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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 …

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.

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.

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.

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 - 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 …

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 …

The Changing Concept Of Change: The Derivative From Fermat To Weierstrass, Judith V. Grabiner

Pitzer Faculty Publications and Research

Historically speaking, there were four steps in the development of today's concept of the derivative, which I list here in chronological order. The derivative was first used; it was then discovered; it was then explored and developed; and it was finally defined. That is, examples of what we now recognize as derivatives first were used on an ad hoc basis in solving particular problems; then the general concept lying behind them these uses was identified (as part of the invention of calculus); then many properties of the derivative were explained and developed in applications both to …

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.

Pressure Method For The Numerical Solution Of Transient, Compressible Fluid Flown, Donald Greenspan, Vincenzo Casulli

Mathematics Technical Papers - Archive

In this paper the pressure method for incompressible fluid flow simulation is extended and applied to the numerical simulation of compressible fluid flow. The governing equations, obtained from the physical principles of conservation of momentum, mass and energy, are first studied from a characteristic point of view. Then they are discretized with a semi-implicit finite difference technique in such a fashion that the Courant stability condition on the time step is not required. The resulting algorithm is fast, accurate and applies to problems with arbitrarily large speed of sound. As an example, the computer simulation of the von Kármán vortex …

Volterra Integral Equations In Abstract Cones And Monotone Iterative Technique, G. R. Shendge

Mathematics Technical Papers - Archive

The objective of this paper is to develop monotone technique for obtaining extremal solutions of Volterra integral equations in abstract Banach spaces via coupled lower and upper quasi-solutions. To generate the iterates, different schemes are given which would be of special interest from computational point of view.

Determining A Fair Border, Theodore P. Hill

Research Scholars in Residence

In a general class of measure-partitioning or fair-division problems, the extremal case occurs when the measures are proportional. Applications are given to classical and recent fair-division problems, and to statistical decision theory.

Derivation And Test Of Predictions Of A Discrete Latent State Model For Signed Number Addition Test Performance, Kentaro Yamamoto

Dissertations and Theses

This study is an investigation of the performance of a discrete latent state model devised by Paulson (1982) to account for signed-number arithmetic test data gathered by Birenbaum and Tatsuoka (1980). One hundred twenty nine students took a test which consists of sixteen item types with four parallel arithmetic items of each type. The present study utilizes the five addition item types of four items each; hence, there are four parallel subtests. Responses to the addition items can be analyzed in terms of two components: the sign component (is the sign correct?), and the absolute value component (is the size …