Mathematics Commons^™

A Scheme Over Prime Spectrum Of Modules, Ahmad Abbasi, Dawood Hassanzadeh Lelekami

Turkish Journal of Mathematics

Let R be a commutative ring with nonzero identity and let M be an R-module with X=Spec(M). It is introduced a scheme O_X on the prime spectrum of M and some of its properties have been investigated.

Global And Finitistic Dimension Of Hopf-Galois Extensions, Ling Liu, Qiaoling Guo

Turkish Journal of Mathematics

Let H be a Hopf algebra over a field k and A/B a right H-Galois extension. Then in this note a spectral sequence for Ext will be constructed which yields the estimate for global dimension of A in terms of the corresponding data for H and B. As an application, we obtain the Maschke-type theorems for crossed products and twisted smash products. Finally, the relationship of finitistic dimensions between A and B will be given, if H is semisimple.

Some Properties On The Baer-Invariant Of A Pair Of Groups And V_G-Marginal Series, Mohammad Reza Rismanchian, Mehdi Araskhan

Turkish Journal of Mathematics

The aim of this paper is to present some properties of the Baer-invariant of a pair of groups with respect to a given variety of groups V. We derive some equalities and inequalities of the Baer-invariant of a pair of finite groups, as long as V is considered to be a Schur-Baer variety. Moreover, we present a relative version of the concept of lower marginal series and give some isomorphisms among V_G-marginal factor groups. Also, we conclude a generalized version of the Stallings' theorem.

New Trace Formula For The Matrix Sturm-Liouville Equation With Eigenparameter Dependent Boundary Conditions, Chuan Fu Yang

Turkish Journal of Mathematics

A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained.

Contact 3-Structure Qr-Warped Product Submanifold In Sasakian Space Form, Esmaiel Abedi, Ghorbanali Haghighatdoost, Mohammad Ilmakchi, Zahra Nazari

Turkish Journal of Mathematics

In the present paper we obtain sharp estimates for the squared norm of the second fundamental form in terms of the mapping function for contact 3-structure CR-warped products isometrically immersed in Sasakian space form.

On Nash\'S 4-Sphere And Property 2r, Motoo Tange

Turkish Journal of Mathematics

D. Nash defined a family of homotopy 4-spheres in [11]. Proving that his manifolds S_{m,n,m',n'} are all real S^4, we show that they have handle decomposition with no 1-handles, two 2-handles and two 3-handles. The handle structures give new potential counterexamples to the Property 2R conjecture.

Finite Rings And Wilson's Theorem, Yasuyuki Hirano, Manabu Matsuoka

Turkish Journal of Mathematics

In this paper we consider the product of all elements in the group of units in a finite ring and we generalize Wilson's theorem to finite rings. As an application, we study some generalizations of Wilson's theorem on residually finite Dedekind domains. And we also give some examples for such rings. Moreover we study some generalizations of Wilson's theorem on rings of matrices over a finite commutative ring.

On Theta Pair For A Proper Subalgebra, Ali Reza Salemkar, Sara Chehrazi, Hamid Mohammadzadeh

Turkish Journal of Mathematics

For a proper subalgebra K of a finite dimensional Lie algebra L, a pair (A,B) of subalgebras of L is called a \theta-pair if L = \langle A,K\rangle, B is the largest ideal of L contained in A\cap K and for each proper subalgebra C/B of A/B which is an ideal of L/B, we have L\neq C+K. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.

Towards Interference-Immune And Channel-Aware Multicarrier Schemes: Filters, Lattices, And Interference Issues, Alphan Sahin

USF Tampa Graduate Theses and Dissertations

In this dissertation, multicarrier schemes are reviewed within the framework of Gabor Systems. Their fundamental elements; what to transmit, i.e., symbols, how to transmit, i.e., filters or pulse shape, and where/when to transmit, i.e., lattices are investigated extensively. The relations between different types of multicarrier schemes are discussed.

Within the framework of Gabor systems, a new windowing approach, edge windowing, is developed to address the out-of-band (OOB) radiation problem of orthogonal frequency division multiplexing (OFDM) based multicarrier schemes. To the best of our knowledge, for the first time, the diversity on the range of the users is exploited to suppress …

Expression And Computation Of Generalized Stirling Numbers, Tian-Xiao He

Scholarship

Here presented is a unified expression of Stirling numbers and their generalizations by using generalized factorial functions and generalized divided difference. Three algorithms for calculating the Stirling numbers and their generalizations based on our unified form are also given, which include a comprehensive algorithm using the characterization of Riordan arrays.

Polynomial Knot And Link Invariants From The Virtual Biquandle, Alissa S. Crans, Allison Henrich, Sam Nelson

Mathematics, Statistics and Data Science Faculty Works

The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which determine both the generalized Alexander polynomial (also known as the Sawollek polynomial) for virtual knots and the classical Alexander polynomial for classical knots. For a fixed monomial ordering <, the Gr\"obner bases for these ideals are computable, comparable invariants which fully determine the elementary ideals and which generalize and unify the classical and generalized Alexander polynomials. We provide examples to illustrate the usefulness of these invariants and propose questions for future work.

An Adaptive Total Variation Algorithm For Computing The Balanced Cut Of A Graph, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht

Mathematics, Statistics and Data Science Faculty Works

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced cut energy as well as convergence of the algorithm. In practice the total variation minimization step is never solved exactly. Instead, an accuracy parameter is specified and the total variation minimization terminates once this level of accuracy is reached. The choice of this parameter can vastly impact both the computational time of the overall algorithm as well as the accuracy of …

C.P. Modules And Their Applications, Qiongling Liu, Jianlong Chen

Turkish Journal of Mathematics

Let R be a ring. A left R-module M is called a c.p. module if every cyclic submodule of M is projective. This notion is a generalization of left p.p. rings in the general module theoretic setting. The aim of this article is to investigate these modules. Some characterizations and properties are given. As applications, the connections among Baer rings, p.p. rings and von Neumann regular rings are studied.

Integral Polytopes And Polynomial Factorization, Fati̇h Koyuncu

Turkish Journal of Mathematics

For any field F, there is a relation between the factorization of a polynomial f \in F[x_1,...,x_n] and the integral decomposition of the Newton polytope of f. We extended this result to polynomial rings R[x_1,...,x_n] where R is any ring containing some elements which are not zero-divisors. Moreover, we have constructed some new families of integrally indecomposable polytopes in \mb giving infinite families of absolutely irreducible multivariate polynomials over arbitrary fields.

A Nonlocal Parabolic Problem In An Annulus For The Heaviside Function In Ohmic Heating, Fei Liang, Hongjun Gao, Charles Bu

Turkish Journal of Mathematics

In this paper, we consider the nonlocal parabolic equation u_t=\Delta u+\frac{\lambda H(1-u)}{\big(\int_{A_{\rho, R}} H(1-u)dx\big)^2}, x\in A_{\rho, R} \subset R^2, t>0, with a homogeneous Dirichlet boundary condition, where \lambda is a positive parameter, H is the Heaviside function and A_{\rho, R} is an annulus. It is shown for the radial symmetric case that: there exist two critical values \lambda_* and \lambda^*, so that for 0

Approximation By Iterates Of Beta Operators, Purshottam Narain Agrawal, Karunesh Kumar Singh, Vikas Kumar Mishra

Turkish Journal of Mathematics

In this paper, we study the degree of approximation by an iterative combination T_{n,k} of the beta operators introduced by Upreti [8].

On Characterization And Stability Of Alternate Dual Of G-Frames, Ali Akbar Arefijamaal, Soheila Ghasemi

Turkish Journal of Mathematics

One of the essential applications of frames is that they lead to expansions of vectors in the underlying Hilbert space in terms of the frame elements. In this decomposition, dual frames have a key role. G-frames, introduced by Sun, cover many other recent generalizations of frames. In this paper, we give some characterizations of dual g-frames. Moreover, we prove that if two g-frames are close to each other, then we can find duals of them which are close to each other.

Scalar Curvature And Symmetry Properties Of Lightlike Submanifolds}, Cyriaque Atindogbe, Oscar Lungiambudila, Joel Tossa

Turkish Journal of Mathematics

In this paper, the induced Ricci tensor and the extrinsic scalar curvature on lightlike submanifolds are obtained. This scalar quantity extend the result given by C. Atindogbe in [1]. An example of extrinsic scalar curvature on one class of 2-degenerate manifolds is provided. We investigate lightlike submanifolds which are locally symmetric, semi-symmetric, Ricci semi-symmetric in indefinite spaces form. In the coisotropic case, we show that, under some conditions, these lightlike submanifolds are totally geodesic.

Paracontact Semi-Riemannian Submersions, Yilmaz Gündüzalp, Bayram Şahi̇n

Turkish Journal of Mathematics

In this paper, we first define the concept of paracontact semi-Riemannian submersions between almost paracontact metric manifolds, then we provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost paracontact structure of the total manifold. The study is focused on fundamental properties and the transference of structures defined on the total manifold. Moreover, we obtain various properties of the O'Neill's tensors for such submersions and find the integrability of the horizontal distribution. We also find necessary and sufficient conditions for a paracontact semi-Riemannian submersion to be totally geodesic. Finally, …

Asymptotics Of The Ruin Probability With Claims Modeled By \\Alpha-Stable Aggregated Ar(1) Process, Karina Perilioglu, Donata Puplinskaite

Turkish Journal of Mathematics

We study the asymptotics of the ruin probability in a discrete time risk insurance model with stationary claims following the aggregated heavy-tailed AR(1) process discussed in Puplinskaite and Surgailis (2010). The present work is based on the general characterization of the ruin probability with claims modeled by stationary \alpha-stable process in Mikosch and Samorodnitsky (2000). We prove that for the aggregated AR(1) claims' process, the ruin probability decays with exponent \alpha(1-H), where H \in [1/\alpha, 1) is the asymptotic self-similarity index of the claim process, 1< \alpha < 2. This result agrees with the decay rate of the ruin probability with claims modeled by increments of linear fractional motion in Mikosch and Samorodnitsky (2000) and also with other characterizations of long memory of the aggregated AR(1) process with infinite variance in Puplinskaite and Surgailis (2010).