Physical Sciences and Mathematics Commons^™

A Mathematical Regression Of The U.S. Gross Private Domestic Investment 1959-2001, Byron E. Bell

Byron E. Bell

SUMMARY OF PROJECT What did I do? A study of the role the U.S. stock markets and money markets have possibly played in the Gross Private Domestic Investment (GPDI) of the United States from the year 1959 to the year 2001 and I created a Multiple Linear Regression Model (MLRM).

Multiattribute Acceptance Sampling Plans., Anup Majumdar Dr.

Doctoral Theses

Irrespective of the type of product, evaluation of conformity to specified requirements of its quality characteristics is an integral part of quality assurance. Although they form a set of necessary verification activities almost at all stages of production, these activities, known as inspection do not add value to the product on their own and are to be kept at their minimum. The sampling inspection where a portion of a collection of product units is inspected on a set of characteristics with a view to making decision about acceptance or otherwise becomes relevant in this context.The number of elements of the …

Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C-algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give …

Radiationless Travelling Waves In Saturable Nonlinear Schrödinger Lattices, T. R. O. Melvin, A. R. Champneys, Panos Kevrekidis, J. Cuevas

Panos Kevrekidis

The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for isolated coupling strength values. Genuinely localized traveling waves are computed as a function of the system parameters for the first time. The relevant solutions exist only for finite velocities.

Sequences, Series, And Function Approximation, Lawrence Stout

Lawrence N. Stout

Sequences are important in approximation: the usual representation of real numbers using decimals is in fact the process of giving a sequence of rational numbers approximation the real number in question successively better as more decimal places are given. These decimal approximation sequences are actually rather special: successive decimal approximations never get smaller (so the sequence is monotone nondecreasing) and two approximations which agree to the kth decimal place differ by at most 10-k (so the sequence is a Cauchy sequence: to make two values in the sequence close to each other all you need to do is take them …

Robustness With Respect To Sampling For Stabilization Of Riesz Spectral Systems, Richard Rebarber, Stuart Townley

Department of Mathematics: Faculty Publications

We suppose that a continuous-time feedback is input–output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying idealized sample-and-hold to this continuous-time feedback is also input–output stabilizing if the sampling time is small enough. This question has been previously addressed for fairly general systems under various conditions. In this note, we restrict our attention to Riesz spectral systems, for which we generalize the existing results. Specifically, we give two relatively simple conditions which, combined, are sufficient for the sampled-data controller to be stabilizing. The first condition is a spectrum decomposition for the …

Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study multiobjective optimization problems with equilibrium constraints (MOECs) described by generalized equations in the form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models particularly arise from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex …

Composition Operators With Maximal Norm On Weighted Bergman Spaces, Brent J. Carswell, Christopher Hammond

Mathematics Faculty Publications

We prove that any composition operator with maximal norm on one of the weighted Bergman spaces is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H², where every inner function induces a composition operator with maximal norm.

Congruences For The Coefficients Of Weakly Holomorphic Modular Forms, Stephanie Treneer

Mathematics Faculty Publications

Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup Γ₀ (N). In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.

Induction Of Characters And Finite P-Groups, Edith Adan-Bante

Faculty Publications

Let G be a finite p-group, where p is an odd prime number, H be a subgroup of G and θ ∈ Irr(H) be an irreducible character of H. Assume also that | G : H | = p². Then the character θ^G of G induce by θ is either a multiple of an irreducible character of G, or has at least ^p+1/₂ distinct irreducible constituents.

N–Localization Property, Andrzej Rosłanowski

Mathematics Faculty Publications

This paper is concerned with n–localization property introduced by Newelski and Roslanowski in [10] and getting it for CS iterations of forcing notions.

Lowness And Π Nullsets, Rod Downey, Andre Nies, Rebecca Weber, Liang Yu

Dartmouth Scholarship

We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Lof randomness.

Selected Problems Of Inference On Branching Processes And Poisson Shock Model, Satrajit Roychoudhury

Dissertations

This dissertation explores the development of statistical methodology for some problems of branching processes and poisson shock model.

Branching process methods have become extremely popular in recent days. This dissertation mainly explores two fundamental inference problems of Galton-Watson processes. The first problem is concerned with statistical inference regarding the nature of the process. Two methodologies have been developed to develop a statistical test for the null hypothesis that the process is supercritical versus an alternative hypothesis that the process is non-supercritical. Another problem we investigate involves the estimation of the 'age' of a Galton-Watson Process. Three different methods are discussed …

Some Heuristics About Elliptic Curves, Mark Watkins

Mathematics - All Scholarship

We give some heuristics for counting elliptic curves with certain properties. In particular, we re-derive the Brumer-McGuinness heuristic for the number of curves with positive/negative discriminant up to X, which is an application of lattice-point counting. We then introduce heuristics (with refinements from random matrix theory) that allow us to predict how often we expect an elliptic curve E with even parity to have L(E,1)=0. We find that we expect there to be about c₁X^19/24(log X)^3/8 curves with |Delta|< X with even parity and positive (analytic) rank; since Brumer and McGuinness predict cX^5/6 total curves, this implies that asymptotically almost all even parity curves have rank 0. We …

Essays On Individual And Collective Powers In A Voting Body., Sonali Roy Dr.

Doctoral Theses

MotivationThe issue of measurement of voting power is a very important topic of discussion in social science these days. The concept of voting power concerns any collective decision making body (or, equivalently, a collectivity) which makes ‘yes’ or ‘no’ decisions on any issue, by the process of voting. Examples of such bodies abound in today’s world. The United Nations Security Council, The Council of Ministers in the European Union, the Parliament of the republic of India, the board room of any corporate house etc., are all examples of such decision making bodies.The voting process of each of these bodies is …

Preprojective Representations Of Valued Quivers And Reduced Words In The Weyl Group Of A Kac-Moody Algebra, Mark Kleiner, Allen Pelley

Mathematics - All Scholarship

This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. As a consequence, for any Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced …

Categorification Of The Colored Jones Polynomial And Rasmussen Invariant Of Links, Anna Beliakova, Stephan Wehrli

Mathematics - All Scholarship

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that, for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples, where this invariant is a …

A Complete Characterization Of Maximal Symmetric Difference-Free Families On {1,…N}., Travis Gerarde Buck

Electronic Theses and Dissertations

Prior work in the field of set theory has looked at the properties of union-free families. This thesis investigates families based on a different set operation, the symmetricc difference. It provides a complete characterization of maximal symmetric differencefree families of subsets of {1, . . . n}

Movie Math: Mathematical Talent = Mental Illness, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Sequences Of Reflection Functors And The Preprojective Component Of A Valued Quiver, Mark Kleiner, Helene R. Tyler

Mathematics - All Scholarship

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan …

On The Nondegeneracy Of Constant Mean Curvature Surfaces, Nick Korevaar, Robert Kusner, Jesse Ratzkin

Robert Kusner

We prove that many complete, noncompact, constant mean curvature (CMC) surfaces $f:\Sigma \to \R^3$ are nondegenerate; that is, the Jacobi operator Δf+|Af|2 has no L2 kernel. In fact, if Σ has genus zero and f(Σ) is contained in a half-space, then we find an explicit upper bound for the dimension of the L2 kernel in terms of the number of non-cylindrical ends. Our main tool is a conjugation operation on Jacobi fields which linearizes the conjugate cousin construction. Consequences include partial regularity for CMC moduli space, a larger class of CMC surfaces to use in gluing constructions, and a surprising …

Assessing The Effect Of Prior Distribution Assumption On The Variance Parameters In Evaluating Bioequivalence Trials, Dawud A. Ujamaa

Mathematics Theses

Bioequivalence determines if two drugs are alike. The three kinds of bioequivalence are Average, Population, and Individual Bioequivalence. These Bioequivalence criteria can be evaluated using aggregate and disaggregate methods. Considerable work assessing bioequivalence in a frequentist method exists, but the advantages of Bayesian methods for Bioequivalence have been recently explored. Variance parameters are essential to any of theses existing Bayesian Bioequivalence metrics. Usually, the prior distributions for model parameters use either informative priors or vague priors. The Bioequivalence inference may be sensitive to the prior distribution on the variances. Recently, there have been questions about the routine use of inverse …

Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang

Mathematics Research Reports

We study adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Secondly, we demonstrate by numerical examples that an adaptive procedure with a posteriori error estimator based on PPR does produce adaptive meshes satisfy our mesh density assumption, and the recovered gradient by PPR is indeed supercoveregent in the adaptive process.

Nash Equilibria In Cauchy-Random Zero-Sum And Coordination Matrix Games, David P. Roberts

Mathematics Publications

We consider zero-sum games (A, − A) and coordination games (A,A), where A is an m-by-n matrix with entries chosen independently with respect to the Cauchy distribution. In each case, we give an exact formula for the expected number of Nash equilibria with a given support size and payoffs in a given range, and also asymptotic simplications for matrices of a fixed shape and increasing size. We carefully compare our results with recent results of McLennan and Berg on Gaussian random bimatrix games (A,B), and describe how …

Teaching Time Savers: Style Points, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I began as an assistant professor, I had a pretty good sense of how much time it would take for me to prepare for each class. After a few conversations with my new colleagues, I even had a good sense of how much time I should devote to tasks like office hours and committee work. Somewhere in the middle of grading my first exam, though, it became painfully clear that I had underestimated the amount of time I would need to grade exams!

Exponents For B-Stable Ideals, Eric Sommers, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Let G be a simple algebraic group over the complex numbers containing a Borel subgroup B. Given a B-stable ideal I in the nilradical of the Lie algebra of B, we define natural numbers m 1, m 2,. . .,m k which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types A n, B n, C n and some other types. When I = 0, we recover the usual exponents of G by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré polynomial of the …

Adaptive Discontinuous Galerkin Finite Element Methods For Second And Fourth Order Elliptic Partial Differential Equations, Michael A. Saum

Doctoral Dissertations

A unified mathematical and computational framework for implementation of an adaptive discontinuous Galerkin (DG) finite element method (FEM) is developed using the symmetric interior penalty formulation to obtain numerical approximations to solutions of second and fourth order elliptic partial differential equations. The DG-FEM formulation implemented allows for h-adaptivity and has the capability to work with linear, quadratic, cubic, and quartic polynomials on triangular elements in two dimensions. Two different formulations of DG are implemented based on how fluxes are represented on interior edges and comparisons are made. Explicit representations of two a posteriori error estimators, a residual based type and …

The Effect Of Using A Video-Case Curriculum To Promote Preservice Teachers’ Development Of A Reflective Stance Towards Mathematics Teaching, Shari L. Stockero

Dissertations

This study investigates the effects of using a coherent video-case curriculum in a university methods course. In particular, three issues are addressed: (1) howthe use of a video-case curriculum affects the reflective stance of preservice teachers; (2) the extent to which a reflective stance developed while reflecting on other teachers' practice transfers to reflecting on one's own practice; and (3) how preservice teachers' reflective stance that is developed via sustained and focused reflection using a video-case curriculum compares to the reflective stance of peers who engaged in less sustained and focused reflection. Althoughvideo cases are increasingly being used in teacher …

Chainability And Hemmingsen's Theorem, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

On the surface, the definitions of chainability and Lebesgue covering dimension ⩽1 are quite similar as covering properties. Using the ultracoproduct construction for compact Hausdorff spaces, we explore the assertion that the similarity is only skin deep. In the case of dimension, there is a theorem of E. Hemmingsen that gives us a first-order lattice-theoretic characterization. We show that no such characterization is possible for chainability, by proving that if κ is any infinite cardinal and AA is a lattice base for a nondegenerate continuum, then AA is elementarily equivalent to a lattice base for a continuum Y …

Cohomological Dimension With Respect To Nonabelian Groups, Atish Jyoti Mitra

Doctoral Dissertations

This dissertation addresses three aspects of cohomological dimension of metric spaces with respect to nonabelian groups.

In the first part we examine when the Eilenberg-Maclane space (n = 1) of the abelianization of a solvable group being an absolute extensor of a metric space implies the Eilenberg-Maclane space of the group itself is an absolute extensor. We also give an elementary approach to this problem in the case of nilpotent groups and 2-dimensional metric spaces.

The next part of the dissertation is devoted to generalizations of the Cencelj- Dranishnikov theorems relating extension properties of nilpotent CW complexes to its homology …