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An Application Of Modified Sigmoid Function To A Class Of $Q-$ Starlike And $Q-$ Convex Analytic Error Functions, Arzu Akgül
Turkish Journal of Mathematics
In this study, in the open unit disc $\Lambda$, by applying the $q-$ derivative operator and the fractional $q-$ derivative operator and by using the principle of subordination between analytic functions, we introduce some new interesting subclasses of $q-$ starlike and $q-$ convex analytic functions associated with error functions and modified sigmoid functions.
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Representation Variety Of Free Or Surface Groups And Reidemeister Torsion, Fati̇h Hezenci̇, Yaşar Sözen
Turkish Journal of Mathematics
For $G \in \left\{ \mathrm{GL}(n,\mathbb{C}) , \mathrm{SL}(n,\mathbb{C})\right\} ,$ we consider $G-$valued representations of free or surface group with genus $ >1.$ We establish a formula for computing Reidemeister torsion of such representations in terms of Atiyah-Bott-Goldman symplectic form for $G.$ Furthermore, we apply the obtained results to hyperbolic 3-manifolds.
Some Relations Between Almost Paracontact Metric Manifolds And Almost Parahermitian Manifolds, Nüli̇fer Özdemi̇r, Neci̇p Erdoğan
Some Relations Between Almost Paracontact Metric Manifolds And Almost Parahermitian Manifolds, Nüli̇fer Özdemi̇r, Neci̇p Erdoğan
Turkish Journal of Mathematics
In this study, almost paracontact metric manifolds and almost para-Hermitian manifolds are considered. The relations between almost paracontact metric manifolds and almost para-Hermitian manifolds are investigated and certain results are acquired. Examples of almost para-Hermitian manifolds are presented using the determined relations.
A Series Evaluation Technique Based On A Modified Abel Lemma, John Maxwell Campbell, Marco Cantarini
A Series Evaluation Technique Based On A Modified Abel Lemma, John Maxwell Campbell, Marco Cantarini
Turkish Journal of Mathematics
We introduce a technique for determining infinite series identities through something of a combination of the modified Abel lemma on summation by parts and a method of undetermined coefficients. We succeed in applying our technique in our proving a nontrivial variant of Gauss' hypergeometric identity, giving us an evaluation for a family of ${}_{3}F_{2}(1)$-series with three free parameters, and to establish a ${}_{3}F_{2}(-1)$-variant of Kummer's hypergeometric identity. Also, we apply the technique upon which this article is based to formulate a new and simplified proof of a remarkable series evaluation recently derived by Cantarini via the generalized Clebsch-Gordan integral.
A Class Of Finsler Measure Spaces Of Constant Weighted Ricci Curvature, Songting Yin, Xiaohuan Mo, Ling Zhu
A Class Of Finsler Measure Spaces Of Constant Weighted Ricci Curvature, Songting Yin, Xiaohuan Mo, Ling Zhu
Turkish Journal of Mathematics
The weight Ricci curvature plays an important role in studying global Finsler geometry. In this paper, we study a class of Finsler measure spaces of constant weighted Ricci curvature. We explicitly construct new families of such complete Finsler measure spaces. In particular, we find an eigenfunction and its eigenvalue for such spaces, generalizing a result previously only known in the case of Gaussian shrinking soliton. Finally, we give necessary and sufficient conditions on the coordinate functions for these spaces to be Euclidean measure spaces.
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
A Matrix-Collocation Method For Solutions Of Singularly Perturbed Differential Equations Via Euler Polynomials, Deni̇z Elmaci, Şuayi̇p Yüzbaşi, Nurcan Baykuş Savaşaneri̇l
Turkish Journal of Mathematics
In this paper, a matrix-collocation method which uses the Euler polynomials is introduced to find the approximate solutions of singularly perturbed two-point boundary-value problems (BVPs). A system of algebraic equations is obtained by converting the boundary value problem with the aid of the collocation points. After this algebraic system, the coefficients of the approximate solution are determined. This error analysis includes two theorems which consist of an upper bound of errors and an error estimation technique. The present method and error analysis are applied to three numerical examples of singularly perturbed two-point BVPs. Numerical examples and comparisons with other methods …
Ranks And Presentations For Order-Preserving Transformations With One Fixed Point, Joerg Koppitz, Somnuek Worawiset
Ranks And Presentations For Order-Preserving Transformations With One Fixed Point, Joerg Koppitz, Somnuek Worawiset
Turkish Journal of Mathematics
In the present paper, we consider the semigroup $O_{n,p}$ of all order-preserving full transformations $\alpha $ on an n-elements chain $X_{n}$% , where $p\in X_{n}$ is the only fixed point of $\alpha $. The nilpotent semigroup $O_{n,p}$ was first studied by Ayik et al. in 2011. Moreover, $% O_{n,1}$ is the maximal nilpotent subsemigroup of the Catalan Monoid $C_{n}$. Its rank is the difference of the $(n-1)$th and the $(n-2)$th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup $O_{n,p}$. We will calculate the rank of $O_{n,p}$ for $% p>1$ …
Symmetric Polynomials In Free Associative Algebras, Silvia Boumova, Vesselin Drensky, Deyan Dzhundrekov, Martin Kassabov
Symmetric Polynomials In Free Associative Algebras, Silvia Boumova, Vesselin Drensky, Deyan Dzhundrekov, Martin Kassabov
Turkish Journal of Mathematics
By a result of Margarete Wolf in 1936, we know that the algebra $K\langle X_d\rangle^{Sym(d)}$ of symmetric polynomials in noncommuting variables is not finitely generated. In 1984, Koryukin proved that if we equip the homogeneous component of degree $n$ with the additional action of $Sym(n)$ by permuting the positions of the variables, then the algebra of invariants $K\langle X_d\rangle^G$ of every reductive group $G$ is finitely generated. First, we make a short comparison between classical invariant theory of finite groups and its noncommutative counterpart. Then, we expose briefly the results of Wolf. Finally, we present the main result of our …
A Variant Of Rosset's Approach To The Amitsur-Levitzki Theorem And Some $\Mathbb{Z}_{2}$-Graded Identities Of $\Mathrm{M}_{N}(E)$, Szilvia Homolya, Jen Szigeti
A Variant Of Rosset's Approach To The Amitsur-Levitzki Theorem And Some $\Mathbb{Z}_{2}$-Graded Identities Of $\Mathrm{M}_{N}(E)$, Szilvia Homolya, Jen Szigeti
Turkish Journal of Mathematics
In the spirit of Rosset's proof of the Amitsur-Levitzki theorem, we show how the standard identiy (for matrices over a commutative base ring) and the addition of external Grassmann variables can be used to derive a certain $\mathbb{Z}_{2}$-graded polynomial identity of $\mathrm{M}_{n}(E)$.
On The Restricted Graded Jacobson Radical Of Rings Of Morita Context, Puguh Wahyu Prasetyo, Hidetoshi Marubayashi, Indah Emilia Wijayanti
On The Restricted Graded Jacobson Radical Of Rings Of Morita Context, Puguh Wahyu Prasetyo, Hidetoshi Marubayashi, Indah Emilia Wijayanti
Turkish Journal of Mathematics
The class of rings $\mathcal{J}=\{A (A,\circ)$ forms a group$\}$ forms a radical class and it is called the Jacobson radical class. For any ring $A$, the Jacobson radical $\mathcal{J}(A)$ of $A$ is defined as the largest ideal of $A$ which belongs to $\mathcal{J}$. In fact, the Jacobson radical is one of the most important radical classes since it is used widely in another branch of abstract algebra, for example, to construct a two-sided brace. On the other hand, for every ring of Morita context $T=\begin{pmatrix} R & V \\ W & S \end{pmatrix}$, we will show directly by the structure …
Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ
Introducing Selective D-Separability In Bitopological Spaces, Selma Özçağ
Turkish Journal of Mathematics
We introduce $\sf D$-separability and its game-theoretic version, $\sf D^+$-separability in bitopological spaces, and investigate their relationships with $d$-separability and a weaker form of $\sf H$-separability which will be called ${\sf DH}$-separability. Further we give the connection of these notions with the selective versions of separability-types properties under the bitopological context. We also obtain some results about the $d$-separability properties of bitopological spaces which are slightly different from those one expects for the classical case
Birotational Hypersurface And The Second Laplace-Beltrami Operator In The Four Dimensional Euclidean Space ${\Mathbb{E}}^{4}$, Erhan Güler, Yusuf Yayli, Hasan Hi̇lmi̇ Hacisali̇hoğlu
Birotational Hypersurface And The Second Laplace-Beltrami Operator In The Four Dimensional Euclidean Space ${\Mathbb{E}}^{4}$, Erhan Güler, Yusuf Yayli, Hasan Hi̇lmi̇ Hacisali̇hoğlu
Turkish Journal of Mathematics
We consider the birotational hypersurface $\mathbf{x(}u,v,w\mathbf{)}$ with the second Laplace-Beltrami operator in the four dimensional Euclidean space ${\mathbb{E}}^{4}.$ We give the $i$-th curvatures of $\mathbf{x}$. In addition, we compute the second Laplace-Beltrami operator of the birotational hypersurface satisfying $\Delta ^{II}\mathbf{x=}\mathcal{A}% \mathbf{x}$ for some $4\times 4$ matrix $\mathcal{A}$.
On The Geometry Of Lift Metrics And Lift Connections On The Tangent Bundle, Esmaeil Peyghan, Davood Seifipour, Adara Blaga
On The Geometry Of Lift Metrics And Lift Connections On The Tangent Bundle, Esmaeil Peyghan, Davood Seifipour, Adara Blaga
Turkish Journal of Mathematics
We study lift metrics and lift connections on the tangent bundle $TM$ of a Riemannian manifold $(M,g)$. We also investigate the statistical and Codazzi couples of $TM$ and their consequences on the geometry of $M$. Finally, we prove a result on $1$-Stein and Osserman structures on $TM$, whenever $TM$ is equipped with the complete lift connection.
Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas
Universality Of An Absolutely Convergent Dirichlet Series With Modified Shifts, Antanas Laurincikas, Renata Macaitiene, Darius Siauciunas
Turkish Journal of Mathematics
In the paper, a theorem on approximation of a wide class of analytic functions by generalized shifts $\zeta_{u_T}(s+i\varphi(\tau))$ of an absolutely convergent Dirichlet series $\zeta_{u_T}(s)$ which in the mean is close to the Riemann zeta-function is obtained. Here $\varphi(\tau)$ is a monotonically increasing differentiable function having a monotonic continuous derivative such that $\varphi(2\tau)\max\limits_{\tau\leqslant t\leqslant 2\tau} \frac{1}{\varphi'(t)} \ll \tau$ as $\tau\to\infty$, and $u_T\to\infty$ and $u_T\ll T^2$ as $T\to\infty$.
Explicit Examples Of Constant Curvature Surfaces In The Supersymmetric ${C}P^{2}$ Sigma Model, İsmet Yurduşen
Explicit Examples Of Constant Curvature Surfaces In The Supersymmetric ${C}P^{2}$ Sigma Model, İsmet Yurduşen
Turkish Journal of Mathematics
The surfaces constructed from the holomorphic solutions of the supersymmetric (susy) ${C}P^{N-1}$ sigma model are studied. By obtaining compact general expansion formulae having neat forms due to the properties of the superspace in which this model is described, the explicit expressions for the components of the radius vector as well as the elements of the metric and the Gaussian curvature are given in a rather natural manner. Several examples of constant curvature surfaces for the susy ${C}P^{2}$ sigma model are presented.
Curvature Identities For Einstein Manifolds Of Dimensions 5 And 6, Yunhee Euh, Jihun Kim, Jeonghyeong Park
Curvature Identities For Einstein Manifolds Of Dimensions 5 And 6, Yunhee Euh, Jihun Kim, Jeonghyeong Park
Turkish Journal of Mathematics
Patterson discussed the curvature identities on Riemannian manifolds based on the skew-symmetric properties of the generalized Kronecker delta, and a curvature identity for any 6-dimensional Riemannian manifold was independently derived from the Chern-Gauss-Bonnet Theorem. In this paper, we provide the explicit formulae of Patterson's curvature identity that holds on 5-dimensional and 6-dimensional Einstein manifolds. We confirm that the curvature identities on the Einstein manifold derived from the Chern-Gauss-Bonnet Theorem are the same as the curvature identities deduced from Patterson's result. We also provide examples that support the theorems.
On The $2$-Class Group Of Some Number Fields Of $2$-Power Degree, Idriss Jerrari, Abdelmalek Azizi
On The $2$-Class Group Of Some Number Fields Of $2$-Power Degree, Idriss Jerrari, Abdelmalek Azizi
Turkish Journal of Mathematics
Let $K$ be an imaginary cyclic quartic number field whose $2$-class group is isomorphic to $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/2\mathbb{Z}$, and let $K^*$ denote the genus field of $K$. In this paper, we compute the rank of the $2$-class group of $K^*_n$ the $n$-th layer of the cyclotomic $Z_2$-extension of $K^*$.
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Quasi $J$-Submodules, Ece Yetki̇n Çeli̇kel, Hani Khashan
Turkish Journal of Mathematics
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. The aim of this paper is to extend the notion of quasi $J$-ideals of commutative rings to quasi $J$-submodules of modules. We call a proper submodule $N$ of $M$ a quasi $J$-submodule if whenever $r\in R$ and $m\in M$ such that $rm\in N$ and $r\notin(J(R)M:M)$, then $m\in M$-$rad(N)$. We present various properties and characterizations of this concept (especially in finitely generated faithful multiplication modules). Furthermore, we provide new classes of modules generalizing presimplifiable modules and justify their relation with (quasi) $J$-submodules. Finally, for a submodule $N$ …
Spinor Representation Of Framed Mannheim Curves, Bahar Doğan Yazici, Zehra İşbi̇li̇r, Murat Tosun
Spinor Representation Of Framed Mannheim Curves, Bahar Doğan Yazici, Zehra İşbi̇li̇r, Murat Tosun
Turkish Journal of Mathematics
In this paper, we obtain spinor with two complex components representations of Mannheim curves of framed curves. Firstly, we give the spinor formulas of the frame corresponding to framed Mannheim curve. Later, we obtain the spinor formulas of the frame corresponding to framed Mannheim partner curve. Moreover, we explain the relationships between spinors corresponding to framed Mannheim pairs and their geometric interpretations. Finally, we present some geometrical results of spinor representations of framed Mannheim curves.
A Characterization Of Abelian Group Codes In Terms Of Their Parameters, Fatma Altunbulak Aksu, İpek Tuvay
A Characterization Of Abelian Group Codes In Terms Of Their Parameters, Fatma Altunbulak Aksu, İpek Tuvay
Turkish Journal of Mathematics
In 1979, Miller proved that for a group $G$ of odd order, two minimal group codes in $\mathbb{F}_2G$ are $G$-equivalent if and only if they have identical weight distribution. In 2014, Ferraz-Guerreiro-Polcino Milies disproved Miller's result by giving an example of two non-$G$-equivalent minimal codes with identical weight distribution. In this paper, we give a characterization of finite abelian groups so that over a specific set of group codes, equality of important parameters of two codes implies the $G$-equivalence of these two codes. As a corollary, we prove that two minimal codes with the same weight distribution are $G$-equivalent if …
Minimal Legendrian Submanifolds Of $\Mathbb S^{9}$ With Nonnegative Sectional Curvature, Shujie Zhai, Heng Zhang
Minimal Legendrian Submanifolds Of $\Mathbb S^{9}$ With Nonnegative Sectional Curvature, Shujie Zhai, Heng Zhang
Turkish Journal of Mathematics
In this paper, we established a complete classification of 4-dimensional compact minimal Legendrian submanifolds with nonnegative sectional curvature in the 9-dimensional unit sphere.
(Co)Limit Calculations In The Category Of 2-Crossed $R$-Modules, Eli̇s Soylu Yilmaz
(Co)Limit Calculations In The Category Of 2-Crossed $R$-Modules, Eli̇s Soylu Yilmaz
Turkish Journal of Mathematics
In this work, we obtain how to construct finite limits and colimits for 2-crossed $R$-Modules over groups denoted with $\mathbf{X_2Mod/R}$. We give direct construction of the pullback object to show that this category has finite products over the terminal object. We also show finite coproducts and (co)completeness.
Some Asymptotic Results For The Continued Fraction Expansions With Odd Partial Quotients, Gabriela Ileana Sebe, Dan Lascu
Some Asymptotic Results For The Continued Fraction Expansions With Odd Partial Quotients, Gabriela Ileana Sebe, Dan Lascu
Turkish Journal of Mathematics
We present and develop different approaches to study the asymptotic behavior of the distribution functions in the odd continued fractions case. Firstly, by considering the transition operator of the Markov chain associated with these expansions on a certain Banach space of complex-valued functions of bounded variation, we make a brief survey of the solution in the Gauss-Kuzmin-type problem. Secondly, we use the method of Szüsz to obtain a similar asymptotic result and to give a good estimate of the convergence rate involved.
Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin
Continuation Value Computation Using Malliavin Calculus Under General Volatility Stochastic Process For American Option Pricing, Mohamed Kharrat, Fabian Bastin
Turkish Journal of Mathematics
American options represent an important financial instrument but are notoriously difficult to price, especially when the volatility is not constant. We explore the conditions required to apply Malliavin calculus to price American options when the volatility follows a general stochastic differential process, and develop the expressions to compute the continuation value at any time before the expiration date, given the current asset price and volatility. The developed methodology can then be applied to price American options.
On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
On The Application Of Euler's Method To Linear Integro Differential Equations And Comparison With Existing Methods, Deni̇z Elmaci, Nurcan Baykuş Savaşaneri̇l, Fadi̇me Dal, Mehmet Sezer
Turkish Journal of Mathematics
In this study, a collocation method using Euler method for solving systems of linear integro-differential equations is presented. Thesolution process is illustrated and various physically relevant results are obtained. Comparison of the obtained results with exactsolutions and solutions obtained by other methods show that the proposed method is an effective and highly promising for linear integro-differential equation systems. All of numerical calculations have been made on a computer using a program written in Matlab.
A New Subclass Of Certain Analytic Univalent Functions Associated With Hypergeometric Functions, Alaatti̇n Akyar
A New Subclass Of Certain Analytic Univalent Functions Associated With Hypergeometric Functions, Alaatti̇n Akyar
Turkish Journal of Mathematics
The main objective of the present paper is to give with using the linear operator theory and also hypergeometric representations of related functions a new special subclass $\mathcal{TS}_{p}(2^{-r},2^{-1}), r\in \mathbb{ Z }^{+}$ of uniformly convex functions and in addition a suitable subclass of starlike functions with negative Taylor coefficients. Furthermore, the provided trailblazer outcomes in presented study are generalized to certain functions classes with fixed finitely many Taylor coefficients.
Efficient Nyberg-Rueppel Type Of Ntru Digital Signature Algorithm, Ferdi̇ Elverdi̇, Sedat Akleylek, Bariş Bülent Kirlar
Efficient Nyberg-Rueppel Type Of Ntru Digital Signature Algorithm, Ferdi̇ Elverdi̇, Sedat Akleylek, Bariş Bülent Kirlar
Turkish Journal of Mathematics
Message recovery is an important property in Nyberg-Rueppel type digital signature algorithms. However, the security of Nyberg-Rueppel type digital signature algorithms depends on the hard problems which might be vulnerable to quantum attacks. Therefore, quantum resistant Nyberg-Rueppel type digital signature algorithms with message recovery property are needed. Since NTRU-based cryptosystems are one of the best studied quantum-resistant schemes, using traditional NTRU encryption scheme has several advantages on the message recovery property. In this paper, we define Nyberg-Rueppel type of NTRU digital signature algorithm. It is carried out by combining NTRU-based encryption and signature algorithms. In the proposed scheme, efficient message …