Physical Sciences and Mathematics Commons^™

Periodic Solutions Of Nonlinear Boundary Value Problems, V. Lakshmikantham, R. Kannan

Mathematics Technical Papers

One of the well known techniques in the theory of nonlinear boundary value problems (BVP) is the method of differential inequalities or the method of upper and lower solutions. The method of "Alternative Problems", a global variant of the Lyapunov-Schmidt method, has been used in the study of problems at resonance. The investigation of periodic BVP's forms an important subclass of problems at resonance. Our aim is to combine the two approaches to discuss nonlinear problems at resonance. We restrict ourselves in this paper to the discussion of periodic boundary value problems. In Section 1, we shall indicate the method …

Contribution To Theories Of Repetitive Sampling Strategies., Raghunath Arnab Dr.

Doctoral Theses

A common practical problem to whlch a survey - sampler has frequently to address himself 1s one of sampling a given finite population on successive occasions. One of the relevant issues requiring one's attention then 1s to adopt a suitable sampling strategy to estimate the population total of a variate of interest an the current occasion in an optimal manner. Here one has of necessity to take care to utilize the accumalated data on that variate procured in course of the survey along with other auxdliary information on one or more additional variables that may also incidentally be available, Several …

Scs 55: Mc Direct Limits, John R. Isbell

Seminar on Continuity in Semilattices

No abstract provided.

The King Chicken Theorems, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

Offshore Oil/Gas Lease Bidding And The Weibull Distributions, Danny D. Dyer

Mathematics Technical Papers

It is the purpose of this paper to study the use of the Weibull distribution as an acceptable model for the distribution of the bids on a lease. A multi-sample test procedure of the Weibull-bids hypothesis will be given and implemented to show that the Weibull distribution provides a better statistical fit than does the lognormal distribution for the group of 13-, 14-, 15-, and 16-bid leases.

Computer Studies Of The Classical Oxygen Molecule, Donald Greenspan

Mathematics Technical Papers

A classical, simplistic model of the molecular dynamics of 02 is developed for interactions which are not readily amenable to quantum mechanical analysis. All electron-electron interactions are included. Extensive computer examples are described and the reasonableness of the Born-Oppenheimer approximation is explored.

Scs 54: Cl-Projective Limits Of Distributive Continuous Lattices Are Distributive, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

No abstract provided.

Determination Of Probability Measures Through Group Actions., Inder Kumar Rana Dr.

Doctoral Theses

One of the fundamental problems in Measure Theory is the following: given a measurable space (x, B,), to find subclasses D of B, such that whenever for two probability measures u and v on (X, B,), u(B) = v(3) for every B c D, then u(B) = v(B) for every Be B,. The first basic theorem of Measure Theory, viz., the Caratheodory Extension Theorem says that any sub-algebra D of B, which generates B, has the above mentioned property.Let (X, B, ) be a given measurable space. A subclass n of 3, is called a determining class for a class …

Statistical Analysis Of Nonestimable Functionals., Dibyen Majumdar Dr.

Doctoral Theses

Our interent will be centred around the Gaunn Markov model (Y,X6,2A), where Y ls a randon variable asnuning values in R" with expectation and dispersion natrix given byE(Y) = XA (1.1) (1.2) * X in Rnxm and A In the subset of nonnegative definite (n.n.d.) natrices of RAre known. Unless apecifled to the contrary, A will be assuted to be positive definite (p.d.). The unknown paraneter vector B varies in Ag, a subset of Rand o? in, will alvays be the positive half of the real line, unless otherwine specifled, and 1ikewfse satiafien the minimum requirement dim (n,) = m.Historically, …

On Some Non Uniform Rates Of Convergence To Normality With Applications., Ratan Dasgupta Dr.

Doctoral Theses

We obtain non-uniform rates of convergence to normality of the partial sums in a triangular array of random variables, where variables in each array are independently distributed. Section 2 of this chapter generalizes the results of Michel (1976) mainly in the direction of considering a triangular array of rand om variables. A slight generality in the moment assumptions is also made. The later extension is quite in spirit with Katzs (1963) extension of the classical Berry-Esseen theorem. Since by Tomkins theorem (see Tomkins (1971) or Stout (1974)) the laws of the iterated logarithm are directly related to the zone where …

Some Problems On Econometric Regression Analysis., Maitreyi Chaudhuri Dr.

Doctoral Theses

Very often in eoonometrio enslysis one adopts the classical lineer regression model. The classical linear regression model is given by If, in addition, e is assumed to be normally Ä‘istributed, the model is called classical normal1 linear regression mode1.Ordinary least squares (0LS) methods of estimation and hypothesis testing are besed on this ndal, d eveluton copy of CV POFO But the assumptions on É›is and- xs may not be fulfilled in reality; or, in other words, the model may not be correctly specified. Cne class of problems arises when some of the regressors are omitted from the equation and/or scme …

Geological Depletion And Locational Advantage In The Analysis Of Mineral Extraction Programmes., Sudhir Dattatray Chitale Dr.

Doctoral Theses

The aim of the study is to evolve optimal pro- duction and linkage plans, to meet and oxogenously specified, spatially distributed time profile of damands from a set of spatially dispersed coking coal bearing geological blocks. The plans are optimal in the sense of minimun discounted present value of the sun of production, washing and transport costa.Pocussing our attention on a geological block consisting of many coal seams, we work with it as if it was operated as one production conplex. Geological depletion in ea ch block is formalised by estimat ing a Block Level Cumulative Cest Function (BLCCF) based …

Quasi-Solutions And Monotone Method For Systems Of Nonlinear Boundary Value Problems, A. S. Vatsala, V. Lakshmikantham

Mathematics Technical Papers

In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for initial and boundary value problems of ordinary differential systems, it becomes necessary to impose a condition generally known as quasi-monotone property [1,3,5]. In systems which represent physical situations such as a model governing the combustion of a material, quasi-monotonicity is not satisfied, see [4]. However a kind of mixed monotone property holds. To deal with such situations the notion of quasi-solutions was systematically developed in [4]. In this paper, we investigate monotone iterative method for systems of nonlinear boundary value problems when the system possesses …

Quasi-Solutions, Vector Lyapunov Functions And Monotone Method, S. Leela, V. Lakshmikantham, M. N. Oguztoreli

Mathematics Technical Papers

It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale interconnected dynamical and control systems. [3,4,5,11-15]. Several Lyapunov functions result in a natural way in the study of such systems by the decomposition and aggregation method [1-4,12-14]. However an unpleasant fact in this approach is the requirement of quasi-monotone property on the comparison system since comparison systems with a desired property like stability exist without satisfying quasi-monotone property. Also in the study of comparison theorems and extremal solutions for differential systems one usually imposes this quasi-monotone property. …

Embedding Discrete Flows On R In A Continuous Flow, P. L. Sharma, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

The problem of determining when a given discrete flow on a topological space is embeddable in some continuous flow was mentioned by G. R. Sell ("Topological Dynamics and Ordinary Differential Equations," Van Nostrand, New York, 1971) in his book on topological dynamics. In this book, the theory of generalized dynamical systems is exploited in the qualitative study of differential equations. Even more complicated is the problem of simultaneously embedding two or more discrete flows in a single continuous flow. We examine both of these problems when the underlying topological space is the space R of the real numbers. © 1980.

Tolerance Intervals For A Class Of Ifr Distributions With A Threshold Parameter, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

One-sided upper and lower tolerance intervals based on type II censored data are obtained. Under certain conditions the tolerance factors can be obtained from known results on the 2-parameter exponential distribution. Copyright © 1980 by the Institute of Electrical and Electronics Engineers, Inc.

Asymptotic Numbers: Ii. Order Relation, Infinitesimals And Interval Topology, Todor D. Todorov

Mathematics

It has been shown in [8] that the set of asympototic numbers A is a system of generalized numbers including isomorphically the set of real numbers R, as well as the field of formal power (asymptotic) series. In the present paper, which is a continuation of [8], an order relation in A is introduced due to A turning out to be a totally-ordered set. The consistency between the order relation and the algebraic operations in A is investigated and in particular, it is shown that the inequalities in A can be added and multiplied as in the set of …

Asymptotic Numbers: I. Algebraic Properties, Todor D. Todorov

Mathematics

The set of asymptotic numbers A introduced in Refs. [1] and [3] is a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers. The purpose of this paper is to study in detail the algebraic properties of A which are a little unusual, in a cenain sense, as compared with the known algebraic structures (rings. fields, etc.) This is necessary for the investigation of the class of asymptotic functions [2.4], which are on their part, generalized functions similar to the distributions of Schwartz but allowing the operation of …

Transformational Geometry Unit, Elizabeth Ann O'Neill

All Graduate Projects

The study included the development and writing of a unit on transformational geometry which involved a holistic approach including the cognitive, psychomotor, and affective domains. This unit was taught to the eighth grade class in the Oakville School District in Oakville, Washington. The results showed support that the teaching of this unit was effective.

How To Handle An Equation, Richard C. Heyser

Unpublished Writings

"This part might also be called 'math for those who hate math' because I [Heyser] intend to discuss, in words, what the foregoing math symbolism is about." In this paper draft, Heyser explains several mathematical equations for measuring sound.

Untitled (Subject: Energy), Richard C. Heyser

Unpublished Writings

Fundamental energy relations are explored as a basis for the measurement of physical systems. By considering finite dimensional observations in linear Hilbert space it is shown that a necessary and sufficient condition for the conservation of energy is the partitioning of any observation of that energy into two components which will be related through the Hilbert transform. The consequence of this relationship is demonstrated for the equilibrium storage of energy, point-wave duality in measurements, significance of complex representations involving circular form, the meaning of minimum phase and all-pass properties, and the introduction of new measurement characterizations such as the energy-time …

The Pattern Of Twos, Richard C. Heyser

Unpublished Writings

Rather than explaining the meanings behind the phases of sound measurement, Richard C. Heyser explains the relationships between these phases, which he calls the Pattern of Twos.

The Two Parts Of Energy, Richard C. Heyser

Unpublished Writings

In this paper, Richard C. Heyser explains the theories behind measuring sound by discussing its energy. Using what he calls abstract geometry, Heyser argues that measuring the transfer properties (that is, pressure and velocity) of sound's energy aids in the discovery of its amplitude and phase (or in-phase and quadrature).

Závisí Matematická Pravda Od Času?, Judith V. Grabiner

Pitzer Faculty Publications and Research

This is a Slovak translation of Judith Grabiner's "Is Mathematical Truth Time-Dependent?," published in Volume 81 of American Mathematical Monthly (April 1974).

Energry Loss Through Storage, Richard C. Heyser

Unpublished Writings

Richard C. Heyser prepared this article for submission in Science magazine. The process of storing energy under equilibrium conditions loses work that could have been obtained directly from the source of energy. This is independent of the form of the energy and can be extended to the analysis of situations otherwise difficult to formulate in a common description, such as multiple energy conversions involving solar, electrical, chemicl, and mechanical storage.

Understanding Energy, Richard C. Heyser

Unpublished Writings

In this paper, Richard C. Heyser explains how the conservation of total energy, the law stating that energy can be neither created nor destroyed in any process, is the underlying principle behind measuring sound through time delay spectrometry (TDS).

A Function In The Number Theory, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The definition of this function is:

S(n) is the smallest integer such that S(n)! is divisible by n.

It had become known as Smarandache Function.

A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.

On The Evaluation Of Powers And Monomials, Nicholas Pippenger

All HMC Faculty Publications and Research

Let $y_1 , \cdots ,y_p $ be monomials over the indeterminates $x_1 , \cdots ,x_q $. For every $y = (y_1 , \cdots ,y_p )$ there is some minimum number $L(y)$ of multiplications sufficient to compute $y_1 , \cdots ,y_p $ from $x_1 , \cdots ,x_q $ and the identity 1. Let $L(p,q,N)$ denote the maximum of $L(y)$ over all $y$ for which the exponent of any indeterminate in any monomial is at most $N$. We show that if $p = (N + 1^{o(q)} )$ and $q = (N + 1^{o(p)} )$, then $L(p,q,N) = \min \{ p,q\} \log N …

Two Point Boundary Value Problem With Jumping Nonlinearities, Alfonso Castro

All HMC Faculty Publications and Research

We prove that a certain two point BVP with jumping nonlinearities has a solution. Our result generalizes that of [2]. We use variational methods which permit giving a minimax characterization of the solution. Our proof exposes the similarities between the variational behavior of this problem and that of other semilinear problems with noninvertible linear part (see [5]).