Mathematics Commons^™

Resolution Of Local Inconsistency In Identification, Douglas Ray Anderson, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper reports an algorithm for the resolution of local inconsistency in information-theoretic identification. This problem was first pointed out by Klir as an important research area in reconstructability analysis. Local inconsistency commonly arises when an attempt is made to integrate multiple data sources, i.e., contingency tables, which have differing common margins. For example, if one ha)s an AB table and a BC table, the B margins obtained from the two tables may disagree. If the disagreement can be assigned to sampling error, then one can arrive at a compromise B margin, adjust the original AB and BC tables to …

Symmetrically Continuous Function Which Is Not Countably Continuous, Krzysztof Ciesielski

Faculty & Staff Scholarship

We construct a symmetrically continuous function f : R → R such that for some X ⊂ R of cardinality continuum f|X is of Sierpi´nskiZygmund type. In particular such an f is not countably continuous. This gives an answer to a question of Lee Larson.

Characterizing Derivatives By Preimages Of Sets, Krzysztof Ciesielski

Faculty & Staff Scholarship

In this note we will show that many classes F of real functions f : R → R can be characterized by preimages of sets in a sense that there exist families A and D of subsets of R such that F = C(D, A), where C(D, A) = {f ∈ R R : f −1 (A) ∈ D for every A ∈ A}. In particular, we will show that there exists a Bernstein B ⊂ R such that the family ∆ of all derivatives can be represented as ∆ = C(D, A), where A = S c∈R {(−∞, c),(c, …

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.

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 …

About Some Normal Subgroups Of Hecke Groups, İsmail Naci Cangül

Turkish Journal of Mathematics

In this work we study the suucture of some special normal subgroups of Hecke groups. Particwarly those of genus O and 1 are studied by means of the regwar map theory which has been a growing subject in recent years. As a nice application, we calcwate the total number of genus 1 normal subgroups for a given index.

Nv-P-Groups With Nilpotent Centralizers, Ali Osman Asar, Aynur Yalincaklioğlu

Turkish Journal of Mathematics

In this work a sufficient condition is given for an NC-p-group to have an epimorphic image which is an NF-p-group.

An Application Of Monodromy Groupoid, Osman Mucuk

Turkish Journal of Mathematics

The monodromy groupoid was first inlioduced by Pradines in [7] and developed by Mucuk in [6] In this paper we give an application of the monodromy groupoid.

Locally Topological Groupoids, Osman Mucuk

Turkish Journal of Mathematics

The notion of Iocally topological groupoid was introduced by Aof and Brown in [2]. On the other hand in [6] by Mackenzie a topological groupoid MG, called monodromy groupoid, is constructed. In this paper we prove that this groupoid MG gives a Iocally topological groupoid.

The Spectra And Fine Spectra For P-Cesáro Operators, Cafer Coşkun

Turkish Journal of Mathematics

In [6], Rhaly computed the spectrum of p-Cesaro operator on the Hilbert space l_2 = {x = (x_k): \Sigma_k IX_kl^2 < infinite}. In the present paper, we study the spectrum and fine spectrum for p-Cesáro operators acting on C_o, the space of null sequences.

Painlevé Analysis And Infinite Lie Symmetries Of The Complex Modified Korteweg-De Vries-Ii Equation, Abulgassim Ali Muhammad, Mehmet Can

Turkish Journal of Mathematics

The Painleve analysis developed by Weiss et al. [9] for nonlinear partial differential equations is applied to the CMKdV-II equation. It has been shown that this equation passes the Painleve test. By specializing the arbitrary functions that appear in the phi series expansions found in the test, one obtains a system of partial differential equations for the formally arbitrary data. For specific systems, and conjectured in general, these equations are integrable. The form of the resulting reduction enables the identification of integrable reductions of the original systems. Assuming u_i = \upsilon_i = 0, i >= 2 we obtain conditions to …

Augmented Graded Rings, Mashhoor Refai

Turkish Journal of Mathematics

In this paper we study the augmented graded rings and give the ralationship between these rings and stronger properties of graded rings.

On The Theory Of A Certain Class Of Quadratic Pencils Of Matrices And Its Applications, G.Sh. Guseinov, G. Oturanç

Turkish Journal of Mathematics

This paper is devoted to the study of the properties of eigenvalues and eigenvectors of quadratic pencil \lambda^2C - \lambdaR - J , where C is a positive diagonal matrix, R is an arbitrary real diagonal matrix, J is a ,, tridiagonal" real symmetric and positive matrix. The obtained results are then used to solve the corresponding system of differential equations with boundary and initial conditions. Kev Words: Quadratic pencijs, eigenvalues, eigenvectors.

Near Ultrafilters And Luc-Compactification Of Real Numbers, Mahmut Koçak

Turkish Journal of Mathematics

In this work we will investigate some of the topological properties of the Luc compactification of real numbers R in terms of the concept of near ultrafilters.

On The Solution Of The E.P.D. Equation Using Finite Integral Transformations, Neşe Dernek

Turkish Journal of Mathematics

In this paper, a solution is given for the following initial boundary value problem: \Delta=u_{tt}+k/t+u_t+g(x, t) (t>0) u(0, t)=u(a, t)=0 u(x, 0)=f(x), u_t(x, 0)=0 where x, a \epsilon R^n, t is the time variable, k < 1, k ? -1, -2, -3, . . . is a real parameter, \Delta is the n dimensional Laplace operator, f and g real analytic functions. The equation in this problem is known as the nonhomogeneous Euler-Poisson-Darboux (E.P.D.) Equation. The solution is obtained using finite integral transformation technique and is the sum of two uniformly and absolutely convergent power series.

Locally Nilpotent P-Groups Whose Proper Subgroups Are Nc-Groups, A.O. Asar, A. Yalincaklioğlu

Turkish Journal of Mathematics

Let G be a locally nilpotent p-group in which every proper subgroup is an NC-group. It is shown that G is itself an NC-group if either (i) the normal closure of every finite subgroup of G is a Chernikov extension of a CC-group or (ii) every proper normal subgroup of G is the union of an ascending chain of normal CCsubgroups.

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.

Darboux Like Functions That Are Characterizable By Images, Preimages And Associated Sets, Krzysztof Ciesielski

Faculty & Staff Scholarship

For arbitrary families A and B of subsets of R let C(A,B)= {f| f: R-->R and the image f[A] is in B for every A in A} and C^-1 (A,B)= {f| f: R-->R and the inverse image f^-1(B) is in A for every B in B}. A family F of real functions is characterizable by images (preimages) of sets if F=C(A,B) (F=C^-1(A,B), respectively) for some families A and B. …

Particle Modeling Of Liquid Drop Formation On A Solid Surface In 3-D, Mark Korlie

Department of Mathematics Faculty Scholarship and Creative Works

Using a molecular aggregate approach and classical Newtonian dynamics, we show how to simulate a liquid drop formation on a horizontal solid surface in three-dimensional space. We use sets of quasi-molecular particles which interact in accordance with classical molecular-type formulas. For application, the liquid is taken to be water while the solid surface is taken to be graphite. The resulting dynamical equations for the particles are large systems of second-order, nonlinear, ordinary differential equations which must be solved by a numerical method. Computer simulations of the results and related contact angle calculations are presented and discussed. The results are in …

Particle Simulation Of Carbon Dioxide Bubbles In Water, Mark Korlie, D. Greenspan

Department of Mathematics Faculty Scholarship and Creative Works

Using a molecular aggregate approach and classical molecular dynamics type formulas, a method that can be used to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, the motion of carbon dioxide bubbles in water. The resulting equations are solved numerically. The rise of the bubbles and the motion of the water near the bubbles are described.

Irreducible K-To-1 Maps Onto Grids, Susan M. Parker

Honors Theses

In this paper we explore the existence of exactly k-to-1 continuous functions between graphs, and more specifically 2-to-1 continuous function between graphs that are irreducibly 2-to-1, meaning that no restriction of the function to a subgraph is 2-to-l. We show how to construct such functions in some general cases, and then more specifically onto rectangular grids. We have in mind an application to distributed networks and signal verification.

Steiner Trees Over Generalized Checkerboards, Meta M. Voelker '97

Honors Projects

To minimize the length of a planar network, we can build a Steiner minimal tree that is, a tree consisting of the original network points, as well as additional, strategically-placed (Steiner) points. Chung, Gardner and Graham [2] investigated building Steiner trees over grids of unit squares. We generalize their ideas to grids of rhombuses, and show that two near-optimal Steiner trees exist for each grid, one built from Steiner trees over rhombuses and one built from Steiner trees over isosceles triangles. Further, we conjecture that for grids with an odd number of layers, only the small angle of the rhombus …

Scattering From Stellar Acoustic-Gravity Potentials: Ii. Phase Shifts Via The First Born Approximation, J. A. Adam, I. Mckaig

Mathematics & Statistics Faculty Publications

Using the first Born approximation, properties of the scattering phase shift are investigated for waves that are scattered by a schematic representation of a large-scale “stellar potential,” i.e., one for which the star itself is viewed as the potential inducing a phase shift in an incoming wave. In particular, the phase shift properties are examined as functions of the relative wavenumber (α) and the azimuthal wavenumber (l), high l-values being of interest in helioseismology.

Eigenvalue And Eigenvector Determination For Damped Gyroscopic Systems, D. P. Malone, Don L. Cronin, Timothy W. Randolph

Mechanical and Aerospace Engineering Faculty Research & Creative Works

No abstract provided.

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 …

Convolution And Fourier-Feynman Transforms, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper, for a class of funtionals on Wiener space of the form F(x) = exp{∫^T₀ f(t, x(t)) dt}, we show that the Fourier-Feynman transform of the convolution product is a product of Fourier-Feynman transforms. This allows us to compute the transform of the convolution product without computing the convolution product.

Collected Papers, Vol. 2, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

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 …

Hartogs' Phenomenon For Polyregular Functions And Projective Dimension Of Related Modules Over A Polynomial Ring, W. W. Adams, P. Loustaunau, V. P. Palamadov, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we prove that the projective dimension of Mn = R^4/(An) is 2n -1, where R is the ring of polynomials in 4n variables with complex coefficients and (An) is the module generated by the columns of a 4x4n matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of n quaternionic variables. As a corollary we show that the sheaf R of regular functions has flabby dimension 2n -1, and we prove a cohomology vanishing theorem for open sets in the space Hn of quaternions. We …

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.