Digital Commons Network^™

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.

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

Department of Mathematics Facuty 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 …

Data Compression Based On The Cubic B-Spline Wavelet With Uniform Two-Scale Relation, S. K. Yang, C. H. Cooke

Mathematics & Statistics Faculty Publications

The aim of this paper is to investigate the potential artificial compression which can be achieved using an interval multiresolution analysis based on a semiorthogonal cubic B-spline wavelet. The Chui-Quak [1] spline multiresolution analysis for the finite interval has been modified [2] so as to be characterized by natural spline projection and uniform two-scale relation. Strengths and weaknesses of the semiorthogonal wavelet as regards artificial compression and data smoothing by the method of thresholding wavelet coefficients are indicated.

A Multiple-Precision Division Algorithm, David M. Smith

Mathematics Faculty Works

The classical algorithm for multiple-precision division normalizes digits during each step and sometimes makes correction steps when the initial guess for the quotient digit turns out to be wrong. A method is presented that runs faster by skipping most of the intermediate normalization and recovers from wrong guesses without separate correction steps.

On Affine Selection And Separation Of Vector Valued Functions, S. Alpay, Z. Ercan

Turkish Journal of Mathematics

Let K be a Choquet simplex, E a Fr\'{e}chet space and \Phi: K \ra 2^E a map such that \Phi(x) is closed and convex for each x \in K. A sufficient condition is given for \Phi to have a continuous affine selection.This is employed to prove a separation theorem for vector valued semicontinuous functions from a Choquet simplex into an ordered Fr\'{e}chet space.

On Functions That Are Trivial Cocycles For A Set Of Irrationals. Ii, Lawrence W. Baggett, Herbert A. Medina, Kathy D. Merrill

Mathematics Faculty Works

Two results are obtained about the topological size of the set of irrationals for which a given function is a trivial cocycle. An example of a continuous function which is a coboundary with non-L(1) cobounding function is constructed.

On Transitive And Fully Transitive Abelian P-Groups, D. Carroll, Brendan Goldsmith

Articles

It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.

Paracompact Subspaces In The Box Product Topology, Peter Nyikos, Leszek Piatkiwicz

Faculty Publications

No abstract provided.

Zeros Of Derivatives Of Dirichlet L-Functions, C. Yalçin Yildirim

Turkish Journal of Mathematics

In this paper diverse results on the location and number of zeros of derivatives of Dirichlet L-functions are proved.

Mathematical Rebuses, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Geometrical Modeling Of Material Aging, Alexander Chudnovsky, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

Material aging is understood as changes of material properties with time. The aging is usually observed as an improvement of some properties and a deterioration of others. For example an increase of rigidity and strength and reduction in toughness with time are commonly observed in engineering materials. In an attempt to model aging phenomena on a continuum (macroscopical) level one faces three major tasks. The first is to identify an adequate age parameter that represents, on a macroscopic scale, the micro and sub microscopical features, underlying the aging phenomena such as nucleation, growth and coalescence of microdefects, physico-chemical transformations etc. …

On Non-Holonomic Second-Order Connections With Applications To Continua With Microstructure, Marek Elźanowski, Serge Preston

Mathematics and Statistics Faculty Publications and Presentations

Motivated by the theory of uniform elastic structures we try to determine the conditions for the local flatness of locally integrable connections on non-holonomic frame bundles of order 2. Utilizing the results of Yuen as well as our results for the holonomic case, we show that the locally integrable non-holonomic 2-connection is locally flat if, and only if, its projection to the bundle of linear frames is symmetric and the so-called inhomogeneity tensor vanishes. In the last section of this short paper we show how these results can be interpreted in the framework of the theory of uniformity of simple …

Configuration Spaces And Imbedding Invariants, Raoul Bott

Turkish Journal of Mathematics

No abstract provided.

Contact Structures And Foliations On 3-Manifolds, Yakov M. Eliashberg, William P. Thurston

Turkish Journal of Mathematics

No abstract provided.

Lectures On Seiberg-Witten Invariants, Selman Akbulut

Turkish Journal of Mathematics

No abstract provided.

The Multi-Monopole Equations For K\"Ahler Surfaces, James A. Bryan, Richard Wentworth

Turkish Journal of Mathematics

The purpose of this paper is to introduce a natural generalization of the Seiberg-Witten equations having more than one Spinor field ("monopole") and to study the moduli space of solutions in the case of a K\"ahler surface. We find an explicit algebro-geometric construction of the moduli space. In the course of our construction, we prove an existence and uniqueness result for a generalization of the Kazdan-Warner equation.

The Minimal Genus Of An Embedded Surface Of Non-Negative Square In A Rational Surface, Daniel Ruberman

Turkish Journal of Mathematics

No abstract provided.

A Note On The Geography Of Symplectic Manifolds, Andras Stipsicz

Turkish Journal of Mathematics

No abstract provided.

Star Topological Groupoids, O. Mucuk

Turkish Journal of Mathematics

In [4] a construction on topological groups was given. In this paper we generalize this costruction to more general topological groupoids and have a similar structure on the topological groupodis.

Operations With The Periodic Decimal Expansions, H. Ardahan

Turkish Journal of Mathematics

In this paper, we prove the rules of direct addition and subtraction for the finite decimal expansions of fractions which are periodic. It has been shown that these rules are valid for the fractions which can be expanded as a periodic decimal with p figures in the period or have the mixed decimal part containing \nu non-periodic and p periodic figures. Also, it has been given a rule of multiplication for these periodic decimals by 10^{\nu}, \nu\in\Bbb N. Last of all, if a rational fraction has a period of length p, then it can be expressed by a decimal expansion, …

A Note On Intuitionistic Sets And Intuitionistic Points, D. Çoker

Turkish Journal of Mathematics

The purpose of this note is to define the so-called "intuitionistic sets" and "intuitionistic points", and obtain their fundamental properties.

Finite Dimensional Attractors For A Class Of Semilinear Wave Equations, A. Eden, V. Kalantarov

Turkish Journal of Mathematics

In this paper we give a self-contained survey of results related with the global attractors for a class of nonlinear wave equations with damping or viscosity terms. In particular, we prove the existence of a finite dimensional attractor and estimate its fractal dimension by imbedding it in an exponential attractor. Some results on global stability, existence of finite dimensional attractors were already partially discussed in Kalantarov [44] and in Eden et. al. [25], however we simplify the framework by introducing a unified approach to both the existence of attractors through \alpha-contractions and the construction of exponential attractors via some Lipschitzianity …

An Extension Of The Binomial Theorem With Application To Stability Theory, Z. Zahreddinea

Turkish Journal of Mathematics

We show how it is possible to put different stability types such as Routh-Hurwitz and Schur-Cohn on common grounds by establishing direct links between them. In the process, we obtain natural and elegant extensions of both Pascal's rule and the binomial theorem, which prove useful in establishing our main results. A M S subject classification: Primary 34D, Secondary 93D.

A Note On Gamma Rings, M. Sapanci, A. Nakajimaz

Turkish Journal of Mathematics

Let M be a \Gamma-ring and D a non-zero left derivation on M. We show that if there exists an element m in M such that D(m) is a right non-zero divisor, then M is commutative.

Fixed Points And Completeness, Z. Liu

Turkish Journal of Mathematics

We give five necessary and sufficient conditions for a metric space to be complete.

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 Spaces Of Generalized Dirichlet Series, M. Dragilev

Turkish Journal of Mathematics

It is considered the relationship between spaces L_f(\lambda,\sigma) and subspaces of the space A_1(\bar{A}_1) of analytic functions in the open (closed) unit disc, generated by systems F(\alpha_nz), n\in N, if they constitute a basis in their closure.

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

Legacy ETDs

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.

An Almost Periodic Function Of Several Variables With No Local Minimum, Gregory S. Spradlin

Publications

No abstract provided.

An Almost Periodic Function Of Several Variables With No Local Minimum, Gregory S. Spradlin

Gregory S. Spradlin