patricio, P AU - Puystjens, R T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - A class of sufficient conditions is given to ensure that the sum a + b in a ring R , is equivalent to a sum x + y , which is an orthogonal Pierce decomposition. This is then used to show that a lower triangular matrix, with a regular diagonal is equivalent to its diagonal iff the matrix admits a lower triangular von Neumann inverse. DA - 2005/5/15/ PY - 2005/5/15/ DO - 10.1016/j.laa.2004.10.002 VL - 401 SP - 381-391 SN - 1873-1856 KW - rings KW - triangular matrices KW - von Neumann regularity KW - diagonalization ER - TY - JOUR TI - Bosonic realizations of higher-level toroidal Lie algebras AU - Jing, NH AU - Misra, K AU - Tan, SB T2 - PACIFIC JOURNAL OF MATHEMATICS AB - We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A1 using vertex operators based on bosonic elds. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k0;k1) with k00. We also construct a smaller module of level (k0;0) for the toroidal algebra from the Fock space using certain screening vertex operator, and this later representation generalizes the higher-level construction of the ane Lie algebra 2. DA - 2005/4// PY - 2005/4// DO - 10.2140/pjm.2005.219.285 VL - 219 IS - 2 SP - 285-301 SN - 0030-8730 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-30544448525&partnerID=MN8TOARS KW - toroidal Lie algebra KW - vertex operator KW - bosonic realization ER - TY - JOUR TI - An optimal optical flow AU - Ito, K T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - The problem of determining optical flow for the image registration problem is discussed. Feedback solutions are proposed, and it is shown that they are optimal for certain optimal control formulations of the problem. Well-posedness of the proposed feedback solutions is analyzed, and numerical findings are presented. DA - 2005/// PY - 2005/// DO - 10.1137/S0363012904433444 VL - 44 IS - 2 SP - 728-742 SN - 0363-0129 KW - optical flow KW - feedback solution ER - TY - JOUR TI - A parameter sensitivity methodology in the context of HIV delay equation models AU - Banks, HT AU - Bortz, DM T2 - JOURNAL OF MATHEMATICAL BIOLOGY AB - A sensitivity methodology for nonlinear delay systems arising in one class of cellular HIV infection models is presented. Theoretical foundations for a typical sensitivity investigation and illustrative computations are given. DA - 2005/6// PY - 2005/6// DO - 10.1007/s00285-004-0299-x VL - 50 IS - 6 SP - 607-625 SN - 1432-1416 KW - sensitivity analysis KW - parameter sensitivity methodology KW - HIV Models ER - TY - JOUR TI - A stochastic control model of investment, production and consumption AU - Fleming, W. H. AU - Pang, T. T2 - Quarterly of Applied Mathematics AB - We consider a stochastic control model in which an economic unit has productive capital and also liabilities in the form of debt. The worth of capital changes over time through investment as well as through random Brownian fluctuations in the unit price of capital. Income from production is also subject to random Brownian fluctuations. The goal is to choose investment and consumption controls which maximize total expected discounted HARA utility of consumption. Optimal control policies are found using the method of dynamic programming. In case of logarithmic utility, these policies have explicit forms. DA - 2005/// PY - 2005/// DO - 10.1090/s0033-569x-04-00941-1 VL - 63 IS - 1 SP - 71-87 ER - TY - JOUR TI - Instantaneous multiple-depth soil mechanical impedance sensing from a moving vehicle AU - Chukwu, E. AU - Bowers, C. G. T2 - Transactions of the ASAE AB - A three-depth soil mechanical impedance sensor was developed and tested within a laboratory soil bin. Soilmechanical impedance measurements were made on a continuous basis at three simultaneous depths of 178, 279, and 381 mmfrom one end of the soil bin to the other using three prismatic tips and three Omega LCF500 load cells. This article discusseshow the sensor can be used for measuring the soil mechanical impedances that plant roots encounter during normal growth.The soil sensor also offers excellent opportunities to study the forces acting on soil-engaging implements and subsequentcontrol of tillage tools. Compaction created from past tillage machinery operation and trafficking by heavy equipmentsometimes forms plowpans in crop fields. These layers, as well as other naturally occurring dense soil layers that impedewater infiltration and root penetration, can be located using the three-depth soil mechanical impedance sensor. Thelaboratory experiment for testing and verifying the devices performance showed that the three-depth sensor can measuredifferences in soil mechanical impedance with depth and location and that these impedances correlate well withcorresponding cone penetrometer measurements. DA - 2005/// PY - 2005/// DO - 10.13031/2013.18492 VL - 48 IS - 3 SP - 885-894 ER -