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- Oscillation (23)
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Articles 1051 - 1080 of 2494
Full-Text Articles in Physical Sciences and Mathematics
$Q$-Counting Hypercubes In Lucas Cubes, Eli̇f Saygi, Ömer Eğeci̇oğlu
$Q$-Counting Hypercubes In Lucas Cubes, Eli̇f Saygi, Ömer Eğeci̇oğlu
Turkish Journal of Mathematics
Lucas and Fibonacci cubes are special subgraphs of the binary hypercubes that have been proposed as models of interconnection networks. Since these families are closely related to hypercubes, it is natural to consider the nature of the hypercubes they contain. Here we study a generalization of the enumerator polynomial of the hypercubes in Lucas cubes, which $q$-counts them by their distance to the all 0 vertex. Thus, our bivariate polynomials refine the count of the number of hypercubes of a given dimension in Lucas cubes and for $q=1$ they specialize to the cube polynomials of Klavžar and Mollard. We obtain …
A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash
A Comparative Study Of Gauss‒Laguerre Quadrature And An Open Type Mixed Quadrature By Evaluating Some Improper Integrals, Pritikanta Patra, Debasish Das, Rajani Ballav Dash
Turkish Journal of Mathematics
An open type mixed quadrature rule is constructed blending the anti-Gauss 3-point rule with Steffensen's 4-point rule. The analytical convergence of the mixed rule is studied. An adaptive integration scheme is designed based on the mixed quadrature rule. A comparative study of the mixed quadrature rule and the Gauss‒Laguerre quadrature rule is given by evaluating several improper integrals of the form $\int\limits_{0}^{\infty}e^{-x}f(x)dx$. The advantage of implementing mixed quadrature rule in developing an efficient adaptive integration scheme is shown by evaluating some improper integrals.
Reduction Formula Of A Double Binomial Sum, Wenchang Chu
Reduction Formula Of A Double Binomial Sum, Wenchang Chu
Turkish Journal of Mathematics
A class of double sums with binomial coefficients are evaluated by combining finite differences with partial fraction decompositions.
Regularity And Projective Dimension Of The Edge Ideal Of A Generalized Theta Graph, Seyyede Masoome Seyyedi, Farhad Rahmati
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 $G$.
Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Two-Dimensional Generalized Discrete Fourier Transform And Related Quasi-Cyclic Reed‒Solomon Codes, Majid Mazrooei, Lale Rahimi, Najme Sahami
Turkish Journal of Mathematics
Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensional discrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceed to study its computational aspects as well as the inverse transform, which necessitate the development of a faster way to calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linear codes that can be assumed to be a generalization of Reed‒Solomon codes.
Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon
Various Centroids And Some Characterizations Of Catenary Rotation Hypersurfaces, Dong-Soo Kim, Young Ho Kim, Dae Won Yoon
Turkish Journal of Mathematics
We study positive $C^1$ functions $z=f(x), x=(x_1,\cdots, x_n)$ defined on the $n$-dimensional Euclidean space $ \mathbb R^{n}$. For $x=(x_1,\cdots, x_n)$ with nonzero numbers $x_1, \cdots, x_n$, we consider the rectangular domain $I(x)=I(x_1)\times \cdots \times I(x_n)\subset \mathbb R^{n}$, where $I(x_i)= [0, x_i]$ if $x_i>0$ and $I(x_i)= [x_i,0]$ if $x_i
An Effective Application Of Differential Quadrature Method Based Onmodified Cubic B-Splines To Numerical Solutions Of The Kdv Equation, Ali̇ Başhan
Turkish Journal of Mathematics
In this study, numerical solutions of the third-order nonlinear Korteweg--de Vries (KdV) equation are obtained via differential quadrature method based on modified cubic B-splines. Five different problems are solved. To show the accuracy of the proposed method, $L_{2}$ and $L_{\infty }$ error norms of the problem, which has an analytical solution, and three lowest invariants are calculated and reported. The obtained solutions are compared with some earlier works. Stability analysis of the present method is also given.
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
Turkish Journal of Mathematics
In this paper, we study the relationships between the cohomological structure of a space and that of the fixed point set of a finite dimensional pro-torus action on the space.
On Some Multivariate Lcm And Gcd Sums, Khola Algali
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.
Differential Subordination And Radius Estimates For Starlike Functions Associated With The Booth Lemniscate, Nak Eun Cho, Sushil Kumar, Virendra Kumar, V. Ravichandran
Differential Subordination And Radius Estimates For Starlike Functions Associated With The Booth Lemniscate, Nak Eun Cho, Sushil Kumar, Virendra Kumar, V. Ravichandran
Turkish Journal of Mathematics
We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of Ma-Minda starlike functions. In addition, by proving an associated technical lemma, we compute various radii constants such as the radius of starlikeness, radius of convexity, radius of starlikeness associated with the lemniscate of Bernoulli, and other radius estimates for functions in the …
Generalized Geometry Of Goncharov And Configuration Complexes, Muhammad Khalid, Javed Khan, Azhar Iqbal
Generalized Geometry Of Goncharov And Configuration Complexes, Muhammad Khalid, Javed Khan, Azhar Iqbal
Turkish Journal of Mathematics
In this article, a generalized geometry of Goncharov's complex and the Grassmannian complex will be proposed. First, all new homomorphisms will be defined, and then they will be used extensively to connect the Bloch--Suslin and the Grassmannian complex for weight $n=2$ and then Goncharov's complex with Grassmannian complex for weight $n=3$, up to $n=6$. Lastly, and most importantly, generalized morphisms will be presented to cover the geometry of the Goncharov and Grassmannian complex when weight $n= N$. Associated diagrams will be exhibited, proven to be commutative.
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Turkish Journal of Mathematics
Let $R$ be a ring with involution $*$. $R^{m\times n}$ denotes the set of all $m\times n$ matrices over $R$. In this paper, we give a characterization of the pseudo core inverse of $A\in R^{n\times n}$ in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, where $N_l(A)=\{x\in R^{1\times m} xA=0\}$ and $N_r(A)=\{x\in R^{n\times 1}~ ~Ax=0\}.$ Then we obtain necessary and sufficient conditions for $A\in R^{n\times n}$, in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, to be *-DMP. If $R$ is a principal ideal domain (resp. semisimple Artinian ring), then matrices expressed as that form include all $n\times n$ matrices over $R$.
The Equation ${Dd'+D'D=D^2}$ For Derivations On C$^*$-Algebras, Sayed Khalil Ekrami, Madjid Mirzavaziri
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.
Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi
Semisymmetric Contact Metric Manifolds Of Dimension $\Geq 5$, Nasrin Malekzadeh, Esmaiel Abedi
Turkish Journal of Mathematics
We classify semisymmetric contact metric manifolds $M^{2n+1}(\varphi, \xi, \eta, g),~n\geq2$ with $\xi$-parallel tensor $h$, where $2h$ denotes the Lie derivative of the structure tensor $\varphi$ in the direction of the characteristic vector field $\xi$.
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
On The Isospectrality Of The Scalar Energy-Dependent Schrödingerproblems, Tüba Gülşen, Etibar Sadi Panakhov
Turkish Journal of Mathematics
In this study, we discuss the inverse spectral problem for the energy-dependent Schrödinger equation on a finite interval. We construct an isospectrality problem and obtain some relations between constants in boundary conditions of the problems that constitute isospectrality. Above all, we obtain degeneracy of $ K(x,t)-K_{0}{ (x,t)}$ and $L(x,t)-L_{0} (x,t)$ by using a different approach. Some of the main results of our study coincide with results reported by Jodeit and Levitan. However, the method to obtain degeneracy is completely different. Furthermore, we consider all above results for the nonisospectral case.
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
On Oscillation Of Integro-Differential Equations, Said R. Grace, Ağacik Zafer
Turkish Journal of Mathematics
We study the oscillatory behavior of solutions for integro-differential equations of the form $$x'(t) = e(t) -\int_0^t (t-s)^{\alpha-1}k(t, s)f(s, x(s))\, {\rm ds},\quad t\geq 0,$$ where $0
On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk
On Oscillation Of Two-Dimensional Time-Scale Systems With A Forcing Term, Özkan Öztürk
Turkish Journal of Mathematics
The oscillation and nonoscillation theories for nonlinear systems have recently received a lot of attention. We consider a two-dimensional time-scale system and find the oscillation criteria for solutions of the system by using some improper integrals and inequalities. We also give a few examples in order to highlight our main results.
Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak
Descent-Inversion Statistics In Riffle Shuffles, Ümi̇t Işlak
Turkish Journal of Mathematics
The purpose of this paper is to answer a question of Fulman on the asymptotic normality of the number of inversions in riffle shuffles. We will also study asymptotics for the number of descents and the length of the longest alternating subsequences in the same shuffling scheme.
On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine
On The Dimension Of Vertex Labeling Of $K$-Uniform Dcsl Of An Even Cycle, Nageswara Rao Karrey, Germina Kizhekekunnel Augustine
Turkish Journal of Mathematics
In this paper, we discuss the lower bound for the dcsl index $ \delta_k $ of a $k$-uniform dcsl of even cycle $ C_{2n},\ n\geq 2 $, in terms of the dimension of a poset and prove that $dim({\mathscr{F}})\leq \delta_k(C_{2n}) $, where ${\mathscr{F}}$ is the range of any $k$-uniform dcsl $ f $ of $ C_{2n},\ n\geq 2 $.
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions, Xiang Gao, Hui Hu, Zhihui Li
A Result On The Maximal Length Of Consecutive 0 Digits In $\Beta$-Expansions, Xiang Gao, Hui Hu, Zhihui Li
Turkish Journal of Mathematics
Let $\beta>1$ be a real number. For any $x\in[0,1]$, let $r_{n}(x,\beta)$ be the maximal length of consecutive zero digits in the first $n$ digits of the $\beta$-expansion of $x$. In this note, it is proved that for any $0
Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic
Harmonic Quadrangle In Isotropic Plane, Ema Jurkin, Marija Simic Horvath, Vladimir Volenec, Jelena Beban-Brkic
Turkish Journal of Mathematics
The concept of the harmonic quadrangle and the associated Brocard points are introduced and investigated in the isotropic plane by employing suitable analytic methods.
On The Unit Index Of Some Real Biquadratic Number Fields, Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous
On The Unit Index Of Some Real Biquadratic Number Fields, Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous
Turkish Journal of Mathematics
Let $p_1\equiv p_2\equiv1 \pmod 4$ be different prime numbers such that $\left(\dfrac{2}{p_2}\right)=\left(\dfrac{p_1}{p_2}\right)=-\left(\dfrac{2}{p_1}\right)=-1$. Put $\kk=\QQ(\sqrt{2p_1p_2})$ and let $\KK$ be a quadratic extension of $\kk$ contained in its absolute genus field $\kk^{(*)}$. Denote by $k_j$, $1\leq j\leq 3$, the three quadratic subfields of $\KK$. Let $E_{\KK}$ (resp. $E_{k_j}$) be the unit group of $\KK$ (resp. $k_j$). The unit index $\left[E_{\KK}: \prod_{j=1}^3E_{k_j}\right]$ is characterized in terms of biquadratic residue symbols between $2$, $p_1$ and $p_2$ or by the capitulation of $\mathfrak{2}$, the prime ideal of $\QQ(\sqrt{2p_1})$ above $2$, in $\KK$. These results are used to describe the $2$-rank of some CM-fields.
An Explicit Formula Of The Intrinsic Metric On The Sierpinski Gasket Via Code Representation, Mustafa Saltan, Yunus Özdemi̇r, Bünyami̇n Demi̇r
An Explicit Formula Of The Intrinsic Metric On The Sierpinski Gasket Via Code Representation, Mustafa Saltan, Yunus Özdemi̇r, Bünyami̇n Demi̇r
Turkish Journal of Mathematics
The computation of the distance between any two points of the Sierpinski gasket with respect to the intrinsic metric has already been investigated by several authors. However, to the best of our knowledge, in the literature there is not an explicit formula obtained by using the code set of the Sierpinski gasket. In this paper, we obtain an explicit formula for the intrinsic metric on the Sierpinski gasket via the code representations of its points. We finally give an important geometrical property of the Sierpinski gasket with regard to the intrinsic metric by using its code representation.
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Quantitative Voronovskaya- And Grüss-Voronovskaya-Type Theorems By The Blending Variant Of Szã¡Sz Operators Including Brenke-Type Polynomials, Purshottam Narain Agrawal, Behar Baxhaku, Ruchi Chauhan
Turkish Journal of Mathematics
The present paper aims to investigate a class of linear positive operators by combining Szász-Jain operators and Brenke polynomials and studies their approximation properties. We also prove quantitative Voronovskaya-type results and establish Grüss-Voronovskaja-type theorem. Furthermore, we show the rate of convergence for Szász-Jain-Brenke operators to functions having derivative of bounded variation and not having derivative of bounded variation by illustrative graphics using MATLAB.
Integral Representation For Solutions Of The Pseudoparabolic Equation In Matrix Form, Yeşi̇m Sağlam Özkan, Sezayi̇ Hizliyel
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.
The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz
The Productively Lindelöf Property In The Remainders Of Topological Spaces, Seçi̇l Tokgöz
Turkish Journal of Mathematics
A topological space $X$ is called productively Lindelöf if $X\times Y$ is Lindelöf for every Lindelöf space $Y$. We study with remainders and investigate topological spaces with productively Lindelöf remainders.
Weak Convergence Of Probability Measures To Choquet Capacity Functionals, Dietmar Ferger
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 …
A Vectorization For Nonconvex Set-Valued Optimization, Emrah Karaman, İlknur Atasever Güvenç, Mustafa Soyertem, Di̇dem Tozkan, Mahi̇de Küçük, Yalçin Küçük
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.
Digital Lusternik-Schnirelmann Category, Ayse Borat, Tane Vergi̇li̇
Digital Lusternik-Schnirelmann Category, Ayse Borat, Tane Vergi̇li̇
Turkish Journal of Mathematics
In this paper, we define the digital Lusternik-Schnirelmann category cat${}_\kappa$, introduce some of its properties, and discuss how the adjacency relation affects the digital Lusternik-Schnirelmann category.
The Natural Brackets On Couples Of Vector Fields And $1$-Forms, Miroslav Doupovec, Jan Kurek, Wlodzimierz Mikulski
The Natural Brackets On Couples Of Vector Fields And $1$-Forms, Miroslav Doupovec, Jan Kurek, Wlodzimierz Mikulski
Turkish Journal of Mathematics
All natural bilinear operators transforming pairs of couples of vector fields and $1$-forms into couples of vector fields and $1$-forms are found. All natural bilinear operators as above satisfying the Leibniz rule are extracted. All natural Lie algebra brackets on couples of vector fields and $1$-forms are collected.