Mathematics Commons^™

The Cyclic Behavior Of The Constrictive Markov Operators, César Emilio Villarreal Rodríguez

Turkish Journal of Mathematics

Let S be a Polish space, and let M_{\varSigma} be the Banach space of finite signed measures on the Borel \Sigma-algebra \varSigma of S. Given a constrictive Markov operator T:M_{\varSigma}\rightarrow M_{\varSigma}, we use the asymptotic periodic decomposition of T to determine the set of T-invariant distributions in M_{\varSigma} and the set of T-ergodic distributions. We also give the relationship between the asymptotic periodic decomposition and the cycles of the process relative to the operator T.

On The Nilpotent Graph Of A Ring, Mohammad Javad Nikmehr, Soheila Khojasteh

Turkish Journal of Mathematics

Let R be a ring with unity. The nilpotent graph of R, denoted by \Gamma_N(R), is a graph with vertex set Z_N(R)^* = {0 \neq x \in R \mid xy \in N(R) for some 0 \neq y \in R}; and two distinct vertices x and y are adjacent if and only if xy \in N(R), where N(R) is the set of all nilpotent elements of R. Recently, it has been proved that if R is a left Artinian ring, then diam(\Gamma_N(R)) \leq 3. In this paper, we present a new proof for the above result, where R is a finite …

Complex Symplectic Geometry With Applications To Vector Differential Operators, Chuan Fu Yang

Turkish Journal of Mathematics

Let l(y) be a formally self-adjoint vector-valued differential expression of order n on an interval (a, \infty)(-\infty \leq a < \infty) with complex matrix-valued function coefficients and finite equal deficiency indices. In this paper, applying complex symplectic algebra, we give a reformulation for self-adjoint domains of the minimal operator associated with l(y) and classify them.

Global Existence, Decay And Blow Up Solutions For Coupled Nonlinear Wave Equations With Damping And Source Terms, Erhan Pi̇şki̇n, Necat Polat

Turkish Journal of Mathematics

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters.

L^P Solutions Of Infinite Time Interval Bsdes And The Corresponding G-Expectations And G-Martingales, Zhaojun Zong

Turkish Journal of Mathematics

In this paper we study the existence and uniqueness theorem for L^p (1

Polynomial Root Separation In Terms Of The Remak Height, Arturas Dubickas

Turkish Journal of Mathematics

We investigate some monic integer irreducible polynomials which have two close roots. If P(x) is a separable polynomial in Z[x] of degree d \geq 2 with the Remak height R(P) and the minimal distance between the quotient of two distinct roots and unity Sep(P), then the inequality 1/Sep(P) \ll R(P)^{d-1} is true with the implied constant depending on d only. Using a recent construction of Bugeaud and Dujella we show that for each d \geq 3 there exists an irreducible monic polynomial P \in Z[x] of degree d for which R(P)^{(2d-3)(d-1)/(3d-5)} \ll 1/Sep(P). For d=3 the exponent 3/2 is improved …

Finite Groups With Some Weakly S-Supplementally Embedded Subgroups, Tao Zhao

Turkish Journal of Mathematics

A subgroup H of G is said to be weakly s-supplementally embedded in G if there exist a subgroup T of G and an s-permutably embedded subgroup H_{se} of G contained in H such that G=HT and H \cap T \leq H_{se}. In this paper, we investigate the influence of some weakly s-supplementally embedded subgroups on the structure of a finite group G. Some earlier results are unified and generalized.

Surgery In Codimension 3 And The Browder--Livesay Invariants, Friedrich Hegenbarth, Yuri Muranov, Dusan Repovs

Turkish Journal of Mathematics

The inertia subgroup I_n(\pi) of a surgery obstruction group L_n(\pi) is generated by elements that act trivially on the set of homotopy triangulations S(X) for some closed topological manifold X^{n-1} with \pi_1(X) = \pi. This group is a subgroup of the group C_n(\pi), which consists of the elements that can be realized by normal maps of closed manifolds. These 2 groups coincide by a recent result of Hambleton, at least for n \geq 6 and in all known cases. In this paper we introduce a subgroup J_n(\pi) \subset I_n(\pi), which is generated by elements of the group L_n(\pi), which act …

Quasinormability And Diametral Dimension, Ahmet Tosun Terzi̇oğlu

Turkish Journal of Mathematics

Two versions of diametral dimension are shown to coincide for quasinormable Fréchet spaces. The diametral dimension is determined by a single bounded subset in certain cases.

Complete Cotorsion Pairs In The Category Of Complexes, Zhanping Wang, Zhongkui Liu

Turkish Journal of Mathematics

In this paper, we study completeness of cotorsion pairs in the category of complexes of R-modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair (\widetilde{A}, dg\widetilde{B}) and (\overline{A}, \overline{A}^{\perp}) are complete if A is closed under pure submodules and cokernels of pure monomorphisms, where in Gillespie's definitions \widetilde{A} is the class of exact complexes with cycles in A and dg\widetilde{B} is the class of complexes X with components in B such that the complex Hom(A, X) is exact for every complex A \in \widetilde{A}; and \overline{A} is the class of all complexes …

Factorization Of Composite Polynomials Over Finite Fields, Saeid Mehrabi

Turkish Journal of Mathematics

This paper presents the reducibility of some composite polynomials and explicitly determines the factorization over finite fields. Also families of irreducible polynomials over finite fields are introduced.

Dimension Reduction For Power System Modeling Using Pca Methods Considering Incomplete Data Readings, Ting Zhao

Dissertations, Master's Theses and Master's Reports - Open

Principal Component Analysis (PCA) is a popular method for dimension reduction that can be used in many fields including data compression, image processing, exploratory data analysis, etc. However, traditional PCA method has several drawbacks, since the traditional PCA method is not efficient for dealing with high dimensional data and cannot be effectively applied to compute accurate enough principal components when handling relatively large portion of missing data. In this report, we propose to use EM-PCA method for dimension reduction of power system measurement with missing data, and provide a comparative study of traditional PCA and EM-PCA methods. Our extensive experimental …

On Binary And Regular Matroids Without Small Minors, Kayla Davis Harville

Electronic Theses and Dissertations

The results of this dissertation consist of excluded-minor results for Binary Matroids and excluded-minor results for Regular Matroids. Structural theorems on the relationship between minors and k-sums of matroids are developed here in order to provide some of these characterizations. Chapter 2 of the dissertation contains excluded-minor results for Binary Matroids. The first main result of this dissertation is a characterization of the internally 4-connected binary matroids with no minor that is isomorphic to the cycle matroid of the prism+e graph. This characterization generalizes results of Mayhew and Royle [18] for binary matroids and results of Dirac [8] and Lovász …

Special Type Of Subset Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we construct special subset topological spaces using subsets from semigroups or groups or rings or semirings. Such study is carried out for the first time and it is both interesting and innovative. Suppose P is a semigroup and S is the collection of all subsets of P together with the empty set, then S can be given three types of topologies and all the three related topological spaces are distinct and results in more types of topological spaces. When the semigroup is finite, S gives more types of finite topological spaces. The same is true in case …

Subset Non Associative Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of non associative topological space is new and innovative. In general topological spaces are defined as union and intersection of subsets of a set X. In this book authors for the first time define non associative topological spaces using subsets of groupoids or subsets of loops or subsets of groupoid rings or subsets of loop rings. This study leads to several interesting results in this direction.

Over hundred problems on non associative topological spaces using of subsets of loops or groupoids is suggested at the end of chapter two. Also conditions for these non associative subset topological spaces …

Subset Groupoids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of constructing non associative algebraic structures using subsets of a groupoid. Thus subset groupoids are constructed using groupoids or loops. Even if we use subsets of loops still the algebraic structure we get with it is only a groupoid. However we can get a proper subset of it to be a subset loop which will be isomorphic with the loop which was used in the construction of the subset groupoid. To the best of the authors’ knowledge this is the first time non associative algebraic structures are constructed using subsets. We get …

Variance On Topics Of Plane Geometry, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, …

Neutrosophic Emergencies And Incidences, Florentin Smarandache, Stefan Vladutescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Indeterminate Masses, Elements And Models In Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper at the beginning, we make a short history of the logics, from the classical Boolean logic to the most general logic of today neutrosophic logic. We define the general logic space and give the definition of the neutrosophic logic. Then we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses.

The best approach for dealing with such models is the neutrosophic logic, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

Filters Via Neutrosophic Crisp Sets, A. A. Salama, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.