Digital Commons Network^™

On A Differential Sequence In Geometry, E. Ortaçgi̇l

Turkish Journal of Mathematics

We construct an exact differential sequence which indicates certain relations between curvature, local flatness, torsion and simplicity of higher order connections. Our formulas are expressed explicity in terms of the Christoffel symbols of dual \varepsilon-connections.

On The \Ell_{P} Norms Of Almost Cauchy-Toeplitz Matrices, D. Bozkurt

Turkish Journal of Mathematics

In this study, we have given the definition of almost Cauchy-Toeplitz matrix. i.e. its elements are t_{ij}= a(i=j) and t_{ij}=1/(i-j)\, (i\neq j) such that a is a real number. We have found a lower and upper bounds for the \ell_{p} norm of this matrix. Furthermore, we have done the proof of the conjecture that were given by myself for the spectral norm of this matrix.

On (\Sigma,\Tau) Derivations With Module Values, M. Soytürk

Turkish Journal of Mathematics

Let R be a ring, X\neq (0) an R-bi-module, d: R\ra X a(\sigma,\tau)- derivation with module value such that d\sigma=\sigma d, d\tau=\tau d and U\neq (0) an ideal of R. Furthermore the following properties are also satisfied. \begin{eqnarray*} && \mbox{For }x\in X, a\in R\quad x Ra=0 \mbox{ implies } x=0 \mbox{ or } a=0 \ldots\ldots (G_{1})\\ && \mbox{For }a\in R, x\in X \quad a Rx=0 \mbox{ implies } a=0 \mbox{ or } x=0 \ldots\ldots (G_{2}) \end{eqnarray*} \noindent In this paper we have proved the following results; (1) If (G_{1}) (or (G_{2})) is satisfied and for a \in R, d(U) a=0 …

On Noninvertible Mappings Of The Plane: Eruptions, Lora Billings, James H. Curry

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we are concerned with the dynamics of noninvertible transformations of the plane. Three examples are explored and possibly a new bifurcation, or ‘‘eruption,’’ is described. A fundamental role is played by the interactions of fixed points and singular curves. Other critical elements in the phase space include periodic points and an invariant line. The dynamics along the invariant line, in two of the examples, reduces to the one-dimensional Newton’s method which is conjugate to a degree two rational map. We also determine, computationally, the characteristic exponents for all of the systems. An unexpected coincidence is that the …

Homological Topics In The Representation Theory Of Restricted Lie Algebras, Jorg Feldvoss

University Faculty and Staff Publications

We present some recent developments in the application of homological methods to the representation theory of finite dimensional restricted Lie algebras.

Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre

Mathematics and Statistics Faculty Publications

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity.

An Analysis Of Shewhart Quality Control Charts To Monitor Both The Mean And Variability, Keith Jacob Barrs

College of Graduate Studies: Theses & Dissertations (1964–2006)

When monitoring the mean of a continuous quality measure it is often recommended a separate chart be used to monitor the variability. These charts are traditionally designed separately. This project considers them together as a combined charting procedure and gives recommendations for their design. This is based on an average run length (ARL) analysis. The run length distribution is determined using two methods both based on a Markov chain approach.

Macroelements And Orthogonal Multiresolutional Analysis, Jonathan M. Corbett '96

Honors Projects

Orthogonal multiresolutional wavelet analysis in a two dimension setting furnishes a basis for wavelet analysis. Bernstein-Bezier polynomials over simplexes provide elegant expressions of the necessary and sufficient conditions for a shift invariant space generating an orthogonal multiresolution analysis.

Cardinal Invariants Concerning Extendable And Peripherally Continuous Functions, Krzysztof Ciesielski

Faculty & Staff Scholarship

Let F be a family of real functions, F ⊆ R R . In the paper we will examine the following question. For which families F ⊆ R R does there exist g : R → R such that f + g ∈ F for all f ∈ F? More precisely, we will study a cardinal function A(F) defined as the smallest cardinality of a family F ⊆ R R for which there is no such g. We will prove that A(Ext) = A(PR) = c + and A(PC) = 2c , where Ext, PR and PC stand for the …

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

Mathematics

If one reads a typical article on A,B,C,D systems in the control transactions, one finds that most of the algebra involved is non commutative rather than commutative. Thus, for symbolic computing to have much impact on linear systems research, one needs a program which will do non-commuting operations. Mathematica, Macsyma and Maple do not. We have a package, NCAlgebra, which runs under Mathematica which does the basic operations, block matrix manipulations and other things. The package might be seen as a competitor to a yellow pad. Like Mathematica the emphasis is on interaction with the program and flexibility.

The issue …

Complex Dynamics And Multistability In A Damped Harmonic Oscillator With Delayed Negative Feedback, Sue Ann Campbell, Jacques Bélair, Toru Ohira, John Milton

WM Keck Science Faculty Papers

A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems.

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

Mathematics

No abstract provided.

Computer Experiments For Molecular Motions And Chemical Bonding, Donald Greenspan

Mathematics Technical Papers - Archive

It is shown how to simulate first the ground state molecule H. The correct bond length, period, and electron cloud result. The method is then extended to ground state H2 and it is shown that only a new model of the chemical bond can yield the correct bond length, period, and electron cloud.

Secure Trapdoor Hash Functions Based On Public-Key Cryptosystems, Gary R. Greenfield, Sarah Agnes Spence

Department of Math & Statistics Technical Report Series

In this paper we systematically consider examples representative of the various families of public-key cryptosystems to see if it would be possible to incorporate them into trapdoor hash functions, and we attempt to evaluate the resulting strengths and weaknesses of the functions we are able to construct. We are motivated by the following question:

Question 1.2 How likely is it that the discoverer of a heretofore unknown public-key cryptosystem could subvert it for use in a plausible secure trapdoor hash algorithm?

In subsequent sections, our investigations will lead to a variety of constructions and bring to light the non-adaptability of …

Genetic Epidemilogical Analysis Of Complex Disorders., Swapan Nath Dr.

Doctoral Theses

The present study can be broadly classified in the area of genetic epidemiology, which is conventionally defined as a science that deals with the aetiology, distribution, and control of disease in groups of relatives and with inherited causes of disease in populations (Morton 1982, 1993). One of the major goals of genetic epidemiology is the study of the nature and extent of clustering of a disease in families and in defined ethnic groups. The study of a disorder within the genetic epidemiological framework is performed by testing :(1) whether the disorder clusters in families?(2) whether observed familiarity is caused by …

On Texture Image Analysis Using Fractal Geometry Based Features., Nirupam Sarkar Dr.

Doctoral Theses

Visual textureTexture is a property to characterize a region of a scene. A set of natural texture images is shown in Fig. 1.1. A specific texture may be generated due to certain organization of several objects in a region, or due to the reflectance pattern caused by color variation or unevenness of an object surface. Since texture provides a lot of information of a region, texture analysis and synthesis are important components of digital image processing.It is difficult to provide a formal definition of texture although we perceive and recognize texture rather easily. According to Sklansky [152) "A region in …

Sabbatical Leave Proposal, Brenda Marshall

Sabbaticals

I'd like to learn "Mathematica." "Mathematica" is probably the most~ powerful mathematics software available. It was developed and continues to be upgraded at Wolfram Research in Champaign. The U. of I. as well as many colleges and universities across the nation teach some sections of their calculus courses with "Mathematica." Also, several of the high schools in our district have students enrolled in "Calculus with Mathematica" through a distance learning program at the U. of I.

Rectangular Groups, Nick Fiala, Crystal Hanscom, Patrick Keenan, Tung Tran

Mathematical Sciences Technical Reports (MSTR)

We provide an overview of results and conjectures relating to rectangular groups.

Symmetries Of Accola-Maclachlan And Kulkarni Surfaces, Sean A. Broughton, E Bujalance, A F. Costa, J M. Gamboa, G Gromadzki

Mathematical Sciences Technical Reports (MSTR)

For all g greater than or equal to 2, there is a Riemann surface of genus g whose automorphism group has order 8g+8, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and MacLachlan established the existence of such surfaces; we shall call them Accola-MacLachlan surfaces. In this paper we determine the symmetries of surfaces with genus g = 3(mod 4), computing the number of ovals and the separability of the symmetries. The results are then applied to classify the real forms of these complex algebraic curves.

A Statistical Derivation Of The Significant-Digit Law, Theodore P. Hill

Research Scholars in Residence

The history, empirical evidence and classical explanations of the significant-digit (or Benford's) law are reviewed, followed by a summary of recent invariant-measure characterizations. Then a new statistical derivation of the law in the form of a CLT-like theorem for significant digits is presented. If distributions are selected at random (in any "unbiased" way) and random samples are then taken from each of these distributions, the significant digits of the combines sample will converge to the logarithmic (Benford) distribution. This helps explain and predict the appearance of the significant0digit phenomenon in many different empirical contexts and helps justify its recent application …

Neuro-Fuzzy Models For Classification And Rule Generation., Sushmita Mitra Dr.

Doctoral Theses

Machine recognition [1, 2] of patterns can be viewed as a two-fold task, consisting of learning the invariant and common properties of a set of samples characterizing a class, and of deciding a new sample as a possible member of the class by noting that it has properties common to those of the set of samples. In other words, pattern recognition by computers can be described as a transformation from the measurenment space M to the feature space F and finally to the decision space D (1), i.e., M ⟶F⟶D.Here, the mapping 6 : F⟶D is the decision function and …

Tilings In Art And Science, James E, Hall

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics As An Aesthetic Discipline, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

"Modern Mathematics" At Sonoma State University, C. E. Falbo

Humanistic Mathematics Network Journal

No abstract provided.

Letter Division, Paul J. Tobias

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Introductory Algebra: A Just In Time Approach, By Alice Kaseberg, Gayle Smith

Humanistic Mathematics Network Journal

No abstract provided.

Haiku, Frances Rosamond

Humanistic Mathematics Network Journal

No abstract provided.

Attitudes Of Students To Independent Learning, S. Kenneth Houston

Humanistic Mathematics Network Journal

No abstract provided.

From The Editor, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Voices From The Reform Movement, Allyn Jackson

Humanistic Mathematics Network Journal

No abstract provided.