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T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes
T$_{4}$, Urysohn's Lemma, And Tietze Extension Theorem For Constant Filter Convergence Spaces, Tesni̇m Meryem Baran, Ayhan Erci̇yes
Turkish Journal of Mathematics
In this paper, we characterize various local forms of T$_{4}$ constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T$_{4}$ constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T$_{4}$ and general T$_{4}$ constant filter convergence spaces. Finally, we present Urysohn's lemma and Tietze extension theorem for constant filter convergence spaces.
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Oscillation Tests For Nonlinear Differential Equations With Nonmonotone Delays, Nurten Kiliç
Turkish Journal of Mathematics
In this paper, our aim is to investigate a class of first-order nonlinear delay differential equations with several deviating arguments. In addition, we present some sufficient conditions for the oscillatory solutions of these equations. Differing from other studies in the literature, delay terms are not necessarily monotone. Finally, we give examples to demonstrate the results.
Some Soft Topological Properties And Fixed Soft Element Results In Soft Complex Valued Metric Spaces, İzzetti̇n Demi̇r
Some Soft Topological Properties And Fixed Soft Element Results In Soft Complex Valued Metric Spaces, İzzetti̇n Demi̇r
Turkish Journal of Mathematics
In this paper, first, by using the idea of soft complex numbers as in Das and Samanta [8], we introduce the notion of soft complex valued metric spaces and investigate some of their topological aspects. Next, we establish some fixed soft element theorems for various soft mappings on soft complex valued metric spaces, which are the main results of our paper.
Unitals In Projective Planes Of Order 16, Stoicho Dimitrov Stoichev, Mustafa Gezek
Unitals In Projective Planes Of Order 16, Stoicho Dimitrov Stoichev, Mustafa Gezek
Turkish Journal of Mathematics
In this study, we perform computer searches for unitals in planes of order 16. The number of known nonisomorphic unitals in these planes is improved to be 261. Some data related to 2-$(65,5,1)$ designs associated with unitals are given. New lower bounds on the number of unital designs in projective planes of order 16 and 2-$(65,5,1)$ designs are established. The computations show that thirty-nine unitals can be embedded in two or more nonisomorphic projective planes of order 16. Fifteen new connections between planes of order 16 (based on unitals) are found. All unitals found by the algorithms used in this …
Hardy-Copson Type Inequalities For Nabla Time Scale Calculus, Zeynep Kayar, Bi̇llur Kaymakçalan
Hardy-Copson Type Inequalities For Nabla Time Scale Calculus, Zeynep Kayar, Bi̇llur Kaymakçalan
Turkish Journal of Mathematics
This paper is devoted to the nabla unification of the discrete and continuous Hardy-Copson type inequalities. Some of the obtained inequalities are nabla counterparts of their delta versions while the others are new even for the discrete, continuous, and delta cases. Moreover, these dynamic inequalities not only generalize and unify the related ones in the literature but also improve them in the special cases.
Classification Of Genus-$1$ Holomorphic Lefschetz Pencils, Noriyuki Hamada, Kenta Hayano
Classification Of Genus-$1$ Holomorphic Lefschetz Pencils, Noriyuki Hamada, Kenta Hayano
Turkish Journal of Mathematics
In this paper, we classify relatively minimal genus-$1$ holomorphic Lefschetz pencils up to smooth isomorphism. We first show that such a pencil is isomorphic to either the pencil on $P^1\times P^1$ of bidegree $(2,2)$ or a blow-up of the pencil on $P^2$ of degree $3$, provided that no fiber of a pencil contains an embedded sphere (note that one can easily classify genus-$1$ Lefschetz pencils with an embedded sphere in a fiber). We further determine the monodromy factorizations of these pencils and show that the isomorphism class of a blow-up of the pencil on $P^2$ of degree $3$ does not …
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
The concept of $\Gamma$-hypersemigroup has been introduced in Turk J Math 2020; 44 (5): 1835-1851 in which it has in which it has been shown that various results on $\Gamma$-hypersemigroups can be obtained directly as corollaries of more general results from the theory of $le$-semigroups (i.e. lattice ordered semigroups having a greatest element) or $poe$-semigroups. As a continuation of the paper mentioned above, in the present paper, the concept of ordered $\Gamma$-hypersemigroups has been introduced, and their relation to lattice ordered semigroups is given. It has been shown that although the results on ordered $\Gamma$-hypersemigroups cannot be obtained as corollaries …
On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye
On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye
Turkish Journal of Mathematics
Self-orthogonal codes and self-dual codes, on the one hand, and matrix-product codes, on the other, form important and sought-after classes of linear codes. Combining the two constructions would be advantageous. Adding to this combination the relaxation of the underlying algebraic structures to be commutative rings instead of fields would be even more advantageous. The current article paves a path in this direction. The authors study the problem of self-orthogonality and self-duality of matrix-product codes over a commutative ring with identity. Some methods as well as special matrices are introduced for the construction of such codes. A characterization of such codes …
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Fekete-Szegö Problem For A New Subclass Of Analytic Functions Satisfying Subordinate Condition Associated With Chebyshev Polynomials, Muhammet Kamali̇, Murat Çağlar, Erhan Deni̇z, Mirzaolim Turabaev
Turkish Journal of Mathematics
In this paper,we define a class of analytic functions $F_{\left( \beta ,\lambda \right) }\left( H,\alpha ,\delta ,\mu \right) ,$ satisfying the following subordinate condition associated with Chebyshev polynomials \begin{equation*} \left\{ \alpha \left[ \frac{zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\delta }+\left( 1-\alpha \right) \left[ \frac{% zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\mu }\left[ 1+% \frac{zG^{^{\prime \prime }}\left( z\right) }{G^{^{\prime }}\left( z\right) }% \right] ^{1-\mu }\right\} \prec H\left( z,t\right) , \end{equation*}% where $G\left( z\right) =\lambda \beta z^{2}f^{^{\prime \prime }}\left( z\right) +\left( \lambda -\beta \right) zf^{^{\prime }}\left( z\right) +\left( 1-\lambda +\beta \right) f\left( z\right) ,$ $0\leq \alpha \leq 1,$ $% 1\leq \delta \leq …
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir
Turkish Journal of Mathematics
In this paper, the existence and uniqueness of the solutions to impulsive coupled system of fractional differential equations with Caputo--Hadamard are investigated. Furthermore, Ulam's type stability of the proposed coupled system is studied. The approach is based on a Perov type fixed point theorem for contractions.
The Extension Of Step-$N$ Signatures, Kistosil Fahim
The Extension Of Step-$N$ Signatures, Kistosil Fahim
Turkish Journal of Mathematics
In 2009, Gyurko introduced $\Pi$-rough path which extends $p$-rough path. Inspired by this work we introduce the degree-$(\Pi,N)$ signature which can be treated as the step-$N$ signature for some $\Pi$. The degree-$(\Pi,N)$ signature holds some algebraic properties which will be proven in this paper.
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri
Turkish Journal of Mathematics
In this paper, fractional Sturm--Liouville problems of high-order are studied. A simple and efficient approach is presented to determine more eigenvalues and eigenfunctions than other approaches. Existence and uniqueness of solutions of a fractional high-order differential equation with initial conditions is addressed as well as the convergence of the proposed approach. This class of eigenvalue problems is important in finding solutions to linear fractional partial differential equations (LFPDE). This method is illustrated by three examples to signify the efficiency and reliability of the proposed numerical approach.
Mixed Lagrange Function In Minimax Fractional Programming Problems, Shunchin Ho
Mixed Lagrange Function In Minimax Fractional Programming Problems, Shunchin Ho
Turkish Journal of Mathematics
In this paper, the aim of this work to study mixed Lagrange function for the minimax fractional programming problem with nonsmooth exponential $(p,r)$-invex functions with respect to $\eta$. We introduced a new concept of saddle point for a mixed Lagrange function. We present the equivalence between a saddle point of the mixed Lagrange function and an optimal solution in the considered minimax fractional programming problem under appropriate nonsmooth exponential $(p,r)$-invexity hypotheses.
Relationship Between Lattice Ordered Semigroups And Ordered Hypersemigroups, Niovi Kehayopulu
Relationship Between Lattice Ordered Semigroups And Ordered Hypersemigroups, Niovi Kehayopulu
Turkish Journal of Mathematics
It has been shown in Turk J Math 2019; 43 (5): 2592-2601 that many results on hypersemigroups can be obtained directly as corollaries of more general results from the theory of lattice ordered semigroups, $\vee e$-semigroups or $poe$-semigroups. The present note shows that although this is not exactly the case for ordered hypersemigroups, even in this case various results may be suggested from analogous results for $le$, $\vee e$ or $poe$-semigroups and direct proofs derive along the lines of those $le$, $\vee e$ or $poe$-semigroups setting as well; the sets in the investigation provides a further indication that the results …
New Results On Derivatives Of The Shape Operator Of A Real Hypersurface In A Complex Projective Space, Juan De Dios Perez, David Pérez-López
New Results On Derivatives Of The Shape Operator Of A Real Hypersurface In A Complex Projective Space, Juan De Dios Perez, David Pérez-López
Turkish Journal of Mathematics
We consider real hypersurfaces $M$ in complex projective space equipped with both the Levi-Civita and generalized Tanaka-Webster connections. For any nonnull real number $k$ and any symmetric tensor field of type (1,1) $L$ on $M$ we can define a tensor field of type (1,2) on $M$, $L^{(k)}_F$, related to both connections. We study symmetry and skewsymmetry of the tensor $A^{(k)}_F$ associated to the shape operator$A$ of $M$.
On Sense Of Yamakawa Family Of Meromorphic Bi-Univalent And Bi-Subordinate Functions, Fethi̇ye Müge Sakar
On Sense Of Yamakawa Family Of Meromorphic Bi-Univalent And Bi-Subordinate Functions, Fethi̇ye Müge Sakar
Turkish Journal of Mathematics
This study offers three different univalent function families of bi-meromorphic and bi-subordinate functions defined on $\Delta=\{z:z\in\mathbb{C}, 1
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers
Turkish Journal of Mathematics
A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.
(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n
(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n
Turkish Journal of Mathematics
In this paper, we give categorical properties such as pullback, finite product, finite limit, coproduct, colimit and pushout in $\boldsymbol{XHom-Lie/A}$ of the category of Hom-Lie crossed modules.
Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli
Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we present an explicit formula and recurrent relation for generalized Catalan numbers, from which we can give corresponding formulas for Schröder numbers, large and small generalized Catalan numbers for the special cases of our results.
An Application Of Semigroup Theory To The Coagulation-Fragmentation Models, Arijit Das, Nilima Das, Jitraj Saha
An Application Of Semigroup Theory To The Coagulation-Fragmentation Models, Arijit Das, Nilima Das, Jitraj Saha
Turkish Journal of Mathematics
We present the existence and uniqueness of strong solutions for the continuous coagulation-fragmentation equation with singular fragmentation and essentially bounded coagulation kernel using semigroup theory of operators. Initially, we reformulate the coupled coagulation-fragmentation problem into the semilinear abstract Cauchy problem (ACP) and consider it as the nonlinear perturbation of the linear fragmentation operator. The existence of the substochastic semigroup is proved for the pure fragmentation equation. Using the substochastic semigroup and some related results for the pure fragmentation equation, we prove the existence of global nonnegative, strong solution for the coagulation-fragmentation equation.
On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete
On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete
Turkish Journal of Mathematics
The aim of the article is to study the Betti numbers of the tangent cone of Gorenstein monomial curves in affine 4-space. If $C_S$ is a noncomplete intersection Gorenstein monomial curve whose tangent cone is Cohen--Macaulay, we show that the possible Betti sequences are (1,5,5,1), (1,5,6,2) and (1,6,8,3).
On The Distribution Of Coefficients Of Half-Integral Weight Modular Forms And The Bruinier-Kohnen Conjecture, İlker İnam, Zeynep Demi̇rkol Özkaya, Eli̇f Tercan, Gabor Wiese
On The Distribution Of Coefficients Of Half-Integral Weight Modular Forms And The Bruinier-Kohnen Conjecture, İlker İnam, Zeynep Demi̇rkol Özkaya, Eli̇f Tercan, Gabor Wiese
Turkish Journal of Mathematics
This work represents a systematic computational study of the distribution of the Fourier coefficients of cuspidal Hecke eigenforms of level $\Gamma_0(4)$ and half-integral weights. Based on substantial calculations, the question is raised whether the distribution of normalised Fourier coefficients with bounded indices can be approximated by a generalised Gaussian distribution. Moreover, it is argued that the apparent symmetry around zero of the data lends strong evidence to the Bruinier-Kohnen conjecture on the equidistribution of signs and even suggests the strengthening that signs and absolute values are distributed independently.
Hermitian-Toeplitz Determinants For Functions With Bounded Turning, Virendra Kumar, Nak Eun Cho
Hermitian-Toeplitz Determinants For Functions With Bounded Turning, Virendra Kumar, Nak Eun Cho
Turkish Journal of Mathematics
There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order $\alpha$, are obtained. \keywords{Analytic functions, functions with bounded turning of order $\alpha$, Hermitian-Toeplitz determinant
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu
Turkish Journal of Mathematics
We propose and analyze a modified weak Galerkin finite element method (MWG-FEM) for solving singularly perturbed problems of convection-dominated type. The proposed method is constructed over piecewise polynomials of degree $k\geq1$ on interior of each element and piecewise constant on the boundary of each element. The present method is parameter-free and has less degrees of freedom compared to the classical weak Galerkin finite element method. The method is shown uniformly convergent for small perturbation parameters. An uniform convergence rate of $\mathcal {O}((N^{-1}\ln N)^k)$ in the energy-like norm is established on the piecewise uniform Shishkin mesh, where $N$ is the number …
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik
Turkish Journal of Mathematics
In this paper, we obtain a general double-series identity involving the bounded sequence of arbitrary complex numbers. As application of our double-series identity, we establish some reduction formulas for Srivastava--Daoust double hypergeometric function and Gaussian generalized hypergeometric function $_4F_3$. As special cases of our reduction formula for $_4F_3$ lead to some corollaries involving Clausen hypergeometric functions ${_{3}F_{2}}$. Making suitable adjustment of parameters in reduction formulas for $_4F_3$ and ${_{3}F_{2}}$, we obtain some results in terms of elementary functions and some special functions like Lerch generalized zeta function and incomplete beta function.
Affine Ricci Solitons Associated To The Bott Connection On Three-Dimensionallorentzian Lie Groups, Tong Wu, Yong Wang
Affine Ricci Solitons Associated To The Bott Connection On Three-Dimensionallorentzian Lie Groups, Tong Wu, Yong Wang
Turkish Journal of Mathematics
In this paper, we compute the Bott connection and their curvature on three-dimensional Lorentzian Lie groups with three different distributions, then we classify affine Ricci solitons associated to the Bott connection on the spaces under study.
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli
A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli
Turkish Journal of Mathematics
In this paper, we obtain a determinantal expression for weighted Delannoy numbers, from which we give a new recurrence relation for it. For the special case of our formula, we compute central weighted Delannoy number in terms of weighted Delannoy number.
Quasi-Idempotent Ranks Of The Proper Ideals In Finite Symmetric Inverse Semigroups, Leyla Bugay
Quasi-Idempotent Ranks Of The Proper Ideals In Finite Symmetric Inverse Semigroups, Leyla Bugay
Turkish Journal of Mathematics
Let $I_{n}$ and $S_{n}$ be the symmetric inverse semigroup and the symmetric group on a finite chain $X_{n}=\{1,\ldots ,n \}$, respectively. Also, let $I_{n,r}= \{ \alpha \in I_{n}: im(\alpha) \leq r\}$ for $1\leq r\leq n-1$. For any $\alpha\in I_n$, if $\alpha\neq \alpha^2=\alpha^4$ then $\alpha$ is called a quasi-idempotent. In this paper, we show that the quasi-idempotent rank of $I_{n,r}$ (both as a semigroup and as an inverse semigroup) is $\binom{n}{2}$ if $r=2$, and $\binom{n}{r}+1$ if $r\geq 3$. The quasi-idempotent rank of $I_{n,1}$ is $n$ (as a semigroup) and $n-1$ (as an inverse semigroup).
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Korovkin Type Approximation Via Triangular $A-$Statistical Convergence On An Infinite Interval, Seli̇n Çinar, Sevda Yildiz, Kami̇l Demi̇rci̇
Turkish Journal of Mathematics
In the present paper, using the triangular $A-$statistical convergence for double sequences, which is an interesting convergence method, we prove a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued continuous functions on $\left[ 0,\infty \right)\times \left[ 0,\infty \right) $ with the property that have a finite limit at the infinity. Moreover, we present the rate of convergence via modulus of continuity. Finally, we give some further developments.