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2018

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Articles 10861 - 10890 of 11790

Full-Text Articles in Physical Sciences and Mathematics

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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The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano Jan 2018

The Classification Of Rings With Its Genus Of Class Of Graphs, Thangaraj Asir, Karuppiah Mano

Turkish Journal of Mathematics

Let $R$ be a commutative ring, $I$ be a proper ideal of $R$, and $S(I)=\{a\in R : ra\in I \text{ for some } r\in R\sm I\}$ be the set of all elements of $R$ that are not prime to $I$. The total graph of $R$ with respect to $I$, denoted by $T(\Gamma_I(R))$, is the simple graph with all elements of $R$ as vertices, and for distinct $x,y\in R$, the vertices $x$ and $y$ are adjacent if and only if $x+y\in S(I)$. In this paper, we determine all isomorphic classes of commutative Artinian rings whose ideal-based total graph has genus at …

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Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu Jan 2018

Convergence Analysis And Numerical Solution Of The Benjamin-Bona-Mahony Equation By Lie-Trotter Splitting, Fatma Zürnaci, Nurcan Gücüyenen Kaymak, Muaz Seydaoğlu, Gamze Tanoğlu

Turkish Journal of Mathematics

In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.

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On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk Jan 2018

On Reflexivity Of The Bochner Space $L^{P}(\Mu, E)$ For Arbitrary $\Mu$, Bahaetti̇n Cengi̇z, Banu Güntürk

Turkish Journal of Mathematics

Let $(\Omega ,\mathcal{A},\mu )$ be a finite positive measure space, $E$ a Banach space, and $1

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Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu Jan 2018

Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu

Turkish Journal of Mathematics

By means of the modified Abel lemma on summation by parts, we examine a class of terminating balanced $q$-series. Two transformation formulae are established that contain ten summation formulae as consequences.

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Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara Jan 2018

Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara

Turkish Journal of Mathematics

This paper is written to correct the proof of Lemma 2.1$(i)$ in \cite{K} and to add some decomposition results for the class of $PD$-modules defined in \cite{K}.

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A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao Jan 2018

A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao

Turkish Journal of Mathematics

Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_I(R)$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{(x,y,z)}(R)$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik's conjecture is true in the regular local rings case.

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On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer Jan 2018

On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer

Turkish Journal of Mathematics

Let $\Jt$ be the canonical para-complex structure on $\R^4$. In this paper we study $3$-dimensional centro-affine hypersurfaces with a $\Jt$-tangent centro-affine vector field (sometimes called $\Jt$-tangent centro-affine hypersurfaces) as well as $3$-dimensional $\Jt$-tangent affine hyperspheres with the property that at least one null-direction of the second fundamental form coincides with either $\DD^+$ or $\DD^-$. The main purpose of this paper is to give a full local classification of the above-mentioned hypersurfaces. In particular, we prove that every nondegenerate centro-affine hypersurface of dimension $3$ with a $\Jt$-tangent centro-affine vector field that has two null-directions $\DD^+$ and $\DD^-$ must be both an …

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From Excited Charge Dynamics To Cluster Diffusion: Development And Application Of Techniques Beyond Dft And Kmc, Shree Ram Acharya Jan 2018

From Excited Charge Dynamics To Cluster Diffusion: Development And Application Of Techniques Beyond Dft And Kmc, Shree Ram Acharya

Electronic Theses and Dissertations

This dissertation focuses on developing reliable and accurate computational techniques which enable the examination of static and dynamic properties of various activated phenomena using deterministic and stochastic approaches. To explore ultrafast electron dynamics in materials with strong electron-electron correlation, under the influence of a laser pulse, an ab initio electronic structure method based on time-dependent density functional theory (TDDFT) in combination with dynamical mean field theory (DMFT) is developed and applied to: 1) single-band Hubbard model; 2) multi-band metal Ni; and 3) multi-band insulator MnO. The ultrafast demagnetization in Ni reveal the importance of memory and correlation effects, leading to …

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