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Full-Text Articles in Physical Sciences and Mathematics

Stochastic Differential Inequalities Of Ito Type, V. Lakshmikantham, G. S. Ladde Jun 1978

Stochastic Differential Inequalities Of Ito Type, V. Lakshmikantham, G. S. Ladde

Mathematics Technical Papers

It is well known [3] that the method of differential inequalities plays an important role in the qualitative theory of differential equations. It is therefore natural to expect that a similar theory would be equally important in the study of Stochastic differential systems of Ito type. As will be seen that this investigation is not straightforward extension of the deterministic situation and needs special techniques to be utilized. In this paper, we develop the theory of stochastic differential inequality of Ito type, consider the nonnegativity of solutions, prove existence of extremal solutions and derive a comparison result.

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Scs 47: Équivalence Des Espaces De Batdedat Et Des Treillis Algébriques, Karl Heinrich Hofmann May 1978

Scs 47: Équivalence Des Espaces De Batdedat Et Des Treillis Algébriques, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

No abstract provided.

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Scs 46: A Result About O(X), Gerhard Gierz, Jimmie D. Lawson, Michael Mislove May 1978

Scs 46: A Result About O(X), Gerhard Gierz, Jimmie D. Lawson, Michael Mislove

Seminar on Continuity in Semilattices

No abstract provided.

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Topological Properties Of C(X, Y), Chris Alan Schwendiman May 1978

Topological Properties Of C(X, Y), Chris Alan Schwendiman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to examine the important topological properties of the function spaces BC(X,Y) and C(X,Y). Emphasis is given to the relationship between the metrizability of X and the separability of these function spaces. The paper is divided into three major parts: the preliminary definitions and theorems; the relationship between the topological properties of X and BC (X ,Y), for compact X; and the extension of the results of Part II for X not compact and for the case when we have C(X, Y).

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On The Relative Behavior Of Estimators Of Reliability/Survivability, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating May 1978

On The Relative Behavior Of Estimators Of Reliability/Survivability, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating

Mathematics Technical Papers

Based on a decomposition of mean absolute error, a twofold technique is introduced whereby a pairwise comparison of point estimators of reliability/survivability can be made. Given two such estimators, the method examines (a) the "odds" in favor of one of the estimators being closer to the true value than is the other and (b) each estimator's average closeness to the true value not only when it is closer than is the other but also when it is not. Joint consideration of these concepts is shown to form a basis for determining which of the two estimators is preferred in a …

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Calculation Of Galois Groups, Daniel Schnackenberg May 1978

Calculation Of Galois Groups, Daniel Schnackenberg

Theses and Dissertations

In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory and some useful facts about factorization, I develop the important methods of calculating the Galois group and give a proof of the Chebotarev density theorem.

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Separation And Monotonicity Results For The Roots Of The Moment Problem, Jerome Eisenfeld, James Hallmark May 1978

Separation And Monotonicity Results For The Roots Of The Moment Problem, Jerome Eisenfeld, James Hallmark

Mathematics Technical Papers

Consider the system identification problem [see pdf for notation] [see pdf for notation] where u(t) and y(t) are given discretely on the interval [see pdf for notation] and we wish to determine information about the unknown constant matrices A, B, and C. Many techniques are available for approaching this problem. Several of these methods lead to what is known as the moment problem, [1]-[6]. This paper pertains to the moment problem which will now be introduced.

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Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams May 1978

Maximal Residue Difference Sets Modulo P, Duncan A. Buell, Kenneth S. Williams

Faculty Publications

Let p ≡ 1 (mod 4) be a prime. A residue difference set modulo p is a set S = {ai} of integers ai such that (ai/p) = +1 and ((ai - aj)/p) = +1 for all i and j with i ≠ j, where (n/p) is the Legendre symbol modulo p. Let mp be the cardinality of a maximal such set S. The authors estimate the size of mp.

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Scs 45: Antichains And Equational Compactness, Heiko Bauer Apr 1978

Scs 45: Antichains And Equational Compactness, Heiko Bauer

Seminar on Continuity in Semilattices

No abstract provided.

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A Technique In Stability Theory Of Delay-Differential Equations, S. Leela, V. Lakshmikantham Apr 1978

A Technique In Stability Theory Of Delay-Differential Equations, S. Leela, V. Lakshmikantham

Mathematics Technical Papers

In the study of stability theory for delay-differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to choose an appropriate minimal class of functions relative to which the derivative of the Lyapunov function is estimated. This approach has recently been recognized as a very natural method in the study of the qualitative behavior of delay equations.

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Identification Of Linear Time-Invariant Systems, Jerome Eisenfeld Apr 1978

Identification Of Linear Time-Invariant Systems, Jerome Eisenfeld

Mathematics Technical Papers

A new method of identification for linear time-invariant systems with one input is presented. The method requires the estimation of weighted integrals over a finite time interval.

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Non-Splitting Unitary Perfect Polynomials Over Gf(P), 7≤P≤19, Mickie Sue Harbin Apr 1978

Non-Splitting Unitary Perfect Polynomials Over Gf(P), 7≤P≤19, Mickie Sue Harbin

Mathematics Technical Papers

Examples are given of non-splitting unitary perfect polynomials over [see pdf for notation] for [see pdf for notation]. These, together with previous results, establish the existence of infinitely many such polynomials over [see pdf for notation] for each [see pdf for notation]. The given result further supports the conjecture that non-splitting unitary perfect polynomials exist over [see pdf for notation] for each, [see pdf for notation].

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Hammerstein Integral Equations With Indefinite Kernel, Alfonso Castro Mar 1978

Hammerstein Integral Equations With Indefinite Kernel, Alfonso Castro

All HMC Faculty Publications and Research

This paper deals with the problem of finding solutions of the Hammerstein integral equation. It is shown that this problem can be reduced to the study of the critical points of certain functional defined on L2(Ω). Existence of a solution of the Hammersteln integral equation is proved. Some other related results of interest are obtained.

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On The Relative Behavior Of Point Estimators Based On A Decomposition Of Mean Absolute Error, Danny D. Dyer Mar 1978

On The Relative Behavior Of Point Estimators Based On A Decomposition Of Mean Absolute Error, Danny D. Dyer

Mathematics Technical Papers

Let [see pdf for notation] be a family of probability density functions indexed by the parameter [see pdf for notation]. We assume at least one of the [see pdf for notation] is unknown. Based on a random sample of size n from [see pdf for notation], let [see pdf for notation] be two point estimators of the real-valued function [see pdf for notation], where [see pdf for notation] are specified constants, if any. When comparing [see pdf for notation] and [see pdf for notation], it is quite common to examine the ratio of their respective average precisions usually measured by …

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A Further Look At The Comparison Of Normal Percentile Estimators, Danny D. Dyer Mar 1978

A Further Look At The Comparison Of Normal Percentile Estimators, Danny D. Dyer

Mathematics Technical Papers

For the purpose of making a pairwise comparison of point estimators of normal percentiles, a twofold technique is introduced which basically examines ,(a) the "odds" in favor of an estimator being closer to the true value than is a competing estimator and (b) an estimator's average closeness to the true value when it is closer (as well as when it is not) than is a competing estimator. Closeness to the true value is measured through an absolute error loss function. Joint consideration of these concepts is shown to form a basis for determining which of two estimators is preferred in …

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Parabolic Differential Inequalities In Cones, Randy Vaughn, V. Lakshmikantham Mar 1978

Parabolic Differential Inequalities In Cones, Randy Vaughn, V. Lakshmikantham

Mathematics Technical Papers

In this paper we investigate the theory of parabolic differential inequalities in arbitrary cones. After discussing the fundamental results concerning parabolic inequalities in cones, we prove a result on flow-invariance which is then used to obtain a comparison theorem. This comparison result is useful in deriving upper and lower bounds on solutions of parabolic differential equations in terms of the solutions of ordinary differential equations. We treat the Dirichlet problem in this paper since its theory follows the general pattern of ordinary differential equations and requires less restrictive assumptions. The treatment of Neumann problem, on the other hand, demands stronger …

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Some Contribution To Descriptive Set Theory., Haimanti Sarbadhikari Dr. Feb 1978

Some Contribution To Descriptive Set Theory., Haimanti Sarbadhikari Dr.

Doctoral Theses

Current interest in the descriptive theory of sc ts stems largely from the many applications that the classical theory has found in probability theory, functional analysis, dynanic programming etc. As exarples, we cite the fundament al paper of Blackwell 15J wherein he has shown that many of the pathologies of probability theory c an be avoided if one takes the basic probability space to be an analytic set. As another example, we mention that several vritere [7), L23] have shown that in Blackwell's model of dynamic programming 131 the existence of optimal strategies ig related to the cxistence of measurable …

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Scs 44: Remark On Hofmann's Scs Memo 1/18/78, Klaus Keimel, Heiko Bauer Feb 1978

Scs 44: Remark On Hofmann's Scs Memo 1/18/78, Klaus Keimel, Heiko Bauer

Seminar on Continuity in Semilattices

No abstract provided.

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Reaction-Diffusion Inequalities In Cones, Randy Vaughn, V. Lakshmikantham Feb 1978

Reaction-Diffusion Inequalities In Cones, Randy Vaughn, V. Lakshmikantham

Mathematics Technical Papers

Recently there has been a growing interest in the study of nonlinear reaction-diffusion equations [2,3,4,7] because of the fact examples of such equations occur in population genetics [2,5,12,13], nuclear and chemical reactors [2,7,8], conduction of nerve impulses [1,7,15], and several other biological models [1,6,15]. As is the case of ordinary differential equations [9,10], it is natural to expect that the theory of reaction-diffusion inequalities and comparison theorems will play a prominent role in this study. In this paper, we consider reaction-diffusion equations which are weakly coupled relative to an arbitrary cone. We prove a result on flow-invariance which is then …

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Attractivity Amp Hopf Bifurcation, L. Salvadori, P. Negrini Feb 1978

Attractivity Amp Hopf Bifurcation, L. Salvadori, P. Negrini

Mathematics Technical Papers

Consider the one-parameter family of differential equations [see pdf for notation] where [see pdf for notation] and [see pdf for notation]. Here [see pdf for notation] and [see pdf for notation]. Denoting by [see pdf for notation] the eigenvalues of [see pdf for notation] we shall suppose throughout the paper that [see pdf for notation] and [see pdf for notation]. We are concerned with the general problem of asymptotic stability of the periodic orbits arising in the Hopf bifurcation for (1.1). Such property is related to the asymptotic behaviour of the flow relative to 0 (the critical value of the …

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Scs 43: Locally Quasicompact Sober Spaces Are Baire Spaces, Karl Heinrich Hofmann Jan 1978

Scs 43: Locally Quasicompact Sober Spaces Are Baire Spaces, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

No abstract provided.

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A Random Walk In A Random Environment, Edwin Andrew Sanchez Jan 1978

A Random Walk In A Random Environment, Edwin Andrew Sanchez

Mathematics & Statistics ETDs

In this dissertation we consider a model of a random walk, (Zn}, on R(1) where the distribution of (Zn} is dependent on a stochastic process (Yn} and is given by gy(z) where Yn-1 = y . Conditions on the environmental process (Yn} are given for which transience or recurrence of the random walk (Zn} can be detennined. The probability of n absorption and mean time problems are solved when (Yn} is a finite Markov chain and (Zn} is a classical random walk on …

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Fixed Point Theorems In Generalized Hilbert Spaces, Troy L. Hicks, Ed W. Huffman Jan 1978

Fixed Point Theorems In Generalized Hilbert Spaces, Troy L. Hicks, Ed W. Huffman

Mathematics and Statistics Faculty Research & Creative Works

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of semi norms satisfies the parallelogram law. © 1978.

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Convergent Factorial Series Solutions Of Linear Difference Equations, W. J. Fitzpatrick, L. J. Grimm Jan 1978

Convergent Factorial Series Solutions Of Linear Difference Equations, W. J. Fitzpatrick, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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Numerical Experiments With The Multi-Grid Method, Theodore Craig Poling Jan 1978

Numerical Experiments With The Multi-Grid Method, Theodore Craig Poling

Dissertations, Theses, and Masters Projects

No abstract provided.

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The Conjugate Of A Singular Functional Differential Operator, Leon M. Hall Jan 1978

The Conjugate Of A Singular Functional Differential Operator, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

An explicit representation of the conjugate of a singular functional differential operator is given. Some theorems and their corollaries are proven.

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Quasi-Triangular Matrices, Joanne Dombrowski Jan 1978

Quasi-Triangular Matrices, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

It is shown that there exist quasitriangular operators which cannot be represented as quasitriangular matrices.

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Approximation By Discrete Operators, J. J. Swetits, B. Wood Jan 1978

Approximation By Discrete Operators, J. J. Swetits, B. Wood

Mathematics & Statistics Faculty Publications

A discrete, positive, weighted algebraic polynomial operator which is based on Gaussian quadrature is constructed. The operator is shown to satisfy the Jackson estimate and an optimal version is obtained.

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Generalized Connectors, Nicholas Pippenger Jan 1978

Generalized Connectors, Nicholas Pippenger

All HMC Faculty Publications and Research

An $n$-connector is an acyclic directed graph having $n$ inputs and $n$ outputs and satisfying the following condition: given any one-to-one correspondence between inputs and distinct outputs, there exists a set of vertex-disjoint paths that join each input to the corresponding output. It is known that the minimum possible number of edges in an $n$-connector lies between lower and upper bounds that are asymptotic to $3n\log _3 n$ and $6n\log _3 n$ respectively. A generalized $n$-connector satisfies the following stronger condition: given any one-to-many correspondence between inputs and disjoint sets of outputs, there exists a set of vertex-disjoint trees that …

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Relationship Between Stochastic And Differential Models Of Compartmental Systems, Jerome Eisenfeld Jan 1978

Relationship Between Stochastic And Differential Models Of Compartmental Systems, Jerome Eisenfeld

Mathematics Technical Papers

This paper shows that the differential equations model for compartmental systems is consistent with a stochastic description. Consequently, we may employ either a differential equations or a stochastic formulation for either parameter identification, or for physical interpretation, as best suits the purpose. The differential equations parameters, the so-called fractional transfer coefficients, may be determined from the corresponding set of stochastic parameters and vice versa.

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