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Articles 1 - 30 of 140
Full-Text Articles in Physical Sciences and Mathematics
On Armendariz-Like Properties In Amalgamated Algebras Along Ideals, Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi
On Armendariz-Like Properties In Amalgamated Algebras Along Ideals, Abdeslam Mimouni, Najib Mahdou, Mounir El Ourrachi
Turkish Journal of Mathematics
Let $f: A\rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Armendariz-like properties to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ)$ introduced and studied by D'Anna, Finocchiaro, and Fontana in 2009. Our aim is to provide necessary and sufficient conditions for $A\bowtie^fJ$ to be an Armendariz ring, nil-Armendariz ring, and weak Armendariz ring.
Character Analogue Of The Boole Summation Formula With Applications, Mümün Can, Muhammet Ci̇hat Dağli
Character Analogue Of The Boole Summation Formula With Applications, Mümün Can, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we present the character analogue of the Boole summationformula. Using this formula, an integral representation is derived for thealternating Dirichlet $L$-function and its derivative is evaluated at $s=0$.Some applications of the character analogue of the Boole summation formula andthe integral representation are given about the alternating Dirichlet $L$-function. Moreover, the reciprocity formulas for two new arithmetic sums,arising from the summation formulas, and for Hardy--Berndt sum $S_{p}(b,c:\chi)$ are proved.
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
Turkish Journal of Mathematics
Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
Turkish Journal of Mathematics
The intention of this article is to investigate the most important inequalities of $m$-convex functions without using their derivatives. The article also provides a brief survey of general properties of $m$-convex functions.
Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang
Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang
Turkish Journal of Mathematics
This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed $c=c_*$) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves $\phi(x+c_{*}t)$ (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.
Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly
Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly
Turkish Journal of Mathematics
In this paper, sufficient criteria that guarantee the existence of stochastic asymptotic stability of the zero solution of the nonautonomous second-order stochastic delay differential equation \eqref{3e1} were established with the aid of a suitable Lyapunov functional. Two examples are given in the last section to illustrate our main result.
A Note On Locally Graded Minimal Non-Metahamiltonian Groups, Sevgi̇ Atlihan
A Note On Locally Graded Minimal Non-Metahamiltonian Groups, Sevgi̇ Atlihan
Turkish Journal of Mathematics
We prove that a nonperfect locally gradedminimal non-metahamiltonian group $G$ is a soluble group withderived length of at most 4. On the other hand, if $G$ is perfect,then $G/\Phi (G)$ is isomorphic to $A_{5}$, where $\Phi (G)$ isthe Frattini subgroup of $G$ and $A_{5}$ is the alternating group.Moreover, we show that under some conditions,if G is a $p$-group, then G is metabelian, where $p$ is a prime integer.
The Role Of The Ideal Elements In Studying The Structure Of Some Ordered Semigroups, Niovi Kehayopulu
The Role Of The Ideal Elements In Studying The Structure Of Some Ordered Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The aim of writing this paper is given in the title. We want to show that not only the ideals but also the ideal elements play an essential role in studying the structure of some ordered semigroups.We first prove that a $\vee e$-semigroup $S$ is a semilattice of left simple $\vee e$-semigroups if and only if it is decomposable into some pairwise disjoint left simple $\vee e$-subsemigroups of $S$ indexed by a semilattice $Y$. Then we give an example of a semilattice of left simple $\vee e$-semigroups that leads to a characterization of the semilattices of left simple and the …
Stationary Distribution And Global Asymptotic Stability Of A Three-Species Stochastic Food-Chain System, Hong Qiu, Wenmin Deng
Stationary Distribution And Global Asymptotic Stability Of A Three-Species Stochastic Food-Chain System, Hong Qiu, Wenmin Deng
Turkish Journal of Mathematics
This paper intends to study some dynamical properties of a stochasticthree-dimensional Lotka--Volterra system. Under some mild assumptions, we first introduce a simple method to show thatthe model has a global and positive solution almost surely. Secondly,we prove that this model has a stationary distribution. Then we study the global asymptoticstability of the positive solution. Finally, some numerical simulations are introduced toillustrate the theoretical results.
On Tetravalent Normal Edge-Transitive Cayley Graphs On The Modular Group, Hesam Sharifi, Mohammad Reza Darafsheh
On Tetravalent Normal Edge-Transitive Cayley Graphs On The Modular Group, Hesam Sharifi, Mohammad Reza Darafsheh
Turkish Journal of Mathematics
A Cayley graph $\Gamma=Cay(G, S)$ on a group $G$ with respective toa subset $S\subseteq G$, $S=S^{-1}, 1\notın S$, is said to be normaledge-transitive if $N_{\mathbb{A}ut(\Gamma)}(\rho(G))$ is transitiveon edges of $\Gamma$, where $\rho(G)$ is a subgroup of $\mathbb{A}ut(\Gamma)$isomorphic to $G$. We determine all connected tetravalent normaledge-transitive Cayley graphs on the modular group of order $8n$in the case that every element of $S$ is of order $4n$.
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Braided Regular Crossed Modules Bifibered Over Regular Groupoids, Alper Odabaş, Erdal Ulualan
Turkish Journal of Mathematics
We show that the forgetful functor from the category ofbraided regular crossed modules to the category of regular (or whiskered) groupoids is a fibration and also a cofibration.
Arf Numerical Semigroups, Sedat İlhan, Hali̇l İbrahi̇m Karakaş
Arf Numerical Semigroups, Sedat İlhan, Hali̇l İbrahi̇m Karakaş
Turkish Journal of Mathematics
The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup$S$ and its Lipman semigroup $L(S).$ This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.
On Hölder Continuity Of Approximate Solution Maps To Vector Equilibrium Problems, Lam Quoc Anh, Kien Trung Nguyen, Tran Ngoc Tam
On Hölder Continuity Of Approximate Solution Maps To Vector Equilibrium Problems, Lam Quoc Anh, Kien Trung Nguyen, Tran Ngoc Tam
Turkish Journal of Mathematics
In this article, we considerparametric vector equilibrium problems in normed spaces. Sufficientconditions for Hölder continuity of approximate solution mappingswhere they are set-valued are established. As applications of theseresults, the Hölder continuity of the approximate solutionmappings for vector optimization problems and vector variationalinequalities are derived at the end of the paper. Our results arenew and include the existing ones in the literature.
On The Bounds Of The Forgotten Topological Index, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami
On The Bounds Of The Forgotten Topological Index, Suresh Elumalai, Toufik Mansour, Mohammad Ali Rostami
Turkish Journal of Mathematics
The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph $G.$ In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus--Gaddum-type inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.
Extensions Of Quasipolar Rings, Orhan Gürgün
Extensions Of Quasipolar Rings, Orhan Gürgün
Turkish Journal of Mathematics
An associative ring with identity is called quasipolar provided that for each $a\in R$ there exists an idempotent $p\in R$ such that $p\in comm^2(a)$, $a+p\in U(R)$ and $ap\in R^{qnil}$. In this article, we introduce the notion of quasipolar general rings (with or without identity). Some properties of quasipolar general rings are investigated. We prove that a general ring $I$ is quasipolar if and only if every element $a\in I$ can be written in the form $a=s+q$ where $s$ is strongly regular, $s\in comm^2(a)$, $q$ is quasinilpotent, and $sq=qs=0$. It is shown that every ideal of a quasipolar general ring is …
New Statistical Randomness Tests: 4-Bit Template Matching Tests, Fati̇h Sulak
New Statistical Randomness Tests: 4-Bit Template Matching Tests, Fati̇h Sulak
Turkish Journal of Mathematics
For cryptographic algorithms, secret keys should be generated randomly as the security of the system depends on the key and therefore generation of random sequences is vital. Randomness testing is done by means of statistical randomness tests. In this work, we show that the probabilities for the overlapping template matching test in the NIST test suite are only valid for a specific template and need to be recalculated for the other templates. We calculate the exact distribution for all 4-bit templates and propose new randomness tests, namely template matching tests. The new tests can be applied to any sequence of …
Lie Symmetry Analysis And Exact Solutions Of The Sawada-Kotera Equation, Youwei Zhang
Lie Symmetry Analysis And Exact Solutions Of The Sawada-Kotera Equation, Youwei Zhang
Turkish Journal of Mathematics
In the present paper, the Sawada-Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada-Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada-Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equation.
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Turkish Journal of Mathematics
We investigate suborbital graphs for an imprimitive action of the Atkin-Lehner group on a maximal subset of extended rational numbers on which a transitive action is also satisfied. Obtaining edge and some circuit conditions, we examine some combinatorial properties of these graphs.
Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi
Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi
Turkish Journal of Mathematics
In this paper, we study the notion of substantial efficiency for a given multiobjective optimization problem. We provide two characterizations for substantially efficient solutions: the first one is based on a scalar problem and the second one is in terms of a stability concept. Moreover, this paper introduces the notion of quasi-substantial efficiency. Similar to those of substantial efficiency, two characterizations for quasi-substantially efficient solutions are obtained.
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Turkish Journal of Mathematics
In this paper, the authors consider the $\mathcal{P}_{v,2n}$-transform, the $\mathcal{G}_n$-transform, and the $\mathcal{K}_{v,n}$-transform as generalizations of the Widder potential transform, the Glasser transform, and the $\mathcal{K}_v$-transform, respectively. Many identities involving these transforms are given. A number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are presented. Illustrative examples are given for the results.
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
Turkish Journal of Mathematics
In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. We consider that the HBV infection processes act on a time scale different from that of the vital processes. Such a model becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. We apply, as in the paper of Banasiak and M'pika Massoukou: A …
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Turkish Journal of Mathematics
Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Product Of Arbitrary Fibonacci Numbers With Distance 1 To Fibonomial Coefficient, Nuretti̇n Irmak
Turkish Journal of Mathematics
In this paper, we solve completely the Diophantine equation \begin{gather} F_{n_{1}}F_{n_{2}}\ldots F_{n_{k}}\pm 1={m\brack t}_{F} \end{gather} for $t=1$ and $t=2$ where $2$ < $n_{1}$ < $n_{2}$ < $\ldots$ < $n_{k}$ positive integers and ${m\brack t}_{F}$ is the Fibonomial coefficient.
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems, Nawel Arrar, Natalia Djellab, Jean-Bernard Baillon
On The Stochastic Decomposition Property Of Single Server Retrialqueuing Systems, Nawel Arrar, Natalia Djellab, Jean-Bernard Baillon
Turkish Journal of Mathematics
The study of retrial queuing systems presents great analytical difficulties. Detailed results are available for some models, whereas for other models the obtained results revealed poor information and are cumbersome (they contain Laplace transforms, integral expressions, etc.). Therefore, in practice, they present limited performance. Often, to overcome this difficulty, we use an approach based on the stochastic decomposition property that can be possessed by the model. It offers the advantages of simplification of solving complex models. This paper deals with the stochastic decomposition property of an M$^{X}$/G/1 retrial queue with impatient customers and exponential retrial times and of an M/G/1 …
Free Storage Basis Conversion Over Finite Fields, Ersan Akyildiz, Ndangang Yampa Harold, Ahmet Sinak
Free Storage Basis Conversion Over Finite Fields, Ersan Akyildiz, Ndangang Yampa Harold, Ahmet Sinak
Turkish Journal of Mathematics
Representation of a field element plays a crucial role in the efficiency of field arithmetic. If an efficient representation of a field element in one basis exists, then field arithmetic in the hardware and/or software implementations becomes easy. Otherwise, a basis conversion to an efficient one is searched for easier arithmetic. However, this conversion often brings a storage problem for transition matrices associated with these bases. In this paper, we study this problem for conversion between normal and polynomial bases in the extension field $\mathbb{F}_{q^p}$ over $\mathbb{F}_q$ where $q=p^n$. We construct transition matrices that are of a special form. This …
On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
On Certain Semigroups Of Full Contraction Maps Of A Finite Chain, Goje Uba Garba, Muhammad Jamilu Ibrahim, Abdussamad Tanko Imam
Turkish Journal of Mathematics
Let $X_{n}=\{1,2,\ldots,n\}$ with its natural order and let ${\cal T}_{n}$ be the full transformation semigroup on $X_{n}$. A map $\alpha\in{\cal T}_{n}$ is said to be order-preserving if, for all $x,y\in X_{n}$, $x\leq y\Rightarrow x\alpha\leq y\alpha$. The map $\alpha\in{\cal T}_{n}$ is said to be a contraction if, for all $x,y\in X_{n}$, $ x\alpha-y\alpha \leq x-y $. Let ${\cal CT}_{n}$ and ${\cal OCT}_{n}$ denote, respectively, subsemigroups of all contraction maps and all order-preserving contraction maps in ${\cal T}_{n}$. In this paper we present characterisations of Green's relations on ${\cal CT}_{n}$ and starred Green's relations on both ${\cal CT}_{n}$ and ${\cal OCT}_{n}$.
$F$-Biminimal Immersions, Fatma Gürler, Ci̇han Özgür
$F$-Biminimal Immersions, Fatma Gürler, Ci̇han Özgür
Turkish Journal of Mathematics
In the present paper, we define $f$-biminimal immersions. We consider $f$-biminimal curves in a Riemannian manifold and $f$-biminimal submanifolds of codimension $1$ in a Riemannian manifold, and we give examples of $f$-biminimal surfaces. Finally, we consider $f$-biminimal Legendre curves in Sasakian space forms and give an example.
Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu
Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu
Turkish Journal of Mathematics
We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.
When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam
When Zero-Divisor Graphs Are Divisor Graphs, Emad Abu Osba, Osama Alkam
Turkish Journal of Mathematics
Let $R$ be a finite commutative principal ideal ring with unity. In this article, we prove that the zero-divisor graph $\Gamma(R)$ is a divisor graph if and only if $R$ is a local ring or it is a product of two local rings with at least one of them having diameter less than $2$. We also prove that $\Gamma(R)$ is a divisor graph if and only if $\Gamma(R[x])$ is a divisor graph if and only if $\Gamma(R[[x]])$ is a divisor graph.
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
P-Subordination Chains And P-Valence Integral Operators, Erhan Deni̇z, Hali̇t Orhan, Murat Çağlar
Turkish Journal of Mathematics
In the present investigation we obtain some sufficient conditions for the analyticity and the $p$-valence of an integral operator in the unit disk $\mathbb{D}$. Using these conditions we give some applications for a few different integral operators. The significant relationships and relevance to other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.