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Articles 1351 - 1380 of 2494
Full-Text Articles in Physical Sciences and Mathematics
Some Properties Of Alternate Duals And Approximate Alternate Duals Of Fusion Frames, Ali Akbar Arefijamaal, Fahimeh Arabyani Neyshaburi
Some Properties Of Alternate Duals And Approximate Alternate Duals Of Fusion Frames, Ali Akbar Arefijamaal, Fahimeh Arabyani Neyshaburi
Turkish Journal of Mathematics
In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain alternate dual and approximate alternate dual fusion frames. We also study the stability of alternate dual and approximate alternate dual fusion frames.
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.
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 …
Near Optimal Step Size And Momentum In Gradient Descent For Quadratic Functions, Engi̇n Taş, Memmedağa Memmedli̇
Near Optimal Step Size And Momentum In Gradient Descent For Quadratic Functions, Engi̇n Taş, Memmedağa Memmedli̇
Turkish Journal of Mathematics
Many problems in statistical estimation, classification, and regression can be cast as optimization problems. Gradient descent, which is one of the simplest and easy to implement multivariate optimization techniques, lies at the heart of many powerful classes of optimization methods. However, its major disadvantage is the slower rate of convergence with respect to the other more sophisticated algorithms. In order to improve the convergence speed of gradient descent, we simultaneously determine near-optimal scalar step size and momentum factor for gradient descent in a deterministic quadratic bowl from the largest and smallest eigenvalues of the Hessian. The resulting algorithm is demonstrated …
On The Attached Prime Ideals Of Localcohomology Modules Defined By A Pair Of Ideals, Zohreh Habibi, Maryam Jahangiri, Khadijeh Ahmadi Amoli
On The Attached Prime Ideals Of Localcohomology Modules Defined By A Pair Of Ideals, Zohreh Habibi, Maryam Jahangiri, Khadijeh Ahmadi Amoli
Turkish Journal of Mathematics
Let $I$ and $J$ be two ideals of a commutative Noetherian ring $R$ and $M$ be an $R$-module of dimension $d$. For each $i\in N_0$ let $H^{i}_{I,J}(-)$ denote the $i$-th right derived functor of $\Gamma_{I,J}(-)$, where $\Gamma _{I,J}(M):=\{x \in M : I^{n}x\subseteq Jx \ \text {for} \ n\gg 1\}$. If $R$ is a complete local ring and $M$ is finite, then attached prime ideals of $H^{d-1}_{I,J}(M)$ are computed by means of the concept of co-localization. Moreover, we illustrate the attached prime ideals of $H^{t}_{I,J}(M)$ on a nonlocal ring $R$, for $t= \dim M$ and $t= (I,J,M)$, where $(I,J,M)$ is the …
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.
Nonpolynomial Spline Technique For The Solution Of Ninth Order Boundary Value Problems, Ghazala Akram, Zara Nadeem
Nonpolynomial Spline Technique For The Solution Of Ninth Order Boundary Value Problems, Ghazala Akram, Zara Nadeem
Turkish Journal of Mathematics
In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. The comparative analysis shows that the proposed technique gives better results than the homotopy perturbation method and the modified variational iteration method.
Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat
Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat
Turkish Journal of Mathematics
In this work, we extend the uni-dimensional results, already found by Jerbi and Kharrat, for the multidimensional case: we compute the Malliavin weights related to the conditional expectation $\mathbb{E}(P_{t}(X_{t}) (X_{s}))$ for $0 \leq s \leq t$, where the only state variable follows a multidimensional J-process.
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.
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.
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.
Almost Contact Metric Structures Induced By $G_2$ Structures, Nüli̇fer Özdemi̇r, Mehmet Solgun, Şi̇ri̇n Aktay
Almost Contact Metric Structures Induced By $G_2$ Structures, Nüli̇fer Özdemi̇r, Mehmet Solgun, Şi̇ri̇n Aktay
Turkish Journal of Mathematics
We study almost contact metric structures induced by 2-fold vector cross products on manifolds with $G_2$ structures. We get some results on possible classes of almost contact metric structures. Finally, we give examples.
A Characterization Of Nonprime Powers, Raul Duran Diaz, Luis Hernandez Encinas, Agustin Martin Muñoz, Jaime Muñoz Masque, Seok-Zun Song
A Characterization Of Nonprime Powers, Raul Duran Diaz, Luis Hernandez Encinas, Agustin Martin Muñoz, Jaime Muñoz Masque, Seok-Zun Song
Turkish Journal of Mathematics
A criterion is presented in order to decide whether agiven integer is a prime power or not. The criterion associatesto each positive integer $m$ a finite set of integers$\mathcal{S}(m)$, each of them $\le m $ and the propertiesof this set are studied. The notion of complementary pairsin $\mathcal{S}(m)$ is introduced and it is proved that if one isable to determine a complementary pair $n,n^\prime $, thena partial factorization of the odd integer $m$ can be obtainedin polynomial time. Some particular cases and examples of these resultsare given.
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 $4n$.
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 Generalized Kropina Change Of $M$Th Root Finsler Metrics With Special Curvature Properties, Bankteshwar Tiwari, Ghanashyam Kr. Prajapati
On Generalized Kropina Change Of $M$Th Root Finsler Metrics With Special Curvature Properties, Bankteshwar Tiwari, Ghanashyam Kr. Prajapati
Turkish Journal of Mathematics
In the present paper, we consider generalized Kropina change of $m$th root Finsler metrics and prove that every generalized Kropina change of $m$th root Finsler metrics with isotropic Berwald curvature, isotropic mean Berwald curvature, relatively isotropic Landsberg curvature, and relatively isotropic mean Landsberg curvature reduces to the Berwald metric, weakly Berwald metric, Landsberg metric, and weakly Landsberg metric, respectively. We also show that every generalized Kropina change of $m$th root Finsler metrics with almost vanishing $\textbf{H}$-curvature has vanishing $\textbf{H}$-curvature.
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.
On Orthogonal Systems Of Shifts Of Scaling Function On Local Fields Of Positive Characteristic, Gleb Sergeevich Berdnikov, Iuliia Sergeevna Kruss, Sergey Fedorovich Lukomskii
On Orthogonal Systems Of Shifts Of Scaling Function On Local Fields Of Positive Characteristic, Gleb Sergeevich Berdnikov, Iuliia Sergeevna Kruss, Sergey Fedorovich Lukomskii
Turkish Journal of Mathematics
We present a new method for constructing an orthogonal step scaling function on local fields of positive characteristic, which generates multiresolution analysis.
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 …
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a boundary value problem of impulsive differential systems on the whole line with one-dimensional p-Laplacians. By constructing a weighted Banach space and defining a nonlinear operator, together with Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established (Theorems 3.1-3.3). Two examples are given to illustrate the main results.
Finite Volume Approximation Of The Relativistic Burgers Equation On A Schwarzschild-(Anti-)De Sitter Spacetime, Tuba Ceylan, Baver Okutmuştur
Finite Volume Approximation Of The Relativistic Burgers Equation On A Schwarzschild-(Anti-)De Sitter Spacetime, Tuba Ceylan, Baver Okutmuştur
Turkish Journal of Mathematics
The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constant is also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments.
Subspace Condition For Bernstein's Lethargy Theorem, Asuman Güven Aksoy, Monairah Al-Ansari, Caleb Case, Qidi Peng
Subspace Condition For Bernstein's Lethargy Theorem, Asuman Güven Aksoy, Monairah Al-Ansari, Caleb Case, Qidi Peng
Turkish Journal of Mathematics
In this paper, we consider a condition on subspaces in order to improve bounds given in Bernstein's lethargy theorem for Banach spaces. Let $d_1 \geq d_2 \geq \dots d_n \geq \dots > 0$ be an infinite sequence of numbers converging to $0$, and let $Y_1 \subset Y_2 \subset \dots\subset Y_n \subset \dots \subset X$ be a sequence of closed nested subspaces in a Banach space $X$ with the property that $\overline{Y}_{n}\subset Y_{n+1}$ for all $n\ge1$. We prove that for any $c ın (0,1]$ there exists an element $x_c ın X$ such that$$ c d_n \leq \rho(x_c, Y_n) \leq \min (4, \tilde{a}) …
The $T$-Successive Associated Stirling Numbers, $T$-Fibonacci--Stirling Numbers, And Unimodality, Hacene Belbachir, Assia-Fettouma Tebtoub
The $T$-Successive Associated Stirling Numbers, $T$-Fibonacci--Stirling Numbers, And Unimodality, Hacene Belbachir, Assia-Fettouma Tebtoub
Turkish Journal of Mathematics
Using a combinatorial approach, we introduce the \textit{$t$-successive associated Stirling numbers} and we give the recurrence relation and the generating function. We also establish the unimodality of sequence $\genfrac{\{}{\}}{0pt}{}{n-2k}{k}_{k}$ lying over a ray of the second kind's Stirling triangle. Some combinatorial identities are given.
Sufficient Conditions For The Compactifiability Of A Closed One-Form Foliation, Irina Gelbukh
Sufficient Conditions For The Compactifiability Of A Closed One-Form Foliation, Irina Gelbukh
Turkish Journal of Mathematics
We study the foliation defined by a closed $1$-form on a connected smooth closed orientable manifold.We call such a foliation compactifiable if all its leaves are closed in the complement of the singular set.In this paper, we give sufficient conditions for compactifiability of the foliation in homological terms.We also show that under these conditions, the foliation can be defined by closed $1$-forms with the ranks of their groups of periods in a certain range.In addition, we describe the structure of the group generated by the homology classes of all compact leaves of the foliation.
The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇
The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇
Turkish Journal of Mathematics
In this short paper we present a generalization of the Hahn--Banach extensiontheorem for $A$-linear operators. Some theoretical applications andresults are given.
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.
A Novel Kind Of Akns Integrable Couplings And Their Hamiltonian Structures, Yu-Juan Zhang, Wen-Xiu Ma, Ömer Ünsal
A Novel Kind Of Akns Integrable Couplings And Their Hamiltonian Structures, Yu-Juan Zhang, Wen-Xiu Ma, Ömer Ünsal
Turkish Journal of Mathematics
We present a novel hierarchy of AKNS integrable couplings based on a specific semidirect sum of Lie algebras associated with sl$(2)$. By applying the variational identity, we derive a bi-Hamiltonian structure of the resulting coupling systems, thereby showing their Liouville integrability.
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic
Turkish Journal of Mathematics
In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive.The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.
Generalized Crossed Modules And Group-Groupoids, Mustafa Habi̇l Gürsoy, Hati̇ce Aslan, İlhan İçen
Generalized Crossed Modules And Group-Groupoids, Mustafa Habi̇l Gürsoy, Hati̇ce Aslan, İlhan İçen
Turkish Journal of Mathematics
In this present work, we present the concept of a crossed module over generalized groupsand we call it a "generalized crossed module". We also define a generalizedgroup-groupoid. Furthermore, we show that the category of generalized crossedmodules is equivalent to that of generalized group-groupoids whose object sets are abelian generalized group.