Physical Sciences and Mathematics Commons^™

Low-Dimensional Homology Groups Of Mapping Class Groups: A Survey, Mustafa Korkmaz

Turkish Journal of Mathematics

In this survey paper, we give a complete list of known results on the first and the second homology groups of surface mapping class groups. Some known results on higher (co) homology are also mentioned.

Gauge Theory And Stein Fillings Of Certain 3-Manifolds, Andras I. Stipsicz

Turkish Journal of Mathematics

In the following we show that a Stein filling S of the 3-torus T^3 is homeomorphic to D^2 \times T^2. In the proof we also show that if S is Stein and \partial S is diffeomorphic to the Seifert fibered 3-manifold -\Sigma (2,3,11) then b_1(S)=0 and Q_S=H. Similar results are obtained for the Poincaré homology sphere \pm \Sigma (2,3,5); in studying these fillings we apply recent gauge theoretic results, and prove our theorems by determining certain Seiberg-Witten invariants.

Existence Of Solutions For Discontinuous Functional Equations And Elliptic Boundary-Value Problems, Siegfried Carl, Seppo V. Heikkilä

Mathematics and System Engineering Faculty Publications

We prove existence results for discontinuous functional equations in general Lp-spaces and apply these results to the solvability of implicit and explicit elliptic boundary-value problems involving discontinuous nonlinearities. The main tool in the proof is a fixed point result in lattice-ordered Banach spaces proved by the second author. © 2002 Southwest Texas State University.

Oscillation Criteria For A Class Of Partial Functional-Differential Equations Of Higher Order, Tariel Kiguradze, Takaŝi Kusano, Norio Yoshida

Mathematics and System Engineering Faculty Publications

Higher order partial differential equations with functional arguments including hyperbolic equations and beam equations are studied. Sufficient conditions are derived for every solution of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problem to a one-dimensional problem for higher order functional differential inequalities.

Stability Analysis Of Nonlinear Lyapunov Systems Associated With An Nth Order System Of Matrix Differential Equations, Kanuri N. Murty, Michael D. Shaw

Mathematics and System Engineering Faculty Publications

This paper introduces the notion of Lipschitz stability for nonlinear nth order matrix Lyapunov differential systems and gives sufficient conditions for Lipschitz stability. We develop variation of parameters formula for the solution of the nonhomogeneous nonlinear nth order matrix Lyapunov differential system. We study observability and controllability of a special system of nth order nonlinear Lyapunov systems.

A Note On Computing The Generalized Inverse A^(2)_{T,S} Of A Matrix A, Xiezhang Li, Yimin Wei

Department of Mathematical Sciences Faculty Publications

The generalized inverse A T,S (2) of a matrix A is a {2}-inverse of A with the prescribed range T and null space S. A representation for the generalized inverse A T,S (2) has been recently developed with the condition σ (GA| T)⊂(0,∞), where G is a matrix with R(G)=T andN(G)=S. In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose …

On Inequalities And Partial Orderings For Weighted Reliability Measures, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

Inequalities, relations and partial ordering for weighted reliability measures are presented. Inequalities for Lévy distance measure for weighted distributions are obtained in terms of the parent distributions. Reliability inequalities and stability results are established for weighted distributions with monotone hazard and mean residual life functions.

Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova

Mathematics Faculty Publications

The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.

The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao

Mathematics Faculty Publications

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

Conversations Among Women In Mathematics (Program), University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang

Mathematics and Statistics Faculty Publications

We show that any C^1,1 solution to the uniformly elliptic equation F(D²u) = 0 must belong to C^2,α, if the equation has the Liouville property.

Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller

Mathematics and Statistics Faculty Publications

Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.

Absolutely Continuous Jacobi Operators, Steen Pedersen

Mathematics and Statistics Faculty Publications

No abstract provided.

A Recommendation For Determining The Efficacy Of Weight Removal Estimates For The Pacific Cod Longline Cdq Fishery, Anna L. Furniss

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In January 2000, the Alaska Department of Community and Economic Development contacted the National Marine Fisheries Service (NMFS) regarding concerns over the methods used to determine catch estimates for the Pacific Cod Community Development Quota (CDQ) fishery. Currently, NMFS determines catch estimates for the Pacific Cod CDQ fishery based on the data collected by observers from the North Pacific Groundfish Observer Program (NPGOP).

Observer estimates for catch are based on the random sampling methods for a longline fishing vessel as described in the North Pacific Groundfish Observer Manual. These sampling methods provide an official total catch (OTC) estimate for each …

The Classification Of Low Dimensional Nilpotent Lie Algebras, Kimberli C. Tripp

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Nilpotent Lie algebras are the fundamental building blocks for generic (not semi-simple) Lie algebras. In particular, the classification of nilpotent algebras is the first step in classifying and identifying solvable Lie Algebras. The problem of classifying nilpotent Lie algebras was first studied by Umlauf [9] in 1891. More recently, classifications have been given up to dimension six using different techniques by Morosov (1958) [7], Skjelbred and Sund (1977) [8], and up to dimension five by Dixmier (1958) [2]. Using Morosov's method of classification by maximal abelian ideals, Winternitz reproduced the Morosov classification obtaining different canonical forms for the algebras. The …

One-Sided Resonance For Quasilinear Problems With Asymmetric Nonlinearities, Kanishka Perera

Mathematics and System Engineering Faculty Publications

One-sided resonance for quasilinear problems with asymmetric nonlinearities

Resonance Problems With Respect To The Fučík Spectrum Of The P-Laplacian, Kanishka Perera

Mathematics and System Engineering Faculty Publications

We solve resonance problems with respect to the Fučík spectrum of the p-Laplacian using variational methods.

An Upper And Lower Solution Approach For A Generalized Thomas–Fermi Theory Of Neutral Atoms, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

An upper and lower solution theory for boundary value problems modeled from the Thomas-Fermi equation, was presented. The approach was subjected to a boundary condition corresponding to the neutral atom with Bohr radius. The boundary conditions were investigated for the neutral atoms, the ionized atoms and the isolated neutral atoms.

Random Probability Measures With Given Mean And Variance Running Title: Random Probability Measures, Lisa Bloomer, Theodore P. Hill

Research Scholars in Residence

This article describes several natural methods of constructing random probability measures with prescribed mean and variance, and focuses mainly on a technique which constructs a sequence of simple (purely discrete, finite number of atoms) distributions with the prescribed mean and with variances which increase to the desired variance. Basic properties of the construction are established, including conditions guaranteeing full support of the generated measures, and conditions guaranteeing that the final measure is discrete. Finally, applications of the construction method to optimization problems such as Plackett’s Problem are mentioned, and to experimental determination of average-optimal solutions of certain control problems.

Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe

Mathematics Faculty Publications

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka

Richard P. Kubelka

For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)ij]∞i,j=0 as the infinite matrix satisfying k(p,s)ij = 1/px(i+jj) mod p if (i+jj) is divisible by ps and k(p,s)ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geometric patterns that occur in K(p,s). Indeed, if we consider the finite (truncated) versions of K(p,s), we find that they can be decomposed into superpositions of tensor products of certain primitive p x …

Decomposition Of Pascal’S Kernels Mod PS, Richard P. Kubelka

Faculty Publications

For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)_ij]^∞_i,j=0 as the infinite matrix satisfying k(p,s)_ij = 1/p^x(^i+j_j) mod p if (^i+j_j) is divisible by p^s and k(p,s)_ij = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula …

A Specht Module Analog For The Rook Monoid, Cheryl Grood

Mathematics & Statistics Faculty Works

The wealth of beautiful combinatorics that arise in the representation theory of the symmetric group is well-known. In this paper, we analyze the representations of a related algebraic structure called the rook monoid from a combinatorial angle. In particular, we give a combinatorial construction of the irreducible representations of the rook monoid. Since the rook monoid contains the symmetric group, it is perhaps not surprising that the construction outlined in this paper is very similar to the classic combinatorial construction of the irreducible Sn-representations: namely, the Specht modules.

Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher degree for both numerator and denominator polynomials, with particular attention given to cases in which the degrees are equal. We extend work of Ramanujan on continued fractions with rational limits and also consider cases where the limits are irrational.

On Stochastic Inequalities And Comparisons Of Reliability Measures For Weighted Distributions, Broderick O. Oluyede, E. Olusegun George

Department of Mathematical Sciences Faculty Publications

Inequalities, relations and stochastic orderings, as well as useful ageing notions for weighted distributions are established. Also presented are preservation and stability results and comparisons for weighted and length-biased distributions. Relations for length-biased and equilibrium distributions as examples of weighted distributions are also presented.

Hat Derivatives, Stephen B. Maurer , '67

Mathematics & Statistics Faculty Works

No abstract provided.

C-Closed Sets In L-Fuzzy Topological Spaces And Some Of Its Applications, Ali̇ Ahmed Nouh

Turkish Journal of Mathematics

We introduce and study the notion of C-closed sets in L-fuzzy topological spaces. Then, C-convergence theory for nets and ideals is established in terms of C-closedness. Finally, we give a new concept of C-continuity on L-fuzzy topological space by means of L-fuzzy C-closedness and investigate some of its properties and its relationships with other L-fuzzy mappings introduced previously. Then we systematically study the characterizations of this notion with the aid of the C-convergence of L-fuzzy nets and L-fuzzy ideals.

Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger

All HMC Faculty Publications and Research

If G = (V, E) is a graph, the incidence graphI(G) is the graph with vertices I ∪ E and an edge joining v ∈ V and e ∈ E when and only when v is incident with e in G. For G equal to K_n (the complete graph on n vertices) or K_n,n (the complete bipartite graph on n + n vertices), we enumerate the matchings (sets of edges, no two having a vertex in common) in I(G), both exactly (in terms of generating …

A Minimal Regular Ring Extension Of C(X), Melvin Henriksen, Robert M. Raphael, R. G. Woods

All HMC Faculty Publications and Research

Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τ_δ) of continuous real-valued functions on the space (X,Τ_δ), where Τ_δ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τ_δ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τ_δ) are characterized. Necessary, and different sufficient, conditions for the equality …

Renewal Theory For Uniform Random Variables, Steven Robert Spencer

Theses Digitization Project

This project will focus on finding formulas for E[N(t)] using one of the classical problems in the discipline first, and then extending the scope of the problem to include overall times greater than the time t in the original problem. The expected values in these cases will be found using the uniform and exponential distributions of random variables.