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2021

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Unitals In Projective Planes Of Order 16, Stoicho Dimitrov Stoichev, Mustafa Gezek Jan 2021

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 …

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Cover And Contents Jan 2021

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

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Hardy-Copson Type Inequalities For Nabla Time Scale Calculus, Zeynep Kayar, Bi̇llur Kaymakçalan Jan 2021

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.

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Classification Of Genus-$1$ Holomorphic Lefschetz Pencils, Noriyuki Hamada, Kenta Hayano Jan 2021

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 …

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On Ordered $\Gamma$-Hypersemigroups And Their Relation To Lattice Ordered Semigroups, Niovi Kehayopulu Jan 2021

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 …

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On Self-Orthogonality And Self-Duality Of Matrix-Product Codes Over Commutative Rings, Abdulaziz Deajim, Mohamed Bouye Jan 2021

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 …

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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 Jan 2021

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 …

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Existence Results And Ulam-Hyers Stability To Impulsive Coupled System Fractional Differential Equations, Hadjer Belbali, Maamar Benbachir Jan 2021

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.

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The Extension Of Step-$N$ Signatures, Kistosil Fahim Jan 2021

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.

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Theory And Numerical Approaches Of High Order Fractional Sturm-Liouville Problems, Tahereh Houlari, Mohammad Dehghan, Jafar Biazar, Alireza Nouri Jan 2021

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.

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Mixed Lagrange Function In Minimax Fractional Programming Problems, Shunchin Ho Jan 2021

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.

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Relationship Between Lattice Ordered Semigroups And Ordered Hypersemigroups, Niovi Kehayopulu Jan 2021

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 …

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New Results On Derivatives Of The Shape Operator Of A Real Hypersurface In A Complex Projective Space, Juan De Dios Perez, David Pérez-López Jan 2021

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 $M$.

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On Sense Of Yamakawa Family Of Meromorphic Bi-Univalent And Bi-Subordinate Functions, Fethi̇ye Müge Sakar Jan 2021

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

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Weak C-Ideals Of A Lie Algebra, Zeki̇ye Çi̇loğlu Şahi̇n, David Anthony Towers Jan 2021

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.

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(Co)Limits Of Hom-Lie Crossed Module, Ali̇ Ayteki̇n Jan 2021

(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.

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Explicit Formulas And Recurrence Relations For Generalized Catalan Numbers, Muhammet Ci̇hat Dağli Jan 2021

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.

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An Application Of Semigroup Theory To The Coagulation-Fragmentation Models, Arijit Das, Nilima Das, Jitraj Saha Jan 2021

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.

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On The Betti Numbers Of The Tangent Cones For Gorenstein Monomial Curves, Pinar Mete Jan 2021

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).

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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 Jan 2021

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.

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Hermitian-Toeplitz Determinants For Functions With Bounded Turning, Virendra Kumar, Nak Eun Cho Jan 2021

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

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Uniform Convergent Modified Weak Galerkin Method For Convection-Dominated Two-Point Boundary Value Problems, Şuayi̇p Toprakseven, Peng Zhu Jan 2021

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 …

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A General Double Series Identity And Its Application In Hypergeometric Reduction Formulas, Mohammad Idris Qureshi, Shakir Hussain Malik Jan 2021

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.

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Affine Ricci Solitons Associated To The Bott Connection On Three-Dimensionallorentzian Lie Groups, Tong Wu, Yong Wang Jan 2021

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.

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Winning Entry For 2021, Nhi Doan Jan 2021

Winning Entry For 2021, Nhi Doan

Library Research Prize

No abstract provided.

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Runner Up Entry For 2021, Samirah Jaigirdar Jan 2021

Runner Up Entry For 2021, Samirah Jaigirdar

Library Research Prize

No abstract provided.

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Runner Up Entry For 2021, Kerin Krasnoff Jan 2021

Runner Up Entry For 2021, Kerin Krasnoff

Library Research Prize

No abstract provided.

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Runner Up Entry For 2021, Zoe Honigberg Jan 2021

Runner Up Entry For 2021, Zoe Honigberg

Library Research Prize

No abstract provided.

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A New Recursive Formula Arising From A Determinantal Expression For Weighted Delannoy Numbers, Muhammet Ci̇hat Dağli Jan 2021

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.

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Quasi-Idempotent Ranks Of The Proper Ideals In Finite Symmetric Inverse Semigroups, Leyla Bugay Jan 2021

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).

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