Physical Sciences and Mathematics Commons^™

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 …

The Spinor Representation Of Minimal Surfaces, Rob Kusner, Nick Schmitt

Mathematics and Statistics Department Faculty Publication Series

The spinor representation is developed and used to investigate minimal surfaces in R^3 with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of minimal tori and Klein bottles are given. These surfaces compactify in S^3 to yield surfaces critical for the M¨obius invariant squared mean curvature functional W. On the other hand, all Wcritical spheres and real projective planes arise this way. Thus we determine at the same time the moduli spaces of W-critical spheres and real projective planes via the spinor representation.

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

Mathematics

No abstract provided.

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.

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.

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 …

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.

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 …

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.

Tilings In Art And Science, James E, Hall

Humanistic Mathematics Network Journal

No abstract provided.

Mathematizing, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics As An Aesthetic Discipline, J. D. Phillips

Humanistic Mathematics Network Journal

No abstract provided.

A University Mathematician's View Of What's Wrong With University Mathematics Education, Reuben Hersh

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.

The Most Humanistic Mathematician: Florentin Smarandache, Joanne S. Growney

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.

Poem In Arithmetic Space, Larry Seagull

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.

The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

We consider the one-dimensional catalytic branching process intro­duced by Dawson and Fleischmann, which is a modification of the super­ Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example …

A Zeta Function For Flows With Positive Templates, Michael C. Sullivan

Articles and Preprints

A zeta function for a map f : M → M is a device for counting periodic orbits. For a topological flow however, there is not a clear meaning to the period of a closed orbit. We circumvent this for flows which have positive templates by counting the “twists” in the stable manifolds of the periodic orbits.

A Note On Carnot Geodesics In Nilpotent Lie Groups, Christophe Golé, Ron Karidi

Mathematics Sciences: Faculty Publications

We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct a group, with a left invariant bracket-generating distribution, for which some Carnot geodecics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves, which we derive (for any Lie group) explicitly in terms of the structure constants. © 1995 Plenum Publishing Corporation.

Connectionist Models For Certain Tasks Related To Object Recognition., Jayanta Basak Dr.

Doctoral Theses

Recognition of objects in an image, according to Suetens et al. [1), relers to the task of finding and labeling parts of a two-dimensional image of a scene that correspond to the real objects in the scene. Object recognition is necessary in a variety of domains like robot navigation, aerial imagery analysis, industrial inspection and so on. Normally, different strategies for object recognition (1-(5] involve establishing some model for each object, i.e., some general description of each object, and then labeling different parts of the scene according to the knowledge about the models.Object models can have two-dimensional (2D) or three-climensional …

A Nonexistence Result For Abelian Menon Difference Sets Using Perfect Binary Arrays, K. T. Arasu, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A Menon difference set has the parameters (4N², 2N²-N, N²-N). In the abelian case it is equivalent to a perfect binary array, which is a multi-dimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. Suppose that the abelian group H×K×Z_p^α contains a Menon difference set, where p is an odd prime, |K|=p^α, and p^j≡−1 (mod exp (H)) for some j. Using the viewpoint of perfect binary arrays we prove that K must be cyclic. A …