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Construction Of The Holonomy Invariantfoliated Cocycles On The Tangent Bundle Via Formal Integrability, Fatemeh Ahangari
Construction Of The Holonomy Invariantfoliated Cocycles On The Tangent Bundle Via Formal Integrability, Fatemeh Ahangari
Turkish Journal of Mathematics
This paper is dedicated to exhaustive structural analysis of the holonomy invariant foliated cocycles on the tangent bundle of an arbitrary $(m+n)$-dimensional manifold. For this purpose, by applying Spencer theory of formal integrability, sufficient conditions for the metric associated with the semispray $S$ are determined to extend to a transverse metric for the lifted foliated cocycle on $TM$. Accordingly, this geometric structure converts to a holonomy invariant foliated cocycle on the tangent space, which is totally adapted to the Helmholtz conditions.
$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi
$C$-Paracompactness And $C_2$-Paracompactness, Maha Mohammed, Lutfi Kalantan, Hala Alzumi
Turkish Journal of Mathematics
A topological space $X$ is called $C$-paracompact if there exist a paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. A topological space $X$ is called $C_2$-paracompact if there exist a Hausdorff paracompact space $Y$ and a bijective function $f:X\longrightarrow Y$ such that the restriction $f _{A}:A\longrightarrow f(A)$ is a homeomorphism for each compact subspace $A\subseteq X$. We investigate these two properties and produce some examples to illustrate the relationship between them and $C$-normality, minimal Hausdorff, and other properties.
Multiple-Group Adjustment Method In Indirect Adjustment, Changjun Huang, Hongmei Xia, Xike Zhang
Multiple-Group Adjustment Method In Indirect Adjustment, Changjun Huang, Hongmei Xia, Xike Zhang
Turkish Journal of Mathematics
In view of the low accuracy of traditional adjustment, an improved multiple-group adjustment method in indirect adjustment is proposed in this paper. In the process of improved multiple-group adjustment, the first group is first adjusted, and then the adjustment result of the first group and the observation value of the second group are adjusted together, which makes the results in the first-group adjustment meet the overall adjustment results. Finally, the posteriori unit-weight variance value, the coordinated factor matrix of the adjustment result, and the unknown function weight reciprocal are calculated. The experimental results show that the accuracy of multiple-group adjustment …
When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang
When Do Quasinilpotents Lie In The Jacobson Radical?, Peng Cao, Xin Wang
Turkish Journal of Mathematics
In this paper, we give some spectral characterizations of the Jacobson radical; that is, we will show that some conditions with $\lambda$-multiplicativity imply that the set of all quasinilpotent elements equals the Jacobson radical. We also give some conditions to make sure the quasinilpotents lie in the Jacobson radical, using the set of elements with singleton spectra.
Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar
Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar
Turkish Journal of Mathematics
Let $X$ and $Y$ be complex Banach spaces and $\mathbb{D}$ be the open unit disc in the complex plane $\mathbb{C}$. Let $\varphi$ be an analytic self-map of $\mathbb{D}$ and $\psi$ be an analytic operator-valued function from $\mathbb{D}$ into the space of all bounded linear operators from $X$ to $Y.$ The weighted composition operator $W_{\psi,\varphi}:\mathcal{H} \rightarrow\mathcal{H}(\mathbb{D}, Y)$ is defined by $$ W_{\psi,\varphi}( f)(z)=\psi(z)(f(\varphi(z))), \quad \quad (z\in\mathbb{D}, f\in \mathcal{H}),$$ where $\mathcal{H}$ is the space of all analytic $X$-valued functions on $\mathbb{D}$. In this paper we provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators $W_{\psi,\varphi}$ between vector-valued …
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo
Some Classes Of Harmonic Mappings With Analytic Part Defined By Subordination, Shuhai Li, Ma Li-Na, Ao En, Tang Huo
Turkish Journal of Mathematics
Let $S_{H}$ be the class of functions $f=h+\bar{g}$ that are harmonic univalent and sense-preserving in the open unit disk $\mathbb{U}=\{z\in \mathbb{C}: z
On Integrability Conditions, Operators, And The Purityconditions Of The Sasakian Metric With Respect To Lifts Of $F_{\Lambda}(7,1)$-Structure On The Cotangent Bundle, Haşi̇m Çayir
Turkish Journal of Mathematics
There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the $F_{\lambda }(7,1)$-structure. The $F_{\lambda }(7,1)$-structure was first extended in $M^{n}$ to $T^{\ast }(M^{n})$ by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the $F_{a}(K,1)$-structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the $F_{\lambda }(7,1)$-structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the …
A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms, Altan Erdoğan
A Note On Polynomial Expressions For Sums Of Power Of Integers Multiplied By Exponential Terms, Altan Erdoğan
Turkish Journal of Mathematics
The possible polynomial expressions for sums of powers of integers multiplied by an exponential term are investigated. We explicitly give factorization of these polynomials in terms of the roots of Apostol-Bernoulli polynomials. As a special case, alternating sums of powers of integers are also considered, and some new polynomial expressions are given.
Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation, Dursun Irk, Pinar Keski̇n Yildiz, Meli̇s Zorşahi̇n Görgülü
Quartic Trigonometric B-Spline Algorithm Fornumerical Solution Of The Regularized Long Wave Equation, Dursun Irk, Pinar Keski̇n Yildiz, Meli̇s Zorşahi̇n Görgülü
Turkish Journal of Mathematics
In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.
On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol
On The Starlikeness Of P-Valent Functions, Mamoru Nunokawa, Nak Eun Cho, Oh Sang Kwon, Janusz Sokol
Turkish Journal of Mathematics
For an analytic function in open unit disk $\mathbb{D}$, we consider the $p$-valent analogue of the Noshiro-Warschawski univalence condition. We apply the Fejér-Riesz inequality to establish some sufficient conditions for functions to be $p$-valent or to be a Bazilevič function or to be in some other classes.
A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials, Sedat Akleylek, Meryem Soysaldi
A Novel 3-Pass Identification Scheme And Signature Scheme Based On Multivariate Quadratic Polynomials, Sedat Akleylek, Meryem Soysaldi
Turkish Journal of Mathematics
Identification schemes are used to verify identities of parties and signatures. Recently, systems based on multivariate polynomials have been preferred in identification schemes due to their resistance against quantum attacks. In this paper, we propose a quantum secure $3$-pass identification scheme based on multivariate quadratic polynomials. We compare the proposed scheme with the previous ones in view of memory requirements, communication length, and computation time. We define an efficiency metric by using impersonation probability and computation time. According to the comparison results, the proposed one has the same computation time as that of Monteiro et al. and reduces impersonation probability …
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Notes On Certain Analytic Functions, Emel Yavuz Duman, Shigeyoshi Owa
Turkish Journal of Mathematics
Let $\mathcal{A}(n)$ be the class of functions $$f(z)=a_nz^n + a_{n+1}z^{n+1}+\cdots (n\in \mathbb{N}),$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $f(z)\in \mathcal{A}(n)$, Miller and Mocanu in 1978 showed a very interesting result for $f(z)$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Inequalities On Coefficients For Certain Classes Of M-Fold Symmetric And Bi-Univalent Functions Equipped With Faber Polynomial, Fethi̇ye Müge Sakar, Adnan Canbulat
Turkish Journal of Mathematics
In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu
Sectional Curvatures On Weyl Manifolds With A Special Metric Connection, Fatma Özdemi̇r, Mustafa Deni̇z Türkoğlu
Turkish Journal of Mathematics
In this paper, Weyl manifolds, denoted by $WS(g,w,\pi,\mu)$, having a special a semisymmetric recurrent-metric connection are introduced and the uniqueness of this connection is proved. We give an example of $WS(g,w,\pi,\mu)$ with a constant scalar curvature. Furthermore, we define sectional curvatures of $WS(g,w,\pi,\mu)$ and prove that any isotropic Weyl manifold $WS(g,w,\pi,\mu)$ is locally conformal to an Einstein manifold with a semisymmetric recurrent-metric connection, $EWS(g,w,\pi,\mu)$.
Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space, Aigerim Kalybay, Ryskul Oinarov
Kernel Operators And Their Boundedness From Weighted Sobolev Space To Weighted Lebesgue Space, Aigerim Kalybay, Ryskul Oinarov
Turkish Journal of Mathematics
In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
On A Theorem Of Terzioğlu, Asuman Güven Aksoy
On A Theorem Of Terzioğlu, Asuman Güven Aksoy
Turkish Journal of Mathematics
The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioğlu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for $Q$-compact maps.
Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz
Univalent Harmonic Mappings And Hardy Spaces, Ali Ebadian, Saman Azizi, Si̇bel Yalçin Tokgöz
Turkish Journal of Mathematics
The main purpose of this paper is to establish a relationship between univalent harmonic mappings and Hardy spaces. The main result obtained in this paper improves previously published results. Moreover, we generalize some nice results in the analytic case to the harmonic case.
A Broken Cycle Theorem For The Restrained Chromatic Function, Aysel Erey
A Broken Cycle Theorem For The Restrained Chromatic Function, Aysel Erey
Turkish Journal of Mathematics
A restraint $r$ on a graph $G$ is a function that assigns each vertex of the graph a finite subset of $\mathbb{N}$. For each vertex $v$ of the graph, $r(v)$ is called the set of colors forbidden at $v$. A proper coloring of $G$ is said to be permitted by a given restraint $r$ if each vertex $v$ of the graph receives a color that is not from its set of forbidden colors $r(v)$. The restrained chromatic function, denoted by $\pi_r(G,x)$, is a function whose evaluations at integer $x$ values count the number of proper $x$-colorings of the graph $G$ …
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
A Novel Graph-Operational Matrix Method For Solving Multidelay Fractional Differential Equations With Variable Coefficients And A Numerical Comparative Survey Of Fractional Derivative Types, Ömür Kivanç Kürkçü, Ersi̇n Aslan, Mehmet Sezer
Turkish Journal of Mathematics
In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor …
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Harmonic Numbers Associated With Inversion Numbers In Terms Of Determinants, Takao Komatsu, Amalia Pizarro-Madariaga
Turkish Journal of Mathematics
It has been known that some numbers, including Bernoulli, Cauchy, and Euler numbers, have such corresponding numbers in terms of determinants of Hessenberg matrices. There exist inversion relations between the original numbers and the corresponding numbers. In this paper, we introduce the numbers related to harmonic numbers in determinants. We also give several of their arithmetical and/or combinatorial properties and applications. These concepts can be generalized in the case of hyperharmonic numbers.
Hirzebruch-Kummer Covers Of Algebraic Surfaces, Piotr Pokora
Hirzebruch-Kummer Covers Of Algebraic Surfaces, Piotr Pokora
Turkish Journal of Mathematics
The aim of this paper is to show that using some natural curve arrangements in algebraic surfaces and Hirzebruch-Kummer covers, one cannot construct new examples of ball-quotients, i.e. minimal smooth complex projective surfaces of general type satisfying equality in the Bogomolov-Miyaoka-Yau inequality.
A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r
A Discrete Chaotic Dynamical System On The Sierpinski Gasket, Mustafa Saltan, Ni̇sa Aslan, Bünyami̇n Demi̇r
Turkish Journal of Mathematics
The Sierpinski gasket (also known as the Sierpinski triangle) is one of the fundamental models of self-similar sets. There have been many studies on different features of this set in the last decades. In this paper, initially we construct a dynamical system on the Sierpinski gasket by using expanding and folding maps. We then obtain a surprising shift map on the code set of the Sierpinski gasket, which represents the dynamical system, and we show that this dynamical system is chaotic on the code set of the Sierpinski gasket with respect to the intrinsic metric. Finally, we provide an algorithm …
On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu
On Essential Cohomology Of Powerful $P$-Groups, Fatma Altunbulak Aksu
Turkish Journal of Mathematics
For an odd prime $p$, we prove that a finite powerful $p$-group having rank two Frattini quotient has nonzero essential cohomology. We also provide some examples and applications.
An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems, Süleyman Cengi̇zci̇, Srinivasan Natesan, Mehmet Tarik Atay
An Asymptotic-Numerical Hybrid Method For Singularly Perturbed System Of Two-Point Reaction-Diffusion Boundary-Value Problems, Süleyman Cengi̇zci̇, Srinivasan Natesan, Mehmet Tarik Atay
Turkish Journal of Mathematics
This article focuses on the numerical approximate solution of singularly perturbed systems of second-order reaction-diffusion two-point boundary-value problems for ordinary differential equations. To handle these types of problems, a numerical-asymptotic hybrid method has been used. In this hybrid approach, an efficient asymptotic method, the so-called successive complementary expansion method (SCEM) is employed first, and then a numerical method based on finite differences is applied to approximate the solution of corresponding singularly perturbed reaction-diffusion systems. Two illustrative examples are provided to demonstrate the efficiency, robustness, and easy applicability of the present method with convergence properties.
Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov
Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov
Turkish Journal of Mathematics
A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft $T_{i}$-space and the relationships between them are discussed in detail.
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
Young Tableaux And Arf Partitions, Nesri̇n Tutaş, Hali̇l İbrahi̇m Karakaş, Ni̇hal Gümüşbaş
Turkish Journal of Mathematics
The aim of this work is to exhibit some relations between partitions of natural numbers and Arf semigroups. We also give characterizations of Arf semigroups via the hook-sets of Young tableaux of partitions.
A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
A New Class Of Generalized Polynomials Associated With Laguerre And Bernoulli Polynomials, Nabiullah Khan, Talha Usman, Junesang Choi
Turkish Journal of Mathematics
Motivated by their importance and potential for applications in certain problems in number theory, combinatorics, classical and numerical analysis, and other fields of applied mathematics, a variety of polynomials and numbers with their variants and extensions have recently been introduced and investigated. In this paper, we aim to introduce generalized Laguerre-Bernoulli polynomials and investigate some of their properties such as explicit summation formulas, addition formulas, implicit formulas, and symmetry identities. Relevant connections of the results presented here with those relatively simple numbers and polynomials are considered.
Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues
Slant Helices: A New Approximation, Pascual Lucas, Jose Antonio Ortega-Yagues
Turkish Journal of Mathematics
In this paper, we study a weaker version of classic slant helices in Euclidean space $\mathbb{R}^3$ or Minkowski space $\mathbb{R}^3_1$, which will be called general slant helices. We show that any classic slant helix is a general slant helix but the converse is not true. We also obtain equations involving the curvature and torsion that characterize this family of curves.
Categorical Structures Of Lie-Rinehart Crossed Module, Ali̇ Ayteki̇n
Categorical Structures Of Lie-Rinehart Crossed Module, Ali̇ Ayteki̇n
Turkish Journal of Mathematics
In this paper we give constructions of pullback, finite product, finite limit, coproduct, colimit, pushout, etc. in a special full subcategory $\mathfrak{XMod}/\mathcal{L}$ of the category of Lie-Rinehart crossed modules.