Physical Sciences and Mathematics Commons^™

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.

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

Mathematics Technical Papers

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.

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

Mathematics Technical Papers

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

Mathematics Technical Papers

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.

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

Articles

No abstract available

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.

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

Mathematics Technical Papers

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 …

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

Mathematics Technical Papers

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 …

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.

Topoi And Categories Of Fuzzy Sets, Lawrence Stout

Lawrence N. Stout

Let H be a completely distributive lattice and hence a Heyting algebra. Goguen's category of fuzzy sets Set(H) Eytan's logos Fuz(H) and the topos of sheaves on H, Sh(H), are interconnected by pairs of adjoint functors between them. Each of the categories has a predicate calculus. These predicate calculi are related through the functors between the categories. Change of base lattice gives rise to several functors which preserve or reflect specific kinds of statements in the predicate calculi. This paper gives details of the categories, the predicate calculi attached to them, the functors between the categories, and the preservation properties …

Asymptotic Theory Of Perturbed General Disconjugate Equations Ii, William F. Trench

William F. Trench

No abstract provided.

Asymptotic Behavior Of Solutions Of An N-Th Order Differential Equation, William F. Trench

William F. Trench

No abstract provided.

Maximal Functions Measuring Smoothness, Ronald A. Devore, Robert C. Sharpley

Robert Sharpley

Maximal functions which measure the smoothness of a function are introduced and studied from the point of view of their relationship to classical smoothness and their use in proving embedding theorems, extension theorems and various results on differentiation. New spaces of functions which generalize Sobolev spaces are introduced.

Asymptotics Of Differential Systems With Deviating Arguments, William F. Trench

William F. Trench

No abstract provided.

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.

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 …

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 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

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 …

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

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 …

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

On Strategies Of Sampling Finite Populations In One And Two Phases., Arun Kumar Adhikary Dr.

Doctoral Theses

This thesis is being submitted to the Indi an Statibtical Institute (ISI) in fulfilment of the primary requirements for the award of the degree of Doctor of Philosophy in Statistics.No part of this theais was submitted to any other Inatitute for any degree, diploma, certifioate etc.In this thesis we have mainly presented results of our investigation on optimal strategles for surveying finite populations in two phanes using selection procedures with varying probabilities. Incidentally we have added a few more resulta to the available literature on uni-phase sampling as are conaidered important in formulating appropriate doutbe sampling plans. Optimal and pragnatically …

Optimal Block Designs In One And Multi-Way Settings., Sunanda Bagchi Dr.

Doctoral Theses

The study of optimality of block designs formally began with wald (1943) proving a very important optimality property, designated as D-optimality of Iatin Square. Desi gns in a given physical set up. Next Ehrenfield (1955) proved the E-optimality property of Latin Square Designs. Since then, the work in: the area has primarily consisted in evolving a number of useful opti- mality oriteria for oomparing block design in a reasonable set up given and oharacterizing and/or constructing desi gns saiisfying the so called optimality criteria developed. But it was not until 1958, when the theory was given a proper and precise …

Erratum To "Ideals And Centralizing Mappings In Prime Rings", Joseph H. Mayne

Mathematics and Statistics: Faculty Publications and Other Works

No abstract provided.

Scs 80: Compact Ordered Spaces And Prime Wallman Compactifications: Summary Of Results, Oswald Wyler

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.