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Articles 1 - 30 of 267
Full-Text Articles in Physical Sciences and Mathematics
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Faculty Publications
We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.
Large Sets Of Zero Analytic Capacity, John Garnett, Stan T. Yoshinobu
Large Sets Of Zero Analytic Capacity, John Garnett, Stan T. Yoshinobu
Mathematics
We prove that certain Cantor sets with non-sigma-finite one-dimensional Hausdorff measure have zero analytic capacity.
Discrete Maximum Principle For Nonsmooth Optimal Control Problems With Delays, Boris S. Mordukhovich, Ilya Shvartsman
Discrete Maximum Principle For Nonsmooth Optimal Control Problems With Delays, Boris S. Mordukhovich, Ilya Shvartsman
Mathematics Research Reports
We consider optimal control problems for discrete-time systems with delays. The main goal is to derive necessary optimality conditions of the discrete maximum principle type in the case of nonsmooth minimizing functions. We obtain two independent forms of the discrete maximum principle with transversality conditions described in terms of subdifferentials and superdifferentials, respectively. The superdifferential form is new even for non-delayed systems and may be essentially stronger than a more conventional subdifferential form in some situations.
Periodic Points Of The Family Of Tent Maps, Julio R. Hasfura-Buenaga, Phillip Lynch
Periodic Points Of The Family Of Tent Maps, Julio R. Hasfura-Buenaga, Phillip Lynch
Mathematics Faculty Research
No abstract provided.
How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall
How Many Symmetries Does Admit A Nonlinear Single-Input Control System Around An Equilibrium?, Witold Respondek, Issa Amadou Tall
Miscellaneous (presentations, translations, interviews, etc)
We describe all symmetries of a single-input nonlinear control system, that is not feedback linearizable and whose first order approximation is controllable, around an equilibrium point. For a system such that a feedback transformation, bringing it to the canonical form, is analytic we prove that the set of all local symmetries of the system is exhausted by exactly two 1-parameter families of symmetries, if the system is odd, and by exactly one 1-parameter family otherwise. We also prove that the form of the set of symmetries is completely described by the canonical form of the system: possessing a nonstationary symmetry, …
Integrals Of Periodic Functions, Sean F. Ellermeyer, David G. Robinson
Integrals Of Periodic Functions, Sean F. Ellermeyer, David G. Robinson
Faculty and Research Publications
Computing integrals of powers of the sine function is a standard exercise in calculus. The authors show that the first integral is representative of the integral of any periodic function.
A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger
A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger
All HMC Faculty Publications and Research
We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.
Existence Of Solutions Of The Classical Yang-Baxter Equation For A Real Lie Algebra, Jorg Feldvoss
Existence Of Solutions Of The Classical Yang-Baxter Equation For A Real Lie Algebra, Jorg Feldvoss
University Faculty and Staff Publications
We characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner
Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner
Mahurin Honors College Capstone Experience/Thesis Projects
No abstract provided.
On Some Optimal Tests In Finite Mixtures: Constructions And Applications., Chandranath Pal Dr.
On Some Optimal Tests In Finite Mixtures: Constructions And Applications., Chandranath Pal Dr.
Doctoral Theses
Mixtures of distributions are now-a-days playing very important roles in both theoretical and applied statistics. There is an abundance of real-life situations where mixture distributions are being extensively used for modelling data and drawing inference. Several books and monographs on mixtures have so far been published, e.g., Everitt and Hand (1981), Titterington et al. (1985), McLachlan and Basford (1988), McLachlan (1997) etc., which cover a wide area on different aspects of mixture distributions and their applications. The book by Titterington et al. (1985, pp. 16-21), in particular, contains a comprehensive list of references on direct applications of finite mixtures in …
Precision Measurement Of The Spin-Dependent Asymmetry In The Threshold Region Of 3He (E,E'), F. Xiong, D. Dutta, W. Xu, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, S. Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, D. Dale, A. Deur, P. Djawotho, B. W. Filippone, J. M. Finn, H. Gao, R. Gilman, A. V. Glamazdin, C. Glashausser, W. Glockle, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanage, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R. Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojtsekhowski, J. Yeh, P. Zolnierczuk
Precision Measurement Of The Spin-Dependent Asymmetry In The Threshold Region Of 3He (E,E'), F. Xiong, D. Dutta, W. Xu, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, S. Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, D. Dale, A. Deur, P. Djawotho, B. W. Filippone, J. M. Finn, H. Gao, R. Gilman, A. V. Glamazdin, C. Glashausser, W. Glockle, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanage, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R. Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojtsekhowski, J. Yeh, P. Zolnierczuk
Enkeleida K. Lakuriqi
We present the first precision measurement of the spin-dependent asymmetry in the threshold region of 3He (e,e') at Q2 values of 0.1 and 0.2(GeV/c)2. The agreement between the data and nonrelativistic Faddeev calculations which include both final-state interactions and meson-exchange current effects is very good at Q2=0.1(GeV/c)2, while a small discrepancy at Q2=0.2(GeV/c)2 is observed.
Finiteness Notions In Fuzzy Sets, Lawrence Stout
Finiteness Notions In Fuzzy Sets, Lawrence Stout
Scholarship
Finite sets are one of the most fundamental mathematical structures. In the absence of the axiom of choice there are many different inequivalent definitions of finite even in classical logic. When we allow incomplete existence as in fuzzy sets the situation gets even more complicated. This paper gives nine distinct definitions of finite in a fuzzy context together with examples showing how the properties of the underlying lattice of truth values impact the meanings of finite.
Finiteness Notions In Fuzzy Sets, Lawrence Stout
Finiteness Notions In Fuzzy Sets, Lawrence Stout
Lawrence N. Stout
Finite sets are one of the most fundamental mathematical structures. In the absence of the axiom of choice there are many different inequivalent definitions of finite even in classical logic. When we allow incomplete existence as in fuzzy sets the situation gets even more complicated. This paper gives nine distinct definitions of finite in a fuzzy context together with examples showing how the properties of the underlying lattice of truth values impact the meanings of finite.
Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff
Ethnomathematics: Challenging Traditional Notions Of Mathematical Authority, Christopher D. Goff
College of the Pacific Faculty Presentations
No abstract provided.
Marginal And Parametric Analysis Of The Central Optimal Solution, Allen G. Holder, J F. Sturm, S Zhang
Marginal And Parametric Analysis Of The Central Optimal Solution, Allen G. Holder, J F. Sturm, S Zhang
Mathematics Faculty Research
In this paper we investigate the sensitivity analysis of the parameterized central path. First, a complete marginal analysis of the central optimal solution is developed. This analysis explains the differential properties of the central optimal solution with respect to both the cost coefficients and the right-hand side components. We also show that the marginal derivatives are uniformly bounded. Second, we present three conditions for which the parameterized central path converges. Two of these results allow the difficult situation of simultaneous perturbations in the cost coefficients and right-hand side levels.
Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim
Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim
All HMC Faculty Publications and Research
Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Polygonal Chains Cannot Lock In 4d, Roxana Cocan, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that, in all dimensions d ≥ 4, every simple open polygonal chain and every tree may be straightened, and every simple closed polygonal chain may be convexified. These reconfigurations can be achieved by algorithms that use polynomial time in the number of vertices, and result in a polynomial number of “moves.” These results contrast to those known for d = 2, where trees can “lock,” and for d = 3, where open and closed chains can lock.
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
A Polytope Combinatorics For Semisimple Groups, Jared E. Anderson
Mathematics and Statistics Department Faculty Publication Series
Mirkovi and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they may be used to compute weight multiplicities and tensor product multiplicities for representations of a semisimple group. The polytopes are explicitly described for a few low rank groups.
Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini
Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini
Faculty Publications
We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of TGF. Our work extends a previously developed model which considers the interactions between fibroblasts and extracellular matrix, composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix can direct the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGF to alter the properties of the fibroblasts. Thus we are able to simulate experiments …
Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke
Computational Geometry Column 42, Joseph S. B. Mitchell, Joseph O'Rourke
Computer Science: Faculty Publications
A compendium of thirty previously published open problems in computational geometry is presented.
A Differential Equation Model Of North American Cinematic Box-Office Dynamics, David A. Edwards, Ron Buckmire
A Differential Equation Model Of North American Cinematic Box-Office Dynamics, David A. Edwards, Ron Buckmire
Ron Buckmire
No abstract provided.
Sequential Searches: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials Revisited, Don Rawlings
Sequential Searches: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials Revisited, Don Rawlings
Mathematics
No abstract provided.
The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet
The Fine Structure Of The Kasparov Groups I: Continuity Of The Kk-Pairing, Claude Schochet
Mathematics Faculty Research Publications
In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the groups have a natural pseudopolonais structure, and we prove that various KK-structural maps are continuous.
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
All HMC Faculty Publications and Research
A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum lF is replaced by lB =lF − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …
Whose Limit Is It Anyway?, Joseph E. Borzellino
Whose Limit Is It Anyway?, Joseph E. Borzellino
Mathematics
In a tongue-in-cheek manner, we investigate the notion of limit. We illustrate some of its shortcomings and show that addressing these shortcomings can often lead to unexpected consequences.
Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert
Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert
Faculty Publications
WE CONSIDER FACTORS INFLUENCING the build-up of corrugations on dirt roads and the reactions of vehicles to them. We suggest that corrugations are (at least in part) a consequence of a natural tangential oscillation of the tread surface of the car lure that occurs when the vehicle is being driven or braked. Secondly, we suggest that the unpleasant vibration experienced by a vehicle passing over a corrugated road is the result of a beat produced by the difference of the frequency of oscillation of its own tyres and the frequency of the stimulation received by the vehicle due to passage …
Ultraconvergence Of Zz Patch Recovery At Mesh Symmetry Points, Zhimin Zhang, Runchang Lin
Ultraconvergence Of Zz Patch Recovery At Mesh Symmetry Points, Zhimin Zhang, Runchang Lin
Mathematics Research Reports
Ultraconvergence property of the Zienkiewicz-Zhu gradient patch recovery technique based on local discrete least squares fitting is established for a large class of even-order finite elements. The result is valid at all rectangular mesh symmetry points. Different smoothing strategies are discussed. Superconvergence recovery for the Q8 element is proved and ultraconvergence numerical examples are demonstrated.
The Edge Of The Universe-Noneuclidean Wallpaper, Frank A. Farris
The Edge Of The Universe-Noneuclidean Wallpaper, Frank A. Farris
Mathematics and Computer Science
A simple mathematical model of a two-dimensional universe, called the Poincaré Upper Halfplane, illustrates the possibility of a universe with an unattainable edge. In this article, I describe this model -a famous example of a noneuclidean geometry-and explain how conversations with an analytic number theorist led me to create wallpaper patterns for its inhabitants. These are interesting not only for their high "Gee whiz!"factor, but also as a window for observing the features of this unusual geometry.
Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed
Stochastic Functional Differential Equations On Manifolds, Rémi Léandre, Salah-Eldin A. Mohammed
Articles and Preprints
In this paper, we study stochastic functional differential equations (sfde's) whose solutions are constrained to live on a smooth compact Riemannian manifold. We prove the existence and uniqueness of solutions to such sfde's. We consider examples of geometrical sfde's and establish the smooth dependence of the solution on finite-dimensional parameters.
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
All HMC Faculty Publications and Research
We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem