Physical Sciences and Mathematics Commons^™

Set Theoretic Real Analysis, Krzysztof Ciesielski

Faculty & Staff Scholarship

This article is a survey of the recent results that concern real functions (from Rⁿ into R) and whose solutions or statements involve the use of set theory. The choice of the topics follows the author's personal interest in the subject, and there are probably some important results in this area that did not make to this survey. Most of the results presented here are left without the proofs.

Compositions Of Two Additive Almost Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

In the paper we prove that an additive Darboux function f : R → R can be expressed as a composition of two additive almost continuous (connectivity) functions if and only if either f is almost continuous (connectivity) function or dim(ker(f)) 6= 1. We also show that for every cardinal number λ ≤ 2 ω there exists an additive almost continuous functions with dim(ker(f)) = λ. A question whether every Darboux function f : R → R can be expressed as a composition of two almost continuous functions (see [?] or [?]) remains open.

Gorenstein Witt Rings Ii, Robert W. Fitzgerald

Articles and Preprints

The abstract Witt rings which are Gorenstein have been classified when the dimension is one and the classification problem for those of dimension zero has been reduced to the case of socle degree three. Here we classify the Gorenstein Witt rings of fields with dimension zero and socle degree three. They are of elementary type.

Cyclic Permutations In Doubly-Transitive Groups, John P. Mcsorley

Articles and Preprints

Let Ω be a finite set of size n. A cyclic permutation on Ω is a permutation whose cycle decomposition is one cycle of length n. This paper classifies all finite doubly-transitive permutation groups which contain a cyclic permutation. The classification appears in Table 1.

We use (G, Ω) for a finite doubly-transitive permutation group G acting on a finite set Ω. For other notation and definitions see the self-contained article Cameron [1].

An Invariance Property Of Common Statistical Tests, N. Rao Chaganty, A. K. Vaish

Mathematics & Statistics Faculty Publications

Let A be a symmetric matrix and B be a nonnegative definite (nnd) matrix. We obtain a characterization of the class of nnd solutions Σ for the matrix equation AΣA = B. We then use the characterization to obtain all possible covariance structures under which the distributions of many common test statistics remain invariant, that is, the distributions remain the same except for a scale factor. Applications include a complete characterization of covariance structures such that the chisquaredness and independence of quadratic forms in ANOVA problems is preserved. The basic matrix theoretic theorem itself is useful in other characterizing …

A Dual Approach To Constrained Interpolation From A Convex Subset Of Hilbert Space, Frank Deutsch, Wu Li, Joseph D. Ward

Mathematics & Statistics Faculty Publications

Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx∈Xfrom the setK≔C∩A−1(b),whereCis a closed convex subset ofX,Ais a bounded linearoperator fromXinto a finite-dimensional Hilbert spaceY, andb∈Y. The main point of this paper is to show thatPK(x)isidenticaltoPC(x+A*y …

On The Dynamic Behaviour Of A Thermoviscoelastic Body In Frictional Contact With A Rigid Obstacle, Kenneth Kuttler, K. T. Andrews, M. Shillor

Faculty Publications

We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive relation is assumed to be of Kelvin-Voigt type and the frictional heat generation on the contact surface is taken into account. In this setting we establish the existence of a solution to a weak version of the energy-elasticity system which consists of a parabolic equation coupled …

Fuzzy Logic: An Analysis Of Logical Connectives And Their Characterizations, John F. Hamman

Dissertations and Theses @ UNI

The focus of this thesis is to determine exactly which functions serve as appropriate fuzzy negation, conjunction and disjunction functions. To this end, the first chapter serves as motivation for why fuzzy logic is needed, and includes an original demonstration of the inadequacy of many valued logics to resolve the sorites paradox. Chapter 2 serves as an introduction to fuzzy sets and logic. The canonical fuzzy set of tall men is examined as a motivating example, and the chapter concludes with a discussion of membership functions.

Four desirable conditions of the negation function are given in Chapter 3, but it …

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

Review Of Mathematica 3.0, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Constraint Satisfaction Methods For Generating Valid Cuts, John Hooker

John Hooker

No abstract provided.

Essential Laminations In Graph Manifolds, Ramin Naimi, Mark Brittenham, Rachel Roberts

Ramin Naimi

No abstract provided.

Alte Und Neue Ungeloste Probleme In Der Zahlentheorie Und Geoetrie Der Ebene (Online), Stan Wagon

Stan Wagon, Retired

No abstract provided.

Mathematica In Action., Stan Wagon

Stan Wagon, Retired

No abstract provided.

A Challenge Form Leningrad, Stan Wagon

Stan Wagon, Retired

No abstract provided.

What Is A Prime Number?, Stan Wagon, D. Schattschneider, R. Mabry

Stan Wagon, Retired

No abstract provided.

Constructing Essential Laminations In 2-Bridge Knot Surgered 3-Manifolds, Ramin Naimi

Ramin Naimi

A nontrivial knot that can be drawn with only two relative maxima in the vertical direction is called a 2-bridge knot, and one that can be drawn on a torus is called a torus knot. Loosely speaking, a lamination in a manifold M is a foliation of M, except that it can have a nonempty open complement in M, and very loosely speaking, the lamination is essential if each leaf of it L is incompressible, i.e. inclusion of L into M induces an injective homomorphism from π1(L) into π1(M). Our main result is: Theorem 2. Every 3-manifold obtained by surgery …

An Alternative Dunford-Pettis Property, Walden Freedman

Walden Freedman

Numerical Solution Of The Inverse Eigenvalue Problem For Real Symmetric Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

A Nonlinear Deformed Su(2) Algebra With A Two-Color Quasitriangular Hopf Structure, Andrei Ludu

Andrei Ludu

No abstract provided.

Mathematical Instantons With Maximal Order Jumping Lines, Prabhakar Rao

Prabhakar Rao

Some Problems Of Continuum Percolation., Anish Sarkar Dr.

Doctoral Theses

The model of continuum percolation can be described as follows. We start with a homogeneous Poisson point process X. At each point of X we centre a ball with a random radius such that the radii corresponding to different points are independent of each other and also independent of the Poisson process X. In this way, the space is divided into two regiorns, the covered region or the occupied region consisting of the region which is covered by at least one ball, and the uncovered region or the vacant region which is complement of the covered region. In this dissertation …

Computer Assistance In Discovering Formulas And Theorems In System Engineering Ii, J. W. Helton, Mark Stankus, Kurt Schneider

Mathematics

[HSWcdc94] focused on procedures for simplifying complicated expressions automatically. [HScdc95] turned to the adventurous pursuit of developing a highly computer assisted method for “discovering” certain types of formulas and theorems.

It is often the case that some variables in the formulation of a problem are not the natural “coordinates” for solution of the problem. Gröbner Basis Algorithms, which lie at the core of our method, are very good at eliminating unknowns, but have no way of finding good changes of variables. This paper gives a way of incorporating changes of variables into our method.

As an example, we “discover” the …

M-Isometric Transformations Of Hilbert Space, Iii, Jim Alger, Mark Stankus

Mathematics

No abstract provided.

A Note On Distributions Of True Versus Fabricated Data, Theodore P. Hill

Research Scholars in Residence

New empirical evidence and statistical derivations of Benford’s Law have led to successful goodness-of fit tests to detect fraud in accounting data. Several recent case studies support the hypothesis that fabricated data does not conform to expected true digital frequencies.

A Stronger Triangle Inequality, Herb Bailey

Mathematical Sciences Technical Reports (MSTR)

The triangle inequality is basic for many results in real and complex analysis. The geometric form states that the sum of any two sides of a triangle is greater than the third. This was included as Proposition XX in the first book of Euclid's Elements. Many geometric triangle inequalities involving sides, angles, altitudes, inscribed circles and circumscribed circles have been found. Hundreds of these inequalities are summarized in [l] and [2]. A nice geometric proof of the triangle inequality is given in [3].

Gender Discourse In Small Learning Groups Of College-Level Developmental Mathematics Students, Allen W. Emerson

Dissertations

This study was motivated by the question as to whether women’s and men’s membership in different gender communicative cultures gives rise to gender differentiated ways of talking that are implicated in the failure of a mixed-sex group to achieve good mathematical discourse when women and men sit face to face engaged in various mathematical tasks. If so, in what ways and to what effect is gender discourse implicated in the failure of a mixed-sex group to achieve good mathematical discourse?

Models of feminine and masculine discourse styles based on the theory of communicative cultural difference, as well as a model …

From The Editor, Issue 14, 1996, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

What's All The Fuss About?, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

The Triex: Explore, Extract, Explain, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.