Physical Sciences and Mathematics Commons^™

Probabilistic Ways Of Thinking, Garnet Hauger

ACMS Conference Proceedings 1981

Events of the tiniest probabilities occur every day, and yet we tend to think of these events as unusual and even miraculous. So what should be a Christian's response to such events? Beginning with some simple concepts of probability, this paper examines the role that chance plays in our lives.

The Development Of Algebraic Structures During The Nineteenth Century, Richard Stout

ACMS Conference Proceedings 1981

I remember entering the faculty lounge one day while I was in graduate school and hearing a logician chiding some of the algebraists in the room. He said, "Don't you fellows ever get tired of just plus and times?" His remark, said in jest, had more to it than he may have realized. The fact that there is structure to algebra, represented by plus and times, was a vital discovery in the nineteenth century. It would lead algebra away from a reliance on numbers to a much more formal approach, one in which many different types of algebraic structures could …

A Reaction To The Poythress Paper, Paul J. Zwier

ACMS Conference Proceedings 1981

This paper reacts to the metaphor of Vern Sheridan Poythress’s papers, Science as Allegory, exploring what makes a good metaphor and the quality of argument it produces.

Teaching Mathematics Distinctively, Paul J. Zwier

ACMS Conference Proceedings 1981

By examining previously used education models, Paul Zwier how he developed his current methods of teaching mathematically distinctively.

An Integration Of Integrations Of Christianity And Mathematics—A Response To Harold Heie, Gene B. Chase

ACMS Conference Proceedings 1981

There are three general approaches taken to integrate Christianity and Mathematics: the applicational, the incarnation, and the philosophical. This paper discusses these views and responds to the approaches of Harold Heie.

Reality And Imagination In Mathematics And Religion, Dave Neuhouser

ACMS Conference Proceedings 1981

What does either reality or imagination have to do with mathematics? What does either reality or imagination have to do with religion? The thesis of this paper is that mathematics and religion, both, should be closely related to reality and that imagination is essential in both areas. In fact, imagination is essential in our attempts to understand reality.

Introduction (1981), Robert Brabenec

ACMS Conference Proceedings 1981

A Third Conference on Mathematics from a Christian Perspective

Table Of Contents (1981), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1981

No abstract provided.

Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Mathematics Faculty Publications

The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises.

In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions.

Retracts are discussed in section 3, where it is seen that they are not sufficient …

Ratio Comparisons Of Supremum And Stop Rule Expectations, Theodore P. Hill, Robert P. Kertz

Research Scholars in Residence

Suppose X₁,X₂,...,X_n are independent non-negative random variables with finite positive expectations. Let T_n denote the stop rules for X₁,...,X_n. The main result of this paper is that E(max{X₁,...,X_n }) sup{EX_t t ε T_n }. The proof given is constructive, and sharpens the corresponding weak inequalities of Krengel and Sucheston and of Garling.

Existence Theorems For A Class Of Functional Differential Systems, B. G. Pachpatte, G. S. Ladde

Mathematics Technical Papers

In recent papers [2,6], the authors have established existence and comparison theorems for the well known Cauchy problem for ordinary differential equations without using the monotone property on the given system. These results are obtained under the conditions of the type which have been considered in the classical paper of Müller [8]. The interesting feature of the results established in [2,6], is the fact that the solutions of the Cauchy problem remain in the given sector. In this paper, we shall first establish existence and comparison theorems for a class of more general functional differential systems without using monotone property. …

Monotone Method For Equations Describing Transport Phenomena In A Banach Space, A. S. Vatsala, B. G. Pachpatte

Mathematics Technical Papers

Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach space has been recently considered in [2,7] by utilizing monotone iterative method. A special type of B.V.P. of the form [see pdf for notation] in finite dimensional spaces have been recently investigated in [6]. It is of interest to investigate (1.1) in a Banach space since special forms of them occur in transport processes [1,8,9]. In order to develop monotone technique for (1.1) it becomes necessary to develop a comparison Theorem (see Theorem 2.1) which is of interest in itself. The …

An Estimate For The Roots Of Random Algebraic Polynomial With Application, M. Sambandham, G. S. Ladde

Mathematics Technical Papers

An algebraic polynomial with dependent random coefficients is considered. The difference between the sample roots of random algebraic equation and the roots of the mean equation is estimated. As an application the difference between the sample solution of a random difference equation and the solution of the mean difference equation is also obtained.

Asymptotic Expansions And Deficiency., Tapas Kumar Chandra Dr.

Doctoral Theses

The efficiencies intmduced by B.J. G. Pitnan and R. R.Bahadur are both meant to compare the asymptotie perfornance or statistical procedured. However there are nany interesting situations where these eriteria prove inadequate and rurther discrimination 1s necessary. One such attempt of furthor refinenent is the criterion of defieieney.This investigation was undert aken with the ob ject of davelop- Ing tools for studying defieiency of test proceduros vith (1) same Pitman efficieney, OT (11) sane Bahadur efficiency.Deficiency in the first case has been defined by Hodges and Lehumann (1970). Deficiency in the second case vas defined by Chandra and Chosh (1978). …

Linear Monotone Method For Nonlinear Boundary Value Problems In Banach Spaces, V. Lakshmikantham, Stephen R. Bernfeld

Mathematics Technical Papers

One of the most useful techniques in proving the existence of multiple solutions of nonlinear boundary value problems (BVP for short) is the monotone iterative method, which yields monotone sequences that converge to extremal solutions of the problem. Recently, because of applications, this technique has attracted much attention, see [1,3-7,11,12,14,15]. To explain this method, let us consider the scalar BVP (1.1) [see pdf for notation] where [see pdf for notation] and [see pdf for notation], I being the interval [0,1]. Suppose that [see pdf for notation] with [see pdf for notation] on I and (1.2) [see pdf for notation] Then …

Method Of Quasi-Upper And Lower Solutions In Abstract Cones, V. Lakshmikantham, A. S. Vatsala, S. Leela

Mathematics Technical Papers

Let E be a real Banach space with ||•|| and let E* denote the dual of E. Let K C E be a cone, that is, a closed convex subset such that ^K C K for every ^ ≥ 0 and K ^ {-K} = {O}, By means of K a partial order ≤ is defined as v ≤ u if u - v E K. We let K* =[φ E E*: φ(u) ≥ 0 for all u E K]. A cone K is said to be normal if there exists a real number N > 0 such that 0 ≤ …

Periodic Solution For Nonlinear Delay Equation In Higher Order, Sen-Wo Du

Mathematics Technical Papers

In recent years, the existence and uniqueness of 2n-period solution for (1.1) [see pdf for notation] where x E Rn, and e(t,u,v) is a given function with 2^-period in t, have been discussed in several papers [1],[2],[3],[4] by using the Fourier expansion and fixed point method. The delay case is first discussed by W. Layton [5]. Applying similar ideas, we extend the study of (1.1) for any positive integer j.

Role Of Labour In Indian Agriculture., Manabendu Chattopadhyay Dr.

Doctoral Theses

In this stuly, we have analysed some aspects of labour condi- tions and relations in Indian agriculture on the ba si s of available secondary source data.We have started our analysis by taking a look at the origin and growth of the class of agricul tural labourers in the Indian society. Possible explanations for the ori gin and growth of the agricul tural labour class have been reviewed in this context. We then prmceed to examine the trends in employment and unemployment in both the rural and urban sectors of India. The trends are studied in terms of absolute nurbers …

A Method Of Modeling Multirate Two-Dimensional Recursive Digital Filters Author, Albert P. Gerheim

Electrical & Computer Engineering Theses & Dissertations

This dissertation presents a method of modeling two dimensional sampled data systems with two sampling rates in each dimension. This methodology is applied to the problem of synthesizing two dimensional velocity filters using one dimensional prototypes and multirate concepts.

The modeling method includes the replacement of scalar z-transforms of signals by vectors of polynomials, and the replacement of scalar z-transforms of impulse responses by matrices of polynomials.

The synthesis of velocity filters is accomplished through the use of coordinate transformations in the z-transform domain which skew the ω₁ -ω₂ axes on the unit bidisc. The filters synthesized using …

Monotone Method For Nonlinear Boundary Value Problems Arising In Transport Process, B. G. Pachpatte, V. Lakshmikantham

Mathematics Technical Papers

Recently, monotone iterative methods have been successfully employed to prove existence of multiple solutions and point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations (see, [1], [3]-[6], [9]). In the transport process [10] of n different types of particles in a finite rod of length (b-a) the equation governing the particle's density is given by the following linear system of equations [see pdf for notation] where Ai, Bi (i = 0,1,2) are n x n matrices and x,y,p,q are n-vectors. The components x1,...,xn of the vector x represent the n distinct type of …

Bounded Solutions For Some Gradient Type Systems, A. R. Aftabizadeh

Mathematics Technical Papers

C. Corduneanu in [3,TH.1] investigated the existence of a unique bounded solution of the system [see pdf for notation] (1.1) with [see pdf for notation] continuous and of class c(2) in u. In this paper we shall prove the existence of a unique bounded solution of (1.1), stated in [3,TR.1], under weaker conditions, and also we shall discuss the asymptotic behavior of bounded solution of (1.1) on a half-line. We wish to mention that M. M. Belova [1] had similar ideas, but she did consider only a special case (space L2), and without concern for existence. Before we proceed further, …

On Washout In Nonlinear Compartmental Systems, Jerome Eisenfeld

Mathematics Technical Papers

Let x(t) be a solution of a compartmental system. If, for some compartment j, x (t) -> 0 as t -> °°, then we say that compartment j washes out. We show that a compartment washes out if it always reaches (along a fixed path) either the environment or another compartment for which there is no return path. Additional criteria, particularly regarding exponential convergence, are also presented. Examples are drawn from tracer kinetics, enzyme reactions, and epidemic models.

On None Approach To Equilibrium In Compartmental Systems, Jerome Eisenfeld

Mathematics Technical Papers

The question of convergence of a solution of a compartmental system to an equilibrium point, as t -> °°, is of considerable interest [1-6]. Although it was not explicitly stated, the remarks in [1] seem to suggest that in the case of closed systems, of the type specified below, every solution approaches an equilibrium point. These remarks prompted the construction of counter examples, to be presented below, to show that a closed compartmental system may admit periodic solutions as well as aperiodic solutions that do not approach a constant vector.

Flow-Shop Scheduling Problems., N. R. Achuthan Dr.

Doctoral Theses

Researchers attention was drawn to the study of schodulirg problems through mathemtical modelling, probably for the first time, when Johnson (1954) publishod his famous paper in mval research logistic quarterly. Thercafter, mny authors have contimued to contribute to the growth of the theory of scheduling. A vast colloctim of papers related to this area is rogularly published by journals like mamgement science, operations research, operational research quarterly, naval research logistic quarterly, opsearch etc.. A good grasp of the litermture in this arca can be had from the books by Conway et al. (1967), Baker (1974) and Rinnooy Kan (1976).This thesis …

The Threshold Problem For Fitzhugh-Nagumo Equations, C. Corduneanu

Mathematics Technical Papers

No abstract provided.

Quasi-Invariant Manifolds, Stability, And Generalized Hopf Bifurcation, L. Salvadori, Stephen R. Bernfeld

Mathematics Technical Papers

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 Lyapunov-Schmidt method or topological degree arguments (see Marsden and McCracken [8] and Hale [6] and their references). Our approach, on the other bend, 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 [9] and Bernfeld …

Fixed Point Theorems For Expanding Maps, B. B. Williams, A. A. Gillespie

Mathematics Technical Papers

Suppose (X,d) is a metric space, h > 0 and T: X -> X. We shall use the notation T E E(h) to mean [see pdf for notation] for each x,y E X. If h > 1, then T will be called an expanding map. Clearly T E E(h) implies T is a 1-1 function and [see pdf for notation] for each x,y E T(X). In this paper some conditions are found to insure that an expanding map will have a fixed point. It is shown that each finite dimensional Banach space X has the following property: each continuous and expanding map …

Applications Of Differential Inequalities To Persistence And Extinction Problems For Reaction-Diffusion Systems, Linda Joy Allen

Doctoral Dissertations

Systems of nonlinear reaction-diffusion equations representing models of competition, predation, and mutualism are presented and discussed. The models are divided into two categories, patch models and continuous models which can be represented by systems of ordinary differential equations or by systems of partial differential equations, respectively. Within each of these categories there are four types of diffusion mechanisms, random, biased, directed, and predator-prey diffusion. Conditions for system persistence and extinction are sought.

For the patch models, existence, uniqueness, positivity, and boundedness of solutions are discussed. Persistence of a nonnegative component u_i (t) means limsup/t→∞ u_i (t) > 0 versus …

Extended Particles And The Interpretation Of Quantum Mechanics., C. K. Raju Dr.

Doctoral Theses

A now fornulation of the problen of junotion condiiions 1a given, It is pointed out that, if the existing the ory of relativity ie to be consistent with the existence of natter in the form of particles, thon the cannot be continuously aifferentiable everywhere, The mathonatical part of the problem of Junction conditiona is solved by using nonatandard analysis to define prod uo ta and compoaitions vith distributiona, The definitiona are auch that o ontimaed belief in the equations of relativity is justified, As an application, the equations of IRotion for the apherically-synne tric surface layor, at the Schwerzachild-Minkowsici junction, …

Contractual Arrangements In Agriculture : Some Theory And Empirical Evidence., Chandrasekhar Pant Dr.

Doctoral Theses

Tenancy in agriculture is an arrangement between the landowner and tenant in which the tenant paye to the landowner a certain mutually greed sun (or stare) of produce in return for the right to cul ti vate and appropriate the output produced on rentedend. There are different types of tenaney arrangements and often these differences relate to the form of payment of rent. Two of the more prevalent tendancy arrangements are share cropping (or cropshering) sand fixed-rent tendany, Under sh-re- cropping, the rent is a contructed percentage of the output produced on rented land while in a fixed-rent contract the …