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2018

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Articles 1201 - 1230 of 1332

Full-Text Articles in Mathematics

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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Diagonal Lift In The Semi-Cotangent Bundle And Its Applications, Furkan Yildirim Jan 2018

Diagonal Lift In The Semi-Cotangent Bundle And Its Applications, Furkan Yildirim

Turkish Journal of Mathematics

The present paper is devoted to some results concerning the diagonal lift of tensor fields of type (1,1) from manifold M to its semi-cotangent bundle t*M. In this context, cross-sections in the semi-cotangent (pull-back) bundle t*M of cotangent bundle T*M by using projection (submersion) of the tangent bundle TM can be also defined.

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Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul Jan 2018

Fréchet-Hilbert Spaces And The Property Scbs, Eli̇f Uyanik, Murat Hayretti̇n Yurdakul

Turkish Journal of Mathematics

In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioğlu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Fréchet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Fréchet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Fréchet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Fréchet-Hilbert space has the SCBS property.

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Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal Jan 2018

Jakimovski-Leviatan Operators Of Durrmeyer Type Involving Appell Polynomials, Pooja Gupta, Purshottam Narain Agrawal

Turkish Journal of Mathematics

The purpose of the present paper is to establish the rate of convergence for a Lipschitz-type space and obtain the degree of approximation in terms of Lipschitz-type maximal function for the Durrmeyer type modification of Jakimovski-Leviatan operators based on Appell polynomials. We also study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation.

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A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi Jan 2018

A New Class Of Generalized Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi

Turkish Journal of Mathematics

Motivated by their importance and potential for applications in a variety of research fields, recently, various polynomials and their extensions have been introduced and investigated. In this sequel, we modify the known generating functions of polynomials, due to both Milne-Thomson and Dere and Simsek, to introduce a new class of generalized polynomials and present some of their involved properties. As obvious special cases of the newly introduced polynomials, we also introduce so-called power sum-Laguerre--Hermite polynomials and generalized Laguerre and Euler polynomials and we present some of their involved identities and formulas. The results presented here, being very general, are pointed …

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