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Weak-Projective Dimensions, Mohammad Javad Nikmehr, Zahra Poormahmood, Reza Nikandish
Weak-Projective Dimensions, Mohammad Javad Nikmehr, Zahra Poormahmood, Reza Nikandish
Turkish Journal of Mathematics
In this paper, the notions of weak-projective modules and weak-projective dimension over commutative domain R are given. It is shown that over semisimple rings with weak global dimension 1, these modules are equivalent to weak-injective modules. The weak-projective dimension measures how far away a domain is from being a Prüfer domain. Several properties of these modules are also presented.
Graded Multiplication Modules And The Graded Ideal \Theta_G (M), Shahabaddin Ebrahimi Atani, Reza Ebrahimi Atani
Graded Multiplication Modules And The Graded Ideal \Theta_G (M), Shahabaddin Ebrahimi Atani, Reza Ebrahimi Atani
Turkish Journal of Mathematics
Let G be a group and let R be a G-graded commutative ring. For a graded R-module M, the notion of the associated graded ideal \theta_g (M) of R is defined. It is proved that the graded ideal \theta_g (M) is important in the study of graded multiplication modules. Among various application given, the following results are proved: if M is a graded faithful multiplication module, then \theta_g (M) is an idempotent graded multiplication ideal of R such that \theta_g (\theta_g (M)) = \theta_g (M), and every graded representable multiplication R-module is finitely generated.
Coverings Of Lie Groupoids, İlhan İçen, M. Habi̇l Gürsoy, A. Fati̇h Özcan
Coverings Of Lie Groupoids, İlhan İçen, M. Habi̇l Gürsoy, A. Fati̇h Özcan
Turkish Journal of Mathematics
In this work we constitute the category of coverings of the Lie fundamental groupoid associated with a connected smooth manifold. We show that this category is equivalent to the category of universal coverings of a connected smooth manifold. In addition, we prove the equivalence of the category of coverings of a Lie groupoid and the category of actions of this Lie groupoid on a connected smooth manifold. Also we present two side results related to actions of Lie groupoids on the manifolds and coverings of Lie groupoids.
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
Turkish Journal of Mathematics
Let (H,) be a real Hilbert space and let K be a compact and connected subset of H. We show that every continuous mapping T:K \rightarrow K satisfying a mild condition has a fixed point.
Probabilities For Absolute Irreducibility Of Multivariate Polynomials By The Polytope Method, Fati̇h Koyuncu, Ferruh Özbudak
Probabilities For Absolute Irreducibility Of Multivariate Polynomials By The Polytope Method, Fati̇h Koyuncu, Ferruh Özbudak
Turkish Journal of Mathematics
Motivated by the Dubickas's result in [1], which computes the probability of the irreducible polynomials by Eisenstein's criterion for some families of polynomials in Z[x], we calculate the probabilities which represent the ratio of absolutely irreducible multivariate polynomials by the polytope method in some families of polynomials over arbitrary fields.
On Generalized (\Alpha,\Beta)-Derivations Of Semiprime Rings, Faisal Ali, Muhammad Anwar Chaudhry
On Generalized (\Alpha,\Beta)-Derivations Of Semiprime Rings, Faisal Ali, Muhammad Anwar Chaudhry
Turkish Journal of Mathematics
We investigate some properties of generalized (\alpha,\beta)-derivations on semiprime rings. Among some other results, we show that if g is a generalized (\alpha,\beta)-derivation, with associated (\alpha,\beta)-derivation \delta, on a semiprime ring R such that [g(x),\alpha(x)]=0 for all x\in R, then \delta(x)[y,z]=0 for all x,y,z\in R and \delta is central. We also show that if \alpha,\nu,\tau are endomorphisms and \beta,\mu are automorphisms of a semiprime ring R and if R has a generalized (\alpha,\beta)-derivation g, with associated (\alpha,\beta)-derivation \delta, such that g([\mu(x),w(y)])=[\nu(x),w(y)]_{\alpha,\tau}, where w:R\rightarrow R is commutativity preserving, then [y,z]\delta(w(p))=0 for all y,z,p\in R.
Combinatorial Results For Order-Preserving And Order-Decreasing Transformations, Gonca Ayik, Hayrullah Ayik, Meti̇n Koç
Combinatorial Results For Order-Preserving And Order-Decreasing Transformations, Gonca Ayik, Hayrullah Ayik, Meti̇n Koç
Turkish Journal of Mathematics
Let O_n and C_n be the semigroup of all order-preserving transformations and of all order-preserving and order-decreasing transformations on the finite set X_n={1,2,\ldots ,n}, respectively. Let \fix (\alpha )={x\in X_n:x\alpha =x} for any transformation \alpha. In this paper, for any Y\subseteq X_n, we find the cardinalities of the sets O_{n,Y}={\alpha\in O_n:\fix (\alpha)=Y} and C_{n,Y}={\alpha\in C_n: \fix (\alpha )=Y}. Moreover, we find the numbers of transformations of O_n and C_n with r fixed points.
Gpq Modules And Generalized Armendariz Modules, Liang Zhao, Xiaosheng Zhu
Gpq Modules And Generalized Armendariz Modules, Liang Zhao, Xiaosheng Zhu
Turkish Journal of Mathematics
Let M_R be a right R-module. We introduce the concept of right generalized p.q.-Baer modules (or simply, right GPQ modules) to extend the notion of right p.q.-Baer modules. We study on the relationship between the GPQ property of a module M_R and various quasi-Armendariz properties. We prove that every right GPQ module is a quasi-Armendariz module. As a sequence, we obtain a general form of some known results considering the p.q.Baer property of a ring, some known results are extended. Moreover, we prove that for the formal triangular ring R constructed from a pair of rings S, T and a …
Generalized Derivations On Lie Ideals In Prime Rings, Öznur Gölbaşi, Emi̇ne Koç
Generalized Derivations On Lie Ideals In Prime Rings, Öznur Gölbaşi, Emi̇ne Koç
Turkish Journal of Mathematics
Let R be a prime ring with characteristic different from two, U a nonzero Lie ideal of R and f be a generalized derivation associated with d. We prove the following results: (i) If [u,f(u)] \in Z, for all u \in U, then U \subset Z. (ii) (f,d) and (g,h) be two generalized derivations of R such that f(u)v=ug(v), for all u,v \in U, then U \subset Z. (iii) f([u,v])=\pm \lbrack u,v], for all u,v\in U, then U \subset Z.
A Boundary Value Problem For Bitsadze Equation In Matrix Form, Sezayi̇ Hizliyel, Mehmet Çağliyan
A Boundary Value Problem For Bitsadze Equation In Matrix Form, Sezayi̇ Hizliyel, Mehmet Çağliyan
Turkish Journal of Mathematics
In this work, we investigate the solvability of the problem \frac{\partial^2w}{\partial \overline\phi ^2}=f Re\{i\phi(z)w(z)\}=\gamma_1(z),Rew_{\overline\phi}(z)=\gamma_2(z) z \in \partial D in the unit disk of complex plane. Here f , \gamma_1 and \gamma_2 are given m \times s-complex matrix-valued functions; f\in L^{p} (\overline{D}), \gamma_1, \gamma_2 \in C(\partial D) and \phi is a generating solution for Q-holomorphic functions.
On Orders And Types Of Dirichlet Series Of Slow Growth, Yinying Kong, Huilin Gan
On Orders And Types Of Dirichlet Series Of Slow Growth, Yinying Kong, Huilin Gan
Turkish Journal of Mathematics
The present paper has the object of showing some interesting relationship on the maximum modulus, the maximum term, the index of maximum term and the coefficients of entire functions defined by Dirichlet series of slow growth; some properties like Taylor entire functions are obtained.
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.
Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo
Nontrivial Periodic Solutions Of Nonlinear Functional Differential Systems With Feedback Control, Yingxin Guo
Turkish Journal of Mathematics
This paper examines the existence of nontrivial periodic solutions for the nonlinear functional differential system with feedback control: \{\aligned x'(t)=x(t)a(t)-\big[\sum_{i=1}^n a_i(t)\int_0^{+\infty} f(t, x(t-\theta)) d}\varphi_i(\theta) +\sum_{j=1}^m b_j(t) \int_0^{+\infty} f(t,x'(t-\theta))\,d}\phi_j(\theta)+\sum_{\mu=1}^p c_\mu(t) \int_0^{\infty} u(t-\theta)\,d}\delta_\mu(\theta)\big], u'(t)=-\rho(t)u(t)+\sum_{\nu=1}^q \beta_\nu(t) \int_0^{\infty} f(t, x(t-\theta))\,d}\psi_\nu(\theta).\endaligned Under certain growth conditions on the nonlinearity f, several sufficient conditions for the existence of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative.
Existence And Uniqueness Of Solutions To Neutral Stochastic Functional Differential Equations With Infinite Delay In L^P(\Omega,C_H), Haibo Bao
Turkish Journal of Mathematics
In this paper, we shall consider the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay in L^p(\Omega,C_h) space: d[x(t)-G(x_t)]=f(t,x_t)dt+g(t,x_t)dB(t), where we assume f:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,R^n), g:R^+\times L^p(\Omega,C_h) \to L^p(\Omega,L(R^m, R^n)), G: L^p(\Omega,C_h) \to L^p(\Omega,R^n), p>2,\, and B(t) is a given m-dimensional Brownian motion.
On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy
On Maximum Principle And Existence Of Positive Weak Solutions For N\Times N Nonlinear Elliptic Systems Involving Degenerated P-Laplacian Operators, H. M. Serag, S. A. Khafagy
Turkish Journal of Mathematics
We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -\Delta_{P,p}u_i=\sum_{j=1}^na_{ij}(x) u_j ^{p-2}u_j+f_i(x,u_1,u_2, ... ,u_n) in \Omega, u_i=0,\ i=1,2,. n on \partial \Omega \} where the degenerated p-Laplacian defined as \Delta _{P,p}u=div [P(x) \nabla u ^{p-2}\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using ``sub-super solutions method''.
Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇
Korovkin Type Approximation Theorem For Functions Of Two Variables In Statistical Sense, Fadi̇me Di̇ri̇k, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In this paper, using the concept of A-statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical version. We also obtain a Voronovskaya-type theorem \ and some differential properties for sequences of positive linear operators constructed by means of the Bernstein polynomials of two variables.
A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin
A Note On Dominant Contractions Of Jordan Algebras, Farrukh Mukhamedov, Seyi̇t Temi̇r, Hasan Akin
Turkish Journal of Mathematics
We consider two positive contractions T,S:L_1(A,\tau) \longrightarrow L_1(A,\tau) such that T\leq S, here (A, \tau) is a semi-finite JBW-algebra. If there is an n_0 \in N such that S^{n_0}-T^{n_0}
The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen
The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen
Turkish Journal of Mathematics
The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei
A Gap Theorem For Complete Space-Like Hypersurface With Constant Scalar Curvature In Locally Symmetric Lorentz Spaces, Jiancheng Liu, Lin Wei
Turkish Journal of Mathematics
Let M^n be a complete space-like hypersurface with constant scalar curvature in locally symmetric Lorentz space N^{n+1}_1, S be the squared norm of the second fundamental form of M^n in N^{n+1}_1. In this paper, we obtain a gap property of S: if nP\leq \sup S\leq D(n,P) for some constants P and D(n, P), then either \sup S=nP and M^n is totally umbilical, or \sup S=D(n, P) and M^n has two distinct principal curvatures.
B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu
B.-Y. Chen Inequalities For Slant Submanifolds In Quaternionic Space Forms, Gabriel Eduard Vilcu
Turkish Journal of Mathematics
In this paper some B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms are established.
Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han
Extremal Lagrangian Submanifolds In A Complex Space Form N^N(4c), Shichang Shu, Annie Yi Han
Turkish Journal of Mathematics
Let N^n(4c) be the complex space form of constant holomorphic sectional curvature 4c, \varphi: M \to N^n(4c) be an immersion of an n-dimensional Lagrangian manifold M in N^n(4c). Denote by S and H the square of the length of the second fundamental form and the mean curvature of M. Let \rho be the non-negative function on M defined by \rho^2=S-nH^2, Q be the function which assigns to each point of M the infimum of the Ricci curvature at the point. In this paper, we consider the variational problem for non-negative functional U(\varphi)=\int_M\rho^2dv=\int_M(S-nH^2)dv. We call the critical points of U(\varphi) the …
A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen
A Note On The Lyapunov Exponent In Continued Fraction Expansions, Jianzhong Cheng, Lu-Ming Shen
Turkish Journal of Mathematics
Let T:[0,1) \to [0,1) be the Gauss transformation. For any irrational x \in [0,1), the Lyapunov exponent \alpha(x) of x is defined as \alpha(x)=\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) . By Birkoff Average Theorem, one knows that \alpha(x) exists almost surely. However, in this paper, we will see that the non-typical set \{x\in [0,1):\lim_{n\to\infty}\frac{1}{n} \log (T^n)'(x) does not exist\} carries full Hausdorff dimension.
New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo
New Inequalities Similar To Hardy-Hilbert's Inequality, Namita Das, Srinibas Sahoo
Turkish Journal of Mathematics
In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.
The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan
The Riemann Hilbert Problem For Generalized Q-Holomorphic Functions, Sezayi̇ Hizliyel, Mehmet Çağliyan
Turkish Journal of Mathematics
In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.
Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang
Trace Formulae For Schrödinger Systems On Graphs, Chuan-Fu Yang, Zhen-You Huang, Xiao-Ping Yang
Turkish Journal of Mathematics
For Schrödinger systems on metric graphs with \delta'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.
The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali
The Principal Eigencurves For A Nonselfadjoint Elliptic Operator, Aomar Anane, Omar Chakrone, Abdellah Zerouali
Turkish Journal of Mathematics
In this paper we study the existence of the principal eigencurves for a nonselfadjoint elliptic operator. We obtain their variational formulation. We establish also the continuity and the differentiability of the principal eigencurves.
Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota
Structural Properties Of Bilateral Grand Lebesque Spaces, E. Liflyand, E. Ostrovsky, L. Sirota
Turkish Journal of Mathematics
In this paper we study the multiplicative, tensor, Sobolev and convolution inequalities in certain Banach spaces, the so-called Bilateral Grand Lebesque Spaces. We also give examples to show the sharpness of these inequalities when possible.
Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators, Asha Ram Gairola, P. N. Agrawal
Direct And Inverse Theorems For The Bézier Variant Of Certain Summation-Integral Type Operators, Asha Ram Gairola, P. N. Agrawal
Turkish Journal of Mathematics
Recently, the Bézier variant of some well known operators were introduced (cf. [8]-[9]) and their rates of convergence for bounded variation functions have been investigated (cf. [2], [10]). In this paper we establish direct and inverse theorems for the Bézier variant of the operators M_n introduced in [5] in terms of Ditzian-Totik modulus of smoothness \omega_{\varphi^\lambda}(f,t) (0 \leqslant \lambda \leqslant1 ). These operators include the well known Baskakov-Durrmeyer and Szász-Durrmeyer type operators as special cases.
Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type, Yong Ding, Xinfeng Wu
Weak Hardy Space And Endpoint Estimates For Singular Integrals On Space Of Homogeneous Type, Yong Ding, Xinfeng Wu
Turkish Journal of Mathematics
We develop the theory of weak Hardy spaces H^{1,\infty} on space of homogeneous type. As some applications, we show that certain singular integral operators and fractional integral operators are bounded from H^{1,\infty} to L^{1,\infty} and L^{\frac{1}{1-\alpha},\infty}, respectively. We give also the endpoint estimates for Nagel and Stein's singular integrals studied in [10].
On Harmonicity In Some Moufang-Klingenberg Planes, Basri̇ Çeli̇k, Ati̇lla Akpinar, Süleyman Çi̇ftçi̇
On Harmonicity In Some Moufang-Klingenberg Planes, Basri̇ Çeli̇k, Ati̇lla Akpinar, Süleyman Çi̇ftçi̇
Turkish Journal of Mathematics
In this paper we study Moufang-Klingenberg planes M (A) defined over a local alternative ring A of dual numbers. We show that some collineations of M (A) preserve cross-ratio and thus establish a relation between harmonicity and harmonic position.