TY - CHAP TI - Algebraic algorithms AU - Díaz, A. AU - Kaltofen, E. AU - Pan, V. T2 - The computer science and engineering handbook A2 - Tucker, A.B. PY - 1997/// SP - 226–248 PB - CRC Press SN - 9780849329098 ER - TY - JOUR TI - Immersed interface methods for moving interface problems AU - Li, Zhilin T2 - Numerical Algorithms DA - 1997/5// PY - 1997/5// DO - 10.1023/A:1019173215885 VL - 14 SP - 269–293 KW - immersed interface method KW - Stefan problem KW - moving interface KW - discontinuous coefficients KW - singular source term KW - immersed boundary method KW - Cartesian grid KW - heat conduction ER - TY - JOUR TI - Front fixing vs. front tracking for diffusive transport with moving boundaries AU - Heine, J. T. AU - Li, Zhilin AU - McTigue, D. F. T2 - International Journal for Numerical & Analytical Methods in Geomechanics DA - 1997/// PY - 1997/// VL - 21 SP - 653–662 ER - TY - JOUR TI - An Inverse Problem in a Parabolic Equation AU - Li, Zhilin AU - Zheng, K T2 - Electronic Journal of Differential Equations DA - 1997/// PY - 1997/// VL - 1 SP - 193–199 ER - TY - CONF TI - Mixed symbolic-numerical computations with general DAEs AU - Campbell, Stephen L. AU - Hollenbeck, R. AU - Marszalek, W. T2 - Symposium on Differential Algebraic Equations C2 - 1997/// C3 - Proceedings of the Symposium on Differential-Algebraic Equations: Algebraic and Numerical Aspects CY - Grenoble, France DA - 1997/// PY - 1997/5/26/ SP - 23–34 ER - TY - JOUR TI - Observer design for linear time varying descriptor systems AU - Campbell, Stephen L. AU - Delebecque, F. AU - Nikoukhah, R. T2 - Proceedings of the Control Industrial Systems DA - 1997/// PY - 1997/// VL - 1 SP - 507–512 ER - TY - JOUR TI - Highest weight modules of W_(1+∞), Darboux transformations and the bispectral problem AU - Bakalov, B. AU - Horozov, E. AU - Yakimov, M. T2 - Serdica Mathematical Journal DA - 1997/// PY - 1997/// VL - 23 IS - 2 SP - 95–112 ER - TY - BOOK TI - Mechanisms for branching morphogenesis of the lung AU - Lubkin, S. R. A3 - Alt, W. A3 - Deutsch, A. A3 - Dunn, G. DA - 1997/// PY - 1997/// PB - SE - 229-234 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000071666700027&KeyUID=WOS:000071666700027 ER - TY - BOOK TI - PASCO '97: Proceedings of the second international symposium on Parallel symbolic computation A3 - Hong, Hoon A3 - Kaltofen, Erich A3 - Hitz, Markus DA - 1997/// PY - 1997/// DO - 10.1145/266670 PB - ACM Press SN - 0897919513 9780897919517 UR - http://dx.doi.org/10.1145/266670 ER - TY - CONF TI - Stress fluctuations in granular materials AU - Schaeffer, D.G. AU - Shearer, Michael A2 - Chang, C.S. A2 - Misra, A. A2 - Liang, R.Y. A2 - Babic, M. C2 - 1997/// C3 - Mechanics of deformation and flow of particulate materials : proceedings of a symposium, Evanston, Illinois, June 29-July 2, 1997 DA - 1997/// PB - ASCE Publications ER - TY - CONF TI - Models for stress fluctuations in plasticity AU - Schaeffer, D.G. AU - Shearer, Michael T2 - International Conference on Powders & Grains A2 - Behringer, R.P. A2 - Jenkins, J. C2 - 1997/// C3 - Powders & grains 97 : proceedings of the third International Conference on Powders & Grains, Durham, North Carolina, 18-23 May 1997 CY - Durham, North Carolina DA - 1997/// PY - 1997/5/18/ SP - 325-328 PB - Balkema ER - TY - RPRT TI - If a matrix has a single eigenvalue, how sensitive is this eigenvalue? AU - Cho, G.E. AU - Ipsen, I.C.F. A3 - Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University DA - 1997/// PY - 1997/// M1 - CRSC-TR97-20 M3 - Technical Report PB - Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University SN - CRSC-TR97-20 ER - TY - JOUR TI - Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension AU - LeVeque, Randall J. AU - Li, Zhilin T2 - SIAM Journal on Scientific Computing AB - A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper [SIAM J. Numer. Anal., 31(1994), pp. 1019--1044]. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used. DA - 1997/5// PY - 1997/5// DO - 10.1137/s1064827595282532 VL - 18 IS - 3 SP - 709-735 J2 - SIAM J. Sci. Comput. LA - en OP - SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/s1064827595282532 DB - Crossref KW - Stokes flow KW - creeping flow KW - interface tracking KW - discontinuous coefficients KW - immersed interface methods KW - Cartesian grids KW - bubbles ER - TY - CONF TI - Proceedings of the 2nd International Workshop on Parallel Symbolic Computation, PASCO 1997, July 20-22, 1997, Kihei, Hawaii, USA A2 - Hong, Hoon A2 - Kaltofen, Erich A2 - Hitz, Markus A. C2 - 1997/// DA - 1997/// PB - ACM ER - TY - JOUR TI - Multivariate Resultants Under Composition AU - Hong, Hoon DA - 1997/4// PY - 1997/4// VL - 4 SP - ER - TY - JOUR TI - Subresultants Under Composition AU - Hong, Hoon T2 - Journal of Symbolic Computation AB - Composition is an operation of replacing a variable in a polynomial with another polynomial. The main question of this paper is:What happens to subresultants under composition? The main contribution of the paper is to show that the subresultants ``almost'' commute with composition. This generalizes the well-known fact that the resultant is invariant under translation. DA - 1997/4// PY - 1997/4// DO - 10.1006/jsco.1996.0093 VL - 23 IS - 4 SP - 355-365 UR - http://dx.doi.org/10.1006/jsco.1996.0093 ER - TY - JOUR TI - Implicitization of Nested Circular Curves AU - HONG, HOON T2 - Journal of Symbolic Computation AB - A nested circular curve is a real plane curve traced by a point on a circle that rotates around another circle that again rotates around still another circle, and so on. In this paper, we give an efficient method for obtaining an implicit equation of a nested circular curve. DA - 1997/2// PY - 1997/2// DO - 10.1006/jsco.1996.0082 VL - 23 IS - 2-3 SP - 177-189 UR - http://dx.doi.org/10.1006/jsco.1996.0082 ER - TY - JOUR TI - Testing Stability by Quantifier Elimination AU - HONG, HOON AU - LISKA, RICHARD AU - STEINBERG, STANLY T2 - Journal of Symbolic Computation AB - For initial and initial-boundary value problems described by differential equations, stability requires the solutions to behave well for large times. For linear constant-coefficient problems, Fourier and Laplace transforms are used to convert stability problems to questions about roots of polynomials. Many of these questions can be viewed, in a natural way, as quantifier-elimination problems. The Tarski–Seidenberg theorem shows that quantifier-elimination problems are solvable in a finite number of steps. However, the complexity of this algorithm makes it impractical for even the simplest problems. The newer Quantifier Elimination by Partial Algebraic Decomposition (QEPCAD) algorithm is far more practical, allowing the solution of some non-trivial problems. In this paper, we show how to write all common stability problems as quantifier-elimination problems, and develop a set of computer-algebra tools that allows us to find analytic solutions to simple stability problems in a few seconds, and to solve some interesting problems in from a few minutes to a few hours. DA - 1997/8// PY - 1997/8// DO - 10.1006/jsco.1997.0121 VL - 24 IS - 2 SP - 161-187 UR - http://dx.doi.org/10.1006/jsco.1997.0121 ER - TY - JOUR TI - Special Issue on Application of Quantifier Elimination. Foreword of the Guest Editors AU - Hong, Hoon AU - Liska, Richard T2 - Journal of Symbolic Computation AB - No abstract DA - 1997/8// PY - 1997/8// DO - 10.1006/jsco.1997.0117 VL - 24 IS - 2 SP - 123 UR - http://dx.doi.org/10.1006/jsco.1997.0117 ER - TY - JOUR TI - Heuristic Search and Pruning in Polynomial Constraints Satisfaction. AU - Hong, Hoon T2 - Ann. Math. Artif. Intell. DA - 1997/4// PY - 1997/4// DO - 10.1023/A:1018911907086 VL - 19 IS - 3-4 SP - 319-334 UR - https://doi.org/10.1023/A:1018911907086 ER - TY - JOUR TI - Comparison of Several Decision Algorithms for the Existential Theory of the Reals AU - Hong, Hoon DA - 1997/5// PY - 1997/5// VL - 5 SP - ER - TY - JOUR TI - A Hybrid Method for Moving Interface Problems with Application to the Hele–Shaw Flow AU - Hou, Thomas Y. AU - Li, Zhilin AU - Osher, Stanley AU - Zhao, Hongkai T2 - Journal of Computational Physics AB - In this paper, a hybrid approach which combines theimmersed interface methodwith thelevel set approachis presented. The fast version of the immersed interface method is used to solve the differential equations whose solutions and their derivatives may be discontinuous across the interfaces due to the discontinuity of the coefficients or/and singular sources along the interfaces. The moving interfaces then are updated using the newly developed fast level set formulation which involves computation only inside some small tubes containing the interfaces. This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems. Several key steps in the implementation are addressed in detail. This new approach is then applied to Hele–Shaw flow, an unstable flow involving two fluids with very different viscosity. DA - 1997/7// PY - 1997/7// DO - 10.1006/jcph.1997.5689 VL - 134 IS - 2 SP - 236-252 J2 - Journal of Computational Physics LA - en OP - SN - 0021-9991 UR - http://dx.doi.org/10.1006/jcph.1997.5689 DB - Crossref ER - TY - CHAP TI - Formation of Shear Bands in Models of Granular Materials AU - Shearer, M. AU - Garaizar, F. X. AU - Gordon, M. K. T2 - IUTAM Symposium on Mechanics of Granular and Porous Materials AB - In this paper we analyze the behavior of a granular material just prior to the appearance of a shear band. Shear band formation has long been associated with stress and strain localization — the deformation develops abruptly and locally near the site of the shear band (Rudnicki and Rice, 1975). It is also recognized that the phenomenon is connected with a change of type in the governing partial differential equations resulting from a continuum theory (Schaeffer, 1990). PY - 1997/// DO - 10.1007/978-94-011-5520-5_31 SP - 343-352 OP - PB - Springer Netherlands SN - 9789401063241 9789401155205 UR - http://dx.doi.org/10.1007/978-94-011-5520-5_31 DB - Crossref ER - TY - CONF TI - Fast polynomial factorization over high algebraic extensions of finite fields AU - Kaltofen, Erich AU - Shoup, Victor T2 - the 1997 international symposium AB - New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number. When log q = n, where a > 0 is constant, these algorithms are asymptotically faster than previous known algorithms, the fastest of which required time Ω(n(log q)), or Ω(n) in this case, which corresponds to the cost of computing x modulo an n degree polynomial. The new algorithms factor an arbitrary polynomial in time O(n+n). All measures are in fixed precision operations, that is in bit complexity. Moreover, in the special case where all the irreducible factors have the same degree, the new algorithms run in time O(n). In particular, one may test a polynomial for irreducibility in O(n) bit operations. These results generalize to the case where q = p, where p is a small prime number relative to q. C2 - 1997/// C3 - Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97 DA - 1997/// DO - 10.1145/258726.258777 PB - ACM Press SN - 0897918754 UR - http://dx.doi.org/10.1145/258726.258777 DB - Crossref ER - TY - CONF TI - On randomized Lanczos algorithms AU - Eberly, Wayne AU - Kaltofen, Erich T2 - the 1997 international symposium AB - Article Free Access Share on On randomized Lanczos algorithms Authors: Wayne Eberly Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4 Department of Computer Science, University of Calgary, Calgary, Alberta, Canada T2N 1N4View Profile , Erich Kaltofen Department of Mathematics, North Carolina State University, Raleigh, North Carolina Department of Mathematics, North Carolina State University, Raleigh, North CarolinaView Profile Authors Info & Claims ISSAC '97: Proceedings of the 1997 international symposium on Symbolic and algebraic computationJuly 1997 Pages 176–183https://doi.org/10.1145/258726.258776Published:01 July 1997Publication History 23citation416DownloadsMetricsTotal Citations23Total Downloads416Last 12 Months41Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF C2 - 1997/// C3 - Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97 DA - 1997/// DO - 10.1145/258726.258776 PB - ACM Press SN - 0897918754 UR - http://dx.doi.org/10.1145/258726.258776 DB - Crossref ER - TY - JOUR TI - The extent of early viral replication is a critical determinant of the natural history of simian immunodeficiency virus infection. AU - Lifson, Jeffrey D AU - Nowak, Martin A AU - Goldstein, Simoy AU - Rossio, Jeffrey L AU - Kinter, Audrey AU - Vasquez, Gabriela AU - Wiltrout, Theresa A AU - Brown, Charles AU - Schneider, Douglas AU - Wahl, Linda AU - others T2 - Journal of Virology DA - 1997/// PY - 1997/// VL - 71 IS - 12 SP - 9508-9514 ER - TY - RPRT TI - Optimal Design of High Speed Mechanical Systems AU - David, J W AU - Cheng, C Y AU - Choi, T D AU - Kelley, C T AU - Gablonsky, J A3 - North Carolina State University, Center for Research in Scientific Computation DA - 1997/7// PY - 1997/7// M1 - CRSC-TR97-18 PB - North Carolina State University, Center for Research in Scientific Computation SN - CRSC-TR97-18 ER - TY - JOUR TI - Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections AU - Combettes, P.L. T2 - IEEE Transactions on Image Processing AB - Solving a convex set theoretic image recovery problem amounts to finding a point in the intersection of closed and convex sets in a Hilbert space. The projection onto convex sets (POCS) algorithm, in which an initial estimate is sequentially projected onto the individual sets according to a periodic schedule, has been the most prevalent tool to solve such problems. Nonetheless, POCS has several shortcomings: it converges slowly, it is ill suited for implementation on parallel processors, and it requires the computation of exact projections at each iteration. We propose a general parallel projection method (EMOPSP) that overcomes these shortcomings. At each iteration of EMOPSP, a convex combination of subgradient projections onto some of the sets is formed and the update is obtained via relaxation. The relaxation parameter may vary over an iteration-dependent, extrapolated range that extends beyond the interval [0,2] used in conventional projection methods. EMOPSP not only generalizes existing projection-based schemes, but it also converges very efficiently thanks to its extrapolated relaxations. Theoretical convergence results are presented as well as numerical simulations. DA - 1997/4// PY - 1997/4// DO - 10.1109/83.563316 VL - 6 IS - 4 SP - 493-506 J2 - IEEE Trans. on Image Process. OP - SN - 1057-7149 UR - http://dx.doi.org/10.1109/83.563316 DB - Crossref ER - TY - JOUR TI - Hilbertian convex feasibility problem: Convergence of projection methods AU - Combettes, P. L. T2 - Applied Mathematics & Optimization DA - 1997/5// PY - 1997/5// DO - 10.1007/bf02683333 VL - 35 IS - 3 SP - 311-330 J2 - Appl Math Optim LA - en OP - SN - 0095-4616 1432-0606 UR - http://dx.doi.org/10.1007/bf02683333 DB - Crossref ER - TY - JOUR TI - Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection AU - Nowak, M.A. AU - Lloyd, A.L. AU - Vasquez, G.M. AU - Wiltrout, T.A. AU - Wahl, L.M. AU - Bischofberger, N. AU - Williams, J. AU - Kinter, A. AU - Fauci, A.S. AU - Hirsch, V.M. AU - Lifson, J.D. T2 - Journal of Virology DA - 1997/// PY - 1997/// VL - 71 IS - 10 SP - 7518–7525 ER - TY - JOUR TI - Presence of an inducible HIV-1 latent reservoir during highly active antiretroviral therapy AU - Chun, T.-W. AU - Stuyver, L. AU - Mizell, S. B. AU - Ehler, L. A. AU - Mican, J. A. M. AU - Baseler, M. AU - Lloyd, A. L. AU - Nowak, M. A. AU - Fauci, A. S. T2 - Proceedings of the National Academy of Sciences AB - Although highly active antiretroviral therapy (HAART) in the form of triple combinations of drugs including protease inhibitors can reduce the plasma viral load of some HIV-1-infected individuals to undetectable levels, it is unclear what the effects of these regimens are on latently infected CD4+ T cells and what role these cells play in the persistence of HIV-1 infection in individuals receiving such treatment. The present study demonstrates that highly purified CD4+ T cells from 13 of 13 patients receiving HAART with an average treatment time of 10 months and with undetectable (<500 copies HIV RNA/ml) plasma viremia by a commonly used bDNA assay carried integrated proviral DNA and were capable of producing infectious virus upon cellular activation in vitro. Phenotypic analysis of HIV-1 produced by activation of latently infected CD4+ T cells revealed the presence in some patients of syncytium-inducing virus. In addition, the presence of unintegrated HIV-1 DNA in infected resting CD4+ T cells from patients receiving HAART, even those with undetectable plasma viremia, suggests persistent active virus replication in vivo. DA - 1997/11/25/ PY - 1997/11/25/ DO - 10.1073/pnas.94.24.13193 VL - 94 IS - 24 SP - 13193-13197 J2 - Proceedings of the National Academy of Sciences LA - en OP - SN - 0027-8424 1091-6490 UR - http://dx.doi.org/10.1073/pnas.94.24.13193 DB - Crossref ER - TY - JOUR TI - Damage Detection as Inverse Problems for Distributed Parameter Systems: Computational Approaches AU - Banks, H.T. AU - Smith, R.C. AU - Zhang, Y. T2 - International Journal of Applied Electromagnetics and Mechanics DA - 1997/// PY - 1997/// VL - 8 SP - 61–76 ER - TY - JOUR TI - Numerical Recovery of Material Parameters in Euler-Bernoulli Beam Models AU - Smith, R.C. AU - Bowers, K.L. AU - Vogel, C.R. T2 - Journal of Mathematical Systems, Estimation and Control DA - 1997/// PY - 1997/// VL - 7 IS - 2 SP - 157–195 ER - TY - JOUR TI - Bispectral Algebras of Commuting Ordinary Differential Operators AU - Bakalov, B. AU - Horozov, E. AU - Yakimov, M. T2 - Communications in Mathematical Physics AB - We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank N. It combines and unifies the ideas of Duistermaat–Grünbaum and Wilson. Our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators. The method also provides new broad families of bispectral algebras which may help to penetrate deeper into the problem. DA - 1997/12/1/ PY - 1997/12/1/ DO - 10.1007/s002200050244 VL - 190 IS - 2 SP - 331-373 J2 - Communications in Mathematical Physics OP - SN - 0010-3616 1432-0916 UR - http://dx.doi.org/10.1007/s002200050244 DB - Crossref ER - TY - JOUR TI - Bispectrum and Analysis of the Statistics of Electromagnetic Waves Backscattered by Sea Surface AU - Gilman, M.A. T2 - Journal of Computer and System Sciences International DA - 1997/// PY - 1997/// VL - 36 IS - 6 SP - 972–980 ER - TY - CHAP TI - Analytic approximations to the deformation of a thin compressible elastic layer by a rigid indenter AU - Haider, M.A. AU - Holmes, M.H. T2 - Applied Mathematics: Methods and Applications A2 - Oyibo, G. PY - 1997/// SP - 257–288 PB - Nova Science ER - TY - JOUR TI - The extent of early viral replication is a critical determinant of the natural history of simian immunodeficiency virus infection AU - Lifson, J.D. AU - Nowak, M.A. AU - Goldstein, S. AU - Rossio, J.L. AU - Kinter, A. AU - Vasquez, G. AU - Wiltrout, T.A. AU - Brown, C. AU - Schneider, D. AU - Wahl, L. AU - Lloyd, A.L. AU - Williams, J. AU - Elkins, W.R. AU - Fauci, A.S. AU - Hirsch, V.M. T2 - Journal of Virology DA - 1997/// PY - 1997/// VL - 71 IS - 12 SP - 9508–9514 ER - TY - JOUR TI - A Galerkin Method for Linear PDE Systems in Circular Geometries with Structural Acoustic Problems AU - Smith, Ralph C. T2 - SIAM Journal on Scientific Computing AB - A Galerkin method for systems of PDEs in circular geometries is presented with motivating problems being drawn from structural, acoustic, and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at the singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the 2-D wave equation on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems. DA - 1997/3// PY - 1997/3// DO - 10.1137/s1064827594268531 VL - 18 IS - 2 SP - 371-402 J2 - SIAM J. Sci. Comput. LA - en OP - SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/s1064827594268531 DB - Crossref KW - Galerkin method KW - PDEs in circular geometries KW - structural acoustics ER - TY - JOUR TI - THE ESTIMATION OF MATERIAL AND PATCH PARAMETERS IN A PDE-BASED CIRCULAR PLATE MODEL AU - Banks, H.T. AU - Smith, R.C. AU - Brown, D.E. AU - Metcalf, V.L. AU - Silcox, R.J. T2 - Journal of Sound and Vibration AB - The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions from the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio and Kelvin-Voigt damping for the system, as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics. DA - 1997/2// PY - 1997/2// DO - 10.1006/jsvi.1996.0649 VL - 199 IS - 5 SP - 777-799 J2 - Journal of Sound and Vibration LA - en OP - SN - 0022-460X UR - http://dx.doi.org/10.1006/jsvi.1996.0649 DB - Crossref ER - TY - JOUR TI - Artificial Boundary Conditions for Computation of Oscillating External Flows AU - Tsynkov, S. V. T2 - SIAM Journal on Scientific Computing AB - In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused, for example, by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABCs) at the introduced external boundary. The ABCs we are aiming to obtain must meet the following fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABCs for oscillating flows is based on an essential assumption: the Navier--Stokes equations can be linearized in the far field against the free-stream background. To actually compute the ABCs, we represent the far-field solution as a Fourier series in time and then apply the difference potentials method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABCs for time-periodic external flows. Based on our experience in implementing analogous ABCs for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows. DA - 1997/11// PY - 1997/11// DO - 10.1137/s1064827595291145 VL - 18 IS - 6 SP - 1612-1656 J2 - SIAM J. Sci. Comput. LA - en OP - SN - 1064-8275 1095-7197 UR - http://dx.doi.org/10.1137/s1064827595291145 DB - Crossref KW - oscillating flows KW - artificial boundary conditions KW - boundary equations with projections KW - auxiliary problem KW - difference potentials method ER - TY - THES TI - Analysis of partial differential algebraic equations AU - Marszalek, Wieslaw DA - 1997/// PY - 1997/// PB - Raleigh: North Carolina State University ER - TY - JOUR TI - Instantaneous multiple depth soil mechanical impedance sensing from a moving vehicle AU - Chukwu, E. AU - Bowers, C. G. T2 - Paper (American Society of Agricultural Engineers) DA - 1997/// PY - 1997/// IS - 971077 SP - 23 ER - TY - BOOK TI - Computer modeling : from sports to spaceflight--from order to chaos AU - Danby, J. M. A. DA - 1997/// PY - 1997/// PB - Richmond, VA: Willmann-Bell SN - 0943396514 ER - TY - JOUR TI - Generalized polynomial bases and the Bezoutian AU - Mani, V AU - Hartwig, RE T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - A foundation polynomial is used to induce polynomial bases for Fn−1[x], the vector space of polynomials of degree less than n over an arbitrary field F. The associated bases are then used to block diagonalize the Bezout matrix of two polynomials under congruence. DA - 1997/1/15/ PY - 1997/1/15/ DO - 10.1016/0024-3795(95)00585-4 VL - 251 SP - 293-320 SN - 0024-3795 ER - TY - JOUR TI - Use of an epidemiologic model to evaluate feline leukemia virus control measures AU - Romatowski, J. AU - Lubkin, S. R. T2 - Feline Practice DA - 1997/// PY - 1997/// VL - 25 IS - 4 SP - 6-11 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1997XU72500002&KeyUID=WOS:A1997XU72500002 ER - TY - JOUR TI - Mechanisms for Branching Morphogenesis of the Lung AU - Lubkin, Sharon R. T2 - Dynamics of Cell and Tissue Motion AB - The human lung is a dichotomously branched, hollow structure, which forms in a similar manner to other glandular organs such as the kidney, pancreas, mammary and salivary glands. A hollow finger of epithelium grows into surrounding mesenchyme, and branches repeatedly, over some 23 generations. In turn, the surrounding mesenchyme condenses around the epithelium. Although a great deal is known about branching morphogenesis, primarily from studies of the mouse submandibular gland, branching is not a fully understood process. CN - QH647 .D96 1997 DA - 1997/// PY - 1997/// DO - 10.1007/978-3-0348-8916-2_27 SP - 229-234 ER - TY - CHAP TI - Dynamics within tissues stresses, growth, and morphogenesis AU - Lubkin, S. R. AU - Beloussov, L. V. T2 - Dynamics of cell and tissue motion A2 - W. Alt, A. Deutsch A2 - Dunn, G. CN - QH647 .D96 1997 PY - 1997/// SP - 211-284 PB - Basel: Birkhauser Verlag ER - TY - JOUR TI - Limit theorems and a general framework for risk analysis in clonal forestry AU - Bishir, J AU - Roberds, J T2 - MATHEMATICAL BIOSCIENCES AB - Use of clonally propagated plantings in reforestation offers management advantages of phenotypic uniformity and high yields. Disadvantages include low genetic diversity and the possibility that the clone or clones chosen are particularly susceptible to attack by an insect or pathogen unforeseen as a problem at the time of clonal selection. In this paper, we continue consideration of the problem of choosing an optimal number of clones to minimize the risk of plantation failure. We present an analysis in which risk of failure for a plantation is represented by the probability that the proportion, S, of ramets that survive until harvest is less than or equal to a prescribed value. Our approach includes most earlier treatments as special cases. We show that the proportion S converges in distribution and, furthermore, that, under general conditions, a moderate number of clones, usually no more than 20 to 40 and often fewer, provides equivalent or better protection against catastrophic loss than does a large number of clones. DA - 1997/5// PY - 1997/5// DO - 10.1016/S0025-5564(96)00184-8 VL - 142 IS - 1 SP - 1-11 SN - 0025-5564 ER - TY - JOUR TI - Response of ovule development and post-pollen production processes in male-sterile tomatoes to chronic, sub-acute high temperature stress AU - Peet, MM AU - Willits, DH AU - Gardner, R T2 - JOURNAL OF EXPERIMENTAL BOTANY AB - In order to determine the effects of high temperature on ovule development and reproductive processes subsequent to pollen production, nine day/night temperature combinations were imposed over a 9 month period as four separate experiments, each with three treatments, including one common treatment. In order to eliminate known effects of high temperatures on pollen production and stylar position, high temperature treatments were applied only to male-sterile tomatoes (Lycopersicon esculentum Mill.). Pollen was obtained from male-fertile plants given optimal growth conditions. This allowed comparison of mean daily temperatures from 25–29 °C; day/night temperature differentials (DIFs) of 2, 6, and 10°C; day temperatures of 28, 30 and 32°C at night temperatures of 22, 24, and 26°C; and night temperatures of 22, 24 and 26°C at day temperatures of 28, 30 and 32°C. Average weight per fruit and flower number did not demonstrate a consistent pattern of response to high temperature. Other reproductive characteristics (% fruitset, total number and weight of fruit per plant, and seediness index) decreased as mean daily temperature rose from 25°C to 26°C and from 28°C to 29°C. The primary parameter affecting these variables was mean daily temperature, with day temperature having a secondary role. Thus, in determining reproductive responses of tomato to temperatures within this range, day temperature, night temperature and DIFs do not need to be considered independently of their effect on mean daily temperature. If this relationship holds true in other species, and for pre-pollen production pro- cesses as well, modelling the effects of projected climate change should be simplified. DA - 1997/1// PY - 1997/1// DO - 10.1093/jxb/48.1.101 VL - 48 IS - 306 SP - 101-111 SN - 0022-0957 KW - global climate change KW - thermotolerance KW - stress resistance KW - ovule development KW - pollination ER - TY - JOUR TI - Principles of competitive exclusion for discrete populations with reproducing juveniles and adults AU - Franke, JE AU - Yakubu, AA T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS AB - We invent notions of dominance and weak dominance for discrete multi-species systems with competing juveniles and adults. In this model, both the juveniles and adults are allowed to reproduce. We prove that, a dominant species drives the dominated species to extinction. In discrete juvenile-adult systems that do not allow juveniles to reproduce, it is known that weak dominance is equivalent to dominance, provided all the growth functions are exponentials. We show that if juveniles are allowed to reproduce, then a weakly dominant species could be driven to extinction. It all the growth functions are exponential functions, we obtain sufficient conditions that guarantee the equivalence of weak dominance and dominance. DA - 1997/12// PY - 1997/12// DO - 10.1016/S0362-546X(97)00299-X VL - 30 IS - 2 SP - 1197-1205 SN - 0362-546X ER - TY - JOUR TI - Plane shear waves in a fully saturated granular medium with velocity and stress controlled boundary conditions AU - Gordon, MS AU - Shearer, M AU - Schaeffer, D T2 - INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS AB - A one-dimensional system describing small shearing disturbances in a semi-infinite, fully saturated granular medium is studied. The system is fully non-linear as a result of the incrementally non-linear constitutive law for the material. In particular, there are two different wave speeds corresponding to loading or unloading of the material. Global solutions are constructed with boundary data consisting of a single pulse in either velocity or stress. In the case of velocity controlled boundary conditions, the solution is a traveling pulse of increasing kinetic energy which eventually unloads the material, regardless of whether the initial pulse loads or unloads. The solution with stress controlled boundary conditions has these features only if the initial stress pulse unloads the material. If the initial stress pulse is loading then the solution is a slowly traveling pulse of decreasing kinetic energy which is also loading. DA - 1997/5// PY - 1997/5// DO - 10.1016/S0020-7462(96)00080-7 VL - 32 IS - 3 SP - 489-503 SN - 0020-7462 KW - plane shear waves KW - saturated granular material KW - hypoplastic flow rule KW - scale-invariant problem KW - characteristic wave KW - shock wave KW - rarefaction wave KW - wave curve KW - state space KW - kinetic energy ER - TY - JOUR TI - Identification of hysteretic control influence operators representing smart actuators part I: Formulation AU - Banks, HT AU - Kurdila, AJ AU - Webb, G T2 - MATHEMATICAL PROBLEMS IN ENGINEERING AB - A large class of emerging actuation devices and materials exhibit strong hysteresis characteristics during their routine operation. For example, when piezoceramic actuators are operated under the influence of strong electric fields, it is known that the resulting input–output behavior is hysteretic. Likewise, when shape memory alloys are resistively heated to induce phase transformations, the input–output response at the structural level is also known to be strongly hysteretic. This paper investigates the mathematical issues that arise in identifying a class of hysteresis operators that have been employed for modeling both piezoceramic actuation and shape memory alloy actuation. Specifically, the identification of a class of distributed hysteresis operators that arise in the control influence operator of a class of second order evolution equations is investigated. In Part I of this paper we introduce distributed,hysteretic control influence operators derived from smoothed Preisach operators and generalized hysteresis operators derived from results of Krasnoselskii and Pokrovskii. For these classes, the identification problem in which we seek to characterize the hysteretic control influence operator can be expressed as an ouput least square minimization over probability measures defined on a compact subset of a closed half-plane. In Part II of this paper, consistent and convergent approximation methods for identification of the measure characterizing the hysteresis are derived. DA - 1997/// PY - 1997/// DO - 10.1155/S1024123X97000586 VL - 3 IS - 4 SP - 287-328 SN - 1024-123X KW - hysteretic Preisach operators KW - smart materials KW - evolution equations KW - identification ER - TY - JOUR TI - Dynamics of reaction-diffusion systems and applications AU - Pao, CV T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS AB - The dynamics of a system of arbitrary number of nonlinear parabolic equations in terms of the quasisolutions of the corresponding system of elliptic equations is discussed. The conclusions for the general system are used to study the coexistence and permanence of a three-species predator-prey model and a food-chain model arising from ecology. DA - 1997/12// PY - 1997/12// DO - 10.1016/S0362-546X(97)00350-7 VL - 30 IS - 6 SP - 3371-3377 SN - 0362-546X ER - TY - JOUR TI - The influence of material non-uniformity preceding shear-band formation in a model for granular flow AU - Schaeffer, DG AU - Shearer, M T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS AB - The onset of shear-banding in a deforming elastoplastic solid has been linked to change of type of the governing partial differential equations. If uniform material properties are assumed, then (i) deformations prior to shear-banding are uniform, and (ii) the onset of shear-banding occurs simultaneously at all points in the sample. In this paper we study, in the context of a model for anti-plane shearing of a granular material, the effect of a small variation in material properties (e.g. in yield strength) within the sample. Using matched asymptotic expansions, we find that (i) the deformation is extremely non-uniform in a short time period immediately preceding the formation of shear-bands; and (ii) generically, a shear-band forms at a single location in the sample. DA - 1997/10// PY - 1997/10// DO - 10.1017/S0956792597003070 VL - 8 IS - 1997 Oct. SP - 457-483 SN - 0956-7925 ER - TY - JOUR TI - Spline approximation of thin shell dynamics AU - Rosario, R. C. Del AU - Smith, Ralph T2 - International Journal for Numerical Methods in Engineering AB - A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell–Mushtari thin shell equations, it can be easily extended to the Byrne–Flügge–Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material non-homogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method. © 1997 John Wiley & Sons, Ltd. DA - 1997/// PY - 1997/// DO - 10.1002/(sici)1097-0207(19970815)40:15<2807::aid-nme192>3.0.co;2-h VL - 40 IS - 15 SP - 2807–2840 ER - TY - CONF TI - Radiative transfer with asymmetric ground reflection AU - Barichello, L. B. AU - Garcia, R. D. M. AU - Siewert, C. E. C2 - 1997/// C3 - Proceedings of the 2nd Italian-Latinamerican Conference on Applied and Industrial Mathematics - ITLA 97, Roma, 1997 DA - 1997/// SP - 13 M1 - 1997 ER - TY - CHAP TI - Nonlinear delay differential economic systems in W-2((1)) AU - Chukwu, E. N. T2 - Advances in nonlinear dynamics A2 - S. Sivasundaram, A2 - Martynyuk, A. A. CN - QA845 .A35 1997 PY - 1997/// SP - 157-170 PB - Australia: Gordon and Breach ER - TY - CHAP TI - Dynamics of weakly coupled parabolic systems with nonlocal boundary conditions AU - Pao, C. V. T2 - Advances in nonlinear dynamics A2 - S. Sivasundaram, A2 - Martynyuk, A. A. CN - QA845 .A35 1997 [Hill] PY - 1997/// VL - 5 SP - 319-327 PB - Australia: Gordon and Breach ER - TY - JOUR TI - On the convergence of power scaled Cesaro sums AU - Chen, XZ AU - Hartwig, RE T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - Power scaling is combined with Cesáro summation, and necessary and sufficient local conditions are given for the resulting matrix sequence JN(T) to converge. It is shown that this convergence is closely related to path conditions on the one hand as well as suitable bilinear consistency conditions on the other hand. DA - 1997/12// PY - 1997/12// DO - 10.1016/S0024-3795(97)80056-0 VL - 267 SP - 335-358 SN - 0024-3795 ER - TY - JOUR TI - On a variational formulation of the generalized singular value decomposition AU - Chu, MT AU - Funderlic, RE AU - Golub, GH T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS AB - A variational formulation for the generalized singular value decomposition (GSVD) of a pair of matrices $A \in R^{m \times n}$ and $B \in R^{p \times n}$ is presented. In particular, a duality theory analogous to that of the SVD provides new understanding of left and right generalized singular vectors. It is shown that the intersection of row spaces of A and B plays a key role in the GSVD duality theory. The main result that characterizes left GSVD vectors involves a generalized singular value deflation process. DA - 1997/10// PY - 1997/10// DO - 10.1137/S0895479895287079 VL - 18 IS - 4 SP - 1082-1092 SN - 0895-4798 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0031520186&partnerID=MN8TOARS KW - generalized eigenvalue and eigenvector KW - generalized singular value and singular vector KW - stationary value and stationary point KW - deflation KW - duality ER - TY - JOUR TI - Hydrogen transfer between methanogens and fermentative heterotrophs in hyperthermophilic cocultures AU - Muralidharan, V. AU - Rinker, K. D. AU - Hirsh, I. S. AU - Bouwer, E. J. AU - Kelly, R. M. T2 - Biotechnology and Bioengineering AB - Interactions involving hydrogen transfer were studied in a coculture of two hyperthermophilic microorganisms: Thermotoga maritima, an anaerobic heterotroph, and Methanococcus jannaschii, a hydrogenotrophic methanogen. Cell densities of T. maritima increased 10-fold when cocultured with M. jannaschii at 85°C, and the methanogen was able to grow in the absence of externally supplied H2 and CO2. The coculture could not be established if the two organisms were physically separated by a dialysis membrane, suggesting the importance of spatial proximity. The significance of spatial proximity was also supported by cell cytometry, where the methanogen was only found in cell sorts at or above 4.5 μm in samples of the coculture in exponential phase. An unstructured mathematical model was used to compare the influence of hydrogen transport and metabolic properties on mesophilic and hyperthermophilic cocultures. Calculations suggest the increases in methanogenesis rates with temperature result from greater interactions between the methanogenic and fermentative organisms, as evidenced by the sharp decline in H2 concentration in the proximity of a hyperthermophilic methanogen. The experimental and modeling results presented here illustrate the need to consider the interactions within hyperthermophilic consortia when choosing isolation strategies and evaluating biotransformations at elevated temperatures. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 268–278, 1997. DA - 1997/// PY - 1997/// DO - 10.1002/(sici)1097-0290(19971105)56:3<268::aid-bit4>3.0.co;2-h VL - 56 IS - 3 SP - 268-278 ER - TY - JOUR TI - Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity AU - Gunzburger, MD AU - Hou, LS AU - Ravindran, SS T2 - NUMERISCHE MATHEMATIK DA - 1997/8// PY - 1997/8// DO - 10.1007/s002110050285 VL - 77 IS - 2 SP - 243-268 SN - 0029-599X ER - TY - JOUR TI - Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines AU - Tocci, MD AU - Kelley, CT AU - Miller, CT T2 - ADVANCES IN WATER RESOURCES AB - The pressure-head form of Richards' equation (RE) is difficult to solve accurately using standard time integration methods. For example, mass balance errors grow as the integration progresses unless very small time steps are taken. Further, RE may be solved for many problems more economically and robustly with variable-size time steps rather than with a constant time-step size, but variable step-size methods applied to date have relied upon empirical approaches to control step size, which do not explicitly control temporal truncation error of the solution. We show how a differential algebrain equation implementation of the method of lines can give solutions to RE that are accurate, have good mass balance properties, explicitly control temporal truncation error, and are more economical than standard approaches for a wide range of solution accuracy. We detail changes to a standard integrator, DASPK, that improves efficiency for the test problems considered, and we advocate the use of this approach for both RE and other problems involving subsurface flow and transport phenomena. DA - 1997/2// PY - 1997/2// DO - 10.1016/S0309-1708(96)00008-5 VL - 20 IS - 1 SP - 1-14 SN - 0309-1708 ER - TY - JOUR TI - The solution operator in W-p((1)) for systems of neutral type AU - Chukwu, EN AU - Simpson, HC T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS DA - 1997/11// PY - 1997/11// DO - 10.1016/S0362-546X(96)00169-1 VL - 29 IS - 10 SP - 1173-1195 SN - 0362-546X KW - neutral functional differential equation KW - atomic Sobolev space KW - solution operator ER - TY - JOUR TI - The role of orography in determining the Sahelian climate AU - Semazzi, FHM AU - Sun, LQ T2 - INTERNATIONAL JOURNAL OF CLIMATOLOGY AB - We have examined numerical modelling evidence based on the NASA GEOS-1 general circulation model in order to investigate the role of orography in determining the West African summer climate anomalies. Orographic climatic control and the influence of sea-surface temperature (SST) anomaly forcing were investigated by systematic suppression or inclusion of these effects in the numerical experiments. Our main finding is that the orography of Africa plays a major role in determining the climate of the Sahel and the coastal region of West Africa during the northern hemispheric summer season. These orographic effects are comprised of: (i) a quasi-stationary orographic ridge–trough dipole generated by the passage of the low-level prevailing easterlies over the Atlas–Ahaggar mountain complex over northern Africa, and (ii) an elongated zonal windward orographic ridge generated as the cross-equatorial summer monsoons from the South Atlantic Ocean basin ascends over the elevated landmass of West Africa. Over the Sahel, the moist south-westerly flow emanating from the Atlas–Ahaggar orographic trough over the Atlantic Ocean and the dry hot north-easterlies originating from the corresponding orographic windward ridge tend to converge along a zonal axis thus reinforcing the Inter-Tropical Convergence Zone. This results in wetter conditions over the Sahel than would have been the case in the absence of orography. The model simulations show that further to the south along the coastal region of West Africa, the zonal orographic ridge results in drier conditions than in the model runs when orography is suppressed. The net result is a permanent orographic-induced rainfall dipole pattern over West Africa. Further model simulations were conducted in which the 1973 SST anomaly conditions were described with or without the orography of Africa. The 1973 SST anomaly pattern is characterized by positive anomalies in the Southern Hemisphere and negative anomalies in the Northern Hemisphere. The model results show a weaker orographic-induced rainfall dipole pattern across West Africa in response to the 1973 SST anomaly pattern. The net result is wetter conditions along the coastal region and rainfall deficits over the Sahelian zonal strip. © 1997 by the Royal Meteorological Society. DA - 1997/5// PY - 1997/5// DO - 10.1002/(SICI)1097-0088(199705)17:6<581::AID-JOC134>3.0.CO;2-E VL - 17 IS - 6 SP - 581-596 SN - 0899-8418 KW - Sahel KW - orography KW - summer climate anomalies KW - NASA GEOS-1 GCM ER - TY - JOUR TI - Period-doubling bifurcations for systems of difference equations and applications to models in population biology AU - Selgrade, JF AU - Roberds, JH T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS DA - 1997/7// PY - 1997/7// DO - 10.1016/S0362-546X(96)00041-7 VL - 29 IS - 2 SP - 185-199 SN - 1873-5215 KW - discrete models KW - period-doubling bifurcation KW - Henon map KW - population genetics KW - pioneer and climax populations ER - TY - JOUR TI - Numerical solutions of optimal control for thermally convective flows AU - Ravindran, S. S. T2 - International Journal for Numerical Methods in Fluids DA - 1997/// PY - 1997/// VL - 25 IS - 2 SP - 205-223 ER - TY - JOUR TI - Modeling aggregation and growth processes in an algal population model: Analysis and computations AU - Ackleh, AS AU - Fitzpatrick, BG T2 - JOURNAL OF MATHEMATICAL BIOLOGY AB - Aggregation, the formation of large particles through multiple collision of smaller ones is a highly visible phenomena in oceanic waters which can control material flux to the deep sea. Oceanic aggregates more than 1 cm in diameter have been observed and are frequently described to consist of phytoplankton cells as well as other organic matter such as fecel pellets and mucus nets from pteropods. Division of live phytoplankton cells within an aggregate can also increase the size of aggregate (assuming some daughter cells stay in the aggregate) and hence could be a significant factor in speeding up the formation process of larger aggregate. Due to the difficulty of modeling cell division within aggregates, few efforts have been made in this direction. In this paper, we propose a size structured approach that includes growth of aggregate size due to both cell division and aggregation. We first examine some basic mathematical issues associated with the development of a numerical simulation of the resulting algal aggregation model. The numerical algorithm is then used to examine the basic model behavior and present a comparison between aggregate distribution with and without division in aggregates. Results indicate that the inclusion of a growth term in aggregates, due to cell division, results in higher densities of larger aggregates; hence it has the impact to speed clearance of organic matter from the surface layer of the ocean. DA - 1997/3// PY - 1997/3// DO - 10.1007/s002850050062 VL - 35 IS - 4 SP - 480-502 SN - 0303-6812 KW - phytoplankton aggregation KW - size structure population model KW - numerical approximation ER - TY - JOUR TI - Elimination of sub-oxide transition regions at Si-SiO2 interfaces by rapid thermal annealing at 900 degrees C AU - Lucovsky, G AU - Banerjee, A AU - Niimi, H AU - Koh, K AU - Hinds, B AU - Meyer, C AU - Lupke, G AU - Kurz, H T2 - APPLIED SURFACE SCIENCE AB - In many spectroscopic studies, particularly by X-ray photoelectron spectroscopy, XPS, it has been generally assumed that the existence of sub-oxide transition regions at SiSiO2 interfaces were not strongly dependent on synthesis chemistries and processing conditions. This paper presents experimental evidence for a kinetically-limited phase transition at SiSiO2 interfaces at approximately 900°C that can minimize and to a large degree eliminate significant interfacial sub-oxide transition regions. The paper emphasizes a connection between (i) differences in photoluminescence from SiOx bulk films before and after 900°C annealing and (ii) differences in electrical performance of SiSiO2 interfaces and optical second harmonic generation from SiSiO2 interfaces, also before and after 900°C annealing DA - 1997/6// PY - 1997/6// DO - 10.1016/S0169-4332(97)80079-7 VL - 117 SP - 202-206 SN - 1873-5584 KW - Si-SiO2 interfaces KW - sub-oxide transition regions KW - plasma processing KW - rapid thermal annealing ER - TY - JOUR TI - Control of nonlinear delay differential equations in W-2((1)) with economic applications AU - Chukwu, EN T2 - APPLIED MATHEMATICS AND COMPUTATION AB - The control of economic system's growth with delay is formulated to illustrate Euclidean (En) and function space (W2(1)) controllability of a general nonlinear delay equation. Sufficient conditions are given, in terms of the control matrix, for controllability of the general nonlinear system. These conditions are shown to be necessary for W2(1) controllability. The theory is then applied to a simple dynamics of gross national product and interest rate. The concept of function space controllability is very appropriate: once the target is hit, it remains on a certain growing function for some time. DA - 1997/8// PY - 1997/8// DO - 10.1016/S0096-3003(96)00108-7 VL - 85 IS - 1 SP - 17-59 SN - 0096-3003 ER - TY - JOUR TI - A robust control framework for option pricing AU - McEneaney, WM T2 - MATHEMATICS OF OPERATIONS RESEARCH AB - A new approach is taken to the problem of option pricing. In the standard framework, the option pricing problem involves determining a price such that the option writer can guarantee a certain bound on the cost almost surely. Due to this form, the problem may be reformulated in terms of deterministic differential games of the type employed in robust and H ∞ control. Different models yield different prices. The standard model yields the Black and Scholes price. Both a deterministic model and the standard model with the Ito integral replaced by the Stratonovich integral yield the price corresponding to a stop-loss hedging technique. With these methods, it can also easily be shown that for the standard model with a bounded, stochastic volatility, the Black and Scholes price corresponding to the upper bound for volatility is sufficient to hedge the option. DA - 1997/2// PY - 1997/2// DO - 10.1287/moor.22.1.202 VL - 22 IS - 1 SP - 202-221 SN - 0364-765X KW - option pricing KW - Black-Scholes formula KW - robust control KW - viscosity solutions ER - TY - JOUR TI - Schouten-Nijenhuis brackets AU - Norris, LK T2 - JOURNAL OF MATHEMATICAL PHYSICS AB - The Poisson and graded Poisson Schouten–Nijenhuis algebras of symmetric and antisymmetric contravariant tensor fields, respectively, on an n-dimensional manifold M are shown to be n-symplectic. This is accomplished by showing that both brackets may be defined in a unified way using the n-symplectic structure on the bundle of linear frames LM of M. New results in n-symplectic geometry are presented and then used to give globally defined representations of the Hamiltonian operators defined by the Schouten–Nijenhuis brackets. DA - 1997/5// PY - 1997/5// DO - 10.1063/1.531981 VL - 38 IS - 5 SP - 2694-2709 SN - 0022-2488 ER - TY - JOUR TI - Numerical solution of optimal distributed control problems for incompressible flows AU - Hou, LS AU - Ravindran, SS AU - Yan, Y T2 - INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS AB - Abstract We study the numerical solution of optimal control problems associated with the two-dimensional viscous incompressible flows which are governed by the Navier-Stokes equations. Although the techniques apply to more general settings, the presentation is confined to the objectives of minimizing the vorticity in the steady-state case with distributed controls and tracking the velocity field in the nonstationary case with piecewise distributed controls. In the steady-state case, we develop a systematic way to use the Lagrange multiplier rules to derive an optimality system of equations from which an optimal solution can be computed; finite element methods are used to find approximate solutions for the optimality system of equations. In the time-dependent case, a piecewise-in-time optimal control approach is proposed and the fully discrete approximation algorithm for solving the piecewise optimal control problem is defined. Numrical results are presented for both the steady-state and time-dependent optimal control problems. DA - 1997/// PY - 1997/// DO - 10.1080/10618569708940798 VL - 8 IS - 2 SP - 99-114 SN - 1029-0257 KW - optimal control KW - Navier-Stokes equations KW - finite element method KW - fully discrete approximations ER - TY - JOUR TI - Identification of hysteretic control influence operators representing smart actuators, Part II: Convergent approximations AU - Banks, HT AU - Kurdila, AJ AU - Webb, G T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - In a previous paper, the authors investigated the lower semicontinuity properties of two generalizations of the classical Preisach operator: the smoothed Preisach operator and the Krasnoselskii/Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identification problem for the KP operator is well-posed over compact subsets of the Preisach plane. The identification of the hysteretic control influence operator was shown to be equivalent to the identification of a measure in the space of probability measures taken with the weak* topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper. DA - 1997/6// PY - 1997/6// DO - 10.1177/1045389X9700800606 VL - 8 IS - 6 SP - 536-550 SN - 1045-389X ER - TY - JOUR TI - a priori error estimates for numerical methods for scalar conservation laws .2. Flux-splitting monotone schemes on irregular Cartesian grids AU - Cockburn, B AU - Gremaud, PA T2 - MATHEMATICS OF COMPUTATION AB - This paper is the second of a series in which a general theory of a priori error estimates for scalar conservation laws is constructed. In this paper, we focus on how the lack of consistency introduced by the nonuniformity of the grids influences the convergence of flux-splitting monotone schemes to the entropy solution. We obtain the optimal rate of convergence of ( Δ x ) 1 / 2 (\Delta x)^{1/2} in L ( L 1 ) L^{\infty }(L^{1}) for consistent schemes in arbitrary grids without the use of any regularity property of the approximate solution. We then extend this result to less consistent schemes, called p p- consistent schemes, and prove that they converge to the entropy solution with the rate of ( Δ x ) min { 1 / 2 , p } (\Delta x)^{\min \{1/2,p\}} in L ( L 1 ) L^{\infty }(L^{1}) ; again, no regularity property of the approximate solution is used. Finally, we propose a new explanation of the fact that even inconsistent schemes converge with the rate of ( Δ x ) 1 / 2 (\Delta x)^{1/2} in L ( L 1 ) L^{\infty }(L^{1}) . We show that this well-known supraconvergence phenomenon takes place because the consistency of the numerical flux and the fact that the scheme is written in conservation form allows the regularity properties of its approximate solution (total variation boundedness) to compensate for its lack of consistency; the nonlinear nature of the problem does not play any role in this mechanism. All the above results hold in the multidimensional case, provided the grids are Cartesian products of one-dimensional nonuniform grids. DA - 1997/4// PY - 1997/4// DO - 10.1090/S0025-5718-97-00838-7 VL - 66 IS - 218 SP - 547-572 SN - 1088-6842 KW - a priori error estimates KW - irregular grids KW - monotone schemes KW - conservation laws KW - supraconvergence ER - TY - JOUR TI - Weak solutions to a one-dimensional hydrodynamic model of two carrier types for semiconductors AU - Fang, WF AU - Ito, K T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS DA - 1997/3// PY - 1997/3// DO - 10.1016/0362-546X(95)00189-3 VL - 28 IS - 5 SP - 947-963 SN - 0362-546X KW - hydrodynamic model for semiconductors KW - hyperbolic systems KW - viscosity method KW - compensated compactness ER - TY - JOUR TI - Tori invariant under an involutorial automorphism .2. AU - Helminck, AG T2 - ADVANCES IN MATHEMATICS AB - The geometry of the orbits of a minimal parabolick-subgroup acting on a symmetrick-variety is essential in several areas, but its main importance is in the study of the representations associated with these symmetrick-varieties (see for example [5, 6, 20, and 31]). Up to an action of the restricted Weyl group ofG, these orbits can be characterized by theHk-conjugacy classes of maximalk-split tori, which are stable underk-involutionθassociated with the symmetrick-variety. HereHis a openk-subgroup of the fixed point group ofθ. This is the second in a series of papers in which we characterize and classify theHk-conjugacy classes of maximalk-split tori. The first paper in this series dealt with the case of algebraically closed fields. In this paper we lay the foundation for a characterization and classification for the case of nonalgebraically closed fields. This includes a partial classification in the cases, where the base field is the real numbers, p-adic numbers, finite fields, and number fields. DA - 1997/10/15/ PY - 1997/10/15/ DO - 10.1006/aima.1997.1633 VL - 131 IS - 1 SP - 1-92 SN - 0001-8708 ER - TY - JOUR TI - Steady-state solutions of a one-dimensional hydrodynamic model for semiconductors AU - Fang, WF AU - Ito, K T2 - JOURNAL OF DIFFERENTIAL EQUATIONS AB - Steady-stateBVsolutions to a one-dimensional hydrodynamic model for semiconductors are shown to exist as limits of viscous solutions as the viscosity vanishes. DA - 1997/1/20/ PY - 1997/1/20/ DO - 10.1006/jdeq.1996.3203 VL - 133 IS - 2 SP - 224-244 SN - 0022-0396 ER - TY - JOUR TI - Parameter estimation in a structured algal coagulation-fragmentation model AU - Ackleh, AS T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS DA - 1997/3// PY - 1997/3// DO - 10.1016/0362-546X(95)00195-2 VL - 28 IS - 5 SP - 837-854 SN - 0362-546X KW - parameter estimation KW - phytoplankton KW - coagulation KW - fragmentation ER - TY - JOUR TI - Molecular layer epitaxy by real-time optical process monitoring AU - Bachmann, K. J. AU - Hopfner, C. AU - Sukidi, N. AU - Miller, A. E. AU - Harris, C. J. AU - Aspnes, D. E. AU - Dietz, N. A. AU - Tran, Hien AU - Beeler, S. C. AU - Ito, K. AU - Banks, H. T. T2 - Applied Surface Science AB - In this paper we consider modern methods of optical process monitoring and control in the context of atomic layer epitaxy. One specific method, p-polarized reflectance spectroscopy (PRS), is chosen to assess details of layer-by-layer growth. We show that PRS monitoring under conditions of steady-state growth by pulsed chemical beam epitaxy (PCBE) can achieve the deposition of molecular layers of GaP on silicon (100) deposited with a precision of 5%, which can be improved by reducing the growth rate and increasing the period of time averaging of the reflectance data. Since in the nucleation period prior to formation of a contiguous heteroepitaxial film inhomogeneous surface chemistry and roughening complicates the modeling of the overgrowth process, advances in both experimental methods and theory are required for extending the control to non-steady-state growth conditions. Results of simultaneous single-wavelength PR monitoring and laser light scattering measurements in conjunction with atomic force microscopy studies of short period heteroepitaxial overgrowth processes are presented. The extension of PRS to the monitoring of organometallic chemical vapor deposition at higher pressures is also discussed. DA - 1997/// PY - 1997/// DO - 10.1016/S0169-4332(96)00975-0 VL - 112 IS - 1997 Mar. SP - 38–47 ER - TY - JOUR TI - Modeling of nonsymmetrical damage in plate-like structures AU - Banks, HT AU - Emeric, P AU - Plancke, L T2 - MATHEMATICAL AND COMPUTER MODELLING AB - A two-dimensional model for in-plane vibrations of a damped linear elastic Hookean partially clamped plate-like structure with a nonsymmetrical damage is proposed. The model includes both active and passive contributions of piezoelectric ceramic patches bonded to the surface of the structure. Both strong and weak formulations of the equations of motion are presented. The problem is then formulated as a second-order equation in time. The existence, uniqueness of the solutions, and continuity with respect to the data are discussed. DA - 1997/8// PY - 1997/8// DO - 10.1016/S0895-7177(97)00131-3 VL - 26 IS - 3 SP - 55-65 SN - 0895-7177 KW - damped elastic plates KW - in-plane dynamic vibrations KW - nonsymmetric damage KW - well-posedness ER - TY - JOUR TI - Influence of mixed boundary conditions in some reaction-diffusion systems AU - Martin, RH AU - Pierre, M T2 - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS AB - Synopsis We analyse global existence of solutions to a system of two reaction–diffusion equations for whicha ‘balance’ law holds. The main aim is to make clear the influence of different combinations ofboundary conditions on global existence under the assumption that the nonlinearities satisfy polynomial growth estimates. DA - 1997/// PY - 1997/// DO - 10.1017/s0308210500026883 VL - 127 SP - 1053-1066 SN - 0308-2105 ER - TY - JOUR TI - Ultra-thin gate dielectrics prepared by low-temperature remote plasma-assisted oxidation AU - Niimi, H AU - Koh, K AU - Lucovsky, G T2 - NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS AB - Abstract This paper discusses the formation of ultra-thin nitrided gate oxides by a low temperature plasma assisted oxidation process using remotely excited N2O as the source gas for both oxygen and nitrogen atoms. Three aspects of this process are addressed: (i) the differences in oxide growth rates for O2 or N2O plasma oxidation processes; (ii) the reaction pathways for the incorporation of nitrogen at the SiSiO2 interface for the N2O plasma process; and (iii) possible nitrogen atom depletion during processing steps that follow the plasma assisted oxidation/nitridation process. DA - 1997/5// PY - 1997/5// DO - 10.1016/S0168-583X(96)00958-5 VL - 127 SP - 364-368 SN - 0168-583X ER - TY - JOUR TI - The effects of computational delay in descriptor-based trajectory tracking control AU - vonWissel, D AU - Nikoukhah, R AU - Campbell, SL AU - Delebecque, F T2 - INTERNATIONAL JOURNAL OF CONTROL AB - Descriptor Predictive Control (DPC) has been shown to be a useful method for solving nonlinear tracking problems. A rigorous analysis of local stability and performance characteristics of this method has been achieved previously by studying the linear plant under the assumption that the delay introduced in the control due to numerical computation can be neglected. It was shown that, if the plant is controllable and minimum phase, stability is guaranteed and tracking is achieved exponentially with any desired rate of convergence. It was also shown that sometimes DPC must include a specially designed preliminary feedback. In this paper, we carry out a similar analysis by taking into account computational delay, which is unavoidable in actual implementation of DPC. We show, in particular, that under the same assumptions, and provided the special preliminary feedback is used, that the closed loop system remains stable as long as the delay is smaller than a threshold and that exponential tracking is achieved. However, the rate of convergence of the tracking error cannot be chosen arbitrarily because it is constrained by the plant zeros. The delay analysis is used to explain experimental observations in the literature about the occasional failure of previous implementations of the DPC approach at small sampling periods. A nonlinear robotics problem is worked in detail. DA - 1997/5/20/ PY - 1997/5/20/ DO - 10.1080/002071797224289 VL - 67 IS - 2 SP - 251-273 SN - 1366-5820 ER - TY - JOUR TI - Systems of parabolic equations with continuous and discrete delays AU - Pao, CV T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS AB - In this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear “reaction function” may depend on both continuous (infinite or finite) and discrete delays. It is shown that if the reaction function is locally Lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function. For systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system. This approach yields a (global) attractor of the parabolic system, and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system. Application to three model problems in population dynamics and chemical reactions is given. DA - 1997/1/1/ PY - 1997/1/1/ DO - 10.1006/jmaa.1996.5177 VL - 205 IS - 1 SP - 157-185 SN - 1096-0813 ER - TY - JOUR TI - On the inhomogeneous system of isentropic gas dynamics by the viscosity method AU - Fang, WF AU - Ito, K T2 - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS AB - The existence of global weak solutions is shown for the equations of isentropic gas dynamics with inhomogeneous terms by the viscosity method. A generalised version of the method of invariant regions is developed to obtain the uniform L ∞ bounds of the viscosity solutions, and the method of compensated compactness is applied to show the existence of weak solutions as limits of the viscosity solutions. The lower positive bound for the density function is also obtained. As an example, a hydrodynamic model for semiconductors is analysed DA - 1997/// PY - 1997/// DO - 10.1017/s0308210500023647 VL - 127 SP - 261-280 SN - 0308-2105 ER - TY - JOUR TI - On products of EP matrices AU - Hartwig, RE AU - Katz, IJ T2 - LINEAR ALGEBRA AND ITS APPLICATIONS AB - Necessary and sufficient conditions are given for the product of two EP matrices to be EP. Some special cases are considered. DA - 1997/2// PY - 1997/2// DO - 10.1016/0024-3795(95)00693-1 VL - 252 SP - 339-345 SN - 0024-3795 ER - TY - JOUR TI - Minimization of sub-oxide transition regions at Si-SiO2 interfaces by 900 degrees C rapid thermal annealing AU - Lucovsky, G AU - Banerjee, A AU - Hinds, B AU - Claflin, B AU - Koh, K AU - Yang, H T2 - MICROELECTRONIC ENGINEERING AB - Abstract Combining previously reported optical second harmonic generation (SHG) data with i) newly-reported X-ray photoelectron spectroscopy (XPS) data and ii) the Auger electron spectroscopy (AES) results presented in this paper demonstrates that interfacial sub-oxide bonding (SiOx, x DA - 1997/6// PY - 1997/6// DO - 10.1016/s0167-9317(97)00049-x VL - 36 IS - 1-4 SP - 207-210 SN - 0167-9317 ER - TY - JOUR TI - Identification of benzene oxide as a product of benzene metabolism by mouse, rat, and human liver microsomes AU - Lovern, MR AU - Turner, MJ AU - Meyer, M AU - Kedderis, GL AU - Bechtold, WE AU - Schlosser, PM T2 - CARCINOGENESIS AB - Benzene is a ubiquitous environmental pollutant that is known to cause hematotoxicity and leukemia in humans. The initial oxidative metabolite of benzene has long been suspected to be benzene oxide (3,5-cyclohexadiene-1,2-oxide). During in vitro experiments designed to characterize the oxidative metabolism of [14C]benzene, a metabolite was detected by HPLC-radioactivity analysis that did not elute with other known oxidative metabolites. The purpose of our investigation was to prove the hypothesis that this metabolite was benzene oxide. Benzene (1 mM) was incubated with liver microsomes from human donors, male B6C3F1 mice, or male Fischer-344 rats, NADH (1 mM), and NADPH (1 mM) in 0.1 M sodium phosphate buffer (pH 7.4) and then extracted with methylene chloride. Gas chromatography-mass spectrometry analysis of incubation extracts for mice, rats, and humans detected a metabolite whose elution time and mass spectrum matched that of synthetic benzene oxide. The elution time of the benzene oxide peak was approximately 4.1 min, while phenol eluted at approximately 8 min. Benzene oxide also coeluted with the HPLC peak of the previously unidentified metabolite. Based on the 14C activity of this peak, the concentration of benzene oxide was determined to be approximately 18 microM, or 7% of total benzene metabolites, after 18 min of incubation of mouse microsomes with 1 mM benzene. The metabolite was not observed in incubations using heat-inactivated microsomes. This is the first demonstration that benzene oxide is a product of hepatic benzene metabolism in vitro. The level of benzene oxide detected suggests that benzene oxide is sufficiently stable to reach significant levels in the blood of mice, rats, and humans and may be translocated to the bone marrow. Therefore benzene oxide should not be excluded as a possible metabolite involved in benzene-induced leukemogenesis. DA - 1997/9// PY - 1997/9// DO - 10.1093/carcin/18.9.1695 VL - 18 IS - 9 SP - 1695-1700 SN - 0143-3334 ER - TY - JOUR TI - Experimental confirmation of a PDE-based approach to design of feedback controls AU - Banks, HT AU - Smith, RC AU - Brown, DE AU - Silcox, RJ AU - Metcalf, VL T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - Issues regarding the experimental implementation of PDE-based controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surface-mounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vector-valued initial value problem. Optimal control theory is used to determine continuous-time voltages to the patches, and the approximations needed to facilitate discrete-time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady-state vibrations through these techniques are presented. DA - 1997/7// PY - 1997/7// DO - 10.1137/S0363012995285909 VL - 35 IS - 4 SP - 1263-1296 SN - 0363-0129 KW - feedback control KW - piezoceramic actuators KW - PDE model ER - TY - JOUR TI - Computational methods for a curved beam with piezoceramic patches AU - Banks, HT AU - Zhang, Y T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - We develop a computational scheme to approximate the solutions of a mathematical model that describes the vibrations of a curved beam structure. The physical model also includes pairs of piezoceramic patches that can be viewed either as passive devices, changing only the structural properties of the beam, or as active devices used to control vibrations of the beam. As part of our numerical experiments, we compare schemes with a method that employs hybrid B-spline basis elements and a method that employs just one family of B-spline basis elements. We calculate the first four fundamental frequencies and mode shapes of the structure, and we simulate patch-activated vibrations. Finally, we devote a section to investigation of locking phenomena which have been reported for some shell problems. DA - 1997/3// PY - 1997/3// DO - 10.1177/1045389X9700800307 VL - 8 IS - 3 SP - 260-278 SN - 1045-389X ER - TY - JOUR TI - An organizing center for wave bifurcation in multiphase flow models AU - Marchesin, D. AU - Plohr, B. J. AU - Schecter, S. T2 - SIAM Journal on Applied Mathematics AB - We consider a one-parameter family of nonstrictly hyperbolic systems of conservation laws modeling three-phase flow in a porous medium. For a particular value of the parameter, the model has a shock wave solution that undergoes several bifurcations upon perturbation of its left and right states and the parameter. In this paper we use singularity theory and bifurcation theory of dynamical systems, including Melnikov's method, to find all nearby shock waves that are admissible according to the viscous profile criterion. We use these results to construct a unique solution of the Riemann problem for each left and right state and parameter value in a neighborhood of the unperturbed shock wave solution; together with previous numerical work, this construction completes the solution of the three-phase flow model. In the bifurcation analysis, the unperturbed shock wave acts as an organizing center for the waves appearing in Riemann solutions. DA - 1997/// PY - 1997/// DO - 10.1137/s0036139995280683 VL - 57 IS - 5 SP - 1189-1215 ER - TY - JOUR TI - DAEs arising from traveling wave solutions of PDEs AU - Campbell, SL AU - Marszalek, W T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS AB - The study of traveling waves for explicit and implicit PDEs can sometimes result in differential algebraic equations (DAEs) instead of ordinary differential equations. The advantages of using DAEs is discussed as are the implications of DAE theory for the study of traveling waves. A specific type of traveling wave that connects equilibria is examined in more detail. Specific examples are given. DA - 1997/9/15/ PY - 1997/9/15/ DO - 10.1016/S0377-0427(97)00084-8 VL - 82 IS - 1-2 SP - 41-58 SN - 0377-0427 KW - differential algebraic equation KW - DAE KW - traveling waves KW - equilibria KW - magnetohydrodynamics ER - TY - JOUR TI - On pattern formation in reptilian dentition AU - Lubkin, , SR T2 - JOURNAL OF THEORETICAL BIOLOGY AB - Pattern formation of placode initiation in reptilian dental development is modeled with a generalized function, which may represent chemical concentrations, strain energy of mechanically deforming tissues, or other quantities representing a local inhibition of placode formation. The conditions on the generalized model which are necessary to account for all experimental observations are examined in detail. Minimal conditions for the correct sequencing of the tooth primordia are determined, and it is found that all known initial reptilian sequences can be accounted for with the same mechanism, with merely a different choice of parameters. An implication of the modeling results is that the lower jaw of the tuatara (Sphenodon punctatus) has a greater growth rate in its anterior portion than in its posterior portion, whereas the opposite is true of all other reptiles studied. Sequences of tooth initiation are observed robustly in the model which have not hitherto been documentedin vivo, suggesting the as yet undocumented occurrence of such a sequence in a living or extinct reptile. DA - 1997/5/21/ PY - 1997/5/21/ DO - 10.1006/jtbi.1996.0349 VL - 186 IS - 2 SP - 145-157 SN - 0022-5193 UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:A1997XA38000002&KeyUID=WOS:A1997XA38000002 ER - TY - JOUR TI - A mathematical approximation for the solution of a static indentation test AU - Haider, MA AU - Holmes, MH T2 - JOURNAL OF BIOMECHANICS AB - The classical contact problem of the indentation of a thin compressible linear elastic layer bonded to a rigid substrate is considered. Closed-form mathematical approximations of the deformation are presented for the cases of plane indentation by a rectangular block and three dimensional indentation by a plane-ended (axisymmetric) cylinder. The approximations are analyzed in the context of a static indentation test by comparison of applied load values to those obtained using a classical integral transform solution. In the case of plane indentation, the mathematical and classical predictions agree to within 2% relative error for aspect ratios between 0.1 and 1.0 and apparent Poisson ratio between 0.0 and 0.3. Comparisons for the axisymmetric case indicate a similar pattern. The main advantage of the new approach is that it yields closed-form approximations of the static indentation solution which can also capture the essential singular behavior. DA - 1997/7// PY - 1997/7// DO - 10.1016/S0021-9290(97)00024-9 VL - 30 IS - 7 SP - 747-751 SN - 1873-2380 KW - indentation KW - articular cartilage KW - joint contact ER - TY - JOUR TI - Jacobian reuse in explicit integrators for higher index DAEs AU - Campbell, SL AU - Zhong, YC T2 - APPLIED NUMERICAL MATHEMATICS AB - Systems F(y′,y,t) = 0 with Fy′ identically singular are known as differential algebraic equations (DAEs) and occur in a variety of applications. The index v is one measure of numerical difficulty. Most numerical methods for DAEs either require special structure or low index. Two alternative approaches have been proposed for numerically integrating more general higher index DAEs. This paper examines some of the mathematical issues involved in the efficient implementation of the “explicit integration” method. It is first shown that the reuse of Jacobians can lead to the integration of discontinuous vector fields. It is then proven that these discontinuous fields can be successfully integrated. Computational examples back up the theory. A comparison to a standard integrator on an index three control problem illustrates that while the explicit approach can be somewhat more expensive computationally, it can be easier to apply, and does not suffer from order reduction in the higher index variables. DA - 1997/12// PY - 1997/12// DO - 10.1016/S0168-9274(97)00052-4 VL - 25 IS - 4 SP - 391-412 SN - 0168-9274 KW - differential algebraic equation KW - DAE KW - numerical methods ER - TY - JOUR TI - Some identities for Chandrasekhar polynomials AU - Siewert, CE AU - McCormick, NJ T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER AB - Basic techniques of linear algebra are used to derive some identities involving the Chandrasekhar polynomials that play a vital role in the spherical-harmonics (PN) solution to basic radiative-transfer problems. DA - 1997/3// PY - 1997/3// DO - 10.1016/S0022-4073(96)00122-7 VL - 57 IS - 3 SP - 399-404 SN - 0022-4073 ER - TY - JOUR TI - Shape matching with smart material structures using piezoceramic actuators AU - Fitzpatrick, BG T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES AB - In this paper, we consider the problem of driving a flexible structure from an "unforced" equilibrium position to a given desired shape. Within the context of smart materials, we focus on piezoceramic actuators as controls. Our approach is to base the choice of input voltages on a physical model of the structure, with "good" voltage choices being those whose modelbased displacements "'closely" match the desired shape. This shape matching problem is posed as a least squares problem in a Hilbert space that represents the displacement component of the state space of the flexible structure model. Here we treat the structure as a distributed parameter system, so that the state space is infinite dimensional. Thus, we must examine questions of existence of solutions and convergence of approximations. To illustrate our techniques, we give some numerical examples. DA - 1997/10// PY - 1997/10// DO - 10.1177/1045389X9700801007 VL - 8 IS - 10 SP - 876-882 SN - 1045-389X ER - TY - JOUR TI - On the trace of graded automorphisms AU - Jing, NH AU - Zhang, JJ T2 - JOURNAL OF ALGEBRA AB - LetA = ⊕d ≥ 0 Adbe a connected algebra with a graded algebra endomorphism σ. The trace of σ is defined to be Tr(σ, t) = ∑d ≥ 0 tr(σ|Ad)td. We prove that Tr(σ, t) is a rational function ifAis either finitely generated commutative or right noetherian with finite global dimension or regular. A version of Molien's theorem follows in these three cases. IfAis a regular algebra or a Frobenius algebra we prove a reciprocity for the trace. We also partially generalize a theorem of Watanabe on the Gorenstein property to the noncommutative case. DA - 1997/3/15/ PY - 1997/3/15/ DO - 10.1006/jabr.1996.6896 VL - 189 IS - 2 SP - 353-376 SN - 0021-8693 UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0031569313&partnerID=MN8TOARS ER - TY - JOUR TI - On inverse boundary-condition problems in radiative transfer AU - Barichello, LB AU - Garcia, RDM AU - Siewert, CE T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER AB - Abstract Some elementary computations are reported to suggest that a certain type of inverse boundary-condition problem in radiative transfer can, in some cases, be solved quite simply. DA - 1997/3// PY - 1997/3// DO - 10.1016/S0022-4073(96)00095-7 VL - 57 IS - 3 SP - 405-410 SN - 0022-4073 ER - TY - JOUR TI - Analogue of the Bruhat-Chevalley order for reductive monoids AU - Pennell, EA AU - Putcha, MS AU - Renner, LE T2 - JOURNAL OF ALGEBRA AB - The purpose of this paper is to describe the Adherence Order of w x B = B-orbits on a reductive algebraic monoid. By the results of 10 there is already a perfect analogue of the Bruhat decomposition for reductive w x monoids. Indeed, by 10, Corollary 5.8 , if M is reductive with unit group G and maximal torus T : G with Borel subgroup B = T , then the set of two sided B-orbits, B R MrB is canonically identified with a certain finite Ž . inverse monoid R. In fact, R s N T rT , the orbit monoid of the Zariski G Ž . closure of N T in M. By definition, for s , t g R we define the AdherG ence Order by s F t if Bs B : Bt B, where Bt B denotes the Zariski closure in M of Bt B. DA - 1997/10/15/ PY - 1997/10/15/ DO - 10.1006/jabr.1997.7111 VL - 196 IS - 2 SP - 339-368 SN - 0021-8693 ER - TY - JOUR TI - The perturbation theory for the drazin inverse and its applications AU - Wei, Y.-M. AU - Wang, G. R. T2 - Linear Algebra and Its Applications DA - 1997/// PY - 1997/// VL - 258 IS - 1997 June SP - 179-186 ER - TY - JOUR TI - Teaching computational abstract algebra AU - Kaltofen, E T2 - JOURNAL OF SYMBOLIC COMPUTATION AB - We report on the contents and pedagogy of a course in abstract algebra that was taught with the aid of educational software developed within the Mathematica system. We describe the topics covered and the didactical use of the corresponding Mathematica packages, as well as draw conclusions for future such courses from the students' comments and our own experience. DA - 1997/// PY - 1997/// DO - 10.1006/jsco.1996.0104 VL - 23 IS - 5-6 SP - 503-515 SN - 0747-7171 ER - TY - JOUR TI - Risk-sensitive and robust escape criteria AU - Dupuis, P AU - McEneaney, WM T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION AB - The problem of controlling a noisy process so as to prevent it from leaving a prescribed set has a number of interesting applications. In this paper, new approaches to this problem are considered. First, a risk-sensitive criterion for a stochastic diffusion process model is examined, and it is shown that the value is a classical solution of a related PDE. The qualitative properties of this criterion are favorably contrasted with those of existing criteria in the risk-averse limit. It is proved that in the risk-averse limit the value of the risk-sensitive criterion converges to a viscosity solution of a first-order PDE. It is then demonstrated that the value function of a deterministic differential game is also a viscosity solution to the PDE. This game gives a robust control formulation of the escape time problem and is analogous to H$^{\infty}$ control. In particular, the opposing player attempts to push the process out of the prescribed set and suffers an L2 cost for his efforts. Lower bounds on the escape time as a function of this cost are obtained. DA - 1997/11// PY - 1997/11// DO - 10.1137/S0363012995281626 VL - 35 IS - 6 SP - 2021-2049 SN - 0363-0129 KW - exit time control KW - risk-sensitive control KW - large deviations KW - robust control ER - TY - JOUR TI - Risk analyses in clonal forestry AU - Roberds, JH AU - Bishir, JW T2 - CANADIAN JOURNAL OF FOREST RESEARCH-REVUE CANADIENNE DE RECHERCHE FORESTIERE AB - The number of clones to use in plantations is an important problem that must be addressed by practitioners of clonal forestry because of productivity and forest health considerations. This problem has been analyzed from a number of perspectives, but analyses based upon risk of plantation failure have provided special insight about effects produced by an increase in numbers of clones. In this paper, we describe alternative models and methods that have been proposed to investigate the effect of number of clones on risk of plantation failure following an unforeseen catastrophic event. Properties of these models are reviewed and conclusions resulting from the analysis of each model are given. Results from these analyses and recently developed theory indicate that use of 30 to 40 unrelated clones in plantations provides protection against catastrophic failure roughly equivalent to the use of large numbers of unrelated clones. A detailed description of the recently introduced time-to-failure model is also presented, and several examples that illustrate properties of this model are discussed. Finally, some implications regarding the development of breeding populations are identified and explored. Resume : La problOmatique du nombre de clones utilisOs dans les plantations clonales doit Œtre abordOe par les praticiens de la foresterie clonale en raison des implications quielle peut avoir pour la productivitO et la santO des forŒts. Ce problme a OtO OtudiO sous de nombreux angles, mais il siest avOrO que liapproche basOe sur le risque diOchec de plantation a permis de rOvOler les effets rOsultant diune augmentation du nombre de clones utilisOs. Les auteurs de liOtude font la description des mOthodes et modles alternatifs qui ont OtO proposOs pour Otudier lieffet du nombre de clones sur le risque diOchec de plantation suite ‡ un OvOnement catastrophique imprOvisible. Les auteurs prOsentent la revue des caractOristiques ainsi que les conclusions dOcoulant de lianalyse de chacun de ces modles. Les rOsultats de cette analyse ainsi que les considOrations thOoriques dOveloppOes rOcemment indiquent que liutilisation de 30 ‡ 40 clones non apparentOs par plantation procure une protection contre des Ochecs catastrophiques qui est ‡ peu prs Oquivalente ‡ celle qui dOcoule de liutilisation diun grand nombre de clones non apparentOs. Une description dOtaillOe du modle rOcent de «dOlai diOchec» est prOsentOe. Quelques exemples illustrant les caractOristiques de ce modle sont Ogalement discutOs. Enfin, certaines implications relatives au dOveloppement des populations diOlevage sont identifiOes et discutOes. (Traduit par la ROdaction) DA - 1997/3// PY - 1997/3// DO - 10.1139/x96-202 VL - 27 IS - 3 SP - 425-432 SN - 0045-5067 ER - TY - JOUR TI - Plasma-assisted formation of low defect density SiC-SiO2 interfaces AU - Golz, A. AU - Lucovsky, G. AU - Koh, K. AU - Wolfe, D. AU - Niimi, H. AU - Kurz, H. T2 - Journal of Vacuum Science & Technology. B, Microelectronics and Nanometer Structures DA - 1997/// PY - 1997/// VL - 15 IS - 4 SP - 1097-1104 ER - TY - JOUR TI - Optimal control of the growth of wealth of nations: With Austria and USA examples AU - Chukwu, EN T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS DA - 1997/12// PY - 1997/12// DO - 10.1016/S0362-546X(96)00246-5 VL - 30 IS - 2 SP - 1029-1041 SN - 0362-546X KW - optimal control KW - controllability KW - function space controllable KW - economic variables KW - regression KW - delay differential equations KW - stability ER - TY - JOUR TI - Numerical simulation of pattern formation in grain flows AU - Gremaud, PA T2 - APPLIED MATHEMATICS AND COMPUTATION AB - We present numerical computations for the flow of granular materials in hoppers. The algorithm is based on a cellular automaton approach and takes into account various microscopic effects, including “orientational effects”. The formation and the dynamics of density waves, recently discovered in physical experiments, is observed and analyzed computationally. DA - 1997/7// PY - 1997/7// DO - 10.1016/S0096-3003(96)00084-7 VL - 84 IS - 2-3 SP - 145-162 SN - 0096-3003 ER - TY - JOUR TI - Monoid Hecke algebras AU - Putcha, MS T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY AB - This paper concerns the monoid Hecke algebras $\mathcal {H}$ introduced by Louis Solomon. We determine explicitly the unities of the orbit algebras associated with the two-sided action of the Weyl group $W$. We use this to: find a description of the irreducible representations of $\mathcal {H}$, find an explicit isomorphism between $\mathcal {H}$ and the monoid algebra of the Renner monoid $R$, extend the Kazhdan-Lusztig involution and basis to $\mathcal {H}$, and prove, for a $W\times W$ orbit of $R$, the existence (conjectured by Renner) of generalized Kazhdan-Lusztig polynomials. DA - 1997/9// PY - 1997/9// DO - 10.1090/S0002-9947-97-01823-0 VL - 349 IS - 9 SP - 3517-3534 SN - 0002-9947 ER - TY - JOUR TI - Linear differential equations and products of linear forms AU - Singer, MF AU - Ulmer, F T2 - JOURNAL OF PURE AND APPLIED ALGEBRA AB - We show that liouvillian solutions of an n th-order linear differential equation L ( y ) = 0 are related to semi-invariant forms of the differential Galois group of L ( y ) = 0 which factor into linear forms. The logarithmic derivative of such a form F , evaluated in the solutions of L ( y ) = 0, is the first coefficient of a polynomial P ( u ) whose zeros are logarithmic derivatives of solutions of L ( y ) = 0. Together with the Brill equations, this characterization allows one to efficiently test if a semi-invariant corresponds to such a coefficient and to compute the other coefficients of P ( u ) via a factorization of the form F . DA - 1997/5// PY - 1997/5// DO - 10.1016/S0022-4049(97)00027-3 VL - 117 SP - 549-563 SN - 1873-1376 ER - TY - JOUR TI - Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities AU - Figiel, T AU - Hitczenko, P AU - Johnson, WB AU - Schechtman, G AU - Zinn, J T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY AB - The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the p p moment of a sum of independent symmetric random variables to that of the p p and 2 2 moments of the individual variables, are computed in the range 2 > p 4 2>p\le 4 . This complements the work of Utev who has done the same for p > 4 p>4 . The qualitative nature of the extreme cases turns out to be different for p > 4 p>4 than for p > 4 p>4 . The method developed yields results in some more general and other related moment inequalities. DA - 1997/3// PY - 1997/3// DO - 10.1090/S0002-9947-97-01789-3 VL - 349 IS - 3 SP - 997-1027 SN - 0002-9947 KW - Khintchine inequality KW - Rosenthal inequality KW - Orlicz function KW - extremal problem KW - Rademacher functions ER - TY - JOUR TI - Estimation of the convection coefficient in elliptic equations AU - Ito, K AU - Kunisch, K T2 - INVERSE PROBLEMS AB - The parameter estimation problem for the convection coefficient in elliptic equations is considered in the class of -vector fields. The optimality system is characterized and the convergence of the gradient method is proved. To apply the SQP-method to the singular optimality system, a modification involving a feasibility step in the primal and dual variables is introduced. The resulting algorithm has a second-order convergence rate. Numerical experiments are included. DA - 1997/8// PY - 1997/8// DO - 10.1088/0266-5611/13/4/007 VL - 13 IS - 4 SP - 995-1013 SN - 0266-5611 ER - TY - JOUR TI - Computing an eigenvector with inverse iteration AU - Ipsen, ICF T2 - SIAM REVIEW AB - The purpose of this paper is two-fold: to analyze the behavior of inverse iteration for computing a single eigenvector of a complex square matrix and to review Jim Wilkinson's contributions to the development of the method. In the process we derive several new results regarding the convergence of inverse iteration in exact arithmetic. In the case of normal matrices we show that residual norms decrease strictly monotonically. For eighty percent of the starting vectors a single iteration is enough. In the case of non-normal matrices, we show that the iterates converge asymptotically to an invariant subspace. However, the residual norms may not converge. The growth in residual norms from one iteration to the next can exceed the departure of the matrix from normality. We present an example where the residual growth is exponential in the departure of the matrix from normality. We also explain the often significant regress of the residuals after the first iteration: it occurs when the non-normal part of the matrix is large compared to the eigenvalues of smallest magnitude. In this case computing an eigenvector with inverse iteration is exponentially ill conditioned (in exact arithmetic). We conclude that the behavior of the residuals in inverse iteration is governed by the departure of the matrix from normality rather than by the conditioning of a Jordan basis or the defectiveness of eigenvalues. DA - 1997/6// PY - 1997/6// DO - 10.1137/S0036144596300773 VL - 39 IS - 2 SP - 254-291 SN - 1095-7200 KW - eigenvector KW - invariant subspace KW - inverse iteration KW - departure from normality KW - ill-conditioned linear system ER - TY - JOUR TI - Compact rings having a finite simple group of units AU - Cohen, JA AU - Koh, K T2 - JOURNAL OF PURE AND APPLIED ALGEBRA AB - For a compact Hausdorff ring, one observes that the group of units is a totally disconnected compact topological group and is a finite simple group if and only if it possesses no nontrivial closed normal subgroups. Three classification theorems for compact rings are now given. First, those compact rings with identity having a finite simple group of units are identified. Second, a classification of all compact rings A with identity for which 2 is a unit in A, G modulo the center of G is a finite simple group and the length of W is less than or equal to 4 (or equivalently, W is a torsion group) is given where G is the group of units in A and W is the subgroup of G generated by {g∈ G: g2 = 1}. Finally, those compact rings with identity having 2 as a unit and for which W is a nilpotent group are identified. DA - 1997/6/2/ PY - 1997/6/2/ DO - 10.1016/S0022-4049(96)00128-4 VL - 119 IS - 1 SP - 13-26 SN - 0022-4049 ER -