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Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Effect Of Fractional Analysis On Some Special Curves, Aykut Has, Beyhan Yilmaz
Turkish Journal of Mathematics
In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curves is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Caputo fractional analysis that fits the algebraic structure of differential geometry is used. This is because the Caputo fractional derivative of the constant function is zero. This is an important advantage and allows a variety of fractional physical problems to be based on a geometric basis. This effect is examined with the help …
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 …
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 $L^{p,q}_\alpha(\Omega).$
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.
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.
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.
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.
Notes On Totally Geodesic Foliations Of A Complete Semi-Riemannian Manifold, An Sook Shin, Hyelim Han, Hobum Kim
Notes On Totally Geodesic Foliations Of A Complete Semi-Riemannian Manifold, An Sook Shin, Hyelim Han, Hobum Kim
Turkish Journal of Mathematics
In this paper, we prove that the orthogonal complement $\mathcal{F}^{\perp}$ of a totally geodesic foliation $\mathcal{F}$ on a complete semi-Riemannian manifold $(M,g)$ satisfying a certain inequality between mixed sectional curvatures and the integrability tensor of $\mathcal{F}^{\perp}$ is totally geodesic. We also obtain conditions for the existence of totally geodesic foliations on a complete semi-Riemannian manifold $(M,g)$ with bundle-like metric $g$.
Some Remarks On Parameterized Inequalities Involving Conformable Fractional Operators, Ci̇han Ünal, Fati̇h Hezenci̇, Hüseyi̇n Budak
Some Remarks On Parameterized Inequalities Involving Conformable Fractional Operators, Ci̇han Ünal, Fati̇h Hezenci̇, Hüseyi̇n Budak
Turkish Journal of Mathematics
In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems.
The Normalized Miller-Ross Function And Its Geometric Properties, Khaled Mehrez
The Normalized Miller-Ross Function And Its Geometric Properties, Khaled Mehrez
Turkish Journal of Mathematics
The main objective of this paper is to study certain geometric properties (like univalence, starlikeness, convexity, close-to-convexity) for the normalized Miller-Ross function. The various results, which we have established in the present investigation, are believed to be new, and their importance is illustrated by several interesting consequences and examples. Furthermore, some of the main results improve the corresponding results available in the literature [15].
A Calculus For Intuitionistic Fuzzy Values, Enes Yavuz
A Calculus For Intuitionistic Fuzzy Values, Enes Yavuz
Turkish Journal of Mathematics
We introduce $^\oplus$calculus and $^\otimes$calculus for intuitionistic fuzzy values and prove some basic theorems by using multiplicative calculus which has useful tools to represent the concepts of introduced calculi. Besides, we construct some isomorphic mappings to interpret the relationships between $^\oplus$calculus and $^\otimes$calculus. This paper reveals also new calculi for fuzzy sets in particular.
Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez
Atomic Systems In Krein Spaces, Osmin Ferrer Villar, Edilberto Arroyo Ortiz, José Naranjo Martínez
Turkish Journal of Mathematics
In the present article, we establish a definition of atomic systems in the Krein spaces, specifically, we establish the fundamental tools of the theory of atomic systems in the formalism of the Krein spaces and give a complete characterization of them. We also show that the atomic systems do not depend on the decomposition of the Krein space.
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
The Set Of Arf Numerical Semigroups With Given Frobenius Number, María Ángeles Moreno-Frías, Jose Carlos Rosales
Turkish Journal of Mathematics
A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$
A Note On Half Of Some Med Semigroups Of Maximal Or Almost Maximal Length, Ahmet Çeli̇k
A Note On Half Of Some Med Semigroups Of Maximal Or Almost Maximal Length, Ahmet Çeli̇k
Turkish Journal of Mathematics
In this study, we have shown that numerical semigroups $M=<3,C+1,C+2>$ and $M=<3,C,C+2>$ have maximal or almost maximal length, with conductor $C$, where $C\equiv0(3)$ and $C\equiv2(3),$ respectively. We also examined whether half of these numerical semigroups were of maximal or almost maximal length.
Neumann Boundary Value Problem For The Beltrami Equation In A Ring Domain, İlker Gençtürk
Neumann Boundary Value Problem For The Beltrami Equation In A Ring Domain, İlker Gençtürk
Turkish Journal of Mathematics
In this paper, the Neumann boundary value problem for the Beltrami operator is explicitly solved in a circular ring domain, solvability conditions for this problem are also given in explicit forms. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part as combinations of the Cauchy-Riemann and the Beltrami operators is investigated.
Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak
Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak
Turkish Journal of Mathematics
The main object of this scientific work is firstly to introduce various operators of fractional calculus (that is that fractional integral and fractional derivative(s)) in certain domains of the complex plane, then to determine certain results correlating with normalized analytic functions, which are analytic in certain domains in the complex plane, as a few applications of those operators, and also to present a number of extensive implications of them as special results.
Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen
Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen
Turkish Journal of Mathematics
Let $A_{1}$ and $A_{2}$ be an $\{\alpha_{1}, \beta_{1}, \gamma_{1}\}$-cubic matrix and an $\{\alpha_{2}, \beta_{2}\}$-quadratic matrix, respectively, with $\alpha_{1} \neq \beta_{1}$, $\beta_{1} \neq \gamma_{1}$, $\alpha_{1} \neq \gamma_{1}$ and $\alpha_{2}\neq \beta_{2}$. In this work, we characterize all situations in which the linear combination $A_{3}=a_{1}A_{1}+a_{2}A_{2}$ with the assumption $A_{1}A_{2}=A_{2}A_{1}$ is an $\{\alpha_{3}, \beta_{3}\}$-quadratic matrix, where $a_{1}$ and $a_{2}$ are unknown nonzero complex numbers.
On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök
On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök
Turkish Journal of Mathematics
Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren
Turkish Journal of Mathematics
In this paper, we present some relationships between statistical boundedness and statistical monotonicity of a given sequence and its subsequences. The results concerning statistical boundedness and monotonicity presented here are also closely related to earlier results regarding statistical convergence and are dealing with the Lebesgue measure and with the Baire category.
On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu
On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu
Turkish Journal of Mathematics
This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup properties for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.
K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya
K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya
Turkish Journal of Mathematics
In this paper, we introduce $q-$analogue of Liu-Owa integral operator and define a subclass of $k-$uniformly multivalent starlike functions of order $\gamma, (0\leq\gamma< p; p\in\mathbb{N})$ by using the Liu-Owa $q-$integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of $k-$uniformly multivalent starlike functions of order $\gamma$. Moreover, we determine radii of $k-$uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass.