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On Generalized Robertson--Walker Spacetimes Satisfying Some Curvature Condition, Kadri̇ Arslan, Ryszard Deszcz, Ridvan Ezentaş, Marian Hotlos, Cengi̇zhan Murathan
On Generalized Robertson--Walker Spacetimes Satisfying Some Curvature Condition, Kadri̇ Arslan, Ryszard Deszcz, Ridvan Ezentaş, Marian Hotlos, Cengi̇zhan Murathan
Turkish Journal of Mathematics
We give necessary and sufficient conditions for warped product manifolds (M,g), of dimension \geqslant 4, with 1-dimensional base, and in particular, for generalized Robertson--Walker spacetimes, to satisfy some generalized Einstein metric condition. Namely, the difference tensor R . C - C . R, formed from the curvature tensor R and the Weyl conformal curvature tensor C, is expressed by the Tachibana tensor Q(S,R) formed from the Ricci tensor S and R. We also construct suitable examples of such manifolds. They are quasi-Einstein, i.e. at every point of M rank (S - \alpha g) \leqslant 1, for some \alpha \in R, …
Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski
Counting Pseudo-Anosov Mapping Classes On The 3-Punctured Projective Plane, Blazej Szepietowski
Turkish Journal of Mathematics
We prove that in the pure mapping class group of the 3-punctured projective plane equipped with the word metric induced by certain generating set, the ratio of the number of pseudo-Anosov elements to the number of all elements in a ball centered at the identity tends to one, as the radius of the ball tends to infinity. We also compute growth functions of the sets of reducible and pseudo-Anosov elements.
Regular Poles For The P-Adic Group Gsp_4, Yusuf Danişman
Regular Poles For The P-Adic Group Gsp_4, Yusuf Danişman
Turkish Journal of Mathematics
We compute the regular poles of the L-factors of the admissible and irreducible representations of the group GSp_4, which admit a nonsplit Bessel functional and have a Jacquet module length of at most 2 with respect to the unipotent radical of the Siegel parabolic, over a non-Archimedean local field of odd characteristic. We also compute the L-factors of the generic representations of GSp_4.
On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Turkish Journal of Mathematics
Let R be a commutative ring and I(R) denote the multiplicative group of all invertible fractional ideals of R, ordered by A \leqslant B if and only if B \subseteq A. If R is a Marot ring of Krull type, then R_{(P_i)}, where {P_i}_{i \in I} are a collection of prime regular ideals of R, is a valuation ring and R = \bigcap R_{(P_i)}. We denote by G_i the value group of the valuation associated with R_{(P_i)}. We prove that there is an order homomorphism from I(R) into the cardinal direct sum \coprod_{i \in I} G_i and we investigate the …
Some Rings For Which The Cosingular Submodule Of Every Module Is A Direct Summand, Derya Keski̇n Tütüncü, Ni̇l Orhan Ertaş, Patrick F. Smith, Rachid Tribak
Some Rings For Which The Cosingular Submodule Of Every Module Is A Direct Summand, Derya Keski̇n Tütüncü, Ni̇l Orhan Ertaş, Patrick F. Smith, Rachid Tribak
Turkish Journal of Mathematics
The submodule \overline{Z}(M) = \cap {N M/N is small in its injective hull} was introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if \overline{Z}(M) is a direct summand of M for every R-module M. It is shown that a commutative perfect ring R has (P) if and only if R is semisimple. An example is given to show that this characterization is not true for noncommutative rings. We prove that if R is a commutative ring such that the class {M \in Mod-R \overline{Z}_{R}(M) = 0} is closed under factor modules, then …
On Kapranov's Description Of \Overline{M}_{0,N} As A Chow Quotient, Noah Giansiracusa, William Danny Gillam
On Kapranov's Description Of \Overline{M}_{0,N} As A Chow Quotient, Noah Giansiracusa, William Danny Gillam
Turkish Journal of Mathematics
We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over C that the Hilbert quotient (P^1)^n//_HPGL_2 and Chow quotient (P^1)^n//_{Ch}PGL_2 are isomorphic to \overline{M}_{0,n}. In both cases this is done by explicitly constructing the universal family of orbit closures and then showing that the induced morphism is an isomorphism onto its image. The proofs of these results in many ways reduce to the case n = 4; in an appendix we outline a formalism of this phenomenon relating to certain operads.
Generalized Hypercenter Of A Finite Group, Mohamed Ezzat Mohamed, Mohammed Mosa Alshomrani
Generalized Hypercenter Of A Finite Group, Mohamed Ezzat Mohamed, Mohammed Mosa Alshomrani
Turkish Journal of Mathematics
Let G be a finite group. In this paper, we introduce the concept of super generalized supersolvably embedded subgroup of a group G and give a new characterization of the generalized hypercenter of G.
Oscillation Of Second Order Differential Equations With Mixed Nonlinearities, Zhiting Xu, Aijun Cheng
Oscillation Of Second Order Differential Equations With Mixed Nonlinearities, Zhiting Xu, Aijun Cheng
Turkish Journal of Mathematics
By refining the standard integral averaging technique, in this paper, new oscillation criteria as well as interval oscillation criteria are established for the second order delay differential equation with mixed nonlinearities \begin{equation*} (r(t) x^{\prime}(t) ^{\alpha-1}x^{\prime}(t))^{\prime}+q_0(t) x(\tau_0(t)) ^{\alpha-1}x(\tau_0(t)) +\sum\limits_{i = 1}^nq_i(t) x(\tau_i(t)) ^{\alpha_i-1}x(\tau_i(t)) = 0, \end{equation*} where \alpha>0, \alpha_i>0, i = 1,2,\cdots,n. Our results generalize and improve the known results in the literature. Examples are also given to illustrate the importance of our results.
Existence, Global Nonexistence, And Asymptotic Behavior Of Solutions For The Cauchy Problem Of A Multidimensional Generalized Damped Boussinesq-Type Equation, Erhan Pi̇şki̇n, Necat Polat
Existence, Global Nonexistence, And Asymptotic Behavior Of Solutions For The Cauchy Problem Of A Multidimensional Generalized Damped Boussinesq-Type Equation, Erhan Pi̇şki̇n, Necat Polat
Turkish Journal of Mathematics
We consider the existence, both locally and globally in time, the global nonexistence, and the asymptotic behavior of solutions for the Cauchy problem of a multidimensional generalized Boussinesq-type equation with a damping term.
Relaxed Elastic Line In A Riemannian Manifold, Gözde Özkan, Ahmet Yücesan
Relaxed Elastic Line In A Riemannian Manifold, Gözde Özkan, Ahmet Yücesan
Turkish Journal of Mathematics
We obtain a differential equation with 2 boundary conditions for a relaxed elastic line in a Riemannian manifold. This differential equation, which is found with respect to constant sectional curvature G, geodesic curvature \kappa, and 2 boundary conditions, gives a more direct and more geometric approach to questions concerning a relaxed elastic line in a Riemannian manifold. We give various theorems and results in terms of a relaxed elastic line. Consequently, we examine the concept of a relaxed elastic line in 2- and 3- dimensional space forms.
On Joachimsthal's Theorems In Riemann--Otsuki Space R-O_3, Münevver Yildirim Yilmaz, Mehmet Bektaş
On Joachimsthal's Theorems In Riemann--Otsuki Space R-O_3, Münevver Yildirim Yilmaz, Mehmet Bektaş
Turkish Journal of Mathematics
In this paper we study the Joachimsthal theorem in Riemann--Otsuki space
Half-Lightlike Submanifolds With Planar Normal Sections In R_2^4, Feyza Esra Erdoğan, Rifat Güneş, Bayram Şahi̇n
Half-Lightlike Submanifolds With Planar Normal Sections In R_2^4, Feyza Esra Erdoğan, Rifat Güneş, Bayram Şahi̇n
Turkish Journal of Mathematics
We investigate half-lightlike submanifolds with planar normal sections of 4-dimensional pseudo-Euclidean space. We obtain necessary and sufficient conditions for a half-lightlike submanifold of R_2^4 such that it has degenerate or nondegenerate planar normal sections.
Almost Contact Metric Submersions And Symplectic Manifolds, Augustin Batubenge, Tshikunguila Tshikuna-Matamba
Almost Contact Metric Submersions And Symplectic Manifolds, Augustin Batubenge, Tshikunguila Tshikuna-Matamba
Turkish Journal of Mathematics
In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that this is obtained if the total space is an b-almost Kenmotsu manifold.
A Note On Closed G_2-Structures And 3-Manifolds, Hyunjoo Cho, Sema Salur, Albert Todd
A Note On Closed G_2-Structures And 3-Manifolds, Hyunjoo Cho, Sema Salur, Albert Todd
Turkish Journal of Mathematics
This article shows that given any orientable 3-manifold X, the 7-manifold T^*X \times R admits a closed G_2-structure \varphi = Re \Omega-\omega \wedge dt where \Omega is a certain complex-valued 3-form on T^*X; next, given any 2-dimensional submanifold S of X, the conormal bundle N^*S of S is a 3-dimensional submanifold of T^*X \times R such that \varphi _{N^*S}\equiv 0. A corollary of the proof of this result is that N^*S \times R is a 4-dimensional submanifold of T^*X \times R such that \varphi _{N^*S \times R}\equiv 0.
Covers And Preenvelopes By V-Gorenstein Flat Modules, Xiaoyan Yang
Covers And Preenvelopes By V-Gorenstein Flat Modules, Xiaoyan Yang
Turkish Journal of Mathematics
In this paper, we introduce and study V-Gorenstein flat modules and show the stability of the category of V-Gorenstein flat modules. We investigate the existence of V-Gorenstein flat covers and V-Gorenstein flat preenvelopes for any left R-module. Also we prove that (V-GF,V-GF^\bot) is a perfect hereditary cotorsion pair in B^l(R), where V-GF stands the class of V-Gorenstein flat left R-modules and B^l(R) is the left Bass class. Some applications are given.
On The K-Ring Of The Classifying Space Of The Generalized Quaternion Group, Mehmet Kirdar, Sevi̇lay Özdemi̇r
On The K-Ring Of The Classifying Space Of The Generalized Quaternion Group, Mehmet Kirdar, Sevi̇lay Özdemi̇r
Turkish Journal of Mathematics
We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.
Generalized Higher Commutators Generated By The Multilinear Fractional Integrals And Lipschitz Functions, Huixia Mo, Dongyan Yu, Huiping Zhou
Generalized Higher Commutators Generated By The Multilinear Fractional Integrals And Lipschitz Functions, Huixia Mo, Dongyan Yu, Huiping Zhou
Turkish Journal of Mathematics
Let l \in N and \vec{A}=(A_1,\dots,A_l) and \vec{f}=(f_1,\dots,f_l) be 2 finite collections of functions, where every function A_i has derivatives of order m_i and f_1,\dots,f_l\in L_c^{\infty}(R^n). Let x\notin\cap_{i=1}^lSupp f_i. The generalized higher commutator generated by the multilinear fractional integral is then given by I_{\alpha,m}^{\vec{A}}(\vec{f})(x) =\dint_{(R^n)^m} \frac{\prod\limits_{i=1}^lR_{m_i+1}(A_i;x,y_i)f_{i}(y_i)}{ (x-y_1,\dots ,x-y_m) ^{ln+(m_1+m_2+\dots+m_l)-\alpha}} dy_1\dots dy_l. When D^{\gamma}A_i\in \dot{\Lambda}_{\beta_i}(0
The Property Of Real Hypersurfaces In 2-Dimensional Complex Space Form With Ricci Operator, Dong Ho Lim, Woon Ha Sohn, Seong Soo Ahn
The Property Of Real Hypersurfaces In 2-Dimensional Complex Space Form With Ricci Operator, Dong Ho Lim, Woon Ha Sohn, Seong Soo Ahn
Turkish Journal of Mathematics
Let M be a real hypersurface in a complex space form M_2(c), c \neq 0. In this paper, we prove that S \phi=\phi S on M if and only if M is pseudo-Einstein.
An Alternative Approach To The Adem Relations In The Mod 2 Steenrod Algebra, Neşet Deni̇z Turgay
An Alternative Approach To The Adem Relations In The Mod 2 Steenrod Algebra, Neşet Deni̇z Turgay
Turkish Journal of Mathematics
The Leibniz--Hopf algebra F is the free associative algebra over Z on one generator S^n in each degree n>0, with coproduct given by \Delta(S^n) = \sum_{i+j=n} S^i \otimes S^j. We introduce a new perspective on the Adem relations in the mod 2 Steenrod algebra A_2 by studying the map \pi^\ast dual to the Hopf algebra epimorphism \pi: F \otimes Z/2 \to A_2. We also express Milnor's Hopf algebra conjugation formula in A_2^\ast in a different form and give a new approach for the conjugation invariant problem in A_2^\ast.
Population Dynamical Behaviors Of Stochastic Logistic System With Jumps, Ruihua Wu, Ke Wang
Population Dynamical Behaviors Of Stochastic Logistic System With Jumps, Ruihua Wu, Ke Wang
Turkish Journal of Mathematics
This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established. The critical value of extinction, nonpersistence in the mean, and weak persistence in the mean are obtained. The path-wise and moment properties are also investigated. Finally, some simulation figures are introduced to illustrate the main results.
On A Generalization Of Kelly's Combinatorial Lemma, Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour
On A Generalization Of Kelly's Combinatorial Lemma, Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour
Turkish Journal of Mathematics
Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t -elements subsets of a v -element set was given by Pouzet. We consider a version of this generalization modulo a prime p. We give illustrations to graphs and tournaments.
Frobenius-Like Groups As Groups Of Automorphisms, Güli̇n Ercan, İsmai̇l Şuayi̇p Güloğlu, Evgeny Khukhro
Frobenius-Like Groups As Groups Of Automorphisms, Güli̇n Ercan, İsmai̇l Şuayi̇p Güloğlu, Evgeny Khukhro
Turkish Journal of Mathematics
A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms FH aiming at restrictions on G in terms of C_G(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like …
Hilbert Series Of The Braid Monoid Mb_4 In Band Generators, Zaffar Iqbal, Shamaila Yousaf
Hilbert Series Of The Braid Monoid Mb_4 In Band Generators, Zaffar Iqbal, Shamaila Yousaf
Turkish Journal of Mathematics
L. A. Bokut gave a Gröbner--Shirshov basis of the braid group B_n in band generators. Using this presentation and solving all the ambiguities we construct a linear system for irreducible words and compute the Hilbert series of the braid monoid MB_4.
Gradient Estimates For The Porous Medium Type Equation On Smooth Metric Measure Space, Deng Yihua
Gradient Estimates For The Porous Medium Type Equation On Smooth Metric Measure Space, Deng Yihua
Turkish Journal of Mathematics
The porous medium equation arises in different applications to model diffusive phenomena. In this paper, we obtain several gradient estimates for some porous medium type equations on smooth metric measure space with N-Bakry-Emery Ricci tensor bounded from below. In particular, we improve and generalize some current gradient estimates for the porous medium equations.
Disjoint Supercyclic Powers Of Weighted Shifts On Weighted Sequence Spaces, Yu-Xia Liang, Ze-Hua Zhou
Disjoint Supercyclic Powers Of Weighted Shifts On Weighted Sequence Spaces, Yu-Xia Liang, Ze-Hua Zhou
Turkish Journal of Mathematics
We characterize the disjoint supercyclicity of finitely many different powers of weighted shifts acting on the weighted sequence spaces l^2(N,w), c_0(N,w) , and l^2(Z,w), c_0(Z,w), where w=(w_i)_i is a positive weight sequence satisfying w_i \geq 1 for every i\in N (or i\in Z).
Some New Associated Curves Of A Frenet Curve In E^3 And E^4, Nesi̇be Maci̇t, Mustafa Düldül
Some New Associated Curves Of A Frenet Curve In E^3 And E^4, Nesi̇be Maci̇t, Mustafa Düldül
Turkish Journal of Mathematics
In this paper, firstly, we define a W -direction curve and W -rectifying curve of a Frenet curve in 3-dimensional Euclidean space E^3 by using the unit Darboux vector field W of the Frenet curve and give some characterizations together with the relationships between the curvatures of each associated curve. We also introduce a V -direction curve, which is associated with a curve lying on an oriented surface in E^3. Later, some new associated curves of a Frenet curve are defined in E^4.
Notes On The Tangent Bundle With Deformed Complete Lift Metric, Aydin Gezer, Mustafa Özkan
Notes On The Tangent Bundle With Deformed Complete Lift Metric, Aydin Gezer, Mustafa Özkan
Turkish Journal of Mathematics
In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.