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Articles 121 - 140 of 140
Full-Text Articles in Physical Sciences and Mathematics
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.
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.
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.