Physical Sciences and Mathematics Commons^™

Some Theorems On Fixed Points In Lipschitz And Kannan Type Mappings, B. B. Williams, A. A. Gillespie

Mathematics Technical Papers

No abstract provided.

Shallow Water Problem, Shu-Chen Li

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

The equations in shallow water over an obstacle are nonlinear hyperbolic differential equations. We use the method of lines and GEARB package to numerically solve this problem.

A Note On The Degree Of Approximation With An Optimal, Discrete Polynomial, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

A saturation theorem and an asymptotic theorem are proved for an optimal, discrete, positive algebraic polynomial operator. The operator is based on the Gauss-Legendre quadrature formula.

Incidence Codes Of Posets: Eulerian Posets And Reed-Muller Codes, Kenneth P. Bogart

Dartmouth Scholarship

This paper shows how to construct analogs of Reed-Muller codes from partially ordered sets. In the case that the partially ordered set is Eulerian the length of the code is the number of elements in the poset, the dimension is the size of a selected order ideal and the minimum distance is the minimum size of a principal dual ideal generated by a member of the order ideal. In this case, the majority logic method of decoding Reed-Muller codes works for incidence codes. A number of interesting combinatorial questions arise from the study of these codes.

Interpolating Functions Associated With Second Order Differential, William F. Trench

William F. Trench

No abstract provided.

An Octic Reciprocity Law Of Scholz Type, Duncan A. Buell, Kenneth S. Williams

Faculty Publications

No abstract provided.

Critical Point Theory And The Number Of Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.

A Monte Carlo Power Study Of K-Sample Tests For Exponentiality, Mickie Sue Harbin, Danny D. Dyer

Mathematics Technical Papers

Suppose one has a collection of k independent samples where the ith sample size is [see pdf for notation]. Let [see pdf for notation] denote the ordered observations in the ith sample. A number of test procedures are available to jointly test for exponentiality of the collection of independent samples, that is [see pdf for notation] is the probability density function (pdf) of the ith population. These include the k-sample Durbin (1975) test, the k-sample Shapiro-Wilk (1972) W-exponential test, the k-sample Tiku (1974) test, and a test procedure derived by Dyer (1979) which is based on a characterization of the …

Uniform Factorizations Of Graphs, David Burns

Dissertations

No abstract provided.

Scs 53: Completely Distributive Algebraic Lattices, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

No abstract provided.

On The Existence Of Positive Solutions For Non-Linear Elliptic Equations, Giovanni Vidossich

Mathematics Technical Papers

No abstract provided.

Generalized Hopf Bifurcation And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld

Mathematics Technical Papers

The prevalent approach to the Hopf bifurcation problem is to prove directly the existence of the bifurcating periodic orbits by using such standard procedures as the implicit function theorem, the LiapunovSchmidt method and its known variants, and topological degree arguments (see [7]). The phenomenon of Hopf bifurcation often occurs because of exchange of stability properties of the equilibrium under perturbations (see for instance, Chafee in [7] p. 85-88,Andronov et. al. [1], Marchetti et. al. [6] and Negrini and Salvadori [8]). This connection between the exchange of stability of the equilibrium and the appearance of bifurcating periodic orbits can be carefully …

Practical Stability And Lyapunov Functions, V. Lakshmikantham, Stephen R. Bernfeld

Mathematics Technical Papers

The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations may not assure "practical stability" and vice versa. For example an aircraft may oscillate around a mathematically unstable path, yet its performance may be acceptable. Motivated by this, Weiss and Infante introduced the concept of finite time stability [7]. They were interested in the behavior of systems contained within specified bounds during a fixed time interval. Many problems fall into this category including the travel of a space vehicle between two points and the problem, in a …

Existence Of Extremal Solutions And Comparison Results For Delay Differential Equations In Abstract Cones, R. L. Laughn, A. S. Vatsala

Mathematics Technical Papers

The study of Cauchy problem for ordinary differential equations in a Banach space has been extensive [2,4,10]. It is of interest to look at the corresponding problem for delay differential equations since such equations occur in many physical problems. Existence of solutions of such equations are considered in [6,8,9] using monotonicity conditions and dissipative conditions.In this paper our objective is to prove the existence of extremal solutions for the delay differential equation [see pdf for notation] (1.1) relative to a cone k of the Banach space E. For this purpose, we begin by proving an existence result under a simple …

Generalized Hopf Bifurcation In Rn And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld

Mathematics Technical Papers

No abstract provided.

Comparison, Existence, Uniqueness And Successive Approximations For The Dirichlet Problem Of Elliptic Equations, Giovanni Vidossich

Mathematics Technical Papers

No abstract provided.

A New Computer Approach To Atomic Electron Configuartions With Application To The Elements From Helium Through Oxygen, Donald Greenspan

Mathematics Technical Papers

In this paper a new, computer approach is developed for atomic and molecular dynamics. Though classical in nature, it includes all electron-electron interactions. Experimental ionization energies are used to determine average radial distances and velocities for atoms. Computer examples for symmetric and nonsymmetric electron motions are described and discussed. Auto-ionization results fix the nonadmissibility of a significant class of electron configurations.

On The Existence And Uniqueness Of Periodic Solutions Of Second Order Ordinary Differential Equations, Giovanni Vidossich

Mathematics Technical Papers

No abstract provided.

Ua66/16/2 Ogden Instructional Computing Newsletter, Vol. 1, No. 2, Wku Mathematics & Computer Science

WKU Archives Records

Newsletter created by the Ogden Computer Laboratory to promote services, courses, hardware, software and student activities.

Quasi-Solutions And Their Role In The Qualitative Theory Of Differential Equations, V. Lakshmikantham, K. Deimling

Mathematics Technical Papers

In the study of comparison theorems and extremal solutions for systems of ordinary differential equations [5], one usually imposes a condition on the right hand side known as quasi-monotone nondecreasing property. This property. is also needed in proving comparison theorems for second order, boundary value problems [9] as well as for the initial boundary value problem for parabolic systems [5, 6]. Also, it is well known that in the .method of vector Lyapunov functions which provides an effective tool to investigate the stability of Large Scale Systems [1-4], an unpleasant drawback is the requirement of the quasi-monotone property for the …

Equations With Unbounded Delay: A Survey, V. Lakshmikantham, C. Corduneanu

Mathematics Technical Papers

The theory of equations with delay has been considerably developed during the past 30 years. The first book dedicated to this subject has been published by A. D. Myshkis [180], in 1951, and has been subsequently translated into German (1955) and English (1966). A second Russian edition, that came out in 1972, contains a good deal of references and points out interesting features of the theory of linear equations with delayed argument, including also examples of equations with unbounded delay.

A Comparison Of Several Methods For Solving Second-Order Damped Systems Of Ordinary Differential Equations, Vickie Lynch

Masters Theses

No abstract provided.

Traceability In Graphs, Ronald J. Gould

Dissertations

No abstract provided.

Stochastic Parameters In Compartmental Systems And Structural Identification, Jerome Eisenfeld

Mathematics Technical Papers

Let [see pdf for notation] denote the mean time a particle resides in i having started in j and let [see pdf for notation] denote the probability that a particle reaches i from j. These parameters, expressed in terms of the fractional transfer coefficients, provide an interpretation and a representation of the transfer function which are useful for determining the identifiable parameters in an input-output experiment. In particular the transfer function is expressed in terms of other transfer functions which represent smaller subsystems along the flow.

An Analysis Of A New Partizan Game Using Combinatorial Techniques, James Snodgrass Iii

Masters Theses & Specialist Projects

John Horton Conway's combinatorial game theory was applied to a new partizan game with a complete analysis as the result. Mathematical values were assigned to the countably infinite number of positions in the game. Direct computation of the first eight values and extension via the Principle of Mathematical Induction made the assignments possible.

Examination of these values (which repeat with period 2) shows that the game, played on a strip of squares, can be won by the first player if the strip is of odd length and can be won by the second player if the strip is of even …

A Survey Of Certain K-Sample Test Procedures With Applications To Lpr-5 Data, Danny D. Dyer

Mathematics Technical Papers

When dealing with k independent samples, it is frequently of interest to jointly assess the underlying population distributions. Usually such an assessment is carried out by performing k independent tests; that is, we test the null hypothesis [see pdf for notation] that the population from which the [see pdf for notaion] sample was drawn has some specified distribution. Combining the results of such independent tests may then be carried out by Fisher's method (1950, pp. 99-101). Specifically, let Ti be the test statistic associated with the [see pdf for notaion] sample. Suppose large values of Ti are considered critical for …

On The Asymptotic Theory Of Quantiles And L-Statistics., Kesar Singh Dr.

Doctoral Theses

Let {Xi} be a sequence of r.v.s. nth stage we At the define e.d.f. as Fn (x) = (# Xi, ≤ x :≤ i ≤ n)/n and the ttn sample quantile as Qnt = inf {x : Fn (x) ≥ t} for t > 0 and = en(0+) for t=0. Most of the techniques of studying the process Qnt: 0 ≤ t≤ 1} consist of relating {Qnt} with some suitable linear statistics. The following are some of the commonly used methods for studying quantiles :(i) The Direct Methods In The Independent Case. Here, one can actually find the exact dis tribution …

Scs 52: Bemerkungen Zum "Neuen Lemma", Karl Heinrich Hofmann, Klaus Keimel

Seminar on Continuity in Semilattices

No abstract provided.

Making Curriculum Decisions And The Nature Of Mathematics, Paul Zwier

ACMS Conference Proceedings 1979

This paper explores the pedagogical decisions made by those teaching mathematics by discussing the various values and priorities of a mathematics course.

Mathematics In The Christian Philosophy Of Life, C. Ralph Verno

ACMS Conference Proceedings 1979

It is universally agreed that mathematics is important, that it is indeed very significant in life. This would be admitted even by those who are ignorant of or who dislike mathematics. There would be much less agreement, however, about why mathematics is important or significant. Such disagreement exists even more among mathematicians and mathematics educators. Unhappily many of the Christians who think about such things (and there are not very many who think about them at all) basically share the utilitarian view of many non-Christian thinkers, although endeavoring to place it within a Christian context. They think it is wonderful …