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On The Fundamental Theory Of Nonlinear Second Order Stochastic Boundary Value Problems, G. S. Ladde, Jagdish Chandra, V. Lakshmikantham

Mathematics Technical Papers - Archive

A Study of nonlinear second order stochastic boundary value problems (SBVP for short) is initiated through sample calculus approach. A basic existence result for bounded nonlinearities is established. The method of upper and lower solution processes and a general existence theorem are established. After proving the stochastic version of the needed maximum principle, the monotone iterative technique is developed which yields existence of multiple solution processes of SBVP. Finally, by developing a stochastic comparison result, the important problem of finding error estimates between the sample solutions of SBVP and the solutions of corresponding mean BVP, is considered.

Quasi-Extended Asymptotic Functions, Todor D. Todorov

Mathematics

The class F of "quasi-extended asymptotic functions" introduced in the present paper contains all extended asymptotic functions [8, (3.1)] (in particular, all examples constructed in [9, Sec. 1 ]). But F contains also some new asymptotic functions very similar to tht Schwartz distributions. On the other hand, every two quasi-extended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square &# 948;² of an asymptotic function &# 948; similar to Dirac's delta-function is constructed as an example. The connection with the asymptotic functions introduced in [2] and [4] is established.

A Note On Products Of Infinite Cyclic Groups, Brendan Goldsmith

Articles

In his book [2], Fuchs introduces the notion of a subgroup X of a Specker group P being a product and goes on to establish a Lemma [2, Lemma 95.1] which yields a useful characterization of the quotient and enables an easy derivation of Nunke’s characterization of epimorphic images of the Specker group [4]. Unfortunately this Lemma is incorrect as we show in section 1. In section 2 by suitably strengthening the hypothesis we regain a characterization of the quotient. Throughout, all groups are additively written Abelian groups and our notation follows the standard works of Fuchs [1], [2].

A Modified Crank-Nicolson Method, Ernest David Jordan Jr.

Theses and Dissertations

In order to obtain a numerical solution to the heat equation using finite differences, either implicit or explicit equations are used to formulate a solution. The advantage in an explicit formulation is its simplicity and minimal computer storage requirements while its disadvantage is its instability. The opposite is true for an implicit formulation such as the Crank-Nicolson method; although it is stable it is more difficult to implement and requires a much larger memory capacity. In this paper we examine the accuracy and stability of a hybrid approach, a modified Crank-Nicolson formulation, that combines the advantageous features of both the …

Synchronized Slide-Tapes In The Physics Laboratory, Loren Quan

University of the Pacific Theses and Dissertations

Media play a large part in most of our daily lives. We watch television; we go to the movies; we listen to the radio. For years educators have been adapting media-related technological advancements for the purpose of teaching in the classroom. Here at the Physics Department of the University of the Pacific, we have adapted the medium of synchronized slide-tapes for use in the laboratory component of our calculus-based introductory physics course.

The Frobenius Theorem, Hiroshi Nagao

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

Many theorems in differential geometry which deal with the existence of certain geometrical structures or properties depend upon various existence and uniqueness theorems for differential equations. Because of its wide range of applications one of the most important of these theorems is the Frobenius Theorem for systems of total differential equations. There are four different forms of the Frobenius Theorem. In applications of the theorem one form is often preferable to the others. In this report we -shall prove the Frobenius Theorem, establish the equivalence of these various forms, and discuss a few applications.

Boole's Algebra Isn't Boolean Algebra (Article Review), Calvin Jongsma, John Corcoran

Faculty Work Comprehensive List

Reviewed Title: Boole's Algebra Isn't Boolean Algebra by Theodore Hailperin. Mathematics Magazine, v. 54:4, pp. 172-184. ISSN: 0025-570X

On Some Dependencies Between Functional Forms In Functional Programming Systems, Atanas Radenski

Mathematics, Physics, and Computer Science Faculty Articles and Research

In the present paper, some dependencies between functional forms in functional programming systems are demonstrated. It is shown that any functional form can be expressed by using only the forms composition, condition and construction.

The Method Of Upper, Lower Solutions And Volterra Integral Equations, G. S. Ladde, B. G. Pachpatte, V. Lakshmikantham

Mathematics Technical Papers - Archive

In employing the method of upper and lower solutions to dynamical systems, one is required to impose a certain monotone property on the given system [5,6,11] When the given system does not possess such a monotonic property, stronger forms of upper and lower solutions have to be assumed in order to obtain similar results [4,6,9]. Furthermore, if the system enjoys a mixed monotone property the method of quasi-upper and lower solutions, which is recently introduced, is most useful [7]. In this paper we shall extend these ideas to Volterra integral equations. We want to note that Volterra integral equations and …

An Analysis Of Stress Wave Propagation In Slender Bars Using A Discrete Particle Approach, Donald Greenspan, W. R. Reeves

Mathematics Technical Papers - Archive

In this paper, a discrete particle approach is developed for the quantitative analysis of stress wave propagation in metal bars. Though linear forces are emphasized, nonlinear forces are also considered. Cylindrical, tapered, homogeneous, and nonhomogeneous bars are studied. Computer results show most favorable agreement with available theoretical and experimental results.

Scs 57: On The Duality Of Semilattices, Karl Heinrich Hofmann, Jimmie D. Lawson

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro

All HMC Faculty Publications and Research

In this paper, we study the existence of weak solutions of the problem

□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)

u(t,x) = 0 ; (t,x) є ∂Ω

where □ is the wave operator ∂²/∂t² - ∂²/∂x², G: Rⁿ→R is a function of class C² such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L₂,(Ω))ⁿ and satisfying

f(0,x) = f(π,x) = 0

for all x є [0,π].

Numerical Simulation Of Free Surface Thermally-Influenced Flows For Nonhomogeneous Fluids, Vincenzo Casulli

Mathematics Technical Papers - Archive

In this paper a finite difference technique is presented to simulate the behavior of natural water bodies under the influence of pollutants and temperature differences. The mathematical model which has been discretized is the closed system obtained by combining the Navier-Stokes equations, the heat transfer equation, the diffusion equations, and an equation relating fluid density to both the chemical concentration and the temperature. The numerical method is based on the Marker-and-Cell method which has been extended to consider the volume expansion due to heat transfer and the density variations.

Scs 56: On A Question Of O. Wyler, Karl Heinrich Hofmann, Klaus Keimel

Seminar on Continuity in Semilattices

Source: University archive of the Technische Universität Darmstadt.

Stability And Generalized Hopf Bifurcation Through A Reduction Principle, Stephen R. Bernfeld, L. Salvadori, P. Negrini

Mathematics Technical Papers - Archive

We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques as the Liapunov-Schmidt method or topological degree arguments (see [5] and its references). Our approach, on the other hand, is based upon stability properties of the equilibrium point of the unperturbed system. Andronov et. al. [1] showed the fruitfulness of this approach in studying bifurcation problems in R2 (for more recent papers see Negrini and Salvadori 161 and Bernfeld and Salvadori [2]). In the case …

On The Existence Of Global Variational Principles, Ian M. Anderson, T. Duchamp

Mathematics and Statistics Faculty Publications

In studying physical phenomena one frequently encounters differential equations which arise from a variational principle, i.e. the equations are the Euler-Lagrangequations obtained from the fundamental (or action) integral of a problem in the calculus of variations. Because solutions to the Euler-Lagrange equations determine the possible extrema of the fundamental integral, the first step in the solution of a given problem in the calculus of variations is to obtain the appropriate Euler-Lagrange equations. This state of affairs suggests the so-called inverse problem, viz. does a given differential equation arise from a variational principle and, if so, what is the Lagrangian for …

Feasibility Of Quasi-Random Band Model In Evaluating Atmospheric Radiance, Navin Mirakhur

Mechanical & Aerospace Engineering Theses & Dissertations

The use of the quasi-random band model in evaluating the upwelling atmospheric radiation is investigated. The spectral transmittance and total band absorptance are evaluated for selected molecular bands by using the line-by-line model, quasi-random band model, exponential sum fit method, and empirical correlations, and these are compared with the available experimental results. The atmospheric transmittance and up­ welling radiance have been calculated by using the line-by-line and quasi-random models and are compared with the results of an existing program called LOWTRAN. The results obtained by the exponential sum fit and empirical relations are not in good agreement with experimental results …

Numerical Studies Of Double-Layer Circularization And Gastrulation, Donald Greenspan

Mathematics Technical Papers - Archive

In this paper, certain types of biological cell rearrangements are modeled from a computer point of view. All forces are of a local nature and are patterned on classical atomic and molecular interactions. It is first shown how to induce a double-layered flat tissue to fold into a double-layered circular tissue. Then, it is shown how to induce a section of the circular tissue to pull inward, or gastrulate.

Stability And Asymptotic Equivalence Of Perturbations Of Nonlinear Systems Of Differential Equations, M. E. Lord

Mathematics Technical Papers - Archive

A nonlinear variation of constants method was introduced by Alekseev [1] and applications of this formula to questions of stability and asymptotic equivalence of differential systems was demonstrated by Brauer [2,3,4]. In [6] a different approach to the nonlinear variation of constants method is given. This new approach involves determining the solution of the perturbed system by variation of the starting vector in the unperturbed system. Conceptually this is the method used in obtaining the classical variation of constants formula for perturbations of linear systems. In [6] the method yields two different formulas, one of which is equivalent to the …

Existence And Asymptotic Behavior Of Reaction-Diffusion Systems Via Coupled Quasi-Solutions, G. S. Ladde, A. S. Vatsala, V. Lakshmikantham

Mathematics Technical Papers - Archive

In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for differential systems a property called quasimonotone property is necessary [2,7,10]. However, there are several physical situations wherein such a property is not satisfied [1]. This difficulty has been overcome by introducing the notion of quasi-solutions [3,8,9]. In this paper we consider the reaction-diffusion system in which quasi-monotone property is not satisfied but a mixed quasimonotone property holds. By utilizing fruitfully the notion of quasi-solutions we prove the existence of coupled maximal and minimal solutions. For this purpose we exploit the monotone iterative technique. We then …

Homogeneous Extensions Of C*-Algebras And K-Theory. I, Claude Schochet

Mathematics Faculty Research Publications

No abstract provided.

Fixed Point Theorems For Ppf Mappings Satisfying Inwardness Conditions, Stephen R. Bernfeld, Y. M. Reddy, V. Lakshmikantham

Mathematics Technical Papers - Archive

In this paper we continue our recent development [1] of the theory of fixed point theorems of nonlinear operators whose domain and range are different Banach spaces. In particular we consider the analogues of recent results of Caristi and Kirk [5,6,8] where "inwardness conditions" are used to obtain fixed points. More precisely "inwardness conditions" on a mapping T whose domain K is a proper subspace of its range have been imposed to ensure that T maps points x of K "towards" K. Caristi and Kirk, for example, have considered two different conditions, metrically inward and weakly inward (this is the …

Some Asymptotic Properties Of Maximum Likelihood Procedures., Kasala Subramaniam Dr.

Doctoral Theses

This thesis consists of two parts dealing with maximum likeli. hood procedures in two different frameworks. In the first part (Chapters 1,2 and 3) we consider inference about a parameter which is discrete or separated in the sense that no f(x, e) can be obtained as a "limit" of ff(x,e1)}, + e. (A precise definition of what is meant by & "limit" is given in Chapter 1). In the second part (Chapters 4 and 5) we consider the usual eÅŸtimetion problem of what may be called in constrast to Part I, a contimuous parameter. We assume, we have an exponential …

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

WKU Administration Documents

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

The Riccati Equation Arising In The Control Theory, G. Da Prato

Mathematics Technical Papers - Archive

No abstract provided.

Determining Initial Values For Stiff Systems With Incomplete Initial Data, Yech-Kuang Ning

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Stiff differential equations frequently arise in physical problems due to the existence of greatly differing time constants. One way of solving stiff differential equations is taking the step size very small, another way is using an A-stable or stiffly stable implicit method. The purpose of this thesis is to discuss the method of determining initial values for stiff systems. The algorithm was motivated by a problem from ionospheric physics in which some of the initial values are unknown. If we give those unknown initial values an arbitrary number and integrated with those values, we have an initial transient. However, if …

A New Mathematical Approach To Biological Cell Rearrangement With Applications To The Inversion Of Volvox, Donald Greenspan

Mathematics Technical Papers - Archive

This paper develops a new method for modeling cell rearrangement in both two and three dimensions. The method uses classical molecular type forces and is computer oriented, recursively explicit, and economical. As yet, the approach is simplistic in that switching processes are not related deterministically to chemical, neurological, or genetic precursors. Illustrative computer examples of the inversion of volvox are described and discussed.

On The Discrimination Between The Lognormal And The Weibull Distributions With Applications To Offshore Oil/Gas Lease Bids, Danny D. Dyer

Mathematics Technical Papers - Archive

The competitive sealed bids on an individual offshore oil and gas lease are often assumed to follow a lognormal distribution (Brown, 1969). However, under the lognormality assumption there are known discrepancies between observed and theoretical results. Accordingly, alternative lease bid distributions have been studied. In particular, Dyer (1980) has shown that one would not reject the hypothesis that the bids on certain groups of leases follow Weibull distributions. In this paper, we discuss test procedures for discriminating between a lognormal distribution and a Weibull distribution. The procedure is then applied to the group of 12-, 13-, 14-, 15-, and 16-bid …

A Classical Molecular Approach To Computer Simulation Of Biological Sorting, Donald Greenspan

Mathematics Technical Papers - Archive

Steinberg's theory of sorting is modified by replacing the free energy minimization principle with dynamical equations of a molecular nature. Correct cellular sorting then follows in all cases where the mixture is in a liquid or a near-liquid state. Computer examples are described and discussed, primarily for two dimensional, but also for three dimensional, interactions.

Stochastic Parameters In Compartmental Systems, Jerome Eisenfeld

Mathematics Technical Papers - Archive

Let [see pdf for notation] denote the probability that a particle in compartment j will reach (or enter) compartment i. We present several formulas for obtaining the [see pdf for notation] in terms of the fractional transfer coefficients. The parameter are interesting for their own sake and they are also useful for obtaining qualitative properties of compartmental systems and for interpreting results already obtained. The reachability parameters also play a role in structural identification since they give us a new method for expressing the transfer function.