The Equation ${Dd'+D'D=D^2}$ For Derivations On C$^*$-Algebras,
2018
TÜBİTAK
The Equation ${Dd'+D'D=D^2}$ For Derivations On C$^*$-Algebras, Sayed Khalil Ekrami, Madjid Mirzavaziri
Turkish Journal of Mathematics
Let $\mathcal{A}$ be an algebra. A linear mapping $d:\mathcal{A}\to\mathcal{A}$ is called a derivation if $d(ab)=d(a)b+ad(b)$ for each $a,b\in\mathcal{A}$. Given two derivations $d$ and $d'$ on a C$^*$-algebra $\mathcal{A}$, we prove that there exists a derivation $D$ on $\mathcal A$ such that $dd'+d'd=D^2$ if and only if $d$ and $ d' $ are linearly dependent.
Boolean Differential Operators,
2018
TÜBİTAK
Boolean Differential Operators, Luis Hernandez Encinas, Ángel Martín Del Rey
Turkish Journal of Mathematics
In this work the notion of boolean differential operator is revisited and some new properties are stated.
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems,
2018
TÜBİTAK
Analysis Of Periodic And Asymptotically Periodic Solutions In Nonlinear Coupled Volterra Integro-Differential Systems, Youssef Raffoul
Turkish Journal of Mathematics
In this note, we investigate the existence of periodic and asymptotically periodic solutions of a system of coupled nonlinear Volterra integro-differential equations with infinite delay. We will make use of Schauder fixed point theorem to prove our maps have fixed points.
Regularity And Projective Dimension Of The Edge Ideal Of A Generalized Theta Graph,
2018
TÜBİTAK
Regularity And Projective Dimension Of The Edge Ideal Of A Generalized Theta Graph, Seyyede Masoome Seyyedi, Farhad Rahmati
Turkish Journal of Mathematics
Let $k\geq 3$ and $G=\theta_{n_1,\ldots, n_k}$ be a graph consisting of $k$ paths that have common endpoints. In this paper, we show that the projective dimension of $R/I(G)$ equals $bight I(G)$ or $ bight I(G)+1$. For some special cases, we explain $depth(R/I(G))$ in terms of invariants of graphs. Moreover, we prove the regularity of $R/I(G)$ equals $c_G$ or $c_G+1$, where $c_G$ is the maximum number of 3-disjoint edges in $G$.
On A Class Of Unitary Operators On The Bergman Space Of The Right Half Plane,
2018
TÜBİTAK
On A Class Of Unitary Operators On The Bergman Space Of The Right Half Plane, Namita Das, Jitendra Kumar Behera
Turkish Journal of Mathematics
In this paper, we introduce a class of unitary operators defined on the Bergman space $L_a^2(\mathbb{C}_+)$ of the right half plane $\mathbb{C}_+$ and study certain algebraic properties of these operators. Using these results, we then show that a bounded linear operator $S$ from $L_a^2(\mathbb{C}_+)$ into itself commutes with all the weighted composition operators $W_a, a \in \mathbb{D}$ if and only if $\widetilde{S}(w)=\langle Sb_{\overline{w}},b_{\overline{w}}\rangle, w \in \mathbb{C}_+ $ satisfies a certain averaging condition. Here for $a=c+id \in \mathbb{D}, f \in L_a^2(\mathbb{C}_+), W_af=(f \circ t_a) \frac{M^{\prime}}{M^{\prime} \circ t_a}, Ms=\frac{1-s}{1+s}, t_a(s)=\frac{-ids +(1-c)}{(1+c)s + id}$, and $b_{\overline{w}}(s)=\frac{1}{\sqrt{\pi}} \frac{1+w}{1+\overline{w}} \frac{2 \mbox {Re} w}{(s+w)^2}, w=M\overline {a}, …
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor,
2018
TÜBİTAK
The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski
Turkish Journal of Mathematics
How many linear connections are there with a prescribed Ricci tensor? The question is answered in the analytic case by using the Cauchy-Kowalevski theorem
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals,
2018
TÜBİTAK
Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek
Turkish Journal of Mathematics
In this paper, by applying the $p$-adic $q$-integrals to a family of continuous differentiable functions on the ring of $p$-adic integers, we construct new generating functions for generalized Apostol-type numbers and polynomials attached to the Dirichlet character of a finite abelian group. By using these generating functions with their functional equations, we derive various new identities and relations for these numbers and polynomials. These results are generalizations of known identities and relations including some well-known families of special numbers and polynomials such as the generalized Apostol-type Bernoulli, the Apostol-type Euler, the Frobenius-Euler numbers and polynomials, the Stirling numbers, and other …
An Inequality On The Hodge Number $H^{1,1}$ Of A Fibration And The Mordell-Weil Rank,
2018
TÜBİTAK
An Inequality On The Hodge Number $H^{1,1}$ Of A Fibration And The Mordell-Weil Rank, Cheng Gong, Hao Sun
Turkish Journal of Mathematics
In this paper, we establish some formulas on the Mordell-Weil rank and the Hodge number $h^{1,1}$ for a fibration.
An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus,
2018
TÜBİTAK
An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus, Muhammad Waseem, Muhammad Aslam Noor, Farooq Ahmed Shah, Khalida Inayat Noor
Turkish Journal of Mathematics
In this paper, we develop an efficient technique in the framework of multiplicative calculus and suggest a new class of numerical methods for solving multiplicative nonlinear equations \textit{g}(\textit{x}% ) = 1. We also develop the convergence criteria of the proposed methods. We solve the population growth model and minimization problem, which demonstrate the implementation and efficiency of the new techniques. We also show that these techniques perform much better as compared to the similar ordinary methods for solving ordinary nonlinear equations \textit{f}(\textit{x}) = 0.
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation,
2018
TÜBİTAK
An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar
Turkish Journal of Mathematics
The aim of this paper is to give an alternative solution for the $q$-kinetic equation involving the Riemann--Liouville fractional $q$-integral operator. The solution is obtained in terms of the $q$-Mittag--Leffler functions using inverse $q$-Sumudu transform. As applications, some corollaries are presented to illustrate the main results.
Hyperplanes, Parallelism, And Related Problems In Veronese Spaces,
2018
TÜBİTAK
Hyperplanes, Parallelism, And Related Problems In Veronese Spaces, Krzysztof Petelczyc, Krzysztof Prazmowski, Malgorzata Prazmowska, Mariusz Zynel
Turkish Journal of Mathematics
We determine hyperplanes in Veronese spaces associated with projective spaces and polar spaces, and we analyze the geometry of parallelisms induced by these hyperplanes. We also discuss whether or not parallelisms on Veronese spaces associated with affine spaces can be imposed.
Integral Representation For Solutions Of The Pseudoparabolic Equation In Matrix Form,
2018
TÜBİTAK
Integral Representation For Solutions Of The Pseudoparabolic Equation In Matrix Form, Yeşi̇m Sağlam Özkan, Sezayi̇ Hizliyel
Turkish Journal of Mathematics
In this paper, an integral representation is given for special bounded solutions of pseudoparabolic equations of the form $$ Lw:=\frac{\partial}{\partial t}\left(w_{\overline \phi}+aw+b\overline{w} \right) +cw+d\overline{w} $$ by means of a generating pair of the corresponding class of the generalized $Q$-holomorphic functions in $L_{p,2}(\mathbb{C})$, for $p>2$, where $a,\ b, \ c, \ d$ are functions of $z$ alone.
Bound States And Spectral Singularities Of An Impulsive Schrödinger Equation,
2018
TÜBİTAK
Bound States And Spectral Singularities Of An Impulsive Schrödinger Equation, Emel Yildirim
Turkish Journal of Mathematics
In this paper, we study the analytical properties of the Jost function of an impulsive Schrödinger equation. We also investigate the bound states and spectral singularities of this equation. We present some conditions on the potential function that guarantee that the impulsive Schrödinger equation has a finite number of bound states and spectral singularities with finite multiplicities.
Weak Convergence Of Probability Measures To Choquet Capacity Functionals,
2018
TÜBİTAK
Weak Convergence Of Probability Measures To Choquet Capacity Functionals, Dietmar Ferger
Turkish Journal of Mathematics
In the definition of weak convergence of probability measures it is assumed that the limit is a probability measure as well. We get rid of this assumption and require that the limit merely needs to be a Choquet-capacity functional. In terms of random variables this means that the distributional limit no longer is a random point, but a random closed set, namely one uniquely determined by the Choquet capacity. For our extended notion of weak convergence there is a counterpart of the portmanteau theorem. Moreover, we demonstrate basic relations to the theory of random closed sets with emphasis on weak …
Harmonic Functions Associated With Some Polynomials In Severalvariables,
2018
TÜBİTAK
Harmonic Functions Associated With Some Polynomials In Severalvariables, Fatma Taşdelen Yeşi̇ldal, Rabi̇a Aktaş, Esra Erkus Duman
Turkish Journal of Mathematics
The aim of this paper is to give various properties of homogeneous operators associated with Chan-Chyan-Srivastava polynomials and, by using these results, to obtain harmonic functions by applying Laplace and ultrahyperbolic operators to the Chan-Chyan-Srivastava polynomials.
A Vectorization For Nonconvex Set-Valued Optimization,
2018
TÜBİTAK
A Vectorization For Nonconvex Set-Valued Optimization, Emrah Karaman, İlknur Atasever Güvenç, Mustafa Soyertem, Di̇dem Tozkan, Mahi̇de Küçük, Yalçin Küçük
Turkish Journal of Mathematics
Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.
Bounded Solutions And Asymptotic Stability Of Nonlinear Second-Order Neutral Difference Equations With Quasi-Differences,
2018
TÜBİTAK
Bounded Solutions And Asymptotic Stability Of Nonlinear Second-Order Neutral Difference Equations With Quasi-Differences, Magdalena Nockowska Rosiak
Turkish Journal of Mathematics
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n $$ with respect to $(q_n)$. For $q_n\to1$, $q_n\in(0,1)$ the standard fixed point approach is insufficient to get the existence of the bounded solution, so we combine this method with an approximation technique to achieve our goal. Moreover, for $p\ge 1$ and $\sup q_n
Coframe Bundle And Problems Of Lifts On Itscross-Sections,
2018
TÜBİTAK
Coframe Bundle And Problems Of Lifts On Itscross-Sections, Arif Salimov, Habil Fattaev
Turkish Journal of Mathematics
The main purpose of this paper is to study the complete and horizontal lifts of vector and tensor fields of type (1,1) on cross-sections in the coframe bundle. Explicit formulas of these lifts are obtained. Finally, complete lifts of almost complex structures restricted to almost analytic cross-sections are investigated.
On Ordered Hypersemigroups Given By A Table Of Multiplication And A Figure,
2018
TÜBİTAK
On Ordered Hypersemigroups Given By A Table Of Multiplication And A Figure, Niovi Kehayopulu
Turkish Journal of Mathematics
The aim is to show that from every example of a regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered semigroup given by a table of multiplication and an order, a corresponding example of regular, intraregular, left (right) regular, left (right) quasiregular, semisimple, left (right) simple, simple, or strongly simple ordered hypersemigroup can be constructed having the same left (right) ideals, bi-ideals, quasi-ideals, or interior ideals. On this occasion, some further related results have also been given.
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations,
2018
TÜBİTAK
On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh
Turkish Journal of Mathematics
The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. In this paper, dominated coloring of graphs is compared with (open) packing number of $G$ and it is shown that if $G$ is a graph of order $n$ with $diam(G)\geq3$, then $\chi_{dom}(G)\leq n-\rho(G)$ and if $\rho_0 (G)=2n/3$, then $\chi_{dom}(G)= \rho_0 (G)$, and if $\rho(G)=n/2$, then $\chi_{dom}(G)=\rho(G)$. The dominated chromatic numbers of the …
