Physical Sciences and Mathematics Commons^™

On Intuitionistic Fuzzy Bi-Ideals Of Semigroups, Kyung Ho Kim, Jong Geol Lee

Turkish Journal of Mathematics

We consider the intuitionistic fuzzification of the concept of several ideals in a semigroup S, and investigate some properties of such ideals.

Constructing New K3 Surfaces, Selma Altinok

Turkish Journal of Mathematics

This paper is concerned with a method based on birational geometry and produces dozens of new examples in codimensions 3, 4, 5 etc. The method is called unprojection by Reid. Using this method we construct new examples of K3 surfaces of codimensions 3 and 4 in weighted projective spaces from smaller codimension K3 surfaces whose rings are much simpler. This leads to the existence of almost all candidates for codimension 3 K3 surfaces in the list.

On Jordan Generalized Higher Derivations In Rings, Wagner Cortes, Claus Haetinger

Turkish Journal of Mathematics

I. N. Herstein proved that any Jordan derivation on a prime ring of characteristic not 2 is a derivation. M. Breşar extended this result to semiprime rings, while M. Ferrero and C. Haetinger extended the result to Jordan higher derivations. Recently, M. Ashraf and N. Rehman considered the question of Herstein for a Jordan generalized derivation. This paper extends Ashraf's Theorem. We prove that if R is a 2-torsion-free ring which has a commutator right nonzero divisor, then every Jordan generalized higher derivation on R is a generalized higher derivation.

On Fuzzy Cosets Of Gamma Nearrings, Satyanarayana Bhavanari, Syam Prasad Kuncham

Turkish Journal of Mathematics

In this paper, we consider fuzzy notion of a \Gamma -near ring, introduce the notion of a fuzzy coset and obtained some related important fundamental isomorphism theorems.

On \Delta-I-Continuous Functions, Şazi̇ye Yüksel, A. Açikgöz, T. Noiri

Turkish Journal of Mathematics

In this paper, we introduce a new class of functions called \delta-I-continuous functions. We obtain several characterizations and some of their properties. Also, we investigate its relationship with other types of functions.

Spacelike Normal Curves In Minkowski Space E^3_1, Kazim İlarslan

Turkish Journal of Mathematics

In the Euclidean space E^3, it is well known that normal curves, i.e., curves with position vector always lying in their normal plane, are spherical curves [3]. Necessary and sufficient conditions for a curve to be a spherical curve in Euclidean 3-space are given in [10] and [11]. In this paper, we give some characterizations of spacelike normals curves with spacelike, timelike or null principal normal in the Minkowski 3-space E^3_1.

On The Nilpotency Class Of Lie Rings With Fixed-Point-Free Automorphisms, Pavel Shumyatsky

Turkish Journal of Mathematics

Let L be a solvable Lie ring with derived length s. Assume that L admits an automorphism \phi of prime order p\geq 11 such that C_L(\phi)=0. It is proved that the class of L is less than \frac{(p-2)^{s+1}}{(p-3)^2}.

Su(2) Representations Of The Groups Of Integer Tangles, Tangül Uygur

Turkish Journal of Mathematics

In this work we classify the irreducible SU(2) representations of \Pi_1(S^3\backslash k_n) where k_n is an integer n tangle and as a result we have proved the following theorem: Let n be an odd integer then \mathcal{R}^{\ast}(\Pi_1(S^3 \backslash k_n)) /SO(3) is the disjoint union of n open arcs where \mathcal{R}^{\ast}(\Pi _1(S^3 \backslash k_n)) is the space of irreducible representations.

Weighted Boundedness For A Rough Homogeneous Singular Integral, Hussain Al-Qassem

Turkish Journal of Mathematics

A weighted norm inequality for a homogeneous singular integral with a kernel belonging to a certain block space is proved. Also, some applications of this inequality are obtained. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.

A Multi-Server Markovian Queueing Model With Primary And Secondary Services, Valentina Klimenok, Srinivas R. Chakravarthy, Alexander Dudin

Industrial & Manufacturing Engineering Presentations And Conference Materials

We study a multi-server queueing model in which the arrivals occur according to a Markovian arrival process. An arriving customer either (a) is lost due to all main servers being busy; or (b) enters into service with one of the main servers and leaves the system (as a satisfied primary customer); (c) enters into a service with one of the main servers, gets service in self-service mode, and is impatient to get a final service with one of the main servers, may leave the system (as a dissatisfied secondary customer); or (d) enters into service with one of the main …

Multidimensional Kolmogorov-Petrovsky Test For The Boundary Regularity And Irregularity Of Solutions To The Heat Equation, Ugur G. Abdulla

Mathematics and System Engineering Faculty Publications

This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of ( ) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard -dimensional Brownian motion.

Semantic Notation And Retrieval In Art And Architecture Image Collections, Boyan N. Dimitrov

Mathematics Publications

In this paper we analyze various methods used for semantic annotation and search in a collection of art and architecture images. We discuss the Art and Architecture Thesaurus, WordNet, ULAN and Iconclass ontology. Systems for searching and retrieval art and architecture image collections are presented. We explore if the MPEG 7 descriptors are useful for art and architecture image annotations. For illustrations we use images from Antoni Gaudi architecture and Claude Monet paintings.

Global Stability Of Periodic Orbits Of Non-Autonomous Difference Equations And Population Biology, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of period r is GAS, then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and …

A Tutorial On Radiation Oncology And Optimization, Allen G. Holder, Bill Salter

Mathematics Faculty Research

Designing radiotherapy treatments is a complicated and important task that affects patient care, and modern delivery systems enable a physician more flexibility than can be considered. Consequently, treatment design is increasingly automated by techniques of optimization, and many of the advances in the design process are accomplished by a collaboration among medical physicists, radiation oncologists, and experts in optimization. This tutorial is meant to aid those with a background in optimization in learning about treatment design. Besides discussing several optimization models, we include a clinical perspective so that readers understand the clinical issues that are often ignored in the optimization …

Global Stability Of Periodic Orbits Of Non-Autonomous Difference Equations And Population Biology, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of period r is GAS, then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and …

Geometry Of Jump Systems, Vadim Lyubashevsky, Chad Newell, Vadim Ponomarenko

Mathematics Faculty Research

A jump system is a set of lattice points satisfying a certain "two-step" axiom. We present a variety of results concerning the geometry of these objects, including a characterization of two-dimensional jump systems, necessary (though not sufficient) properties of higher-dimensional jump systems, and a characterization of constant-sum jump systems.

Navy Personnel Planning And The Optimal Partition, Allen G. Holder

Mathematics Faculty Research

One could argue that the Navy's most important resource is its personnel, and as such, workforce planning is a crucial task. We investigate a new model and solution technique that is designed to aid in optimizing the process of assigning sailors to jobs. This procedure attempts to achieve an increased level of sailor satisfaction by providing a list of possible jobs from which a sailor may choose. We show that the optimal partition provided by an interior-point algorithm is particularly useful when designing the job lists. This follows because a strictly complementary solution to the linear programming relaxation observes all …

The Asymptotic Optimal Partition And Extensions Of The Nonsubstitution Theorem, Julio R. Hasfura-Buenaga, Allen G. Holder, Jeffrey Stuart

Mathematics Faculty Research

The data describing an asymptotic linear program rely on a single parameter, usually referred to as time, and unlike parametric linear programming, asymptotic linear programming is concerned with the steady state behavior as time increases to infinity. The fundamental result of this work shows that the optimal partition for an asymptotic linear program attains a steady state for a large class of functions. Consequently, this allows us to define an asymptotic center solution. We show that this solution inherits the analytic properties of the functions used to describe the feasible region. Moreover, our results allow significant extensions of an economics …

Reduction Of The Gibbs Phenomenon Via Interpolation Using Chebyshev Polynomials, Filtering And Chebyshev-Pade' Approximations, Rob-Roy L. Mace

Theses, Dissertations and Capstones

In this manuscript, we will examine several methods of interpolation, with an emphasis on Chebyshev polynomials and the removal of the Gibbs Phenomenon. Included as an appendix are the author’s Mat- Lab implementations of Lagrange, Chebyshev, and rational interpolation methods.

Convergence Analysis Of Mcmc Method In The Study Of Genetic Linkage With Missing Data, Diana Fisher

Theses, Dissertations and Capstones

Computational infeasibility of exact methods for solving genetic linkage analysis problems has led to the development of a new collection of stochastic methods, all of which require the use of Markov chains. The purpose of this work is to investigate the complexities of missing data in pedigree analysis using the Monte Carlo Markov Chain (MCMC) method as compared to the exact results. Also, we attempt to determine an association between missing data in a familial pedigree and the convergence to stationarity of a descent graph Markov chain implemented in the stochastic method for parametric linkage analysis.

In particular, we will …

Dynamic Equations On Changing Time Scales: Dynamics Of Given Logistic Problems, Parameterization, And Convergence Of Solutions, Kelli J. Hall

Theses, Dissertations and Capstones

In this thesis we use the theory of dynamic equations on time scales to understand the changes in dynamics between difference and differen- tial equations by parameterizing the underlying domains. To illustrate where and how these changes occur, we then construct a bifurcation diagram for a simple family of dynamic equations. However, these results are only true if we can move continuously through our domains, i.e, the time scales. In the last part of this thesis, we define what it means to have a convergent sequence of time scales. Then we use this definition to prove that the limit …

Unpredictable Binary Strings, Richard Low, Mark Stamp, R. Craigen, G. Faucher

Faculty Publications, Computer Science

We examine a class of binary strings arising from considerations about stream cipher encryption: to what degree can one guarantee that the number of pairs of entries distance k apart that disagree is equal to the number that agree, for all small k? In a certain sense, a keystream with such a property achieves a degree of unpredictability. The problem is also restated combinatorially in terms of seating arrangements. We examine sequences s of length 2n in which this property holds for all k ≤ Mn, where Mn is the largest number for which this is possible among strings of …

The Stepping Stone Model, Ii: Genealogies And The Infinite Sites Model, Submitted, Iljana Zähle, J. Theodore Cox, Richard Durrett

Mathematics - All Scholarship

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman’s coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by …

Rescaled Lotka-Volterra Models Converge To Super-Brownian Motion, J. Theodore Cox, Edwin A. Perkins

Mathematics - All Scholarship

We show that a sequence of stochastic spatial Lotka–Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.

Stability Properties Of Linear Volterra Integrodifferential Equations With Nonlinear Perturbation, Muhammad Islam, Youssef Raffoul

Mathematics Faculty Publications

A Lyapunov functional is employed to obtain conditions that guarantee stability, uniform stability and uniform asymptotic stability of the zero solution of a scalar linear Volterra integrodifferential equation with nonlinear perturbation.

Boundedness And Stability In Nonlinear Delay Difference Equations Employing Fixed Point Theory, Muhammad Islam, Ernest Yankson

Mathematics Faculty Publications

In this paper we study stability and boundedness of the nonlinear difference equation

x(t+1)=a(t)x(t)+c(t)Δx(t−g(t))+q(x(t),x(t−g(t))).

In particular we study equi-boundedness of solutions and the stability of the zero solution of this equation. Fixed point theorems are used in the analysis.

Positive Operators And Maximum Principles For Ordinary Differential Equations, Paul W. Eloe

Mathematics Faculty Publications

We show an equivalence between a classical maximum principle in differential equations and positive operators on Banach Spaces. Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Finally, we shall present extended applications of the maximum principle that have arisen with the continued study of the qualitative properties of Green’s functions.

2005 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2005 Winter Colloquium

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

On Cographic Matroids And Signed-Graphic Matroids, Dan Slilaty

Mathematics and Statistics Faculty Publications

We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph Σ iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that Σ must be the projective-planar dual signed graph of an actual imbedding of G in the projective plane. As a corollary we get that, if G1, . . . , G29 denote the 29 nonseparable forbidden minors for projective-planar graphs, then the cographic matroids of G1, . . . , G29 are among the forbidden minors for the class of bias matroids …