TY - RPRT
TI - On an adaptive control algorithm for the adaptive optics problems
AU - Chu, Moody
DA - 1999///
PY - 1999///
M3 - Preprint
ER -
TY - JOUR
TI - A Continuous-Time Approach to the Oblique Procrustes Problem
AU - Trendafilov, Nickolay T.
AU - Chu, Moody T.
T2 - Behaviormetrika
DA - 1999/7//
PY - 1999/7//
DO - 10.2333/bhmk.26.167
VL - 26
IS - 2
SP - 167–181
SN - 0385-7417 1349-6964
UR - http://dx.doi.org/10.2333/bhmk.26.167
ER -
TY - JOUR
TI - East Coast Computer Algebra Day '99 (April 24, 1999): Abstracts of invited talks and presented posters
T2 - Association for Computing Machinery SIGSAM Bulletin
AB - article Free Access Share on East Coast Computer Algebra Day '99 (April 24, 1999): abstracts of invited talks and presented posters Editors: Hoon Hong North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C. North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C.View Profile , Erich Kaltofen North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C. North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C.View Profile , Michael Singer North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C. North Carolina State University, Mathematics Department, Box 8205, Raleigh, N.C.View Profile Authors Info & Claims ACM SIGSAM BulletinVolume 33Issue 2June 1999 pp 43–52https://doi.org/10.1145/334714.570085Online:01 June 1999Publication History 0citation106DownloadsMetricsTotal Citations0Total Downloads106Last 12 Months0Last 6 weeks0 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
DA - 1999/6//
PY - 1999/6//
DO - 10.1145/334714.570085
VL - 33
IS - 2
SP - 43-52
ER -
TY - JOUR
TI - Numerical Study of Two Dimensional Electro-migration
AU - Gao, H
AU - Li, Zhilin
AU - Zhao, H
T2 - Journal of Computational Physics
DA - 1999///
PY - 1999///
VL - 152
SP - 281–304
ER -
TY - JOUR
TI - A numerical method for solving heat equations involving interfaces
AU - Li, Zhilin
AU - Shen, Yun-Qui
T2 - Electronic Journal of Differential Equations
DA - 1999///
PY - 1999///
VL - 3
SP - 100–108
ER -
TY - RPRT
TI - Industrial Mathematics Modeling Workshop for Graduate Students series
DA - 1999///
PY - 1999///
M3 - CRSC Technical Reports
ER -
TY - RPRT
TI - Exploiting order variation in mesh refinement for direct transcription methods
AU - Betts, John T.
AU - Huffman, William P.
AU - Biehn, Neil
AU - Campbell, Stephen L.
A3 - Boeing
DA - 1999///
PY - 1999///
M3 - Technical Report
PB - Boeing
ER -
TY - CONF
TI - Detection Signal Design for Failure Detection
AU - Nikoukhah, R.
AU - Campbell, S.L.
AU - Delebecque, F.
T2 - Iranian Conference on Electrical Engineering
C2 - 1999///
C3 - Proceedings of the Iranian Conference on Electrical Engineering
DA - 1999///
PY - 1999///
SP - 45–52
ER -
TY - CONF
TI - A subgradient projection algorithm for nondifferentiable signal recovery
AU - Luo, J.
AU - Combettes, P.L.
T2 - Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing
C2 - 1999///
C3 - Proceedings of the IEEE Workshop on Nonlinear Signal and Image Processing
CY - Antalya, Turkey
DA - 1999///
PY - 1999/6/20/
SP - 452–456
ER -
TY - CONF
TI - On the genericity of the modular polynomial GCD algorithm
AU - Kaltofen, Erich
AU - Monagan, Michael B.
T2 - the 1999 international symposium
C2 - 1999///
C3 - Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99
DA - 1999///
DO - 10.1145/309831.309861
PB - ACM Press
SN - 1581130732
UR - http://dx.doi.org/10.1145/309831.309861
DB - Crossref
ER -
TY - CONF
TI - Symbolic computation in Java
AU - Bernardin, Laurent
AU - Char, Bruce
AU - Kaltofen, Erich
T2 - the 1999 international symposium
C2 - 1999///
C3 - Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99
DA - 1999///
DO - 10.1145/309831.309946
PB - ACM Press
SN - 1581130732
UR - http://dx.doi.org/10.1145/309831.309946
DB - Crossref
ER -
TY - CONF
TI - Efficient algorithms for computing the nearest polynomial with a real root and related problems
AU - Hitz, Markus A.
AU - Kaltofen, Erich
AU - Lakshman, Y. N.
T2 - the 1999 international symposium
C2 - 1999///
C3 - Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99
DA - 1999///
DO - 10.1145/309831.309937
PB - ACM Press
SN - 1581130732
UR - http://dx.doi.org/10.1145/309831.309937
DB - Crossref
ER -
TY - JOUR
TI - Level one representations of quantum affine algebras Uq(C n (1))
AU - Jing, N.
AU - Koyama, Y.
AU - Misra, K.C.
T2 - Selecta Mathematica, New Series
DA - 1999///
PY - 1999///
VL - 5
IS - 2
SP - 243-255
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-53149123269&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Level one representations of Uq(G2 (1))
AU - Jing, N.
T2 - Proceedings of the American Mathematical Society
DA - 1999///
PY - 1999///
VL - 127
IS - 1
SP - 21-27
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-22444452806&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Level two vertex representations of G(1) 2
AU - Jing, N.
AU - Lyerly, C.M.
T2 - Communications in Algebra
DA - 1999///
PY - 1999///
VL - 27
IS - 9
SP - 4355-4362
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0033243918&partnerID=MN8TOARS
ER -
TY - JOUR
TI - HLA alleles determine human T-lymphotropic virus-I (HTLV-I) proviral load and the risk of HTLV-I-associated myelopathy
AU - Jeffery, Katie JM
AU - Usuku, Koichiro
AU - Hall, Sarah E
AU - Matsumoto, Wataru
AU - Taylor, Graham P
AU - Procter, Jeanette
AU - Bunce, Mike
AU - Ogg, Graham S
AU - Welsh, Kenneth I
AU - Weber, Jonathan N
AU - others
T2 - Proceedings of the National Academy of Sciences
DA - 1999///
PY - 1999///
VL - 96
IS - 7
SP - 3848-3853
ER -
TY - JOUR
TI - The The lack of influence of the right-hand side on the accuracy of linear system solution
AU - Banoczi, J. M.
AU - Chiu, N. C.
AU - Cho, G. E.
AU - Ipsen, I. C. F.
T2 - SIAM Journal on Scientific Computing
AB - It is commonly believed that a fortunate right-hand side b can significantly reduce the sensitivity of a system of linear equations Ax=b. We show, both theoretically and experimentally, that this is not true when the system is solved (in floating point arithmetic) with Gaussian elimination or the QR factorization: the error bounds essentially do not depend on b, and the error itself seems to depend only weakly on b. Our error bounds are exact (rather than first-order); they are tight; and they are stronger than the bound of Chan and Foulser.
We also present computable lower and upper bounds for the relative error. The lower bound gives rise to a stopping criterion for iterative methods that is better than the relative residual. This is because the relative residual can be much larger, and it may be impossible to reduce it to a desired tolerance.
DA - 1999///
PY - 1999///
DO - 10.1137/S106482759630526X
VL - 20
IS - 1
SP - 203–227
KW - linear system
KW - right-hand side
KW - condition number
KW - backward error
KW - stopping criterion
ER -
TY - CONF
TI - Global artificial boundary conditions for computation of external flow problems with propulsive jets
AU - Tsynkov, Semyon
AU - Abarbanel, Saul
AU - Nordstrom, Jan
AU - Ryaben'kii, Victor
AU - Vatsa, Veer
T2 - 14th Computational Fluid Dynamics Conference
AB - We propose new global artificial boundary conditions (ABC''s) for computation of flows with propulsive jets. The algorithm is based on application of the difference potentials method (DPM). Previously, similar boundary conditions have been implemented for calculation of external compressible viscous flows around finite bodies. The proposed modification substantially extends the applicability range of the DPM-based algorithm. In the paper, we present the general formulation of the problem, describe our numerical methodology, and discuss the corresponding computational results. The particular configuration that we analyze is a slender three-dimensional body with boat-tail geometry and supersonic jet exhaust in a subsonic external flow under zero angle of attack. Similarly to the results obtained earlier for the flows around airfoils and wings, current results for the jet flow case corroborate the superiority of the DPM-based ABC''s over standard local methodologies from the standpoints of accuracy, overall numerical performance, and robustness.
C2 - 1999/11//
C3 - 14th Computational Fluid Dynamics Conference
DA - 1999/11//
DO - 10.2514/6.1999-3351
VL - 2
SP - 836-846
PB - American Institute of Aeronautics and Astronautics
UR - http://dx.doi.org/10.2514/6.1999-3351
DB - Crossref
N1 - AIAA Paper No. 99–3351
RN - AIAA Paper No. 99–3351
ER -
TY - RPRT
TI - Long-Time Numerical Integration of the Three-Dimensional Wave
Equation in the Vicinity of a Moving Source
AU - Ryaben’kii, V. S.
AU - Turchaninov, V. I.
AU - Tsynkov, S. V.
A3 - ICASE
DA - 1999///
PY - 1999///
M1 - 99–23, NASA/CR–1999–209350
PB - ICASE
SN - 99–23, NASA/CR–1999–209350
UR - https://ntrs.nasa.gov/search.jsp?R=19990062251
ER -
TY - JOUR
TI - The use of lacunae of the 3D-wave equation for computing a
solution at large time values
T2 - Mat. Model.
DA - 1999///
PY - 1999///
VL - 11
IS - 12
SP - 113-126
UR - https://mathscinet.ams.org/mathscinet-getitem?mr=1761052
N1 - [in Russian]
RN - [in Russian]
ER -
TY - RPRT
TI - IFFCO: Implicit Filtering for Constrained Optimization, Version 2
AU - Choi, T D
AU - Eslinger, O J
AU - Gilmore, P
AU - Patrick, A
AU - Kelley, C T
AU - Gablonsky, J M
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 1999/7//
PY - 1999/7//
M1 - CRSC-TR99-23
PB - North Carolina State University, Center for Research in Scientific Computation
SN - CRSC-TR99-23
ER -
TY - RPRT
TI - {Newton-Krylov-Schwarz} Methods for {R}ichards' Equation
AU - Jenkins, E W
AU - Berger, R C
AU - Hallberg, J P
AU - Howington, Stacy E
AU - Kelley, C T
AU - Schmidt, Joseph H
AU - Stagg, Alan
AU - Tocci, M D
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 1999/10//
PY - 1999/10//
M1 - CRSC-TR99-32
PB - North Carolina State University, Center for Research in Scientific Computation
SN - CRSC-TR99-32
ER -
TY - CONF
TI - A Model to Simulate the Interaction between Groundwater and Surface Water
AU - Howington, S E
AU - Berger, R C
AU - Hallberg, J P
AU - Peters, J F
AU - Stagg, A K
AU - Jenkins, E W
AU - Kelley, C T
T2 - North Carolina State University, Center for Research in Scientific Computation
C2 - 1999/8//
C3 - Proceedings of the High Performance Computing Users' Group Meeting
CY - Monterrey, CA
DA - 1999/8//
M1 - CRSC-TR99-27
ER -
TY - JOUR
TI - Hard-constrained inconsistent signal feasibility problems
AU - Combettes, P.L.
AU - Bondon, P.
T2 - IEEE Transactions on Signal Processing
AB - We consider the problem of synthesizing feasible signals in a Hilbert space in the presence of inconsistent convex constraints, some of which must imperatively be satisfied. This problem is formalized as that of minimizing a convex objective measuring the amount of violation of the soft constraints over the intersection of the sets associated with the hard ones. The resulting convex optimization problem is analyzed, and numerical solution schemes are presented along with convergence results. The proposed formalism and its algorithmic framework unify and extend existing approaches to inconsistent signal feasibility problems. An application to signal synthesis is demonstrated.
DA - 1999///
PY - 1999///
DO - 10.1109/78.782189
VL - 47
IS - 9
SP - 2460-2468
J2 - IEEE Trans. Signal Process.
OP -
SN - 1053-587X
UR - http://dx.doi.org/10.1109/78.782189
DB - Crossref
KW - convex feasibility problem
KW - fixed point
KW - Hilbert space
KW - inconsistent constraints
KW - monotone operator
KW - optimization
KW - signal synthesis
ER -
TY - JOUR
TI - On the origins of the Lotka-Volterra Equations
AU - Haydon, D.T.
AU - Lloyd, A.L.
T2 - The Bulletin of the Ecological Society of America
DA - 1999///
PY - 1999///
VL - 80
IS - 3
SP - 205–206
ER -
TY - JOUR
TI - Dynamics of Macrophage and T Cell Infection by HIV
AU - Wodarz, Dominik
AU - Lloyd, Alun L.
AU - Jansen, Vincent A.A.
AU - Nowak, Martin A.
T2 - Journal of Theoretical Biology
AB - We analyse mathematical models comparing the in vivo dynamics of macrophage- and T cell infection by HIV. Experiments suggest that HIV can only replicate in activated T cells whereas cell activation may not be required for successful replication in macrophages. These assumptions lead to fundamentally different conditions required to establish a persistent infection in the two cell types. While persistent replication in macrophages is achieved if the basic reproductive ratio of the virus, R0, exceeds unity, the establishment of T cell infection may depend on a complex balance between host and viral parameters as well as initial conditions. More specifically, the replication rate of HIV needs to lie above a threshold level and the immune responsiveness of the host below a certain threshold for persistent T cell infection to be possible. In addition, initial virus load has to be intermediate and the initial abundance of CTLs low. Mathematical models predict that macrophage infection may be essential for the successful establishment of HIV in the primary phase of the infection. Acting as a reservoir, they allow the virus to evolve towards increased replication kinetics as well as away from immune recognition, thus paving the way for the rise of exclusively T cell tropic strains using the CXCR4-coreceptor.
DA - 1999/1//
PY - 1999/1//
DO - 10.1006/jtbi.1998.0816
VL - 196
IS - 1
SP - 101-113
J2 - Journal of Theoretical Biology
LA - en
OP -
SN - 0022-5193
UR - http://dx.doi.org/10.1006/jtbi.1998.0816
DB - Crossref
ER -
TY - JOUR
TI - HLA alleles determine human T-lymphotropic virus-I (HTLV-I) proviral load and the risk of HTLV-I-associated myelopathy
AU - Jeffery, K. J. M.
AU - Usuku, K.
AU - Hall, S. E.
AU - Matsumoto, W.
AU - Taylor, G. P.
AU - Procter, J.
AU - Bunce, M.
AU - Ogg, G. S.
AU - Welsh, K. I.
AU - Weber, J. N.
AU - Lloyd, A. L.
AU - Nowak, M. A.
AU - Nagai, M.
AU - Kodama, D.
AU - Izumo, S.
AU - Osame, M.
AU - Bangham, C. R. M.
T2 - Proceedings of the National Academy of Sciences
AB - The risk of disease associated with persistent virus infections such as HIV-I, hepatitis B and C, and human T-lymphotropic virus-I (HTLV-I) is strongly determined by the virus load. However, it is not known whether a persistent class I HLA-restricted antiviral cytotoxic T lymphocyte (CTL) response reduces viral load and is therefore beneficial or causes tissue damage and contributes to disease pathogenesis. HTLV-I-associated myelopathy (HAM/TSP) patients have a high virus load compared with asymptomatic HTLV-I carriers. We hypothesized that HLA alleles control HTLV-I provirus load and thus influence susceptibility to HAM/TSP. Here we show that, after infection with HTLV-I, the class I allele HLA-A*02 halves the odds of HAM/TSP (P < 0.0001), preventing 28% of potential cases of HAM/TSP. Furthermore, HLA-A*02(+) healthy HTLV-I carriers have a proviral load one-third that (P = 0.014) of HLA-A*02(-) HTLV-I carriers. An association of HLA-DRB1*0101 with disease susceptibility also was identified, which doubled the odds of HAM/TSP in the absence of the protective effect of HLA-A*02. These data have implications for other persistent virus infections in which virus load is associated with prognosis and imply that an efficient antiviral CTL response can reduce virus load and so prevent disease in persistent virus infections.
DA - 1999/3/30/
PY - 1999/3/30/
DO - 10.1073/pnas.96.7.3848
VL - 96
IS - 7
SP - 3848-3853
J2 - Proceedings of the National Academy of Sciences
LA - en
OP -
SN - 0027-8424 1091-6490
UR - http://dx.doi.org/10.1073/pnas.96.7.3848
DB - Crossref
ER -
TY - JOUR
TI - A simple relationship between viral load and survival time in HIV-1 infection
AU - Arnaout, R. A.
AU - Lloyd, A. L.
AU - O'Brien, T. R.
AU - Goedert, J. J.
AU - Leonard, J. M.
AU - Nowak, M. A.
T2 - Proceedings of the National Academy of Sciences
AB - Despite important recent insights into the short-term dynamics of HIV-1 infection, our understanding of the long-term pathogenesis of AIDS remains unclear. Using an approach that places rapid progressors, typical progressors, and nonprogressors on a single clinical spectrum of disease progression, we quantitate the previously reported relationship between viral load and survival time. We introduce the concept of viral constant, present evidence that this quantity is conserved across patients, and explore the immunopathological implications of this finding. We conclude with a quantitative approach for assessing the benefits of a given regime of antiviral therapy.
DA - 1999/9/28/
PY - 1999/9/28/
DO - 10.1073/pnas.96.20.11549
VL - 96
IS - 20
SP - 11549-11553
J2 - Proceedings of the National Academy of Sciences
LA - en
OP -
SN - 0027-8424 1091-6490
UR - http://dx.doi.org/10.1073/pnas.96.20.11549
DB - Crossref
KW - prognosis
KW - CD4(+) cell count
KW - CD4(+) cell decline
KW - antiviral therapy
KW - statistical analysis
ER -
TY - JOUR
TI - Deformation of chains via a local symmetric group action
AU - Hersh, Patricia
T2 - The Electronic Journal of Combinatorics
DA - 1999///
PY - 1999///
VL - R27
ER -
TY - JOUR
TI - On Lacunae-Based Algorithm for Numerical Solution of 3D Wave Equation for Arbitrarily Large Time
AU - Ryaben’kii, V.S.
AU - Turchaninov, V.I.
AU - Tsynkov, S.V.
T2 - Mathematical Modeling
DA - 1999///
PY - 1999///
VL - 11
IS - 12
SP - 113–127
ER -
TY - JOUR
TI - Global Smooth Solutions and Large Time Behavior of the One-Dimensional Navier–Stokes Equations
AU - Pang, Tao
T2 - Journal of Mathematical Analysis and Applications
AB - The system of balance laws of mass, momentum and energy for a viscous, heat-conductive, one-dimensional real gas (Navier-Stokes equations) is considered. The existence of globally defined smooth solution to an initial boundary value problem is established. Because of the boundary conditions' effect, vacuum will be developed as time tends to infinity.
DA - 1999/7//
PY - 1999/7//
DO - 10.1006/jmaa.1999.6287
VL - 235
IS - 2
SP - 395-417
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1006/jmaa.1999.6287
DB - Crossref
ER -
TY - JOUR
TI - Structured tree outflow condition for blood flow in larger systemic arteries
AU - Olufsen, Mette S.
T2 - American Journal of Physiology-Heart and Circulatory Physiology
AB - A central problem in modeling blood flow and pressure in the larger systemic arteries is determining a physiologically based boundary condition so that the arterial tree can be truncated after a few generations. We have used a structured tree attached to the terminal branches of the truncated arterial tree in which the root impedance is estimated using a semianalytical approach based on a linearization of the viscous axisymmetric Navier-Stokes equations. This provides a dynamic boundary condition that maintains the phase lag between blood flow and pressure as well as the high-frequency oscillations present in the impedance spectra. Furthermore, it accommodates the wave propagation effects for the entire systemic arterial tree. The result is a model that is physiologically adequate as well as computationally feasible. For validation, we have compared the structured tree model with a pure resistance and a windkessel model as well as with measured data.
DA - 1999/1//
PY - 1999/1//
DO - 10.1152/ajpheart.1999.276.1.h257
VL - 276
IS - 1
SP - H257-H268
J2 - American Journal of Physiology-Heart and Circulatory Physiology
LA - en
OP -
SN - 0363-6135 1522-1539
UR - http://dx.doi.org/10.1152/ajpheart.1999.276.1.h257
DB - Crossref
KW - arterial modeling
KW - mathematical modeling
KW - arterial outflow boundary condition
ER -
TY - JOUR
TI - Synchronicity, chaos and population cycles: spatial coherence in an uncertain world
AU - Lloyd, Alun L
AU - May, Robert M
T2 - Trends in Ecology & Evolution
DA - 1999/11//
PY - 1999/11//
DO - 10.1016/s0169-5347(99)01717-6
VL - 14
IS - 11
SP - 417-418
J2 - Trends in Ecology & Evolution
LA - en
OP -
SN - 0169-5347
UR - http://dx.doi.org/10.1016/s0169-5347(99)01717-6
DB - Crossref
ER -
TY - JOUR
TI - Cohomology of Conformal Algebras
AU - Bakalov, Bojko
AU - Kac, Victor G.
AU - Voronov, Alexander A.
T2 - Communications in Mathematical Physics
AB - The notion of a conformal algebra encodes an axiomatic description of the operator product expansion of chiral fields in conformal field theory. On the other hand, it is an adequate tool for the study of infinite-dimensional Lie algebras satisfying the locality property. The main examples of such Lie algebras are those “based” on the punctured complex plane, such as the Virasoro algebra and loop Lie algebras. In the present paper we develop a cohomology theory of conformal algebras with coefficients in an arbitrary module. It possesses standards properties of cohomology theories; for example, it describes extensions and deformations. We offer explicit computations for the most important examples. To Bertram Kostant on his seventieth birthday
DA - 1999/2/1/
PY - 1999/2/1/
DO - 10.1007/s002200050541
VL - 200
IS - 3
SP - 561-598
J2 - Communications in Mathematical Physics
OP -
SN - 0010-3616 1432-0916
UR - http://dx.doi.org/10.1007/s002200050541
DB - Crossref
ER -
TY - JOUR
TI - Nim-Regularity of Graphs
AU - Reading, Nathan
T2 - The Electronic Journal of Combinatorics
DA - 1999///
PY - 1999///
VL - 6
IS - 1
SP - Research Paper 11, 8
UR - http://www.combinatorics.org/Volume_6/Abstracts/v6i1r11.html
ER -
TY - THES
TI - Decomposition and Enumeration in Partially Ordered Sets
AU - Hersh, Patricia
DA - 1999/5//
PY - 1999/5//
M3 - Ph.D. thesis
PB - Massachusetts Institute of Technology
ER -
TY - CHAP
TI - Undercompressive waves in driven thin film flow: Theory, computation, and experiment
AU - Shearer, Michael
AU - Bertozzi, A.L.
AU - Munch, A.
T2 - Trends in Mathematical Physics
A2 - Alexiades, V.
A2 - Siopsis, G.
PY - 1999/7/28/
DO - 10.1090/amsip/013/04
VL - 13
SP - 43-68
PB - American Mathematical Society
SN - 9780821820063 9781470438043
UR - http://dx.doi.org/10.1090/amsip/013/04
ER -
TY - JOUR
TI - On exact n-step domination
AU - Hersh, Patricia
T2 - Discrete Mathematics
AB - We generalize to n steps the notion of exact 2-step domination introduced by Chartrand et al. (Math. Bohem. 120 (1995) 125–134) and suggest a related minimization problem for which we find a lower bound. A graph G is an exact n -step domination graph if there is some set of vertices in G such that each vertex in the graph is distance n from exactly one vertex in the set. We prove that such subsets have order at least ⌊ log 2 n⌋+2 and limit how much better a bound is possible. We also prove a related conjecture of Alavi et al. (Graph Theory, Combinatorics, and Applications, vol. 1, Wiley, New York, 1991, pp. 1–8) that if each vertex in a connected graph G has exactly one vertex distance n from it then the diameter is n unless G is a path consisting of 2 n vertices.
DA - 1999/7//
PY - 1999/7//
DO - 10.1016/s0012-365x(99)00024-2
VL - 205
IS - 1-3
SP - 235-239
J2 - Discrete Mathematics
LA - en
OP -
SN - 0012-365X
UR - http://dx.doi.org/10.1016/s0012-365x(99)00024-2
DB - Crossref
ER -
TY - JOUR
TI - External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics
AU - Tsynkov, Semyon V.
T2 - SIAM Journal on Scientific Computing
AB - We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow numerically, we discretize the governing equations (Navier--Stokes) on a finite-difference grid. Prior to the discretization, we obviously need to truncate the original unbounded domain by introducing an artificial computational boundary at a finite distance from the body; otherwise, the number of discrete variables will not be finite. This artificial boundary is typically the external boundary of the domain covered by the grid. The flow problem (both continuous and discretized) formulated on the finite computational domain is clearly subdefinite unless supplemented by some artificial boundary conditions (ABCs) at the external computational boundary. In this paper, we present an innovative approach to constructing highly accurate ABCs for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderón's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) of Ryaben'kii. The resulting ABCs appear spatially nonlocal but are particularly easy to implement along with the existing flow solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic and transonic flow regimes. As demonstrated by the computational experiments and comparison with the standard local methods, the DPM-based ABCs allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable speedup of multigrid convergence.
DA - 1999/1//
PY - 1999/1//
DO - 10.1137/s1064827597318757
VL - 21
IS - 1
SP - 166-206
J2 - SIAM J. Sci. Comput.
LA - en
OP -
SN - 1064-8275 1095-7197
UR - http://dx.doi.org/10.1137/s1064827597318757
DB - Crossref
KW - external flows
KW - infinite-domain problems
KW - artificial boundary conditions
KW - far-field linearization
KW - boundary projections
KW - generalized potentials
KW - difference potentials method
KW - auxiliary problem
KW - separation of variables
ER -
TY - JOUR
TI - Factors affecting the adoption of transgenic crops: Some evidence from southeastern US cotton farmers
AU - Marra, M. C.
T2 - AgBioTechNet: The Online Service for Agricultural Biotechnology
DA - 1999///
PY - 1999///
VL - 1
SP - 1
ER -
TY - JOUR
TI - On numbers of clones needed for managing risks in clonal forestry
AU - Bishir, J.
AU - Roberds, J. H.
T2 - Forest Genetics
DA - 1999///
PY - 1999///
VL - 6
IS - 3
SP - 149
ER -
TY - JOUR
TI - Undercompressive shocks in thin film flows
AU - Bertozzi, AL
AU - Munch, A
AU - Shearer, M
T2 - PHYSICA D-NONLINEAR PHENOMENA
AB - Equations of the type ht+(h2−h3)x=−ϵ3(h3hxxx)x arise in the context of thin liquid films driven by the competing effects of a thermally induced surface tension gradient and gravity. In this paper, we focus on the interaction between the fourth order regularization and the nonconvex flux. Jump initial data, from a moderately thick film to a thin precurser layer, is shown to give rise to a double wave structure that includes an undercompressive wave. This wave, which approaches an undercompressive shock as ϵ→0, is an accumulation point for a countable family of compressive waves having the same speed. The family appears through a series of bifurcations parameterized by the shock speed. At each bifurcation, a pair of traveling waves is produced, one being stable for the PDE, the other unstable. The conclusions are based primarily on numerical results for the PDE, and on numerical investigations of the ODE describing traveling waves. Fourth order linear regularization is observed to produce a similar bifurcation structure of traveling waves.
DA - 1999/12/10/
PY - 1999/12/10/
DO - 10.1016/s0167-2789(99)00134-7
VL - 134
IS - 4
SP - 431-464
SN - 1872-8022
KW - undercompressive shock
KW - capillarity
KW - thin films
KW - Marangoni stress
KW - fourth order diffusion
KW - numerical simulation
KW - hyperbolic conservation law
ER -
TY - JOUR
TI - Numerical methods for systems of nonlinear parabolic equations with time delays
AU - Pao, CV
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - The purpose of this paper is to investigate some numerical aspects of a class of coupled nonlinear parabolic systems with time delays. The system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations. The mathematical analysis of the nonlinear system is by the method of upper and lower solutions and its associated monotone iterations. Three monotone iterative schemes are presented and it is shown that the sequence of iterations from each one of these iterative schemes converges monotonically to a unique solution of the finite difference system. A theoretical comparison result for the various monotone sequences and error estimates for the three monotone iterative schemes are obtained. It is also shown that the finite difference solution converges to the classical solution of the parabolic system as the mesh size decreases to zero.
DA - 1999/12/1/
PY - 1999/12/1/
DO - 10.1006/jmaa.1999.6619
VL - 240
IS - 1
SP - 249-279
SN - 1096-0813
ER -
TY - BOOK
TI - Recent developments in quantum affine algebras and related topics: Representations of affine and quantum affine algebras and their applications, North Carolina State University, May 21-24, 1998 / Naihuan Jing, Kailash C. Misra, editors
AU - Jing, Naihuan
AU - Misra, K. C.
CN - QA252.3 .R43 1999
DA - 1999///
PY - 1999///
DO - 10.1090/conm/248
PB - Providence, RI: American Mathematical Society
SN - 0821811991
ER -
TY - JOUR
TI - On the variance of the random sphere of influence graph
AU - Hitczenko, P
AU - Janson, S
AU - Yukich, JE
T2 - RANDOM STRUCTURES & ALGORITHMS
AB - We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in Rd, grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 139–152, 1999
DA - 1999/3//
PY - 1999/3//
DO - 10.1002/(SICI)1098-2418(199903)14:2<139::AID-RSA2>3.0.CO;2-E
VL - 14
IS - 2
SP - 139-152
SN - 1042-9832
ER -
TY - JOUR
TI - Crack jump conditions for elliptic problems
AU - Wiegmann, A
AU - Li, Z
AU - LeVeque, RJ
T2 - APPLIED MATHEMATICS LETTERS
AB - We derive jump conditions for a potential function and its derivatives across a crack. A crack is a “thin” region of very different conductivity, for example a fracture in otherwise homogeneous material. Such a sharp change of material properties introduces a discontinuity in the coefficient of the elliptic equation governing the potential. The crack cannot be neglected, because it substantially alters the behavior of the potential. Numerically, it is very difficult to resolve the potential near the crack. A strategy is to treat the crack as a lower dimensional interface (hypersurface). Jump conditions across the crack for the potential and its derivatives are necessary for the development of numerical schemes for this approach. Besides the jump conditions, we also give an analytic example of their validity.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00083-X
VL - 12
IS - 6
SP - 81-88
SN - 0893-9659
KW - jump conditions
KW - transmission problem
KW - elliptic crack problems
ER -
TY - JOUR
TI - Mathematical and experimental analysis of localization of anti-tumour antibody-enzyme conjugates
AU - Jackson, TL
AU - Lubkin, , SR
AU - Siemers, NO
AU - Kerr, DE
AU - Senter, PD
AU - Murray, JD
T2 - BRITISH JOURNAL OF CANCER
AB - Considerable research has been aimed at improving the efficacy of chemotherapeutic agents for cancer therapy. A promising two-step approach that is designed to minimize systemic drug toxicity while maximizing activity in tumours employs monoclonal antibody (mAb)–enzyme conjugates for the activation of anticancer prodrugs. We present, analyse and numerically simulate a mathematical model based on the biology of the system to study the biodistribution, pharmacokinetics and localization properties of mAb–enzyme conjugates in tumour tissue. The model predictions were compared with experimental observations and an excellent correlation was found to exist. In addition, the critical parameters affecting conjugate half-life were determined to be the inter-capillary half-distance and the antibody–antigen binding affinity. An approximation is presented relating the per cent injected dose per gram to inter-capillary half-distance and time. Finally, the model was used to examine various dosing strategies in an attempt to determine which regimen would provide the best biodistribution results. We compared the results of administering a uniform dose of fusion protein via bolus injection, multiple injections and continuous infusion. The model predicts that dosing strategy has little effect on the amount of conjugate that localizes in the tumour.
DA - 1999/8//
PY - 1999/8//
DO - 10.1038/sj.bjc.6690592
VL - 80
IS - 11
SP - 1747-1753
SN - 1532-1827
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000081900300011&KeyUID=WOS:000081900300011
ER -
TY - CONF
TI - Mesh refinement that exploits order variation
AU - Betts, J. T.
AU - Huffman, W. P.
AU - Biehn, N.
AU - Campbell, S.L.
C2 - 1999///
C3 - Proceedings of the Workshop: Optimalsteuerungsprobleme in der Luft- und Raumfahrt, Universitat Greifswald, 7/8 Oktober 1999 (Sonderforschungsbereich; 255)
DA - 1999///
SP - 1-12
PB - Munchen: Hieronymus
ER -
TY - JOUR
TI - Modeling of nonlinear hysteresis in elastomers under uniaxial tension
AU - Banks, HT
AU - Pinter, GA
AU - Potter, LK
AU - Gaitens, MJ
AU - Yanyo, LC
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - As a fundamental component of an overall program in modeling smart material damping devices, we consider inactive host material models for moderate to highly filled rubbers undergoing uniaxial tensile deformations. Beginning from a neo-Hookean strain energy function formulation for nonlinear extension, we develop general constitutive models for both quasi-static and dynamic deformations of a viscoelastic rod. The constitutive laws are nonlinear and contain hysteresis through a Boltzmann superposition integral term. The resulting integropartial differential equations models are shown to be equivalent to the usual Lagrangian dynamic distributed parameter models coupled with linear ordinary differential equations for internal variables (internal strains). Comprehensive well-posedness results (existence, uniqueness and continuous dependence) are summarized in a discussion of theoretical aspects of the systems. The models are validated with experiments designed and carried out explicitly for this study. In particular, quasi-static Instron experimental data are used in a least squares inverse problem formulation to estimate nonlinear elastic and nonlinear viscoelastic contributions to the general stress-strain constitutive laws proposed. It is shown that the models provide an excellent prediction of nested hysteresis loops manifested in the data. These models are then used as initial estimates in determining the nonlinear hysteretic constitutive laws for the dynamic experiments. It is shown that in cases of more highly filled rubbers, multiple internal variable models lead to best fits to the data.
DA - 1999/2//
PY - 1999/2//
DO - 10.1106/8M8M-F8DQ-GJ2V-PGK1
VL - 10
IS - 2
SP - 116-134
SN - 1045-389X
ER -
TY - JOUR
TI - Two-dimensional photonic crystal Fabry-Perot resonators with lossy dielectrics
AU - Beaky, MM
AU - Burk, JB
AU - Everitt, HO
AU - Haider, MA
AU - Venakides, S
T2 - IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES
AB - Square and triangular lattice two-dimensional (2D) photonic crystals (PCs) composed of lossy dielectric rods in air were constructed with a microwave bandgap between 4-8 GHz. Fabry-Perot resonators of varying length were constructed from two of these PCs of adjustable thickness and reflectivity. The quality factor of cavity modes supported in the resonators was found to increase with increasing PC mirror thickness, but only to a point dictated by the lossiness of the dielectric rods. A 2-D periodic Green's function simulation was found to model the data accurately and quickly using physical parameters obtained in separate measurements. Simple rules are developed for designing optimal resonators in the presence of dielectric loss.
DA - 1999/11//
PY - 1999/11//
DO - 10.1109/22.798003
VL - 47
IS - 11
SP - 2085-2091
SN - 1557-9670
KW - dielectric loss
KW - Fabry-Perot resonator
KW - photonic crystal
ER -
TY - JOUR
TI - Estimation of the effective permeability in magnetorheological fluids
AU - Simon, TM
AU - Ito, K
AU - Banks, HT
AU - Reitich, F
AU - Jolly, MR
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - Magnetorheological (MR) fluids constitute examples of controllable ("smart") fluids, whose Theological properties vary in response to an applied magnetic field. These fluids typically consist of micron-sized, magnetizable particles dispersed in a nonpermeable carrier fluid. The essential characteristic of MR fluids is that they may be continuously and reversibly varied from a state of free flowing liquids in the absence of an applied magnetic field to that of stiff semi-solids in a moderate field. Understanding the magnetic properties of MR fluids is crucial to the design of MR fluid-based devices and it also provides valuable insight into the character of the microstructure responsible for their field-dependent rheology. Prediction of the overall magnetic properties of MR composites is a challenging task, however, due to the highly nonlinear and strongly spatially variable nature of the magnetization of the constituents. In this paper we propose a model for this behavior that is based on the mathematical theory of homogenization. We derive effective equations that govern the magnetic response of (periodically arranged) particle-chains through magnetic saturation. Comparisons of numerical results for these equations with experimental data show good agreement which suggests that our approach could be useful in the design of improved MR fluids.
DA - 1999/11//
PY - 1999/11//
DO - 10.1106/6KW6-7V12-NRQ3-BW6V
VL - 10
IS - 11
SP - 872-879
SN - 1045-389X
ER -
TY - JOUR
TI - Remarks on well-posedness theorems for damped second-order systems
AU - Banks, HT
T2 - APPLIED MATHEMATICS LETTERS
AB - We consider an operator theoretic formulation for distributed damped second-order (in time) forced linear elastic systems. A brief summary of previous well-posedness results is presented along with new results which allow relaxed spatial regularity (which is important in smart material systems applications) on the forcing or input function. Extensions to nonlinear systems are also indicated. The results are presented in a variational format for easy development of finite element approximation methods.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00073-7
VL - 12
IS - 6
SP - 21-24
SN - 0893-9659
ER -
TY - JOUR
TI - Regularity and approximation of systems arising in electromagnetic interrogation of dielectric materials
AU - Banks, HT
AU - Zou, J
T2 - NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
AB - In this paper we are concerned with a mathematical model which describes the electromagnetic interrogation of dielectric materials. We address the well-posedness of the system and regularity of solutions. Then we propose a semi-discrete finite element scheme for approximating the system and prove weak convergence under very mild regularity assumptions on the solutions of the original system. We also establish that the solution has higher regularity in time even though the input source may be a windowed signal of distributional type. This regularity is then utilized to show the strong convergence of the finite element solution.
DA - 1999///
PY - 1999///
DO - 10.1080/01630569908816914
VL - 20
IS - 7-8
SP - 609-627
SN - 0163-0563
ER -
TY - CHAP
TI - Nonlinear descriptor systems
AU - Campbell, Stephen
AU - Nikoukhah, R.
AU - DeLebecque, F.
T2 - Advances in control: Highlights of ECC '99
CN - TJ212.2 .E97 1999
PY - 1999///
DO - 10.1007/978-1-4471-0853-5_9
SP - 247–282
PB - London; New York: Springer-Verlag
ER -
TY - JOUR
TI - Gorensteinness of invariant subrings of quantum algebras
AU - Jing, N
AU - Zhang, JJ
T2 - JOURNAL OF ALGEBRA
AB - We prove Auslander–Gorenstein and GKdim–Macaulay properties for certain invariant subrings of some quantum algebras, the Weyl algebras, and the universal enveloping algebras of finite-dimensional Lie algebras.
DA - 1999/11/15/
PY - 1999/11/15/
DO - 10.1006/jabr.1999.8023
VL - 221
IS - 2
SP - 669-691
SN - 0021-8693
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0033570733&partnerID=MN8TOARS
KW - group actions
KW - invariant subrings
KW - Auslander-Gorenstein property
KW - Macaulay property
ER -
TY - JOUR
TI - Exact separation of eigenvalues of large dimensional sample covariance matrices
AU - Bai, Z. D.
AU - Silverstein, J. W.
T2 - Annals of Probability
DA - 1999///
PY - 1999///
VL - 27
IS - 3
SP - 1536–1555
ER -
TY - JOUR
TI - A trust region method for parabolic boundary control problems
AU - Kelley, CT
AU - Sachs, EW
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - In this paper we develop a trust region algorithm for constrained parabolic boundary control problems. For the computation of a trust region step we propose an iterative scheme which is a projected form of the Steihaug trust region conjugate gradient method. To ensure the good local convergence properties in the terminal phase, a smoothing step at each iteration is added. This step and the projection require the modification of the standard trust region algorithm and its convergence proof. The algorithm has sup-norm convergence in the terminal phase and L2 convergence in the global phase. The results are illustrated for a parabolic boundary control problem.
DA - 1999///
PY - 1999///
DO - 10.1137/S1052623496308965
VL - 9
IS - 4
SP - 1064-1081
SN - 1052-6234
KW - trust region methods
KW - inexact Newton methods
KW - optimal control
ER -
TY - JOUR
TI - A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings
AU - Ito, K
AU - Reitich, F
T2 - INVERSE PROBLEMS
AB - A new method for the reconstruction of two-dimensional periodic structures from scattered far-field data is presented. The approach is based on the recently developed `methods of variation of boundaries' (MVB) for the solution of forward-scattering problems. Here, the inverse problem is formulated as that of minimization of an appropriate nonlinear least-squares cost functional J. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradients algorithm. Through a number of numerical examples it is demonstrated that such globalization may be necessary to overcome the non-convexity of J which, in turn, is shown to persist even when the global minimizer is known to be unique.
DA - 1999/8//
PY - 1999/8//
DO - 10.1088/0266-5611/15/4/315
VL - 15
IS - 4
SP - 1067-1085
SN - 0266-5611
ER -
TY - JOUR
TI - The designing approach of difference schemes by controlling the remainder-effect
AU - Liu, R. X.
AU - Zhang, M. P.
AU - Wang, J.
AU - Liu, X. Y.
T2 - International Journal for Numerical Methods in Fluids
DA - 1999///
PY - 1999///
VL - 31
IS - 2
SP - 523-533
ER -
TY - JOUR
TI - Simulations of particle dynamics in magnetorheological fluids
AU - Ly, HV
AU - Reitich, E
AU - Jolly, MR
AU - Banks, HT
AU - Ito, K
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - We present particle dynamics simulations for the response of magnetorheological (MR) fluids upon application of a magnetic field. The particles motion is considered to be governed by magnetic, hydrodynamic, and repulsive interactions. Fluid-particle interactions are accounted for via Stokes' drag while inter-particle repulsions are modeled through approximate hard-sphere rejections. In accordance with their greater significance, on the other hand (linear) magnetic interactions are fully simulated. The time evolution is considered to be magnetically quasi-static and magnetostatic forces are derived from the solution of (steady) Maxwell's equations, recomputed at each instant in time. For this we use a potential theoretic formulation where the boundary integral equations are solved with a fast multipole approach. We show that the resulting numerical codes can be effectively used to study a number of experimental observables such as effective magnetic permeabilities and response time-scales which are of crucial importance in the design of MR fluids.
DA - 1999/10/10/
PY - 1999/10/10/
DO - 10.1006/jcph.1999.6335
VL - 155
IS - 1
SP - 160-177
SN - 1090-2716
KW - particle dynamics
KW - fast multipole method
KW - MR fluids
KW - effective permeability
KW - response time scale
ER -
TY - JOUR
TI - Real-time optical control of Ga1-xInxP film growth by p-polarized reflectance
AU - Dietz, N
AU - Woods, V
AU - Ito, K
AU - Lauko, I
T2 - JOURNAL OF VACUUM SCIENCE & TECHNOLOGY A
AB - The engineering of advanced optoelectronic integrated circuits implies the stringent control of thickness and composition. These demands led to the development of surface-sensitive real-time optical sensors that are able to move the control point close to the point where the growth occurs, which in a chemical beam epitaxy process is the surface reaction layer, built up of physisorbed and chemisorbed precursor fragments between the ambient and film interface. In this context, we explored the application of p-polarized reflectance spectroscopy (PRS) for real-time monitoring and control of pulsed chemical beam epitaxy during low-temperature growth of epitaxial Ga1−xInxP heterostructures on Si(001) substrates. A reduced order surface kinetics model has been developed to describe the decomposition and growth kinetics of the involved organometallic precursors and their incorporation in the film deposition. We demonstrate the linkage of the PRS response towards the surface reaction chemistry, composition, film growth rate, and film properties. Mathematical control algorithms are applied that link the PR signals to the growth process control parameters to control the composition and growth rate of epitaxial Ga1−xInxP heterostructures.
DA - 1999///
PY - 1999///
DO - 10.1116/1.581811
VL - 17
IS - 4
SP - 1300-1306
SN - 1520-8559
ER -
TY - JOUR
TI - Mountain supreme early blight-resistant hybrid tomato and its parents, NC EBR-3 and NC EBR-4
AU - Gardner, R. G.
AU - Shoemaker, P. B.
T2 - HortScience
DA - 1999///
PY - 1999///
VL - 34
IS - 4
SP - 745-746
ER -
TY - JOUR
TI - Kalman filtering for general discrete-time linear systems
AU - Nikoukhah, R
AU - Campbell, SL
AU - Delebecque, F
T2 - IEEE TRANSACTIONS ON AUTOMATIC CONTROL
AB - Recursive state estimation problems for explicit and implicit time-invariant linear systems, both for systems with and without unknown inputs, can be formulated as a single problem usually referred to as descriptor Kalman filtering. Solutions to this problem have been proposed in the literature; however, these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system. In this paper, the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions. This method uses a generalization of the shuffle algorithm.
DA - 1999/10//
PY - 1999/10//
DO - 10.1109/9.793722
VL - 44
IS - 10
SP - 1829-1839
SN - 0018-9286
KW - descriptor systems
KW - Kalman filtering
KW - linear systems
KW - singular systems
KW - stochastic systems
ER -
TY - JOUR
TI - Domain wall theory for ferroelectric hysteresis
AU - Smith, RC
AU - Hom, CL
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. First, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theories with domain interactions incorporated through mean field relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. Second, hysteresis is incorporated through the consideration of domain wall dynamics and the quantification of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.
DA - 1999/3//
PY - 1999/3//
DO - 10.1106/LJBM-RW18-MXW1-QXD0
VL - 10
IS - 3
SP - 195-213
SN - 1530-8138
ER -
TY - JOUR
TI - Theoretical analysis of conjugate localization in two-step cancer chemotherapy
AU - Jackson, TL
AU - Lubkin, , SR
AU - Murray, JD
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
DA - 1999/10//
PY - 1999/10//
DO - 10.1007/s002850050195
VL - 39
IS - 4
SP - 353-376
SN - 1432-1416
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000083493300004&KeyUID=WOS:000083493300004
KW - mathematical modeling
KW - cancer chemotherapy
KW - antibody-enzyme conjugate
ER -
TY - JOUR
TI - Methodologies in spectral analysis of large dimensional random matrices, a review - Comment: Complements and new developments
AU - Silverstein, J. W.
T2 - Statistica Sinica
DA - 1999///
PY - 1999///
VL - 9
IS - 3
SP - 667–671
ER -
TY - JOUR
TI - A discrete-ordinates solution for Poiseuille flow in a plane channel
AU - Barichello, LB
AU - Siewert, CE
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 1999/11//
PY - 1999/11//
DO - 10.1007/s000000050189
VL - 50
IS - 6
SP - 972-981
SN - 0044-2275
KW - kinetic theory
KW - gas dynamics
KW - discrete ordinates
ER -
TY - JOUR
TI - Use of a mathematical model of rodent in vitro benzene metabolism to predict human in vitro metabolism data
AU - Lovern, MR
AU - Maris, ME
AU - Schlosser, PM
T2 - CARCINOGENESIS
AB - Benzene, a ubiquitous environmental pollutant, is known to cause leukemia and aplastic anemia in humans and hematotoxicity and myelotoxicity in rodents. Toxicity is thought to be exerted through oxidative metabolites formed in the liver, primarily via pathways mediated by cytochrome P450 2E1 (CYP2E1). Phenol, hydroquinone and trans-trans-muconaldehyde have all been hypothesized to be involved in benzene-induced toxicity. Recent reports indicate that benzene oxide is produced in vitro and in vivo and may be sufficiently stable to reach the bone marrow. Our goal was to improve existing mathematical models of microsomal benzene metabolism by including time course data for benzene oxide, by obtaining better parameter estimates and by determining if enzymes other than CYP2E1 are involved. Microsomes from male B6C3F1 mice and F344 rats were incubated with [(14)C]benzene (14 microM), [(14)C]phenol (303 microM) and [(14)C]hydroquinone (8 microM). Benzene and phenol were also incubated with mouse microsomes in the presence of trans-dichloroethylene, a CYP2E1 inhibitor, and benzene was incubated with trichloropropene oxide, an epoxide hydrolase inhibitor. These experiments did not indicate significant contributions of enzymes other than CYP2E1. Mathematical model parameters were fitted to rodent data and the model was validated by predicting human data. Model simulations predicted the qualitative behavior of three human time course data sets and explained up to 81% of the total variation in data from incubations of benzene for 16 min with microsomes from nine human individuals. While model predictions did deviate systematically from the data for benzene oxide and trihydroxybenzene, overall model performance in predicting the human data was good. The model should be useful in quantifying human risk due to benzene exposure and explicitly accounts for interindividual variation in CYP2E1 activity.
DA - 1999/8//
PY - 1999/8//
DO - 10.1093/carcin/20.8.1511
VL - 20
IS - 8
SP - 1511-1520
SN - 0143-3334
ER -
TY - JOUR
TI - Types of reductive monoids
AU - Li, Zhilin
AU - Putcha, M.
T2 - Journal of Algebra
AB - Let M be a reductive monoid with a reductive unit group G. Clearly there is a natural G × G action on M. The orbits are the J-classes (in the sense of semigroup theory) and form a finite lattice. The general problem of finding the lattice remains open. In this paper we study a new class of reductive monoids constructed by multilined closure. We obtain a general theorem to determine the lattices of these monoids. We find that the (J, σ)-irreducible monoids of Suzuki type and Ree type belong to this new class. Using the general theorem we then list all the lattices and type maps of the (J, σ)-irreducible monoids of Suzuki type and Ree type.
DA - 1999///
PY - 1999///
DO - 10.1006/jabr.1999.7946
VL - 221
IS - 1
SP - 102–116
ER -
TY - JOUR
TI - The immersed finite volume element methods for the elliptic interface problems
AU - Ewing, RE
AU - Li, ZL
AU - Lin, T
AU - Lin, YP
T2 - MATHEMATICS AND COMPUTERS IN SIMULATION
AB - An immersed finite element space is used to solve the elliptic interface problems by a finite volume element method. Special nodal basis functions are introduced in a triangle whose interior intersects with the interface so that the jump conditions across the interface are satisfied. Optimal error estimates in an energy norm are obtained. Numerical results are supplied to justify the theoretical work and to reveal some interesting features of the method.
DA - 1999/11//
PY - 1999/11//
DO - 10.1016/S0378-4754(99)00061-0
VL - 50
IS - 1-4
SP - 63-76
SN - 0378-4754
KW - finite volume
KW - convergence
KW - error estimate
KW - interface problems
ER -
TY - JOUR
TI - Global gevrey regularity for the Benard convection in a porous medium with zero Darcy-Prandtl number
AU - Ly, HV
AU - Titi, ES
T2 - JOURNAL OF NONLINEAR SCIENCE
DA - 1999///
PY - 1999///
DO - 10.1007/s003329900073
VL - 9
IS - 3
SP - 333-362
SN - 0938-8974
ER -
TY - JOUR
TI - Detection and remediation of stagnation in the Nelder-Mead algorithm using a sufficient decrease condition
AU - Kelley, CT
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - The Nelder--Mead algorithm can stagnate and converge to a nonoptimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for all iterations, will guarantee convergence of the Nelder--Mead iteration to a stationary point if the objective function is smooth and the diameters of the Nelder--Mead simplices converge to zero. Failure of this condition is an indicator of potential stagnation. As a remedy we propose a new step, which we call an oriented restart, that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point. We also give results that apply when the objective function is a low-amplitude perturbation of a smooth function. We illustrate our results with some numerical examples.
DA - 1999/11/29/
PY - 1999/11/29/
DO - 10.1137/S1052623497315203
VL - 10
IS - 1
SP - 43-55
SN - 1095-7189
KW - Nelder-Mead algorithm
KW - sufficient decrease
KW - stagnation
ER -
TY - JOUR
TI - Computing Galois groups of completely reducible differential equations
AU - Compoint, E
AU - Singer, MF
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We give an algorithm to calculate a presentation of the Picard–Vessiot extension associated to a completely reducible linear differential equation (i.e. an equation whose Galois group is reductive). Using this, we show how to compute the Galois group of such an equation as well as properties of the Galois groups of general equations.
DA - 1999///
PY - 1999///
DO - 10.1006/jsco.1999.0311
VL - 28
IS - 4-5
SP - 473-494
SN - 0747-7171
ER -
TY - JOUR
TI - Application of the NCAR regional climate model to eastern Africa - 1. Simulation of the short rains of 1988
AU - Sun, LQ
AU - Semazzi, FHM
AU - Giorgi, F
AU - Ogallo, L
T2 - JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES
AB - The National Center for Atmospheric Research (NCAR) Regional Climate Model (RegCM2) is employed to investigate the physical mechanisms that govern the October-December rains over eastern Africa. The model employs the Mercator conformai projection, with a domain of 5580 km × 5040 km centered at 31°E, 4°S, and a horizontal grid point spacing of 60 km. The simulation period is October-December 1988, and the model initial and lateral boundary conditions are taken from ECMWF reanalysis. A number of month-long simulations have been conducted to optimize various parameterizations of the model which include the following factors: cumulus convection, moisture parameterization, radiative transfer formulation, surface processes, boundary layer physics, and the lateral boundary conditions. The model was successfully customized over eastern Africa. The model simulates the large-scale circulation characteristics over the region as well as local features such as the dominant precipitation maxima, the Turkana low-level jet, and the diurnal reversal in the lake/land breeze circulation over Lake Victoria. Several model deficiencies are also identified. They include a negative rainfall bias over the western portions of the domain and the Kenya Highlands and a temperature bias over the tropical forest regions. Systematic analysis of surface water budget reveals that evapotranspiration is a major sink in the water budget over the regions where precipitation is moderate or small, while the role of runoff and drainage becomes important over the regions where precipitation is abundant. The model simulations also suggest that during the short-rains season, the large-scale circulation anomalies play the most important role in shaping the precipitation anomalies.
DA - 1999/3/27/
PY - 1999/3/27/
DO - 10.1029/1998JD200051
VL - 104
IS - D6
SP - 6529-6548
SN - 2169-8996
ER -
TY - JOUR
TI - Application of the NCAR Regional Climate Model to eastern Africa - 2. Simulation of interannual variability of short rains
AU - Sun, LQ
AU - Semazzi, FHM
AU - Giorgi, F
AU - Ogallo, L
T2 - JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES
AB - We have applied the NCAR RegCM2 to the simulation of the interannual variability of precipitation over eastern Africa for the short-rains season by performing a set of experiments for the years 1982 to 1993. The model reproduced the observed interannual variability of precipitation in most of the years. The results show that remote factors play a dominant role in determining the precipitation anomalies. Interannual variability of precipitation over Tanzania is closely related to El Niño events in their mature phase and sea surface temperature (SST) anomalies over the Indian and Atlantic Oceans. The southward shift of the Arabian High results in a southward shift of the zonal component of the Intertropical Convergence Zone (ITCZ), which is responsible for early onset of the rainy season (e.g., 1982 and 1986). The enhanced St. Helena High and weaker Mascarene High lead to the eastward shift of the meridional branch of the ITCZ for the wet years. Model simulations confirmed a strong positive correlation between precipitation anomalies over Lake Victoria and the warm El Niño-Southern Oscillation events, by which enhanced moist westerly flow from the Atlantic Ocean and the mainly easterly flow from the Indian Ocean converge over Lake Victoria during wet years. The interannual variability of precipitation over Lake Victoria and the western Kenya Highlands (WKH) are strongly coupled. Positive precipitation anomalies over the WKH region are usually associated with weaker Arabian High and Mascarene High, which weaken the large-scale divergence over the WKH region and favor the development of convection. The interannual variability of precipitation over eastern Kenya Highlands (EKH) is not directly related to the El Niño events, but the association with a warm SST anomaly pattern over the western Indian Ocean is evident during wet years. An El Niño signal is, however, evident for wet years over the Turkana Channel, warm SST anomalies over the northern Indian Ocean contribute enhanced water vapor transport over the region.
DA - 1999/3/27/
PY - 1999/3/27/
DO - 10.1029/1998JD200050
VL - 104
IS - D6
SP - 6549-6562
SN - 2169-897X
ER -
TY - JOUR
TI - An active set strategy based on the augmented Lagrangian formulation for image restoration
AU - Ito, K.
AU - Kunisch, K.
T2 - RAIRO. Mathematical Modelling and Numerical Analysis
AB - Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by very high noise are included.
DA - 1999///
PY - 1999///
DO - 10.1051/m2an:1999102
VL - 33
IS - 1
SP - 1-21
ER -
TY - JOUR
TI - A concise and accurate solution for a polarization model in radiative transfer
AU - Siewert, CE
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - Abstract The discrete-ordinates method is used to develop a solution to a basic polarization problem in radiative transfer. In particular, a solution for the coupled I and Q components of the Stokes vector is developed for a polarization model based on a mixture of Rayleigh and isotropic scattering. The solution is evaluated for the case of a finite plane-parallel layer that has a polarized beam incident on one surface and which has Lambertian reflection on the other surface.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0022-4073(98)00097-1
VL - 62
IS - 6
SP - 677-684
SN - 0022-4073
ER -
TY - JOUR
TI - Wave speeds for an elastoplastic model for two-dimensional deformations with a nonassociative flow rule
AU - Gordon, M
AU - Garaizar, FX
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - A system of partial differential equations describing elastoplastic deformations in two space dimensions is studied. The constitutive relations for plastic deformation include a nonassociative flow rule and shear strain hardening. After a change of variables, the characteristic speeds of plane wave solutions of the system are computed. For both plastic and elastic deformations, there are two nonzero wave speeds, referred to as
DA - 1999/6//
PY - 1999/6//
DO - 10.1090/qam/1686188
VL - 57
IS - 2
SP - 245-259
SN - 0033-569X
ER -
TY - JOUR
TI - Empirical distribution for linear system identification
AU - Yin, G
AU - Fitzpatrick, BG
AU - Yin, K
T2 - STOCHASTIC ANALYSIS AND APPLICATIONS
AB - Asymptotic properties of empirical distributions of approximate errors for least squares identification are developed in this work. As a preparation, it is first shown that a law of large numbers type of result holds for the empirical distribution. Then a scaled sequence is proved to converge to a Gaussian process with a Brownian bridge component. These results are useful for carrying out statistical inference tasks, goodness of fit tests, and related matters
DA - 1999/3//
PY - 1999/3//
DO - 10.1080/07362999908809601
VL - 17
IS - 2
SP - 295-313
SN - 0736-2994
KW - least squares identification
KW - approximate error
KW - empirical distribution
ER -
TY - JOUR
TI - A fast multilevel algorithm for the solution of nonlinear systems of conductive-radiative heat transfer equations in two space dimensions
AU - Banoczi, JM
AU - Kelley, CT
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined conductive-radiative heat transfer in two space dimensions. This extends our previous work in one space dimension. We formulate the equations as a compact fixed point problem with the temperature as the unknown. The fixed point map requires both a Poisson solve and a transport solve for its evaluation. As a solver for both the transport problem and the full system we apply the Atkinson--Brakhage algorithm, using Newton-GMRES as the solver on the coarse mesh. We compare our solver choices with Newton-GMRES. Under modest stability and convergence assumptions on the transport solver, we prove convergence of the multilevel method for the complete system.
DA - 1999///
PY - 1999///
DO - 10.1137/S1064827597322756
VL - 20
IS - 4
SP - 1214-1228
SN - 1064-8275
KW - conductive-radiative heat transfer
KW - multilevel algorithm
KW - compact fixed point problems
ER -
TY - JOUR
TI - Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
AU - Schulze, MR
AU - Shearer, M
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
DA - 1999/1/1/
PY - 1999/1/1/
DO - 10.1006/jmaa.1998.6186
VL - 229
IS - 1
SP - 344-362
SN - 0022-247X
ER -
TY - PCOMM
TI - Some comments concerning the discrete eigenvalue
AU - Siewert, C. E.
DA - 1999///
PY - 1999///
SP - 439
ER -
TY - JOUR
TI - Pointwise convergence of approximation schemes for parameter estimation in parabolic equations
AU - Banks, HT
AU - Zia, LL
T2 - APPLIED MATHEMATICS LETTERS
AB - A finite element-based approximation scheme is presented for parameter estimation problems for parabolic PDEs on a two-dimensional domain. Pointwise convergence results relating the approximating subspaces to the full infinite-dimensional state space are discussed.
DA - 1999/10//
PY - 1999/10//
DO - 10.1016/S0893-9659(99)00097-X
VL - 12
IS - 7
SP - 27-30
SN - 0893-9659
KW - finite elements
KW - bicubic splines
KW - 2-D domain
KW - transport models
KW - parameter estimation
ER -
TY - JOUR
TI - DAEs arising from traveling wave solutions of PDEs II
AU - Marszalek, W
AU - Campbell, SL
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - The study of traveling wave solutions of PDEs sometimes leads to systems of Differential Algebraic Equations (DAEs). This paper examines a family of DAEs that arise in this manner from the Magnetohydrodynamics (MHD) equations. These DAEs are of interest in their own right, as a source of test problems for DAE numerical integrators, and because of their relationship to the MHD equations.
DA - 1999/1//
PY - 1999/1//
DO - 10.1016/S0898-1221(98)00238-7
VL - 37
IS - 1
SP - 15-34
SN - 0898-1221
KW - differential algebraic equation
KW - magnetohydrodynamics
KW - dynamical systems
ER -
TY - JOUR
TI - Approximation results for parameter estimation in a class of abstract nonlinear hyperbolic systems
AU - Banks, HT
AU - Pinter, GA
T2 - APPLIED MATHEMATICS LETTERS
AB - In this paper, we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0893-9659(99)00091-9
VL - 12
IS - 6
SP - 129-133
SN - 0893-9659
KW - nonlinear hyperbolic systems
KW - parameter estimation
KW - approximation
ER -
TY - JOUR
TI - A minimal mechanism for bacterial pattern formation
AU - Tyson, R
AU - Lubkin, , SR
AU - Murray, JD
T2 - PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
AB - Colonies of Escherichia coli or Salmonella typhimurium form geometrically complex patterns when exposed to, or feeding on, intermediates of the tricarboxylic acid (TCA) cycle. In response to the TCA cycle intermediate, the bacteria secrete aspartate, a potent chemo–attractant. As a result, the cells form high density aggregates arranged in striking regular patterns. The simplest are temporary spots formed in a liquid medium by both E. coli and S. typhimurium. In semi–solid medium S. typhimurium forms concentric rings arising from a low–density bacterial lawn, which are either continuous or spotted, whereas E. coli forms complex patterns arising from a dense swarm ring, including interdigitated spots (also called sunflower spirals), radial spots, radial stripes and chevrons. We present a mathematical model which captures all three of the pattern forming processes experimentally observed in both E. coli and S. typhimurium, using a minimum of assumptions.
DA - 1999/2/7/
PY - 1999/2/7/
DO - 10.1098/rspb.1999.0637
VL - 266
IS - 1416
SP - 299-304
SN - 0962-8452
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000078573000013&KeyUID=WOS:000078573000013
KW - chemotaxis
KW - bacterial patterns
KW - mathematical modelling
KW - bacterial aggregates
KW - spots
KW - stripes
ER -
TY - JOUR
TI - Undercompressive shocks and Riemann problems for scalar conservation laws with non-convex fluxes
AU - Hayes, B
AU - Shearer, M
T2 - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
AB - The Riemann initial value problem is studied for scalar conservation laws whose fluxes have a single inflection point. For a regularization consisting of balanced diffusive and dispersive terms, the travelling wave criterion is used to select admissible shocks. In some cases, the Riemann problem solution contains an undercompressive shock. The analysis is illustrated by exploring parameter space for the Buckley–Leverett flux. The boundary of the set of parameters for which there is a physical solution of the Riemann problem for all data is computed. Within the region of acceptable parameters, the solution hasseveral different forms, depending on the initial data; the different forms are illustrated by numerical computations. Qualitatively similar behaviour is observed in Lax–Wendroff approximations of solutions of the Buckley–Leverett equation with no dissipation or dispersion.
DA - 1999///
PY - 1999///
DO - 10.1017/s0308210500013111
VL - 129
IS - 1999
SP - 733-754
SN - 0308-2105
ER -
TY - JOUR
TI - Optimal design of a high pressure organometallic chemical vapor deposition reactor
AU - Bachmann, KJ
AU - Banks, HT
AU - Hopfner, C
AU - Kepler, GM
AU - LeSure, S
AU - McCall, SD
AU - Scroggs, JS
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - A team composed of material scientists, physicists, and applied mathematicians have used computer simulations as a fundamental design tool in developing a new prototype High Pressure Organometallic Chemical Vapor Deposition (HPOMCVD) reactor for use in thin film crystal growth. Early design of the HPOMCVD reactor dramatically evolved long before any physical reactor was built. This effort offers a strong endorsement of such multidisciplinary, computationally based modeling teams in the design of new products in areas of emerging technologies where heretofore extensive and costly experimental design was the central paradigm.
DA - 1999/4//
PY - 1999/4//
DO - 10.1016/S0895-7177(99)00071-0
VL - 29
IS - 8
SP - 65-80
SN - 0895-7177
ER -
TY - JOUR
TI - NC 109 tomato breeding line: 'Mountain Fresh' F-1 hybrid
AU - Gardner, R. G.
T2 - HortScience
DA - 1999///
PY - 1999///
VL - 34
IS - 5
SP - 941-942
ER -
TY - JOUR
TI - Multiple internal layer solutions generated by spatially oscillatory perturbations
AU - Hale, JK
AU - Lin, XB
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - For a singularly perturbed system of reaction-diffusion equations, we study the bifurcation of internal layer solutions due to the addition of a spatially oscillatory term. In the singular limit, the existence and stability of internal layer solutions are determined by the intersection of a fast jump surface Γ 1 and a slow switching curve C . The case when the intersection is transverse was studied by X.-B. Lin (Construction and asymptotic stability of structurally stable internal layer solutions, preprint). In this paper, we show that when Γ 1 intersects with C tangentially, saddle-node or cusp type bifurcation may occur. Higher order expansions of internal layer solutions and eigenvalue–eigenfunctions are also presented. To find a true internal layer solution and true eigenvalue-eigenfunctions, we use a Newton's method in functions spaces that is suitable for numerical computations.
DA - 1999/5/20/
PY - 1999/5/20/
DO - 10.1006/jdeq.1998.3566
VL - 154
IS - 2
SP - 364-418
SN - 0022-0396
ER -
TY - JOUR
TI - Monte Verde tomato
AU - Gardner, R. G.
T2 - HortScience
DA - 1999///
PY - 1999///
VL - 34
IS - 5
SP - 940
ER -
TY - JOUR
TI - Level two vertex representations of G(2)((1))
AU - Jing, NH
AU - Lyerly, CM
T2 - COMMUNICATIONS IN ALGEBRA
AB - We construct explicitly a level two representation of the affine Lie algebra using interactive bosonic fields.
DA - 1999///
PY - 1999///
DO - 10.1080/00927879908826702
VL - 27
IS - 9
SP - 4355-4362
SN - 0092-7872
KW - Kac-Moody algebras
KW - vertex operators
ER -
TY - JOUR
TI - Distributed matrix-free solution of large sparse linear systems over finite fields
AU - Kaltofen, E
AU - Lobo, A
T2 - ALGORITHMICA
DA - 1999///
PY - 1999///
DO - 10.1007/PL00008266
VL - 24
IS - 3-4
SP - 331-348
SN - 0178-4617
KW - distributed symbolic computation
KW - sparse linear systems
KW - block Wiedemann
KW - outer loop parallelization
ER -
TY - JOUR
TI - A discrete-ordinates solution for a polarization model with complete frequency redistribution
AU - Barichello, LB
AU - Siewert, CE
T2 - ASTROPHYSICAL JOURNAL
AB - The discrete-ordinates method is used to develop a solution to a class of polarization problems in the theory of radiative transfer. The I and Q components of the Stokes vector are used to describe the polarized radiation field, and the model considered allows a mixture of Rayleigh and isotropic scattering with complete frequency redistribution (completely noncoherent scattering) and continuum absorption. In addition to a general formulation for a finite plane-parallel medium, specific computations for both the Doppler and the Lorentz profiles of the line-scattering coefficient are reported for a general problem with internal emission and radiation incident on one surface of the layer.
DA - 1999/3/1/
PY - 1999/3/1/
DO - 10.1086/306834
VL - 513
IS - 1
SP - 370-382
SN - 0004-637X
KW - polarization
KW - radiative transfer
ER -
TY - JOUR
TI - Numerical analysis of coupled systems of nonlinear parabolic equations
AU - Pao, CV
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - This paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method. Three monotone iteration processes for the finite difference system are presented, and the sequences of iterations are shown to converge monotonically to a unique solution of the system, including an existence-uniqueness-comparison theorem. A theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given. Also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary-value problem. An application to a reaction-diffusion model in chemical engineering and combustion theory is given.
DA - 1999/3/5/
PY - 1999/3/5/
DO - 10.1137/S0036142996313166
VL - 36
IS - 2
SP - 393-416
SN - 0036-1429
KW - system of parabolic equations
KW - finite difference equations
KW - monotone iterative methods
KW - reaction-diffusion-convection
KW - convergence and error analysis
ER -
TY - JOUR
TI - Hecke algebras and semisimplicity of monoid algebras
AU - Putcha, MS
T2 - JOURNAL OF ALGEBRA
AB - We begin by constructing Hecke algebras for arbitrary finite regular monoids M . We then show that the semisimplicity of the complex monoid algebra C M is equivalent to the semisimplicity of the associated Hecke algebras and a condition on induced group characters. We apply these results to finite Lie-type monoids M . We show that the monoid algebra FM over a field F is semisimple if and only if the characteristic of F does not divide the order of the unit group G . This is accomplished by developing formulas for the unities of C J , J a J -class of M . The unity is explicitly given when G is a simply connected Chevalley group and J is associated with a Borel subgroup of G .
DA - 1999/8/15/
PY - 1999/8/15/
DO - 10.1006/jabr.1999.7868
VL - 218
IS - 2
SP - 488-508
SN - 0021-8693
ER -
TY - JOUR
TI - Estimates for the Nash-Sofer preconditioner for the reduced Hessian for some elliptic variational inequalities
AU - Choi, TD
AU - Kelley, CT
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - The purpose of this paper is to present a class of examples to show how the quality of the Nash--Sofer preconditioner can be directly estimated. This class of examples includes certain discretized elliptic variational inequalities. We use sparsity and locality properties of discretizations of elliptic operators and smoothing properties of their inverses to estimate the quality of the preconditioner. One consequence of our results is that if the Hessian is the five-point discretization of a certain type of strongly elliptic operator with homogeneous Dirichlet boundary conditions on an $n \times n$ mesh and the preconditioner is a fast Poisson solver for that discretization, then the condition number of the reduced Hessian can be lowered from O(n2 ) to O(n ln(n)). We illustrate these theoretical results with calculations.
DA - 1999/4/20/
PY - 1999/4/20/
DO - 10.1137/S1052623497323364
VL - 9
IS - 2
SP - 327-341
SN - 1052-6234
KW - preconditioners
KW - reduced Hessian
KW - elliptic variational inequalities
ER -
TY - JOUR
TI - A complete steady state model of solute and water transport in the kidney
AU - Kottler, NE
AU - Tran, HT
AU - Wessell, DE
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The purpose of this paper is to incorporate a detailed model, along with an optimized set of parameters for the proximal tubule, into J. L. Stephenson's current central core model of the nephron. In this model a set of equations for the proximal tubule are combined with Stephenson's equations for the remaining four tubules and interstitium, to form a complete nonlinear system of 34 ordinary differential and algebraic equations governing fluid and solute flow in the kidney. These equations are then discretized by the Crank-Nicholson scheme to form an algebraic system of nonlinear equations for the unknown concentrations, flows, hydrostatic pressure, and potentials. The resulting system is solved via factored secant update with a finite-difference approximation to the Jacobian. Finally, numerical simulations performed on the model showed that the modeled behavior approximates, in a general way, the physiological mechanisms of solvent and solute flow in the kidney.
DA - 1999/3//
PY - 1999/3//
DO - 10.1016/S0895-7177(99)00055-2
VL - 29
IS - 6
SP - 63-82
SN - 1872-9479
KW - transport model
KW - biomathematics
KW - differential algebraic system
KW - inserve problem
KW - numerical methods
ER -
TY - JOUR
TI - Primal-dual strategy for constrained optimal control problems
AU - Bergounioux, M
AU - Ito, K
AU - Kunisch, K
T2 - SIAM JOURNAL ON CONTROL AND OPTIMIZATION
AB - An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For discretized problems sufficient conditions for convergence in finitely many iterations are given. Numerical examples are given and the role of the strict complementarity condition is discussed.
DA - 1999/5/26/
PY - 1999/5/26/
DO - 10.1137/S0363012997328609
VL - 37
IS - 4
SP - 1176-1194
SN - 0363-0129
KW - active set
KW - augmented Lagrangian
KW - primal-dual method
KW - optimal control
ER -
TY - JOUR
TI - Positive solutions and dynamics of some reaction diffusion models in HIV transmission
AU - Yang, ZP
AU - Pao, CV
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
DA - 1999/2//
PY - 1999/2//
DO - 10.1016/S0362-546X(97)00672-X
VL - 35
IS - 3
SP - 323-341
SN - 0362-546X
KW - reaction diffusion equations
KW - positive solutions
KW - dynamics
KW - HIV transmission
KW - numerical solutions
ER -
TY - JOUR
TI - Case study of the physics component of an integrated curriculum
AU - Beichner, R
AU - Bernold, L
AU - Burniston, E
AU - Dail, P
AU - Felder, R
AU - Gastineau, J
AU - Gjertsen, M
AU - Risley, J
T2 - AMERICAN JOURNAL OF PHYSICS
AB - Over a four-year time span, several departments at North Carolina State University offered experimental sections of courses taken by freshman engineering students. The acronym IMPEC (Integrated Math, Physics, Engineering, and Chemistry curriculum) describes which classes were involved. This paper discusses the physics component of the curriculum and describes the impact of the highly collaborative, technology-rich, activity-based learning environment on a variety of conceptual and problem-solving assessments and attitude measures. Qualitative and quantitative research results indicate that students in the experimental courses outperformed their cohorts in demographically matched traditional classes, often by a wide margin. Student satisfaction and confidence rates were remarkably high. We also noted substantial increases in retention and success rates for groups underrepresented in science, math, and engineering. Placing students in the same teams across multiple courses appears to have been the most beneficial aspect of the learning environment.
DA - 1999/7//
PY - 1999/7//
DO - 10.1119/1.19075
VL - 67
IS - 7
SP - S16-S24
SN - 0002-9505
ER -
TY - JOUR
TI - A conjugacy theorem for symmetric spaces
AU - Helminck, AG
AU - Hilgert, J
AU - Neumam, A
AU - Olafsson, G
T2 - MATHEMATISCHE ANNALEN
DA - 1999/4//
PY - 1999/4//
DO - 10.1007/s002080050282
VL - 313
IS - 4
SP - 785-791
SN - 0025-5831
ER -
TY - JOUR
TI - On constructing matrices with prescribed singular values and diagonal elements
AU - Chu, MT
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Similar to the well known Schur-Horn theorem that characterizes the relationship between the diagonal entries and the eigenvalues of a Hermitian matrix, the Sing-Thompson theorem characterizes the relationship between the diagonal entries and the singular values of an arbitrary matrix. It is noted in this paper that, based on the induction principle, such a matrix can be constructed numerically by a fast recursive algorithm, provided that the given singular values and diagonal elements satisfy the Sing-Thompson conditions.
DA - 1999/2/1/
PY - 1999/2/1/
DO - 10.1016/S0024-3795(98)10124-6
VL - 288
IS - 1-3
SP - 11-22
SN - 1873-1856
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0039035737&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Volterra integrodifferential neutral dynamics for the growth of wealth of nations: A controllability theory, with Canada example
AU - Chukwu, E. N.
T2 - Journal of High Energy Physics
DA - 1999///
PY - 1999///
VL - 5
IS - 1-4
SP - 561-577
ER -
TY - JOUR
TI - Model and analysis of chemotactic bacterial patterns in a liquid medium
AU - Tyson, R
AU - Lubkin, , SR
AU - Murray, JD
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
DA - 1999/4//
PY - 1999/4//
DO - 10.1007/s002850050153
VL - 38
IS - 4
SP - 359-375
SN - 0303-6812
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000079977900004&KeyUID=WOS:000079977900004
KW - chemotaxis
KW - partial differential equations
KW - bacteria
KW - mathematical modeling
KW - pattern formation
ER -
TY - JOUR
TI - Invariant algebra and cuspidal representations of finite monoids
AU - Putcha, MS
T2 - JOURNAL OF ALGEBRA
AB - Motivated by the theories of Hecke algebras and Schur algebras, we consider in this paper the algebra C M G of G -invariants of a finite monoid M with unit group G . If M is a regular “balanced” monoid, we show that C M G is a quasi-hereditary algebra. In such a case, we find the blocks of C M G to be the “sections” of the blocks of C M . We go on to develop a theory of cuspidal representations for balanced monoids. We then apply our results to the full transformation semigroup and the multiplicative monoid of triangular matrices over a finite field.
DA - 1999/2/15/
PY - 1999/2/15/
DO - 10.1006/jabr.1998.7634
VL - 212
IS - 2
SP - 721-737
SN - 0021-8693
ER -
TY - JOUR
TI - Fast and accurate numerical approaches for Stefan problems and crystal growth
AU - Li, ZL
AU - Soni, B
T2 - NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
AB - New numerical approaches for moving boundary interface applications tailored for Stefan problems and crystal growth simulation are proposed in this article. The focus is on the issues of accuracy and speed-up. A modified Crank-Nicolson method that is second-order accurate and stable is developed. The alternating directional implicit (ADI) method is also developed to speed up the simulation for a certain class of problems. The ADI method is shown to be asymptotically stable and at least first-order accurate. Numerical results, however, show that the ADI method actually provides second-order accuracy if the velocity can be calculated accurately. The level set method is used to update the moving interface so that the topological changes can be handled easily. Numerical experiments are compared to exact solutions and results in the literature.
DA - 1999/6//
PY - 1999/6//
DO - 10.1080/104077999275848
VL - 35
IS - 4
SP - 461-484
SN - 1040-7790
ER -
TY - JOUR
TI - Exclusionary population dynamics in size-structured, discrete competitive systems
AU - Francke, JE
AU - Yakubu, AA
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - A discrete multi-species size-structured competition model is considered. By using decreasing growth functions, we achieve the self-regulation of species. We develop various biologically significant conditions for global convergence to the extinction state of the dominated species in the competitive system. With an example we illustrate coexistence in a chaotic supr transient. The chaotic attractor has an unusual pulsating nature.
DA - 1999///
PY - 1999///
DO - 10.1080/10236199908808185
VL - 5
IS - 3
SP - 235-249
SN - 1023-6198
KW - extinction
KW - Lyapunov function
KW - chaotic attractor
ER -
TY - JOUR
TI - Calculating the Galois group of L-1(L-2(y))=0, L-1,L-2 completely reducible operators
AU - Berman, PH
AU - Singer, MF
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - In Calculating Galois groups of completely reducible linear operators, Compoint and Singer describe a decision procedure that computes the Galois group of a completely reducible linear differential operator with rational or algebraic function coefficients (i.e., a linear differential operator that is the least common left multiple of irreducible operators or, equivalently, one whose Galois group is a reductive group). At present, it is unknown how to calculate the Galois group of a general operator. In this paper, we push beyond the completely reducible case by showing how to compute the Galois group of an operator of the form L1∘L2 where L1 and L2 are completely reducible and have rational function coefficients. We begin by showing how to compute the Galois group of an equation of the form L(y)=b with L completely reducible. This corresponds to the case of L1∘L2 where L1=D−b′/b. We then show how one can reduce the general case to the above case and give several examples.
DA - 1999/6/17/
PY - 1999/6/17/
DO - 10.1016/S0022-4049(99)00003-1
VL - 139
IS - 1-3
SP - 3-23
SN - 0022-4049
ER -
TY - JOUR
TI - Representation of GaP formation by a reduced order surface kinetics model using p-polarized reflectance measurements
AU - Beeler, S
AU - Tran, HT
AU - Dietz, N
T2 - JOURNAL OF APPLIED PHYSICS
AB - This contribution presents results on the parameter estimation of rate constants and optical response factors in a reduced order surface kinetics (ROSK) model, which has been developed to describe the decomposition kinetics of the organometallic precursors involved and their incorporation into the film deposition. As a real-time characterization technique, we applied p-polarized reflectance spectroscopy (PRS) during low temperature growth of epitaxial GaP heterostructures on Si(001) substrates by pulsed chemical beam epitaxy. The high surface sensitivity of PRS allows us to follow alterations in the composition and thickness of the surface reaction layer as they are encountered during periodic precursor supply. Linkage of the PRS response to the ROSK model provides the base for the parameter estimation of the reduced order surface kinetics model, giving insights into the organometallic precursor decomposition and growth kinetics.
DA - 1999/7/1/
PY - 1999/7/1/
DO - 10.1063/1.370783
VL - 86
IS - 1
SP - 674-682
SN - 1089-7550
ER -
TY - JOUR
TI - Periodic solutions of parabolic systems with nonlinear boundary conditions
AU - Pao, CV
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper is concerned with the existence and stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions. The approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for parabolic initial-boundary value problems. A sufficient condition for the stability of a periodic solution is also given. These results are applied to three model problems arising from chemical kinetics, ecology, and population biology.
DA - 1999/6/15/
PY - 1999/6/15/
DO - 10.1006/jmaa.1999.6412
VL - 234
IS - 2
SP - 695-716
SN - 1096-0813
ER -
TY - JOUR
TI - A numerical study of electro-migration voiding by evolving level set functions on a fixed Cartesian grid
AU - Li, ZL
AU - Zhao, HK
AU - Gao, HJ
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - A numerical method for studying migration of voids driven by surface diffusion and electric current in a metal conducting line is developed. The mathematical model involves moving boundaries governed by a fourth order nonlinear partial differential equation which contains a nonlocal term corresponding to the electrical field and a nonlinear term corresponding to the curvature. Numerical challenges include efficient computation of the electrical field with sufficient accuracy to afford fourth order differentiation along the void boundary and to capture singularities arising in topological changes. We use the modified immersed interface method with a fixed Cartesian grid to solve for the electrical field, and the fast local level set method to update the position of moving voids. Numerical examples are performed to demonstrate the physical mechanisms by which voids interact under electromigration.
DA - 1999/6/10/
PY - 1999/6/10/
DO - 10.1006/jcph.1999.6249
VL - 152
IS - 1
SP - 281-304
SN - 0021-9991
ER -
TY - JOUR
TI - Well-posedness for a class of abstract nonlinear parabolic systems with time delay
AU - Banks, HT
AU - Musante, CJ
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
DA - 1999/3//
PY - 1999/3//
DO - 10.1016/S0362-546X(98)00053-4
VL - 35
IS - 5
SP - 629-648
SN - 0362-546X
KW - nonlinear parabolic distributed parameter systems with delays
KW - existence
KW - uniqueness
KW - variational form
KW - toxicokinetic modeling
KW - liver transport models
ER -
TY - JOUR
TI - On the size of a random sphere of influence graph
AU - Chalker, TK
AU - Godbole, AP
AU - Hitchzenko, P
AU - Radcliff, J
AU - Ruehr, OG
T2 - ADVANCES IN APPLIED PROBABILITY
AB - We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, X i , draw an open ball (‘sphere of influence’) with radius equal to the distance to X i 's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d ; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.
DA - 1999/9//
PY - 1999/9//
DO - 10.1017/S0001867800009307
VL - 31
IS - 3
SP - 596-609
SN - 1475-6064
KW - Azuma-Hoeffding inequality
KW - random graphs
KW - sphere of influence graphs
ER -
TY - BOOK
TI - Iterative Methods for Optimization
AU - Kelley, C T
AB - This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke& Jeeves, implicit filtering, MDS, and Nelder& Mead schemes in a unified way.
CN - QA402.5 .K44 1999
DA - 1999///
PY - 1999///
DO - 10.1137/1.9781611970920
PB - SIAM
SN - 0898714338
ER -
TY - JOUR
TI - Concerning derivations of lie algebras
AU - Stitzinger, Ernest
AU - Turner, R.
T2 - Linear & Multilinear Algebra
AB - Schur showed that if the center of a group has finite index, then the commutator subgroup is finite. By replacing inner automorphisms by automorphisms, Hegarty obtained a variation of Schur's result. The Lie algebra analogue of Schur's result is well-known. We obtain a strong Lie algebra version of Hegarty's result.
DA - 1999///
PY - 1999///
DO - 10.1080/03081089908818596
VL - 45
IS - 1999
SP - 329–331
ER -
TY - JOUR
TI - Vertex operators for twisted quantum affine algebras
AU - Jing, NH
AU - Misra, KC
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - We construct explicitly the q q -vertex operators (intertwining operators) for the level one modules V ( Λ i ) V(\Lambda _i) of the classical quantum affine algebras of twisted types using interacting bosons, where i = 0 , 1 i=0, 1 for A 2 n − 1 ( 2 ) A_{2n-1}^{(2)} ( n ≥ 3 n\geq 3 ), i = 0 i=0 for D 4 ( 3 ) D_4^{(3)} , i = 0 , n i=0, n for D n + 1 ( 2 ) D_{n+1}^{(2)} ( n ≥ 2 n\geq 2 ), and i = n i=n for A 2 n ( 2 ) A_{2n}^{(2)} ( n ≥ 1 n\geq 1 ). A perfect crystal graph for D 4 ( 3 ) D_4^{(3)} is constructed as a by-product.
DA - 1999/4//
PY - 1999/4//
DO - 10.1090/S0002-9947-99-02098-X
VL - 351
IS - 4
SP - 1663-1690
SN - 0002-9947
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-22644451731&partnerID=MN8TOARS
KW - quantum affine algebras
KW - q-vertex operators
ER -
TY - JOUR
TI - The index of an infinite dimensional implicit system
AU - Campbell, SL
AU - Marszalek, W
T2 - MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS
AB - The idea of the index of a differential algebraic equation (DAE) (or implicit differential equation) has played a fundamental role in both the analysis of DAEs and the development of numerical algorithms for DAEs. DAEs frequently arise as partial discretizations of partial differential equations (PDEs). In order to relate properties of the PDE to those of the resulting DAE it is necessary to have a concept of the index of a possibly constrained PDE. Using the finite dimensional theory as motivation, this paper will examine what one appropriate analogue is for infinite dimensional systems. A general definition approach will be given motivated by the desire to consider numerical methods. Specific examples illustrating several kinds of behavior will be considered in some detail. It is seen that our definition differs from purely algebraic definitions. Numerical solutions, and simulation difficulties, can be misinterpreted if this index information is missing.
DA - 1999/3//
PY - 1999/3//
DO - 10.1076/mcmd.5.1.18.3625
VL - 5
IS - 1
SP - 18-42
SN - 1387-3954
KW - numerical analysis
KW - ordinary differential equations on manifolds
KW - overdetermined systems
KW - partial differential equations on manifolds (AMS Classification)
ER -
TY - JOUR
TI - Global attractivity and convergence to a two-cycle in a difference equation
AU - Franke, JE
AU - Hoag, JT
AU - Ladas, G
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - We obtain conditions under which every positive solution of a difference equation of the form y n+1=y n-1 f(y n-1, y n ), n=0, 1, 2, … is attracted to its positive equilibrium. We also obtain conditions under which every positive solution approaches a two-cycle, which may be an equilibrium. The results apply to a population model with two age classes
DA - 1999///
PY - 1999///
DO - 10.1080/10236199908808180
VL - 5
IS - 2
SP - 203-209
SN - 1023-6198
KW - global attractivity
KW - two-cycle
KW - population model
ER -
TY - JOUR
TI - Geodesic deviation in Regge calculus
AU - Chakrabarti, S
AU - Gentle, AP
AU - Kheyfets, A
AU - Miller, WA
T2 - CLASSICAL AND QUANTUM GRAVITY
AB - Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of general relativity on two different levels. We show that the continuum and simplicial descriptions coincide when the cumulative effect of the Regge contributions over an infinitesimal element of area is considered. This comparison provides a quantitative relation between the curvature of the continuous description and the deficit angles of Regge calculus. The results presented might also be of help in developing generic ways of including matter terms in the Regge equations.
DA - 1999/7//
PY - 1999/7//
DO - 10.1088/0264-9381/16/7/315
VL - 16
IS - 7
SP - 2381-2391
SN - 0264-9381
ER -
TY - JOUR
TI - Efficient eigenvalue calculations in radiative transfer
AU - Siewert, CE
AU - Wright, SJ
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - An efficient method is used to compute the eigenvalues required in a discrete-ordinates solution to a special class of radiative-transfer problems. The basis for this computation is an algorithm for finding eigenvalues of a matrix that consists of the sum of a diagonal matrix and a rank-one matrix, a form that can arise in a discrete-ordinates solution of some basic transport problems. To illustrate the efficiency of the approach, a radiative-transfer problem relevant to a non-gray model with scattering that allows complete frequency redistribution is discussed.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0022-4073(98)00099-5
VL - 62
IS - 6
SP - 685-688
SN - 0022-4073
ER -
TY - JOUR
TI - Convergence analysis of the immersed interface method
AU - Huang, HX
AU - Li, ZL
T2 - IMA JOURNAL OF NUMERICAL ANALYSIS
AB - A rigorous error analysis is given for the immersed interface method (IIM) applied to elliptic problems with discontinuities and singularities. The finite difference scheme using IIM is shown to satisfy the conditions of a maximum principle for a certain class of problems. Comparison functions are constructed to obtain error bounds for some of the approximate solutions. The asymptotic error expansion provides further useful insights and details of the behaviour and convergence properties of IIM, which leads to a sharper estimate of the error bound. Second-order convergence of IIM is indicated by the analysis. Numerical examples are also given to support the analytical results.
DA - 1999/10//
PY - 1999/10//
DO - 10.1093/imanum/19.4.583
VL - 19
IS - 4
SP - 583-608
SN - 0272-4979
ER -
TY - JOUR
TI - Constrained convergence
AU - Hartwig, RE
AU - Semrl, P
T2 - ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
DA - 1999///
PY - 1999///
DO - 10.1216/rmjm/1181071685
VL - 29
IS - 1
SP - 177-195
SN - 0035-7596
ER -
TY - JOUR
TI - Computation of nonclassical solutions to Hamilton-Jacobi problems
AU - Gremaud, PA
AU - Ide, NR
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - This paper is devoted to the construction of numerical methods for the approximation of nonclassical solutions to multidimensional Hamilton--Jacobi equations for both scalar and vectorial problems. Recent theoretical results have yielded existence of solutions in many cases for which the usual viscosity approach was ill-suited or not applicable. The selection criterion used here is based on a viscoelasticity/capillarity approach, common in solid mechanics. Numerical methods adapted to this framework are built. Consistency of the model equation with the given selection criterion is essential. It is achieved here through the use of high-order finite difference schemes. By considering applications to potential well problems, the convergence of the methods are investigated.
DA - 1999/10/26/
PY - 1999/10/26/
DO - 10.1137/S1064827597327668
VL - 21
IS - 2
SP - 502-521
SN - 1064-8275
KW - Hamilton-Jacobi
KW - viscosity solution
KW - nonconvex
KW - systems
KW - numerical viscosity
ER -
TY - JOUR
TI - Codimension-one Riemann solutions: Classical missing rarefaction cases
AU - Schecter, S
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - This paper is the third in a series that undertakes a systematic investigation of Riemann solutions of systems of two conservation laws in one spatial dimension. Sixty-three codimension-one degeneracies of such solutions have been identified at which strict hyperbolicity is maintained. In this paper, 18 of the degeneracies (9 pairs), constituting the most classical degeneracies, are studied in detail. Precise conditions for a codimension-one degeneracy are identified in each case, as are conditions for folding of the Riemann solution surface, which can occur in 4 of the cases. Such folding gives rise to local multiplicity or nonexistence of Riemann solutions.
DA - 1999/9/20/
PY - 1999/9/20/
DO - 10.1006/jdeq.1998.3590
VL - 157
IS - 2
SP - 247-318
SN - 0022-0396
KW - conservation law
KW - Riemann problem
KW - viscous profile
ER -
TY - JOUR
TI - A discrete-ordinates solution for heat transfer in a plane channel
AU - Siewert, CE
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - A recently established version of the discrete-ordinates method is used to develop a solution to a class of problems in the theory of rarefied-gas dynamics where temperature and density effects are coupled. In particular, accurate solutions for the temperature perturbation, the density perturbation, and the heat flux are developed and evaluated for the flow, described by the Bhatnagar, Gross, and Krook model, of a rarefied gas between two parallel plates at which arbitrary and unequal accommodation is allowed. Numerical results are obtained for various choices of the accommodation coefficients and a wide range of the inverse Knudsen number.
DA - 1999/6/10/
PY - 1999/6/10/
DO - 10.1006/jcph.1999.6244
VL - 152
IS - 1
SP - 251-263
SN - 0021-9991
ER -
TY - JOUR
TI - A discrete-ordinates solution for a non-grey model with complete frequency redistribution
AU - Barichello, LB
AU - Siewert, CE
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - The discrete-ordinates method is used to develop a solution to a class of non-grey problems in the theory of radiative transfer. The model considered allows for scattering with complete frequency redistribution (completely non-coherent scattering) and continuum absorption. In addition to a general formulation for semi-infinite and finite plane-parallel media, specific computations, for both the Doppler and the Lorentz profiles of the line-scattering coefficient, are discussed in regard to a half-space application concerning a linearly varying Planck function and also in regard to a basic problem from which, except for the conservative case, the classical X and Y functions can be extracted.
DA - 1999/8//
PY - 1999/8//
DO - 10.1016/S0022-4073(98)00096-X
VL - 62
IS - 6
SP - 665-675
SN - 0022-4073
ER -
TY - JOUR
TI - Solving difference equations in finite terms
AU - Hendriks, PA
AU - Singer, MF
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We define the notion of a Liouvillian sequence and show that the solution space of a difference equation with rational function coefficients has a basis of Liouvillian sequences iff the Galois group of the equation is solvable. Using this we give a procedure to determine the Liouvillian solutions of such a difference equation.
DA - 1999/3//
PY - 1999/3//
DO - 10.1006/jsco.1998.0251
VL - 27
IS - 3
SP - 239-259
SN - 0747-7171
ER -
TY - JOUR
TI - Level one representations of U-q(G(2)((1)))
AU - Jing, NH
T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - We construct a level one representation of the quantum affine algebra $U_q(G_2^{(1)})$ by vertex operators from bosonic fields.
DA - 1999/1//
PY - 1999/1//
DO - 10.1090/S0002-9939-99-04740-1
VL - 127
IS - 1
SP - 21-27
SN - 0002-9939
KW - quantum Z-operators
KW - vertex operators
ER -