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Minimal Norm Constrained Interpolation, Larry Dean Irvine

Mathematics & Statistics Theses & Dissertations

In computational fluid dynamics and in CAD/CAM a physical boundary, usually known only discreetly (say, from a set of measurements), must often be approximated. An acceptable approximation must, of course, preserve the salient features of the data (convexity, concavity, etc.) In this dissertation we compute a smooth interpolant which is locally convex where the data are locally convex and is locally concave where the data are locally concave.

Such an interpolant is found by posing and solving a minimization problem. The solution is a piecewise cubic polynomial. We actually solve this problem indirectly by using the Peano kernel theorem to …

On Universal Tests For The Truth Of World Views: Their Existence And Identifiability, William Buttelmann, Paul Fienberg

ACMS Conference Proceedings 1985

In his book, Christian Apologetics, Norman Geisler proposes a universal test for the truth of world views. We examine this concept and find that it raises serious difficulties. This paper first presents some basic definitions for "world view" and "truth-value of a world view," then studies the concept of a universal test for the truth of world views in light of these definitions. Geisler has proposed what amounts to a universal decision procedure to determine the truth-value of world views. We show that, in the general case, no such universal decision procedure exists. Whether or not such universal tests for …

Selected Bibliography Of Donald Maccrimmon Mackay, Gene B. Chase

ACMS Conference Proceedings 1985

A selected bibliography of Donald MacCrimmon MacKay, including his written works and biographical sources.

The Significance Of Formally Undecidable Propositions For The Use Of Classical Logic In Theological Arguments, Gordon E. Whitney

ACMS Conference Proceedings 1985

No abstract provided.

Faith And Mathematics - A Different Perspective, James E. Mann, Jr.

ACMS Conference Proceedings 1985

No abstract provided.

Artificial Intelligence? - A Christian Appraisal, Donald M. Mackay

ACMS Conference Proceedings 1985

No abstract provided.

Is Rational Thinking The Best Thinking?, Richard Laatsch

ACMS Conference Proceedings 1985

No abstract provided.

Undergraduate Mathematical Modeling: When And What To Teach, Frank R. Giordano, Maurice D. Weir

ACMS Conference Proceedings 1985

No abstract provided.

Introduction (1985), Robert Brabenec

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Table Of Contents (1985), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1985

A Fifth Conference on Mathematics from a Christian Perspective

Edited by Robert L. Brabenec, Wheaton College

Σary N=0, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Rapid Computation Of The Energy States Of Two-Electron Atoms And Ions With An Explicit Formula For The Excited States Of Helium, Donald Greenspan

Mathematics Technical Papers - Archive

A new computational approach is developed for the energy states of two electron atoms and ions. The theory incorporates a classical interpretation of electron pairing and requires Only simple numerical methodology for its implementation. Accurate computer results are described and discussed. These results lead directly to an explicit formula for the excited states of helium. Also, extension to the hydrogen molecule [see pdf for notation] is indicated.

Non Relativistic Kapitza-Dirac Scattering, Evangelos A. Coutsias, J.K. Mciver

Branch Mathematics and Statistics Faculty and Staff Publications

We use techniques of singular perturbation theory to investigate the scattering of nonrelativistic charged particles by a standing light wave (Kapitza-Dirac scattering). Unlike previous treatments, we give explicit results for the effects of the time-dependent part of the field. For low field intensity or low particle energy, we show that the leading-order effects can be found from an averaged equation, and we compute corrections. For the strong fields that can be produced by modern lasers and/or high particle energies, we show that the time dependence of the potential leads to focusing. Our methods can be applied to other problems with …

Brownian Motion Applied To Partial Differential Equations, Steven M. Mckay

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This work is a study of the relationship between Brownian motion and elementary, linear partial differential equations. In the text, I have shown that Brownian motion is a Markov process, and that Brownian motion itself, and certain Stochastic processes involving Brownian motion are also martingales. In particular, Dynkin's formula for Brownian motion was shown. Using Dynkin's formula and Brownian motion, I then constructed solutions for the classical Dirichlet problem and the heat equation, given by Δu=0 and u_t= 1/2Δu+g, respectively. I have shown that the bounded solution is unique if Brownian motion will always exit the domain of …

The Reconstruction Conjecture In Graph Theory, Susan M. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this paper we show that specific classes of graphs are reconstructible; we explore the relationship between the reconstruction and edge-reconstruction conjectures; we prove that several classes of graphs are actually Harary to the reconstructible; and we give counterexamples reconstruction and edge-reconstruction conjectures for infinite graphs.

Some Spectral Properties Of Three And Four Body Scrodinger Operators By The Methods Of Time Dependent Scattering Theory., M. Krishna Dr.

Doctoral Theses

In the present work we shall deal with the asymptotic completeness problem in three and four (Quantum Mechanical) particle scattering. This thesis is divided into three chapters. In the first chapter we give an introduction to Scattering Phencmenon and give a description of the N-particle completeness problem.Then we collect some results preliminary to the later chapters and some results that would complete a discussion of the problem.The second chapter consists of some technical results and a reduction of the asymptotic completeness problem in N-particlerscattering via time dependent methods. The last chapter has two sections. The first section deals with verifying …

An Asymptotic Result In Forced Oscillations Of Pendulum-Type Equations, R. Kannan, R. Ortega

Mathematics Technical Papers - Archive

The forced pendulum-type equation is given by [see pdf for notation] where [see pdf for notation] is continuous and T-periodic and p(t) is[see pdf for notation] -periodic. When g(x) = a sin x, a > 0, we obtain the classical pendulum equation. The question of existence of [see pdf for notation] periodic solution of (1.1) for a given p(t) has been studied recently in [1], [3], [5] (cf. [4] for an extensive bibliography). Throughout this paper we denote by [see pdf for notation] the average of [see pdf for notation]. Some of the existence literature obtains sufficient conditions on the magnitudes …

Multivalued Maps And Multivalued Differential Equations, K. Deimling

Mathematics Technical Papers - Archive

Everybody meets multivalued maps very early in his mathematical education, as inverses of maps which are not one-to-one, but in elementary lectures the multivalued aspect is usually suppressed by means of elementary tricks or restrictions which make sense for practical purposes; think of [see pdf for notation] which has the inverse[see pdf for notation], from [see pdf for notation] (the subsets of R); or think of a linear operator [see pdf for notation] with kernel [see pdf for notation]; in which case one uses the trick to consider [see pdf for notation], defined by [see pdf for notation] which is …

Test Derivation For Cmos Iterative Logic Arrays, Ravi Sharma

Electrical & Computer Engineering Theses & Dissertations

Testability criteria for stuck-open (s-op) faults in one-dimensional unilateral iterative logic arrays (ILA) of CMOS combinational cells are considered in this thesis. A functional fault model to represents-op faults i~ an ILA cell is given. The procedure to detect as-op fault needs a pair of test vectors. The first is used to set up the initial conditions required to test the fault and the second is the test which distinguishes between the good and the bad circuit. Based on this approach necessary and sufficient conditions are given for the testability of as-op fault in a CMOS ILA cell. These conditions …

Scs 96: Generators And Weights Of Completely Distributive Lattices, Marcel Erné

Seminar on Continuity in Semilattices

No abstract provided.

Scs 95: Fixed Point Constructions For Standard Completions, Marcel Erné

Seminar on Continuity in Semilattices

No abstract provided.

Ua66/10/2 Newsletter, Wku Mathematics

WKU Administration Documents

Newsletter created by and about the WKU Mathematics department.

Efficient Nonlinear Parameter Estimation For Exponential Type, Least Square Approximation, Donald Greenspan

Mathematics Technical Papers - Archive

A computer algorithm is described for fitting data sets by least squares to the functions [see pdf for notation]. A non matrix form of Newton's method is utilized which is economical, easily implementable, and exceptionally fast. Computer examples are described and discussed.

Remarks On Bellman's Structural Identifiability, Jerome Eisenfeld

Mathematics Technical Papers - Archive

This paper remarks on unidentifiable compartmental systems. Emphasis is placed on detecting properties of the system directly from the compartmental diagram without resort to complicated analysis. New concepts are introduced. One is separability, a condition in which two or more parameters enter the identification equations only as a certain combination thereby preventing their identification. Concepts from linear algebra such as span, basis, and dimension are adopted to "parameter spaces". A necessary and sufficient condition for interval identification is presented.

Rapid Approximation Of The Energy States Of Three-Electron Systems, Donald Greenspan

Mathematics Technical Papers - Archive

In this paper, we show how to approximate rapidly the energy states of systems with one electron in the second ring. Using known energy states and average radii of two-electron systems in ground state, the Method requires only the computer solution of a single nonlinear equation in one unknown. This can always be accomplished by Newton's method when applied with a correct initial guess. Computational results for [see pdf for notation] are compared with available quantum mechanical estimates.

Some Studies In Analysis And Recognition Of 2 Dimensional Shapes., Swapan Kumar Parui Dr.

Doctoral Theses

Analysis and recognition of 2-dimensional shapes constitute an important problem in the fields of Pattern Recognition, Image Analysis, Computer Vision, Robotics and other related areas of research. If we look at the problem from the point of view of image or scene analysis, in a sense, the antire subject of automatic scene analysis might be defined as the problem of describing and recognizing the shape of the ob jects in an image. Shape is the primal intrinsic property for the vision system because we associate the definitions of objects with shape, rather than with colour or reflectivity, for example.According to …

Statistical Models For Consumer Behaviour In India., Amita Majumder Dr.

Doctoral Theses

The present dissertation is about analysis of consumer behaviour ba sed on time-serios consumption data in the framework of a static complete demand system with special reference to India.On the methodological side, the the proposes two station demand systems. One of them is based on a modification of the Simple Non-additivo Model (SNAM) of Deaton (1976) - a generalisation of Stone's Linear Expenditure System (LES) - that overcomes the limitations of the LES ariaing from the additivity of its underfying direct preference structure. The other system is based on the Frice Independent Generalized Linearity (FIGL) of Maellbaucr (1975). Both the …

A Political Economy Study Of An Indigeneous Irrigation System., Nirmal Sengupta Dr.

Doctoral Theses

The present thesis is the study of a specifio indigenoous irrigation eystem following the general method of politioal coonomy. A couple of yeara baok when I had written for the firet time ubout this little-known but widespread irr igation aystem the artiole had driwn ocnaiderublo attention. The prosent study is a much detailed expooition of the sama syetem. The age old eystem of irrigaticn howover, 1e not mere ly a matter of historionl interest. It alao raisos many different quastione regarding developmant strategy and planning. I have devolop. the study so aia to be able finally, to deal with suoh …

Ada: A New Programming Language., Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

In an attempt to control defense software costs while maintaining system reliability, the DOD (Department of Defense) has sponsored the development of a new programming language, called Ada. While Ada supports many of the features found in Fortran and Pascal, it has additional features making it easier and more reliable to use in large complex engineering software systems. Currently, the DOD is requiring that many new defense software systems be written in Ada. The author reviews the history of Ada's development and examines the primary constructs of the language. The philosophy behind Ada program design is reviewed by designing and …

Automorphisms And Range Families Of Transformation Semigroups, Inessa Levi

Faculty Bibliography

No abstract provided.