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Existence Of Solutions In A Closed Set For Delay Differential Equations In Banach Spaces, V. Moauro, S. Leela

Mathematics Technical Papers - Archive

The study of the Cauchy problem for ordinary differential equations in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed in such a study are (i) finding monotonicity type conditions which guarantee the existence as well as uniqueness of solutions and (ii) finding compactness type conditions which assure only the existence of solutions [3,4]. It is also known [10,12] that in order to prove the existence of solutions in a closed subset F of the Banach space, a boundary condition of the type [see pdf for notation] is required.

Asymptotic Properties Of A Nonlinear Diffusion Process Arising In Articular Cartilage, Van C. Mow, Jerome Eisenfeld

Mathematics Technical Papers - Archive

There has been considerable effort put forth to analyse degenerative Joint diseases in terms of the principles of mechanics and hydrodynamics [8]. This effort has led to mathematical models which are systems of nonlinear partial differential equations (see e.g., [6] and [7]). The mathematical models are based on assumptions concerning the nature of the physical system which are not a priori known. Therefore laboratory experiments are performed with an eye towards validating the mathematical models. This paper deals with a particular mathematical model, a nonlinear diffusion equation, which has been proposed by Mow and Monsour [4], [5] to describe the …

Positive Perturbations Of Unbounded Operators, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

General Moment Methods For A Class Of Nonlinear Models, Stephen W. Cheng, Jerome Eisenfeld

Mathematics Technical Papers - Archive

This paper deals with the following problems: (i) the development of a general theory which incorporates several methods as special cases; (ii) the applicability of moment methods to a class of nonlinear problems, (iii) the specification of the class of admissible weighting functions; (iv) the estimation of the number of parameters; (v) the elimination of the cut-off error in the analysis of fluorescence decay data.

Stability Of Differential Systems With Impulsive Perturbations In Terms Of Two Measures, S. Leela

Mathematics Technical Papers - Archive

The study of differential systems of the form (1.1) [see pdf for notation] where [see pdf for notation] denotes the distributional derivative of [see pdf for notation], a function of bounded variation (that is, differential systems with impulsive perturbations, also called measure differential equations), is both interesting and important because most models for biological neural nets,pulse frequency modulation systems, automatic control problems with impulsive inputs and many physical processes are best described by such equations [1-3,8,10,12,13]. Since the solutions of (1.1) are discontinuous (that is, functions of bounded variation), the investigation of the stability properties of (1.1) by the usual …

Characterizations Of Inner Product Spaces., John Lee Roy Williams

Masters Theses

"The parallelogram law and several extensions and generalizations which characterize inner product spaces among normed linear spaces are given. The characterization problem is motivated by its usefulness in foundations of general quantum theories and examples are given.

The technique of proving that a normed linear space is an inner product space by showing that its unit sphere is an ellipsoid is emphasized. Using this technique, a new integral characterization is obtained"-- Abstract, p. ii

Strict Convexity In Locally Convex Spaces And Fixed Point Theorems In Generalized Hilbert Spaces, Ed Wilburn Huffman

Doctoral Dissertations

"A new definition of strict convexity is introduced for locally convex spaces. Examples are given and several characterizations of strict convexity are established for locally convex spaces whose generating family of semi norms satisfies the parallelogram law.

Some fundamental fixed-point theorems are proved for locally convex spaces whose generating family of semi norms satisfies the parallelogram law. Other fixed-point theorems are proved for strictly convex locally convex spaces which are also F-spaces"-- Abstract, p. ii

Stochastic Integration, Diane Knipfer

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

Differential equations have been used to model physical systems, but in many processes this has not been sufficient due to the presence of random occurrences in the system. One method of dealing with this problem is to model the system as a stochastic or random process.

A stochastic process, x, is a function mapping the product of a probability space, Ω, and a subset of the real numbers, TcR, into the real numbers, x: Ω*T→R. In many physical situations, T can be thought of as representing time and Ω as all possible outcomes of the process. For a fixed t …

A Topological Structure On The Structure Sheaf,, Lawrence Stout

Scholarship

No abstract provided.

Scs 29: On The Closedness Of The Set Of Primes In Continuous Lattices, Karl Heinrich Hofmann, Oswald Wyler

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

A Proof Of Convergence For The Tridiagonal Ql Algorithm In Floating-Point Arithmetic, James George Sanderson

Mathematics & Statistics ETDs

Numerous routines are available to find the eigenvalues of a real symmetric tridiagonal matrix. Since it is known to converge in exact arithmetic, the tridiagonal QL algorithm with origin shift is widely used. Here we analyze the algorithm in floating-point arithmetic. This analysis suggests two modifications to the EISPACK implementation TQLl that enable one to prove correctness and hence convergence of the routine.

Also, it is known that the implicit and explicit versions of the QL algorithm produce the same results in exact arithmetic. A counter-example to the floating-point analog of this theorem is presented.

Scs 28: The Lattice Of Open Subsets Of A Topological Space, Klaus Keimel, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 27: Closure Operators And Kernel Operators In Cl, Michael Mislove

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Graph Multiplicities, David Burns

Masters Theses

No abstract provided.

Scs 26: A Reply To An Editorial, Dana S. Scott

Seminar on Continuity in Semilattices

No abstract provided.

Scs 25: Observations, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 24: An Editorial, Karl Heinrich Hofmann, Klaus Keimel

Seminar on Continuity in Semilattices

No abstract provided.

Scs 23: Non-Continuous Lattices, Jimmie D. Lawson

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 22: Representations Of Colimits In Cl, Part Ii, Gerhard Gierz

Seminar on Continuity in Semilattices

No abstract provided.

Scs 22: Representations Of Colimits In Cl, Part I, Gerhard Gierz

Seminar on Continuity in Semilattices

No abstract provided.

Scs 21: ≤ (N), James H. Carruth, Charles E. Clark, E. L. Evans, James W. Lea, R. L. Wilson

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 20: More On The Coproduct. Errata And Addenda, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Letter Dated October 13, 1976 To Jimmie D. Lawson, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Accompanied by October 5, 1976 memo by Gerhard Gierz and Klaus Keimel.

An Error In The Copower Considerations, Gerhard Gierz, Klaus Keimel

Seminar on Continuity in Semilattices

Accompanies October 13, 1976 letter from Karl Heinrich Hofmann to Jimmie D. Lawson.

Scs 19: Several Remarks, Klaus Keimel, Michael Mislove

Seminar on Continuity in Semilattices

Contents:

1. The closed subsemilattices of a continuous lattice form a continuous lattice
2. When do the prime elements of a distributive lattice form a closed subset
3. Remarks on lower semicontinuous function spaces
4. Remarks on the continuity of the congruence lattice of the continuous lattice

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 18: Continuous Lattices And Universal Algebra, Alan Day

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

Scs 17: The Space Of Lower Semicontinuous Functions Into A Cl-Object, Applications (Part I): Copowers In Cl, Karl Heinrich Hofmann

Seminar on Continuity in Semilattices

Correction to scan at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html

The Use Of Prior Observations In Constructing Prediction Intervals For The Normal Distribution, Charles B. Davis

Mathematics & Statistics ETDs

A prediction interval procedure uses information contained in a sample together with other relevant information to produce an interval which will contain the next observation to be taken from the population with confidence no less than a pre-determined /J. One prediction inter­val procedure renders another "inadmissible" at the fJ level if (1) both procedures maintain the B confidence level and (2) the former produces intervals which are at least as "short" as, and sometimes "shorter" than, those produced by the latter; "short" is defined in a natural fashion in terms of expected length or expected upper (lower) limit. as is …

Mathematical Modeling In Medicine, Jerome Eisenfeld

Mathematics Technical Papers - Archive

Although the involvement of mathematics in medicine is still relatively recent, the discipline has become attractive to the mathematics community, and in fact, medically oriented articles presently appear in several mathematics journals. We call the reader's attention to the following journals: Bulletin of Mathematical Biology (continues The Bulletin of Mathematical Biophysics), Biomathematics (also called Revue de Bio-Mathematique), SIAM Journal in Applied Mathematics (a new series devoted to biomathematics will appear shortly), Math Biosciences, Biomedical Engineering, IEEE Transactions in Biomedical Engineering, Journal of Biomechanics, Biological Cybernetics, Computers in Biology and Medicine, Journal of Theoretical Biology, and Biometrics. Each year there are …

Scs 16: The Random Unit Interval (Another Example Of A Cl-Object), Karl Heinrich Hofmann, John R. Liukkonen

Seminar on Continuity in Semilattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html