Digital Commons Network^™

Uniqueness Of Positive Solutions For A Class Of Elliptic Boundary Value Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.

Perturbation Of Periodic Boundary-Conditions, Larry Turyn

Mathematics and Statistics Faculty Publications

We consider perturbations of the problem (*) - x'' + bx = lambda ax, x(0) - x(1) = 0 = x'(0) - x'(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that a(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)A - epsilon …

Representations Of Algebras Over A Complete Discrete Valuation Ring, Brendan Goldsmith, Manfred Dugas, Rudiger Gobel

Articles

No abstract available

Math 752 Algebraic Topology Ii - Winter '84, David Handel

Mathematics Faculty Research Publications

A collection of notes for the course MAT 752, Algebraic Topology II, prepared by Professor David Handel of the Wayne State University Mathematics Department. This course builds on MAT 751, Algebraic Topology I, and the notes include examples, exercises, and suggestions for further reading.

On A Class Of Strongly Nonlinear Dirichlet Boundary-Value Problems: Beyond Pohozaev's Results, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

Let [see pdf for notation] be an open bounded domain with closure [see pdf for notation] and smooth boundary [see pdf for notation]. Consider the class of nonlinear boundary-value problems defined by [see pdf for notation] with [see pdf for notation] regular enough,[see pdf for notation] and where [see pdf for notation] denotes Laplacian. If n = 2, it is known that the boundary-value problem (1.1) possesses nontrivial, classical eigensolutions (with appropriate eigenvalues ^) even if ø grows exponentially fasts if n ≥ 3, it is also known that problem (1.1) has, with ^ starshaped, no nontrivial, classical solutions as …

On Monotone Formulae With Restricted Depth, Maria M. Klawe, Wolfgang J. Paul, Nicholas J. Pippenger, Mihalis Yannakakis

All HMC Faculty Publications and Research

We prove a hierarchy theorem for the representation of monotone Boolean functions by monotone Boolean functions by monotone formulae with restricted depth. Specifically, we show that there are functions with Π_k-formulae of size n for which every Σ_k-formula has size exp Ω(n^1/(k-1)). A similar lower bound applies to concrete functions such as transitive closure and clique. We also show that any function with a formula of size n (and any depth) has a Σ_k-formula of size exp O(n^1/(k-1)). Thus our hierarchy theorem is the best possible.

A Discrete Model For The Recovery Of Oil From A Reservoir, Cristobal Vargas-Jarillo

Mathematics Technical Papers - Archive

In this work we simulate oil recovery by means of a molecular type approach. This means that we consider the solid and liquid materials to be composed of a finite number of particles, which are approximants for molecules. Porous flow is studied qualitatively under the assumption that particles of rock, oil and the flooding flow interact with each other locally by means of a compensating LennardJones type potential and are also under the influence of gravity. Extensive computations are described and discussed in which initial data and parameters are varied. A comparison is made with actual physical experiments.

Homotopy Equivalences On 3-Manifolds, Gerard A. Venema

University Faculty Publications and Creative Works

Suppose M3 is a 3-manifold and f: M3 ⟶ X is a homotopy equivalence onto an ANR X. In this paper the cellularity properties of point preimages under f are studied. It is shown that for every open cover α of X there exists an open cover β of X such that if f is a β-equivalence then each f-1(x) is α-cellular in M3 X R1. In fact, the (open) cellularity occurs in a continuous fashion and so the map f can be approximated by a Euclidean bundle map.

A Class Of Elliptic Partial Differential Equations With Exponential Nonlineraities, Pierre A. Vuillermot

Mathematics Technical Papers - Archive

This is the second of a series of papers devoted to systems of ordinary and partial differential equations with exponential nonlinearities [20], in which we prove the existence of at least a countable infinity of one- parameter families of nontrivial, Hölder continuous solutions for a class of second-order, strongly nonlinear Dirichlet boundary-value problems in two and more dimensions. Let Y be a C(2)-Young function, namely a twice continuously differentiable, even convex lR—valued function on IR such that[see pdf for notation] and[see pdf for notation]. By C(2)-function, we shall mean a function which is twice continuously differentiable everywhere except possibly at …

Particle Modeling Of Unstable Mode Configurations And Elastic Bending Of Deformable Shells, Vincenzo Casulli, Donald Greenspan

Mathematics Technical Papers - Archive

A new particle-type of modeling is developed for the simulation of phenomena related to the bending of elastic shells. Application is made to the determination of unstable equilibrium modes and to the simulation of snap-through inversion. Computer examples are described and discussed.

A Mathematical Curiosity In Estimating The Radius Of The First Ring Electrons Of An Arbitary Atom, Donald Greenspan

Mathematics Technical Papers - Archive

In this note, we explore an elementary method for approximating the radii and speeds of first ring electrons in atoms. The approach uses only a single algebraic equation with parameters. Any particular atom under study defines all the parameters. A simple hand calculator technique always applies for solving any resulting equation. Results are given through calcium and, to three decimal places, are shown, unexpectedly, to be essentially identical to available quantum mechanics calculations.

Approximate Tolerance Limits And Confidence Limits On Reliability For The Gamma Distribution, Lee J. Bain, Max Engelhardt, Wei Kei Shiue

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

An Essentially Semi-Rigid Class Of Modules, Brendan Goldsmith

Articles

No abstract available

The Relationship Of Self-Concept, Sex, Age, Major, Anxiety, Mathematics Background, And Mathematics Ability To The Level Of Mathematics And Statistical Anxiety Among College Juniors, David John Maysick

Dissertations

Problem. One's choice of career has significant effect upon one's future life in terms of earning potential and social interaction. Mathematics/statistical anxiety and the mathematics avoidance often accompanying such anxiety, can influence career choice, causing otherwise talented people to limit their future. The purpose of this study was to determine from selected variables--particularly self-concept--which, if any, were related to the problem of mathematics and/or statistical anxiety.

Method. The statistical sample used was 350 juniors. Stratification was by degree of mathematics content in subject's major field of study. For the study, subjects had to be in the same major category as …

Neural Population Modeling And Psychology: A Review, Daniel S. Levine

Mathematics Technical Papers - Archive

The development of neural population modeling as it relates to psychology is traced from the early 1940s to the present. The evolution of the field has been from descriptions of randomly connected neurons transmitting all-or-none signals to analyses of structured multi-level net-works whose dynamics involve several different spatial and temporal scales. The cybernetic revolution of the 1940s led to the incorporation into digital neural models of such concepts as linear threshold logic, redundant computation. and information. Each of these concepts has more recently been synthesized with learning to generate a set of adaptive neural models. Concurrently, a variety of data …

A Note On Irreducibility And Weak Covering Properties, Joe Mashburn

Mathematics Faculty Publications

A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N₁-compactness. …

It is shown in this paper that T₁ δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T₁ nor …

Effects Of Thermal Spread On The Space Charge Limit Of An Electron Beam, Evangelos A. Coutsias

Branch Mathematics and Statistics Faculty and Staff Publications

An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally to the beam temperature T near T = O.

Generalisations Et Generalites, Florentin Smarandache, Eleonora Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

"Généralisations et Généralités" , pourquoi ce titre? Parce Que l'auteur a voulu rassembler ici Quelques-unes de ses recherches originales C Qui sont donc des "s~n:§rali tés") , df'2ls diverses branches des mathématiques (algèl)re, thôorie des nombres, Gométrie, analyse, linguistique, mathématiQues distrayantes) , mêlne si les articles qui composent ce recueil n'ont pas toujours de liaison entre eux.

Scs 84: The Zariski Topology On Semilattices And Essential Extensions, Gerhard Gierz, Albert R. Stralka

Seminar on Continuity in Semilattices

No abstract provided.

Scs 83: Continuous Lattices, General Convexity Spaces, And A Fixed-Point Theorem, Klaus Keimel

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

On Isomorphic Decompositions Of Graphs, Sergio Ruiz

Dissertations

A decomposition of a nonempty graph G is a collection of subgraphs G(,1), G(,2), ... , G(,k) of G such that their edge sets form a partition of the edge set of G. If G(,i) is isomorphic to a fixed graph H for each i, then G has an isomorphic decomposition into the graph H or, equivalently, G is H-decomposable. Several topics, each concerning isomorphic decompositions, are investigated in this dissertation.

An historical introduction to the subject of isomorphic decompositions is given in Chapter I. We also present there some new information on finding regular graphs that are H-decomposable for …

Scs 82: Compactifying Distributive Lattices, Gerhard Gierz, Albert R. Stralka

Seminar on Continuity in Semilattices

No abstract provided.

Almost Sure Stability Of Partial Sums Of Uniformly Bounded Random Variables, Theodore P. Hill

Research Scholars in Residence

Suppose a₁ , a₂ ,... is a sequence of real numbers with a_n → ∞. If lim sup(X₁+ ... + X_n)/a_n = α a.s. for every sequence of independent nonnegative uniformly bounded random variables X₁,X₂,... satisfying some hypothesis condition A, then for every (arbitrarily-dependent) sequence of nonnegative uniformly bounded random variables Y₁,Y₂, ... , lim sup(Y₁+ ... + Y_n)/a_n = α a.s. on the set where the conditional distributions (given the past) satisfy …

Scs 81: Intrinsic Topologies On Semilattices Of Finite Breadth, Gerhard Gierz, Jimmie D. Lawson, Albert R. Stralka

Seminar on Continuity in Semilattices

No abstract provided.

The Combinatorics Of Certain Products, Don Rawlings

Mathematics

A combinatorial interpretation for the coefficients in the expansion of Π(1 + ux^jy^k)(1 - ux^jy^k)^-1 is given.

The Role Of Nonreal Eigenvalues In The Identification Of Cycles In A Compartmental System, Jerome Eisenfeld, S. M. Grundy, W. F. Beltz

Mathematics Technical Papers - Archive

The paper concerns the relationship between the cycles in the graph of a compartmental system and the modes of the impulse response function associated with an input-output experiment. Suppose that there is at least one oscillatory mode, [see pdf for notation]. Let [see pdf for notation] be the slowest mode. The main result is that the system contains a cycle of length three or longer and that the length of the longest cycle is at least [see pdf for notation]. The paper also deals with the problem of estimating cycle length from discrete data.

Statistical Analysis Of Economic Activities For Developement In Nepal., Bishnu Pant Dr.

Doctoral Theses

The main objective of this study has been the statistical analysis by the use of those statistical and quantitative tools that could be considered appropriate for applications in an underdeveloped economy, where in usually lies sufficient data and information gaps, towards a proper diagnosis of the problems and prospects of economic activities in its diversified regional environments. This study is conducted with reference to an underdeveloped country, Nepal, where detailed regional analyses have hardly been attempted earlier, to evaluate the regional structures of economic activities for the purpose of clarifying oar visions for a proper kind of regional planning. Though …

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

On First Countable, Countably Compact Spaces. I: (Omega-1,Omega-1-Star)-Gaps, Peter J. Nyikos, Jerry E. Vaughan

Faculty Publications

No abstract provided.

Existence Of Coupled Quasi-Solutions Of Systems Of Nonlinear Reaction-Diffusion Equations, V. Lakshmikantham, G. S. Ladde

Mathematics Technical Papers - Archive

Systems of nonlinear parabolic initial boundary value problems arise in many applications such as epidemies, ecology, biochemistry, biology, chemical and nuclear engineering. Constructive methods of proving existence results for such problems, which can also provide numerical procedures for the computation of solutions, are of greater value than theoretical existence results. The method of upper and lower solutions coupled with monotone iterative technique has been employed successfully to prove existence of multiple solutions of nonlinear reaction-diffusion equations, in special case, by various authors [3,4,5,10,11,15 181. Recently, in [6,17] weakly coupled systems of reaction diffusion equations, when the nonlinear terms are independent …