Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems,
2011
Durham University
Reliable A-Posteriori Error Estimators For Hp-Adaptive Finite Element Approximations Of Eigenvalue/Leigenvector Problems, Stefano Giani, Luka Grubisic, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We present reliable a-posteriori error estimates for hp-adaptive finite element approxima- tions of eigenvalue/eigenvector problems. Starting from our earlier work on h adaptive finite element approximations we show a way to obtain reliable and efficient a-posteriori estimates in the hp-setting. At the core of our analysis is the reduction of the problem on the analysis of the associated boundary value problem. We start from the analysis of Wohlmuth and Melenk and combine this with our a-posteriori estimation framework to obtain eigenvalue/eigenvector approximation bounds.
Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation,
2011
University of Nevada, Las Vegas
Boundary Element Method (Bem) And Method Of Fundamental Solutions (Mfs) For The Boundary Value Problems Of The 2-D Laplace's Equation, Ermes Anthony Salgado-Ibarra
UNLV Theses, Dissertations, Professional Papers, and Capstones
In this thesis we study the solution of the two dimensional Laplace equation by the boundary Element method (BEM) and the method of fundamental solutions (MFS). Both the BEM and MFS used to solve boundary value problems involving the Laplace equation 2-D settings. Both methods rely on the use of fundamental solution of the Laplace's equation (the solution of Laplace's equation in the distributional sense). We will contrast and compare the results we get using the BEM with results we get using the MFS.
The Schroedinger Equation With Potential In Random Motion,
2011
University at Albany, State University of New York
The Schroedinger Equation With Potential In Random Motion, Marius Beceanu, Soffer Avy
Mathematics and Statistics Faculty Scholarship
We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
Geometric Structures On Matrix-Valued Subdivision Schemes,
2011
University of Missouri-St. Louis
Geometric Structures On Matrix-Valued Subdivision Schemes, James J. Smith
Dissertations
Surface subdivision schemes are used in computer graphics to generate visually smooth surfaces of arbitrary topology. Applications in computer graphics utilize surface normals and curvature. In this paper, formulas are obtained for the first and second partial derivatives of limit surfaces formed using 1-ring subdivision schemes that have 2 by 2 matrix-valued masks. Consequently, surface normals, and Gaussian and mean curvatures can be derived. Both quadrilateral and triangular schemes are considered and for each scheme both interpolatory and approximating schemes are examined. In each case, we look at both extraordinary and regular vertices. Every 3-D vertex of the refinement polyhedrons …
Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards,
2011
Illinois Math and Science Academy
Extreme Math Makeover: Mathematics Assessment And Reporting In The Era Of The Common Core Standards, Glenn W. "Max" Mcgee
Publications & Research
This presentation discusses the need to develop high quality performance based assessments of the Common Core Mathematical Standards and Mathematical Practices. Several examples of performance assessments from high achieving countries as well as from the 2009 PISA test are included.
Topological Properties Of Invariant Sets For Anosov Maps With Holes,
2011
Brigham Young University - Provo
Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons
Theses and Dissertations
We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.
Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers,
2011
University of Florida
Biomimetic Broadband Antireflection Gratings On Solar-Grade Multicrystalline Silicon Wafers, Blayne M. Phillips, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
The authors report a simple and scalable bottom-up technique for fabricating broadband antireflection gratings on solar-grade multicrystalline silicon (mc-Si) wafers. A Langmuir-Blodgett process is developed to assemble close-packed silica microspheres on rough mc-Si substrates. Subwavelength moth-eye pillars can then be patterned on mc-Si by using the silica microspheres as structural template. Hemispherical reflectance measurements show that the resulting mc-Si gratings exhibit near zero reflection for a wide range of wavelengths. Both experimental results and theoretical prediction using a rigorous coupled-wave analysis model show that close-packed moth-eye arrays exhibit better antireflection performance than non-close-packed arrays due to a smoother refractive index …
Combinatorics Of Two-Toned Tilings,
2011
Harvey Mudd College
Combinatorics Of Two-Toned Tilings, Arthur T. Benjamin, Phyllis Chinn, Jacob N. Scott '11, Greg Simay
All HMC Faculty Publications and Research
We introduce the function a(r, n) which counts tilings of length n + r that utilize white tiles (whose lengths can vary between 1 and n) and r identical red squares. These tilings are called two-toned tilings. We provide combinatorial proofs of several identities satisfied by a(r, n) and its generalizations, including one that produces kth order Fibonacci numbers. Applications to integer partitions are also provided.
Support Varieties And Representation Type Of Self-Injective Algebras,
2011
University of South Alabama
Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg [7]: If a finite dimensional self-injective algebra has a module of complexity at least 3 and satisfies some finiteness assumptions on Hochschild cohomology, then the algebra is wild. We show directly how this is related to the analogous theory for Hopf algebras that we developed in [23]. We give applications to many different types of algebras: Hecke algebras, reduced universal enveloping algebras, small half- quantum groups, and Nichols (quantum symmetric) algebras.
Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics,
2011
Western Kentucky University
Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz
Masters Theses & Specialist Projects
Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …
An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow,
2011
University of California, Davis
An Analysis Of The Effect Of Stress Diffusion On The Dynamics Of Creeping Viscoelastic Flow, Becca Thomases
Mathematics Sciences: Faculty Publications
The effect of stress diffusivity is examined in both the Oldroyd-B and FENE-P models of a viscoelastic fluid in the low Reynolds (Stokes) limit for a 2D periodic time-dependent flow. A local analytic solution can be obtained when assuming a flow of the form u=Wi-1(x,-y), where Wi is the Weissenberg number. In this case the width of the birefringent strand of the polymer stress scales with the added viscosity as ν1/2, and is independent of the Weissenberg number. Also, the " expected" maximum extension of the polymer coils remains finite with any stress diffusion and scales as Wi·ν-1/2. These predictions …
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming,
2011
Technische Universität Bergakademie Freiberg, Germany
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho
Mathematics Research Reports
This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …
Compositions, Partitions, And Fibonacci Numbers,
2011
Georgia Southern University
Compositions, Partitions, And Fibonacci Numbers, Andrew Sills
Mathematical Sciences: Faculty Publications
A bijective proof is given for the following theorem: the number of compositions of n into odd parts equals the number of compositions of n+ 1 into parts greater than one. Some commentary about the history of partitions and compositions is provided.
Constructing Large Numbers With Cheap Computers,
2011
Illinois Wesleyan University
Constructing Large Numbers With Cheap Computers, Andrew Shallue, Steven Hayman
Scholarship
No abstract provided.
Why Probability Appears In Quantum Mechaincs,
2011
Syracuse University
Why Probability Appears In Quantum Mechaincs, Jerome Blackman, Wu Teh Hsiang
Mathematics - All Scholarship
Early in the development of quantum theory Bohr introduced what came to be called the Copenhagen interpretation. Specifically, the square of the absolute value of the wave function was to be used as a probability density. There followed lengthy arguments about this ranging from alternative universes to Schrodinger's cat. Einstein famously remarked "I am convinced that He (God) does not play dice." The purpose of this paper is to present a mathematical model of the measuring process that shows that the Copenhagen interpretation can actually follow from the fact that the time development of quantum systems is governed by the …
A Modified Stokes-Einstein Equation For Aβ Aggregation,
2011
LSU Health Sciences Center - New Orleans
A Modified Stokes-Einstein Equation For Aβ Aggregation, Srisairam Achuthan, Bong Jae Chung, Preetam Ghosh, Vijayaraghavan Rangachari, Ashuwin Vaidya
Department of Mathematics Faculty Scholarship and Creative Works
Background: In all amyloid diseases, protein aggregates have been implicated fully or partly, in the etiology of the disease. Due to their significance in human pathologies, there have been unprecedented efforts towards physiochemical understanding of aggregation and amyloid formation over the last two decades. An important relation from which hydrodynamic radii of the aggregate is routinely measured is the classic Stokes-Einstein equation. Here, we report a modification in the classical Stokes-Einstein equation using a mixture theory approach, in order to accommodate the changes in viscosity of the solvent due to the changes in solute size and shape, to implement a …
A Generalization Of The Fujisawa–Kuh Global Inversion Theorem,
2011
Trinity University
A Generalization Of The Fujisawa–Kuh Global Inversion Theorem, M. Radulescu, S. Radulescu, Eduardo C. Balreira
Mathematics Faculty Research
We discuss the problem of global invertibility of nonlinear maps defined on the finitedimensional Euclidean space via differential tests. We provide a generalization of theFujisawa-Kuh global inversion theorem and introduce a generalized ratio conditionwhich detects when the pre-image of a certain class of linear manifolds is non-emptyand connected. In particular, we provide conditions that also detect global injectivity.
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions,
2011
Bulgarian Academy of Sciences,
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev
Articles
Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2xZ2 reduction group allow breather-like solitons. Finally it is demonstrated that …
Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries,
2011
Syracuse University
Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller
Mathematics - All Scholarship
This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and T*b (r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) in R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r ↓ 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in Lp. In many instances these are seen to be equivalent to relative stability of the process X itself. The …
Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries,
2011
Syracuse University
Small And Large Time Stability Of The Time Taken For A Lévy Process To Cross Curved Boundaries, Philip S. Griffin, Ross A. Maller
Mathematics - All Scholarship
This paper is concerned with the small time behaviour of a Levy process X. In particular, we investigate the stabilities of the times, Tb(r) and Tb*(r), at which X, started with X0 = 0, first leaves the space-time regions {(t, y) ∈ R2 : y ≤ rtb, t ≥ 0} (one-sided exit), or {(t, y) in R2 :|y| ≤ rtb, t ≥ 0} (two-sided exit), 0 ≤ b < 1, as r -> 0. Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence …
