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Articles 241 - 270 of 2595
Full-Text Articles in Physical Sciences and Mathematics
The Adjoint Reidemeister Torsion For Compact 3-Manifolds Admitting A Unique Decomposition, Esma Di̇ri̇can Erdal
The Adjoint Reidemeister Torsion For Compact 3-Manifolds Admitting A Unique Decomposition, Esma Di̇ri̇can Erdal
Turkish Journal of Mathematics
Let $M$ be a triangulated, oriented, connected compact $3$-manifold with a connected nonempty boundary. Such a manifold admits a unique decomposition into $\triangle$-prime $3$-manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact $3$-manifolds without a corrective term.
Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova
Boundary Value Problem For A Loaded Fractional Diffusion Equation, Arsen V. Pskhu, Murat I. Ramazanov, Minzilya Kosmakova
Turkish Journal of Mathematics
In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of …
Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel
Characterizations Of The Commutators Involving Idempotents In Certain Subrings Of $M_{2}(\Mathbb{Z})$, Tufan Özdi̇n, Günseli̇ Gümüşel
Turkish Journal of Mathematics
In this paper, we characterize the idempotency, cleanness, and unit-regularity of the commutator $[E_1, E_2]=E_1E_2-E_2E_1$ involving idempotents $E_1,E_2$ in certain subrings of $M_{2}(\mathbb{Z})$.
On The Frobenius Norm Of Commutator Of Cauchy-Toeplitz Matrix And Exchange Matrix, Süleyman Solak, Mustafa Bahşi̇
On The Frobenius Norm Of Commutator Of Cauchy-Toeplitz Matrix And Exchange Matrix, Süleyman Solak, Mustafa Bahşi̇
Turkish Journal of Mathematics
Matrix commutator and anticommutator play an important role in mathematics, mathematical physic, and quantum physic. The commutator and anticommutator of two $n\times n$ complex matrices $A$ and $B$ are defined by $\left[ A,B% \right] =AB-BA$ and $\left( A,B\right) =AB+BA$, respectively. Cauchy-Toeplitz matrix and exchange matrix are two of the special matrices and they have excellent properties. In this study, we mainly focus on Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix. Moreover, we give upper and lower bounds for the Frobenius norm of the commutator of Cauchy-Toeplitz matrix and exchange matrix.
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
What Can Lattices Do For Hypersemigroups?, Niovi Kehayopulu
Turkish Journal of Mathematics
This is from Birkhoff, the "father of lattice theory" in Trends in Lattice Theory. Van Nostrand 1970: "Lattices can do things for you, no matter what kind of mathematician you are!". The aim of this paper is to show that the $le$-semigroups (lattice ordered semigroups possessing a greatest element) play the main role in studying the ordered hypersemigroups. From many results on lattice ordered semigroups corresponding results on ordered semigroups can be obtained. The converse is also possible but the beauty and simplicity of "order" makes it easier to investigate the lattice ordered semigroup at first. After getting the results …
Generalization Of Statistical Limit-Cluster Points And The Concepts Of Statistical Limit Inferior-Superior On Time Scales By Using Regular Integral Transformations, Ceylan Yalçin
Turkish Journal of Mathematics
With the aid of regular integral operators, we will be able to generalize statistical limit-cluster points and statistical limit inferior-superior ideas on time scales in this work. These two topics, which have previously been researched separately from one another sometimes only in the discrete case and other times in the continuous case, will be studied at in a single study. We will investigate the relations of these concepts with each other and come to a number of new conclusions. On some well-known time scales, we shall analyze these ideas using examples.
A Note On $Ss$-Supplement Submodules, Emi̇ne Önal Kir
A Note On $Ss$-Supplement Submodules, Emi̇ne Önal Kir
Turkish Journal of Mathematics
In this paper, we describe $ss$-supplement submodules in terms of a special class of endomorphisms. Let $R$ be a ring with semisimple radical and $P$ be a projective $R-$module. We show that there is a bijection between ss-supplement submodules of $P$ and ss-supplement submodules of $End_{R}(P)$. Moreover, we define radical-s-projective modules as a generalization of projective modules. We prove that every $ss$-supplement submodule of a projective $R-$module is radical-s-projective over the ring $R$ with semisimple radical. We show that over $SSI$-ring $R$, every radical-s-projective $R-$module is projective. We provide that over a ring $R$ with semisimple radical, every $ss$-supplement submodule …
Bi-Periodic Incomplete Horadam Numbers, Eli̇f Tan, Mehmet Dağli, Amine Belkhir
Bi-Periodic Incomplete Horadam Numbers, Eli̇f Tan, Mehmet Dağli, Amine Belkhir
Turkish Journal of Mathematics
In this paper, we introduce bi-periodic~incomplete~Horadam numbers as a natural generalization of incomplete Horadam numbers. We study their basic properties and provide recurrence relations. In particular, we derive the generating function of these numbers.
Boundedness Of Bergman Projections Acting On Weighted Mixed Norm Spaces, Ivana Savkovic
Boundedness Of Bergman Projections Acting On Weighted Mixed Norm Spaces, Ivana Savkovic
Turkish Journal of Mathematics
We prove that Bergman projections on weighted mixed norm spaces on smoothly bounded domains in $\mathbb{R}^n$ are bounded for a certain range of parameters of such spaces and assuming certain conditions on weights. The proof relies on estimates of integral means of $M_p(P_\gamma f, r)$ in terms of integral means of $f$. This result complements earlier result on boundedness of $P_\gamma$ on a closely related space $L^{p,q}_\alpha(\Omega).$
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
On The Hilbert Series Of The Tangent Cones For Some 4-Generated Pseudosymmetric Monomial Curves, Ni̇l Şahi̇n
Turkish Journal of Mathematics
In this article, we study Hilbert series of non-Cohen-Maculay tangent cones for some 4-generated pseudosymmetric monomial curves. We show that the Hilbert function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Turkish Journal of Mathematics
This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems for Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay.
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Between Graphical Zonotope And Graph-Associahedron, Marko Pesovic, Tanja Stojadinovic
Turkish Journal of Mathematics
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph, and the last is the graph-associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to $\mathcal{H}$-polytopes.
Some Estimates On The Exponential Stability Of Solutions Of Nonlinear Neutral Type Systems With Periodic Coefficients, Yener Altun
Some Estimates On The Exponential Stability Of Solutions Of Nonlinear Neutral Type Systems With Periodic Coefficients, Yener Altun
Turkish Journal of Mathematics
In this present study, we pay attention to a class of nonlinear neutral type systems (NNSs) with periodic coefficients and construct some assumptions guaranteeing the exponential stability (ES) of the trivial solutions of the system considered. To get specific conditions guaranteeing the ES, we use a modified Lyapunov functional. In conclusion, we get some estimates for the exponential decay of the solutions at infinity with the constructed sufficient conditions. We give two examples to demonstrate the applicability of the results obtained with the constructed assumptions.
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Twisted Dirac Operators And The Kastler-Kalau-Walze Type Theorem For Five Dimensional Manifolds With Boundary, Tong Wu, Sining Wei, Yong Wang
Turkish Journal of Mathematics
In this paper, we prove the Kastler-Kalau-Walze type theorems for twisted Dirac operators on 5-dimensional manifolds with boundary.
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Qualitative Study Of A Second Order Difference Equation, Messaoud Berkal, Juan Francisco Navarro
Turkish Journal of Mathematics
In this paper, we study a second order rational difference equation. We analyze the stability of the unique positive equilibrium of the equation and prove the existence of a Neimark-Sacker bifurcation, validating our theoretical analysis via a numerical exploration of the system.
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
On Max-Min Solutions Of Fuzzy Games With Nonlinear Memberships Functions, Adem Cengi̇z Çevi̇kel
Turkish Journal of Mathematics
In this paper, we deal with two-person zero-sum games with fuzzy goals. We investigated the cases where the membership functions of the players are nonlinear. We examined how the solutions should be if the membership functions of players were exponential functions. In case players' membership functions are exponential, we developed a new method for the maximin solution according to a degree of attainment of the fuzzy goals. An application was made to show the effectiveness of the method.
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
On Conditions Of Regular Solvability For Two Classes Of Third-Order Operator-Differential Equations In A Fourth-Order Sobolev-Type Space, Araz R. Aliev, Nazila L. Muradova
Turkish Journal of Mathematics
In this paper, we study two classes of operator-differential equations of the third order with a multiple characteristic, considered on the whole axis. We introduce the concept of a smooth regular solution of order 1 and obtain sufficient conditions for the "smoothly" regular solvability of these equations.
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Curves And Stick Figures Not Contained In A Hypersurface Of A Given Degree, Edoardo Ballico
Turkish Journal of Mathematics
A stick figure $X\subset \mathbb{P}^r$ is a nodal curve whose irreducible components are lines. For fixed integers $r\ge 3$, $s\ge 2$ and $d$ we study the maximal arithmetic genus of a connected stick figure (or any reduced and connected curve) $X\subset \mathbb{P}^r$ such that $\deg (X)=d$ and $h^0(\mathcal{I}_X(s-1))=0$. We consider Halphen's problem of obtaining all arithmetic genera below the maximal one.
Contiguity Distance Between Simplicial Maps, Ayşe Borat, Mehmetci̇k Pamuk, Tane Vergi̇li̇
Contiguity Distance Between Simplicial Maps, Ayşe Borat, Mehmetci̇k Pamuk, Tane Vergi̇li̇
Turkish Journal of Mathematics
For simplicial complexes and simplicial maps, the notion of being in the same contiguity class is defined as the discrete version of homotopy. In this paper, we study the contiguity distance, $SD$, between two simplicial maps adapted from the homotopic distance. In particular, we show that simplicial versions of $LS$-category and topological complexity are particular cases of this more general notion. Moreover, we present the behaviour of $SD$ under the barycentric subdivision, and its relation with strong collapsibility of a simplicial complex.
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Novel Fano Type Lower Bounds On The Minimum Error Probability Of List $M$-Ary Hypothesis Testing, Berkan Dülek
Turkish Journal of Mathematics
he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Scattering Solutions And Scattering Function Of A Klein-Gordon S-Wave Equation With Jump Conditions, Hali̇t Taş, Yelda Aygar Küçükevci̇li̇oğlu, Elgi̇z Bayram
Turkish Journal of Mathematics
In this work, we are interested in a boundary value problem (BVP) generated by a Klein -Gordon equation (KG) with Jump conditions and a boundary condition. First, we introduce scattering solutions and Jost solution of the problem. Then, we give the scattering function and we prove some properties of it. Lastly, we conclude the paper by a special example.
Numerical Solutions Of Differential Equations Having Cubic Nonlinearity Using Boole Collocation Method, Kübra Erdem Bi̇çer, Hale Gül Dağ
Numerical Solutions Of Differential Equations Having Cubic Nonlinearity Using Boole Collocation Method, Kübra Erdem Bi̇çer, Hale Gül Dağ
Turkish Journal of Mathematics
The aim of the study is to develop a numerical method for the solution of cubic nonlinear differential equations in which the numerical solution is based on Boole polynomials. That solution is in the form of the truncated series and gives approximate solution for nonlinear equations of cubic type. In this method, firstly, the matrix form of the serial solution is set and the nonlinear differential equation is converted into a matrix equation system. By adding the effect of both the conditions of the problem and the collocation points to this system of equations, we obtain the new system of …
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Metrical Almost Periodicity, Metrical Approximations Of Functions And Applications, Belkacem Chaouchi, Marko Kostic, Daniel Velinov
Turkish Journal of Mathematics
In this paper, we analyze Levitan and Bebutov metrical approximations of functions $F :\Lambda \times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n}$, $X$ and $Y$ are complex Banach spaces, and $\rho$ is a general binary relation on $Y$. We also analyze various classes of multidimensional Levitan almost periodic functions in general metric and multidimensional Bebutov uniformly recurrent functions in general metric. We provide several applications of our theoretical results to the abstract Volterra integro-differential equations and the partial differential equations.
Generating Functions For Reciprocal Catalan-Type Sums: Approach To Linear Differentiation Equation And ($P$-Adic) Integral Equations, Damla Gün, Yilmaz Şi̇mşek
Generating Functions For Reciprocal Catalan-Type Sums: Approach To Linear Differentiation Equation And ($P$-Adic) Integral Equations, Damla Gün, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
This article is inspired by the reciprocal Catalan sums associated with problem 11765, proposed by David Beckwith and Sag Harbor. For this reason, partial derivative equations, the first-order linear differentiation equation and integral representations for series and generating functions for reciprocal Catalan-type sums containing the Catalan-type numbers are constructed. Some special values of these series and generating functions, which are given solutions of problem 11765, are found. Partial derivative equations of the generating function for the Catalan-type numbers are given. By using these equations, recurrence relations and derivative formulas involving these numbers are found. Finally, applying the $p$-adic Volkenborn integral …
Locally Product-Like Statistical Submersions, Kazuhi̇ko Takano, Esra Erkan, Mehmet Gülbahar
Locally Product-Like Statistical Submersions, Kazuhi̇ko Takano, Esra Erkan, Mehmet Gülbahar
Turkish Journal of Mathematics
In this paper, the main identities on locally product-like statistical submersions are obtained with the aid of statistical structures and their Riemannian curvature tensors. Some examples of locally product-like statistical submersions are presented. Some results on $F$-invariant, $F^{\ast}$-invariant and antiinvariant locally product-like statistical submersions are given.
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Closure Operators, Irreducibility, Urysohn's Lemma, And Tietze Extension Theorem For Proximity Spaces, Samed Özkan, Muammer Kula, Sümeyye Kula, Tesni̇m Meryem Baran
Turkish Journal of Mathematics
In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of $T_{i}, i=0,1,2$, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and $T_{i}, i=1,2$, proximity spaces. Finally, we present Tietze extension theorem and Urysohn's lemma for proximity spaces.
On Generalized Darboux Frame Of A Spacelike Curve Lying On A Lightlike Surface In Minkowski Space $\Mathbb{E}^{3}_{1}$, Jelena Djordjevic, Emilija Nesovic, Ufuk Öztürk
On Generalized Darboux Frame Of A Spacelike Curve Lying On A Lightlike Surface In Minkowski Space $\Mathbb{E}^{3}_{1}$, Jelena Djordjevic, Emilija Nesovic, Ufuk Öztürk
Turkish Journal of Mathematics
In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on a lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that $\alpha$ has two such frames and obtain generalized Darboux frame's equations. We find the relations between the curvature functions $k_g$, $k_n$, $\tau_g$ of $\alpha$ with respect to its Darboux frame and the curvature functions $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ with respect to generalized Darboux frames. We show that such frames exist along a spacelike straight line lying on a ruled surface which is not entirely lightlike, but contains some lightlike points. We define lightlike ruled surfaces on …
Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia
Global Existence, Asymptotic Behavior And Blow Up Of Solutions For A Kirchhoff-Type Equation With Nonlinear Boundary Delay And Source Terms, Houria Kamache, Nouri Boumaza, Billel Gheraibia
Turkish Journal of Mathematics
The main goal of this work is to study an initial boundary value problem for a Kirchhoff-type equation with nonlinear boundary delay and source terms. This paper is devoted to prove the global existence, decay, and the blow up of solutions. To the best of our knowledge, there are not results on the Kirchhoff type-equation with nonlinear boundary delay and source terms.
Numerical Radius, Berezin Number, And Berezin Norm Inequalities For Sums Of Operators, Najla Altwaijry, Kais Feki, Nicusor Minculete
Numerical Radius, Berezin Number, And Berezin Norm Inequalities For Sums Of Operators, Najla Altwaijry, Kais Feki, Nicusor Minculete
Turkish Journal of Mathematics
The purpose of this article is to explore various inequalities pertaining to the numerical radius of operators in a Hilbert space. Additionally, we present several bounds for the Berezin number and Berezin norm of operators that act on a reproducing kernel Hilbert space. Finally, we establish a necessary and sufficient condition for the triangle inequality related to the Berezin number to hold.
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
On The Relation Between Oscillation Of Solutions Of Differential Equations And Corresponding Equations On Time Scales, Olexandr Stanzhytskyi, Roza Uteshova, Victoriia Tsan, Zoia Khaletska
Turkish Journal of Mathematics
This paper studies oscillatory properties of solutions of a dynamic equation on the set of time scales $\mathbf{T}_\lambda$ provided that the graininess function $\mu_\lambda$ approaches zero as $\lambda\to 0$. We derived the conditions under which oscillation of solutions of differential equations implies that of solutions of the corresponding equations defined on time scales with the same initial data, and vice versa.