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2018

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Regularity And Projective Dimension Of The Edge Ideal Of A Generalized Theta Graph, Seyyede Masoome Seyyedi, Farhad Rahmati Jan 2018

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 $G$.

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On A Class Of Unitary Operators On The Bergman Space Of The Right Half Plane, Namita Das, Jitendra Kumar Behera Jan 2018

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}, …

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The Cauchy-Kowalevski Theorem Applied For Counting Connections With A Prescribed Ricci Tensor, Barbara Opozda, Wlodzimierz M. Mikulski Jan 2018

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

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Construction Of Some New Families Of Apostol-Type Numbers And Polynomials Via Dirichlet Character And $P$-Adic $Q$-Integrals, Yilmaz Şi̇mşek Jan 2018

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 …

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An Inequality On The Hodge Number $H^{1,1}$ Of A Fibration And The Mordell-Weil Rank, Cheng Gong, Hao Sun Jan 2018

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.

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An Efficient Technique To Solve Nonlinear Equations Usingmultiplicative Calculus, Muhammad Waseem, Muhammad Aslam Noor, Farooq Ahmed Shah, Khalida Inayat Noor Jan 2018

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.

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An Application Of $Q$-Sumudu Transform For Fractional $Q$-Kinetic Equation, Sunil Dutt Purohit, Faruk Uçar Jan 2018

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.

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Hyperplanes, Parallelism, And Related Problems In Veronese Spaces, Krzysztof Petelczyc, Krzysztof Prazmowski, Malgorzata Prazmowska, Mariusz Zynel Jan 2018

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.

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Integral Representation For Solutions Of The Pseudoparabolic Equation In Matrix Form, Yeşi̇m Sağlam Özkan, Sezayi̇ Hizliyel Jan 2018

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.

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Bound States And Spectral Singularities Of An Impulsive Schrödinger Equation, Emel Yildirim Jan 2018

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.

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Weak Convergence Of Probability Measures To Choquet Capacity Functionals, Dietmar Ferger Jan 2018

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 …

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Harmonic Functions Associated With Some Polynomials In Severalvariables, Fatma Taşdelen Yeşi̇ldal, Rabi̇a Aktaş, Esra Erkus Duman Jan 2018

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.

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A Vectorization For Nonconvex Set-Valued Optimization, Emrah Karaman, İlknur Atasever Güvenç, Mustafa Soyertem, Di̇dem Tozkan, Mahi̇de Küçük, Yalçin Küçük Jan 2018

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.

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Bounded Solutions And Asymptotic Stability Of Nonlinear Second-Order Neutral Difference Equations With Quasi-Differences, Magdalena Nockowska Rosiak Jan 2018

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

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Coframe Bundle And Problems Of Lifts On Itscross-Sections, Arif Salimov, Habil Fattaev Jan 2018

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.

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On Ordered Hypersemigroups Given By A Table Of Multiplication And A Figure, Niovi Kehayopulu Jan 2018

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.

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On Dominated Coloring Of Graphs And Some Nordhaus--Gaddum-Type Relations, Fatemeh Choopani, Abbas Jafarzadeh, Ahmad Erfanian, Doost Ali Mojdeh Jan 2018

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 …

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On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar Jan 2018

On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar

Turkish Journal of Mathematics

Affine periodicity is a generalization of the notion of conventional periodicity and it is a symmetry property for classes of functions. This study is concerned with the existence of $(Q,T)$-affine periodic solutions of discrete dynamical systems. Sufficient conditions for the main results are proposed due to discrete exponential dichotomy and fixed point theory. Obtained results are also implemented for some economical and biological models. In particular cases, our results cover some existing results in the literature for periodic, antiperiodic, or quasiperiodic solutions of difference equations.

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Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections, Leyla Bugay, Hayrullah Ayik Jan 2018

Generating Sets Of Certain Finite Subsemigroups Of Monotone Partial Bijections, Leyla Bugay, Hayrullah Ayik

Turkish Journal of Mathematics

Let $I_{n}$ be the symmetric inverse semigroup, and let $PODI_{n}$ and $POI_{n}$ be its subsemigroups of monotone partial bijections and of isotone partial bijections on $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups $PODI_{n,r}=\{ \alpha \in PODI_{n}: \im(\alpha) \leq r\}$, $POI_{n,r}=\{ \alpha \in POI_{n}: \im(\alpha) \leq r\}$, and $E_{n,r}=\{ \id_{A}\in I_{n}:A\subseteq X_n\mbox{ and } A \leq r\}$ where $id_{A}$ is the identity map on $A\subseteq X_n$ for $0\leq r\leq n-1$.

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On A Class Of Kazdan--Warner Equations, Yu Fang, Mengjie Zhang Jan 2018

On A Class Of Kazdan--Warner Equations, Yu Fang, Mengjie Zhang

Turkish Journal of Mathematics

Let $(\small{\Si},g)$ be a compact Riemannian surface without boundary and $W^{1,2}(\Si)$ be the usual Sobolev space. For any real number $p>1$ and $\alpha\in\mathbb{R}$, we define a functional $$ J_{\alpha,8\pi}(u)=\frac{1}{2}\le( \int_\Si \nabla_g u ^2dv_g-\alpha (\int_\Si u ^pdv_g)^{2/p}\ri)-8\pi\log\int_\Si he^u dv_g $$ on a function space $\mathcal{H}=\le\{u\in W^{1,2}(\Si):\int_{\Si}u dv_{g}=0\ri\}$, where $h$ is a positive smooth function on $\Si$. Denote $$\lambda_{1,p}(\Si)=\inf_{u\in \mathcal{H},\,\int_\Si u ^p dv_g=1}\int_{\Si} \nabla_{g}u ^{2}\mathrm{d}v_{g}. $$ If $\alpha

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On The Summability Methods Of Logarithmic Type And The Berezin Symbol, Ulaş Yamanci Jan 2018

On The Summability Methods Of Logarithmic Type And The Berezin Symbol, Ulaş Yamanci

Turkish Journal of Mathematics

We prove by means of the Berezin symbols some theorems for the $\left( L\right) $-summability method for sequences and series. Also, we prove a new Tauberian type theorem for $\left( L\right) $-summability.

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Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences, Nares Sawatraksa, Chaiwat Namnak Jan 2018

Green's Relations And Regularity On Some Subsemigroups Of Transformations That Preserve Equivalences, Nares Sawatraksa, Chaiwat Namnak

Turkish Journal of Mathematics

Let $T(X)$ be the full transformation semigroup on a set $X$. For two equivalence relations $E$ and $F$ on $X$ with $F \subseteq E$, let $T(X, E, F) = \{ \alpha \in T(X) : \forall x, y \in X, (x, y)\in E \Rightarrow (x\alpha, y\alpha) \in F \}. $

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Global Attractors For The Semilinear Beam Equationwith Localized Viscosity, Sema Yayla Jan 2018

Global Attractors For The Semilinear Beam Equationwith Localized Viscosity, Sema Yayla

Turkish Journal of Mathematics

In this paper, we deal with the semilinear beam equation with localized viscosity. Under mild conditions on the viscous coefficient, we establish the well-posedness and boundedness of the weak solutions. Then we prove that the semigroup generated by this problem has a smooth global attractor in $H^{3}\left( 0,1\right) \times H_{0}^{1}\left( 0,1\right) $.

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3-Class Groups Of Cubic Cyclic Function Fields, Zhengjun Zhao Jan 2018

3-Class Groups Of Cubic Cyclic Function Fields, Zhengjun Zhao

Turkish Journal of Mathematics

Let $F$ be a global function field over the finite constant field $\mathbb{F}_q$ with $3\mid q-1$, and let $K/F$ be a cubic cyclic function fields extension with Galois group $G=$Gal$(K/F)=$. Denote by $\mathcal{C}(K)$ and $\mathcal{C}(K)_3$ the ideal class group of $K$ and its Sylow 3-subgroup, respectively. Let $\mathcal{C}(K)_3^G=\{[\fa]\in \mathcal{C}(K)_3 \ \sigma[\fa]=[\fa]\}$ and $\mathcal{C}(K)_3^{1-\sigma}=\{[\fa](\sigma[\fa])^{-1} \ [\fa]\in \mathcal{C}(K)_3\}$. In this paper, we present a method for computing the 3-rank of the quotient group $\mathcal{C}(K)_3^G\mathcal{C}(K)_3^{1-\sigma}/\mathcal{C}(K)_3^{1-\sigma}$. Specifically, when $K$ is a cubic Kummer extension of $\mathbb{F}_q(T)$, we determine explicitly the key factors $t$, $x_1,\cdots, x_t$, and $[\mathfrak{A}_1],\cdots, [\mathfrak{A}_t]$ in the process of computing the …

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Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m Jan 2018

Higher Order Generalized Geometric Polynomials, Levent Kargin, Bayram Çeki̇m

Turkish Journal of Mathematics

According to the generalized Mellin derivative, we introduce a new family of polynomials called higher order generalized geometric polynomials and obtain some arithmetical properties of them. Then we investigate the relationship of these polynomials with degenerate Bernoulli, degenerate Euler, and Bernoulli polynomials. Finally, we evaluate several series and integrals in closed forms.

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Legendrian Torus Knots In Lens Spaces, Si̇nem Onaran Jan 2018

Legendrian Torus Knots In Lens Spaces, Si̇nem Onaran

Turkish Journal of Mathematics

In this study, we first classify all topological torus knots lying on the Heegaard torus in lens spaces, and then we study Legendrian representatives of these knots. We classify oriented positive Legendrian torus knots in the universally tight contact structures on the lens spaces up to contactomorphism.

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Variational Problem Involving Operator Curl Associated With $P$-Curl System, Junichi Aramaki Jan 2018

Variational Problem Involving Operator Curl Associated With $P$-Curl System, Junichi Aramaki

Turkish Journal of Mathematics

We shall study the problem of minimizing a functional involving curl of vector fields in a three-dimensional, bounded multiconnected domain with the prescribed tangent component of a given vector field on the boundary. It will be seen that the minimizers are weak solutions of the $p$-curl type system. We shall prove the existence and the estimate of minimizers of a more general functional that contains the $L^p$ norm of the curl of vector fields. We shall also give the continuity with respect to the given data.

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Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen Jan 2018

Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen

Turkish Journal of Mathematics

In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{(4)}(x)+(k_{1}+k_{2})y''(x)+k_{1}k_{2}y(x)=f(x,y(x)), \ \ x\in (0,1),\\ &y(0)=y'(1)=y''(0)=y'''(1)=0,\\ \endaligned \right. $$ which models a statically elastic beam with one of its ends simply supported and the other end clamped by sliding clamps, where $k_{1}

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Graphs Of $Bci/Bck$-Algebras, Atena Tahmasbpour Meikola Jan 2018

Graphs Of $Bci/Bck$-Algebras, Atena Tahmasbpour Meikola

Turkish Journal of Mathematics

The aim of this paper is to study special graphs of $BCI/BCK$-algebras. In this paper, we introduce one kind of graph of $BCI$-algebras based on branches of $X$ and two kinds of graphs of $BCK$-algebras based on ideal $I$. Then we study some of the essential properties of graph theory on the basis of those structures. In particular, we study the planar, outerplanar, toroidal, $K$-connected, chordal, $K$-partite, and Eulerian properties of graph theory.

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On Some Multivariate Lcm And Gcd Sums, Khola Algali Jan 2018

On Some Multivariate Lcm And Gcd Sums, Khola Algali

Turkish Journal of Mathematics

In this paper we obtain an asymptotic formula with a power saving error term for the summation function of a family of generalized least common multiple and greatest common divisor functions of several integer variables.

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