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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.
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.
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
On The Zariski Topology Over An $L$-Module $M$, Fethi̇ Çallialp, Gülşen Ulucak, Ünsal Teki̇r
Turkish Journal of Mathematics
Let $L$ be a multiplicative lattice and $M$ be an $L$-module. In this study, we present a topology said to be the Zariski topology over $\sigma (M),$ the collection of all prime elements of an $L$-module $M.$ We research some results on the Zariski topology over $\sigma (M).$ We show that the topology is a $T_{0}$-space and a $T_{1}$-space under some conditions. Some properties and results are studied for the topology over $\sigma (L)$, the collection of all prime elements of a multiplicative lattice $L.$
Evolution Equations With A Parameter And Application To Transport-Convection Differential Equations, Emile Franc Doungmo Goufo
Evolution Equations With A Parameter And Application To Transport-Convection Differential Equations, Emile Franc Doungmo Goufo
Turkish Journal of Mathematics
We deeply investigate the well-posedness of models taking the form $_0^AD^{\beta }_tu(t) = Au(t),\;\; u(0)= \,f,\;\;\;00$ where $_0^AD^{\beta }_t$ is a derivative with the fractional parameter $\beta$ and $A$ is a closed densely defined operator in a Banach space. We show that, unlike other systems, solutions of our models are not governed by Mittag--Leffler functions and their variants. We extend and adapt Peano's idea to our models and establish conditions for existence and uniqueness of solutions. In particular, relations between the two-parameter solution operator, its resolvent, and its generator are provided; the issue of subordination and prolongation principles are addressed; …
Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici
Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici
Turkish Journal of Mathematics
The trial equation method, which was proposed by Cheng-Shi Liu, is a very powerful method for solving nonlinear differential equations. After the original trial method, some modified versions of the trial equation method were introduced and applied to some famous nonlinear differential equations. Although each modified trial equation method provides a different perspective, they have some weaknesses according to the given differential equations. This is the main reason for introducing modified trial equation methods. This study aims to define a general representation of trial methods for solving nonlinear differential equations. The generalized trial equation method consists of the simple trial …
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
On Golden Semisymmetric Metric $F$-Connections, Aydin Gezer, Çağri Karaman
Turkish Journal of Mathematics
In this paper, we construct a golden semisymmetric metric $F$-connection on a locally decomposable golden Riemannian manifold and investigate some properties of its curvature, conharmonic curvature, Weyl projective curvature, and torsion tensors. Moreover, we define the transposed connection of this connection and study its curvature properties.
On The 3-Dimensional Hopf Bifurcation Via Averaging Theory Of Third Order, Elouahma Bendib, Sabrina Badi, Ammar Makhlouf
On The 3-Dimensional Hopf Bifurcation Via Averaging Theory Of Third Order, Elouahma Bendib, Sabrina Badi, Ammar Makhlouf
Turkish Journal of Mathematics
We apply the averaging theory of third order to polynomial quadratic vector fields in $\mathbb{R}^3$ to study the Hopf bifurcation occurring in that polynomial. Our main result shows that at most $10$ limit cycles can bifurcate from a singular point having eigenvalues of the form $\pm bi$ and $0$. We provide an example of a quadratic polynomial differential system for which exactly $10$ limit cycles bifurcate from a such singular point.
On $\Lambda$-Perfect Maps, Mehrdad Namdari, Mohammad Ali Siavoshi
On $\Lambda$-Perfect Maps, Mehrdad Namdari, Mohammad Ali Siavoshi
Turkish Journal of Mathematics
$\lambda$-Perfect maps, a generalization of perfect maps (i.e. continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some classical results regarding $\lambda$-perfect maps will be extended. In particular, we show that if the composition $fg$ is a $\lambda$-perfect map where $f,g$ are continuous maps with $fg$ well-defined, then $f,g$ are $\alpha$-perfect and $\beta$-perfect, respectively, on appropriate spaces, where $\alpha, \beta\leq\lambda$.
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Warped Product Spaces With Ricci Conditions, Sang Deok Lee, Byung Hak Kim, Jin Hyuk Choi
Turkish Journal of Mathematics
In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
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.
A Note On The Conjugacy Problem For Finite Sylow Subgroups Of Linear Pseudofinite Groups, Pinar Uğurlu Kowalski̇
A Note On The Conjugacy Problem For Finite Sylow Subgroups Of Linear Pseudofinite Groups, Pinar Uğurlu Kowalski̇
Turkish Journal of Mathematics
We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with nonconjugate finite Sylow $2$-subgroups, which was constructed by Platonov.
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Corrigendum: On Density Theorems For Rings Of Krull Type With Zero Divisors, Başak Ay Saylam
Turkish Journal of Mathematics
This corrigendum is written to correct some parts of the paper "On density theorems for rings of Krull type with zero divisors". The proofs of Proposition 2.4 and Proposition 4.3 are incorrect and the current note makes the appropriate corrections.
Minimizing Graph Of The Connected Graphs Whose Complements Are Bicyclic With Two Cycles, Muhammad Javaid
Minimizing Graph Of The Connected Graphs Whose Complements Are Bicyclic With Two Cycles, Muhammad Javaid
Turkish Journal of Mathematics
In a certain class of graphs, a graph is called minimizing if the least eigenvalueof its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, we characterize the minimizinggraph among all the connected graphs that belong to a class of graphs whose complements are bicyclic with two cycles.
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Extension Of The Darboux Frame Into Euclidean 4-Space And Its Invariants, Mustafa Düldül, Bahar Uyar Düldül, Nuri̇ Kuruoğlu, Ertuğrul Özdamar
Turkish Journal of Mathematics
In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4-space $\mathbb{E}^4$. Depending on the linear independency of the curvature vector with the hypersurface's normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in $\mathbb{E}^4$. Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface.
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Quasi-Metric Trees And $Q$-Hyperconvex Hulls, Zechariah Mushaandja, Olivier Olela Otafudu
Turkish Journal of Mathematics
The investigation of metric trees began with J. Tits in 1977. Recently we studied a more general notion of quasi-metric tree. In the current article we prove, among other facts, that the $q$-hyperconvex hull of a $q$-hyperconvex $T_0$-quasi-metric tree is itself a $T_0$-quasi-metric tree. This is achieved without using the four-point property, a geometric concept used by Aksoy and Maurizi to show that every complete metric tree is hyperconvex.
Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi
Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi
Turkish Journal of Mathematics
In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module. In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Turkish Journal of Mathematics
The Schrödinger equation for the eigenvalues of the infinitely deep square well potential is solved within the class of generalised functions. It is found that the ground state consists of a step function like eigenfunction with the eigenvalue zero.
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 For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Asymptotic For A Second-Order Evolution Equation With Convex Potential Andvanishing Damping Term, Ramzi May
Turkish Journal of Mathematics
In this short note, we recover by a different method the new result due to Attouch, Chbani, Peyrouqet, and Redont concerning the weak convergence as $t\rightarrow+\infty$ of solutions $x(t)$ to the second-order differential equation $x^{\prime\prime}(t)+\frac{K}{t}x^{\prime}(t)+\nabla\Phi(x(t))=0,$ where $K>3$ and $\Phi$\ is a smooth convex function defined on a Hilbert space $\mathcal{H}.$ Moreover, we improve their result on the rate of convergence of $\Phi(x(t))-\min\Phi.$
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.
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Generalized $\Ast$-Lie Ideal Of $\Ast$-Prime Ring, Seli̇n Türkmen, Neşet Aydin
Turkish Journal of Mathematics
Let $R$ be a $\ast$-prime ring with characteristic not $2,$ $\sigma, \tau:R\rightarrow R$ be two automorphisms, $U$ be a nonzero $\ast$-$\left( \sigma,\tau\right) $-Lie ideal of $R$ such that $\tau~$commutes with $\ast$, and $a,b$ be in $R.$ $\left( i\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] =0$, then $a\in Z\left( R\right) $ or $U\subset Z\left( R\right) .$ $\left( ii\right) $ If $a\in S_{\ast}\left( R\right) $ and $\left[ U,a\right] _{\sigma,\tau}\subset$ $C_{\sigma,\tau}$, then $a\in Z\left( R\right) ~$or$~U\subset Z\left( R\right) .$ $\left( iii\right) $ If $U\not \subset Z\left( R\right) $ and $U\not \subset C_{\sigma,\tau}$, then there exists a nonzero $\ast$-ideal $M$ of …
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 …
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Singular Dirac Systems In The Sobolev Space, Eki̇n Uğurlu
Turkish Journal of Mathematics
In this paper we construct Weyl's theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, we describe the behavior of the solution belonging to the Sobolev space around the singular point.
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Turkish Journal of Mathematics
In this paper, taking into account the function $\theta $, we introduce a new type of contraction for multivalued maps on metric space. This new concept includes many known contractions in the literature. We then present some fixed point results for closed and bounded set valued maps on complete metric space. Finally, we provide an example to show the significance of the investigation of this paper.
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$, Mehmet Özen, Nazmi̇ye Tuğba Özzai̇m, Nuh Aydin
Cyclic Codes Over $\Mathbb{Z}_{4}+U\Mathbb{Z}_{4}+U^{2}\Mathbb{Z}_{4}$, Mehmet Özen, Nazmi̇ye Tuğba Özzai̇m, Nuh Aydin
Turkish Journal of Mathematics
In this paper, we study cyclic codes over the ring $R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$,where $u^{3}=0$. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over $R$. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over $\mathbb{Z}_4$ by considering Gray images of cyclic codes over $R$.
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki
Stability Analysis Of Nonlinear Fractional Differential Order Systems With Caputo And Riemann--Liouville Derivatives, Javad Alidousti, Reza Khoshsiar Ghaziani, Ali Bayati Eshkaftaki
Turkish Journal of Mathematics
In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann--Liouville derivatives. In particular, we derive conditions for $ {\bf \cal{F}}$-stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.
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 …
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Topological Entropies Of A Class Of Constrained Systems, Yanni Ma, Bingzhe Hou
Turkish Journal of Mathematics
In this paper, we consider a class of constrained systems named double upper bounds $(p,q)$-constrained systems ($(p,q)$-DUB systems in brief), which are one-dimensional subshifts of finite type. We determinate the topological entropies (Shannon capacities) $C(p,q)$ of all $(p,q)$-DUB systems and consequently order all $(p,q)$-DUB systems according to the size of topological entropies. In particular, $C(p, \infty)=C(p+1, p+1)$ are the only equalities possible among the topological entropies of $(p,q)$-DUB systems.
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.