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Articles 1141 - 1170 of 2494
Full-Text Articles in Physical Sciences and Mathematics
On The Numerical Range Of Square Matrices With Coefficients In A Degree $2$ Galois Field Extension, Edoardo Ballico
On The Numerical Range Of Square Matrices With Coefficients In A Degree $2$ Galois Field Extension, Edoardo Ballico
Turkish Journal of Mathematics
Let $L$ be a degree $2$ Galois extension of the field $K$ and $M$ an $n\times n$ matrix with coefficients in $L$. Let $\langle \ ,\ \rangle : L^n\times L^n\to L$ be the sesquilinear form associated to the involution $L\to L$ fixing $K$. We use $\langle \ ,\ \rangle$ to define the numerical range $\mathrm{Num} (M)$ of $M$ (a subset of $L$), extending the classical case $K=\mathbb {R}$, $L=\mathbb {C}$, and the case of a finite field introduced by Coons, Jenkins, Knowles, Luke, and Rault. There are big differences with respect to both cases for number fields and for all …
Block Classical Gram-Schmidt-Based Block Updating In Low-Rank Matrix Approximation, Hasan Erbay, Fati̇h Varçin, Fahretti̇n Horasan, Cenker Bi̇çer
Block Classical Gram-Schmidt-Based Block Updating In Low-Rank Matrix Approximation, Hasan Erbay, Fati̇h Varçin, Fahretti̇n Horasan, Cenker Bi̇çer
Turkish Journal of Mathematics
Low-rank matrix approximations have recently gained broad popularity in scientific computing areas. They are used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncated singular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applications such as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrix is subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULV decomposition. Herein, we propose a BLAS-3 compatible block …
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
On The $J$-Reflexive Operators, Parviz Sadat Hosseini, Bahmann Yousefi
Turkish Journal of Mathematics
A bounded linear operator $T$ on a Banach space $X$ is $J$-reflexive if every bounded operator on $X$ that leaves invariant the sets $J(T,x)$ for all $x$ is contained in the closure of $orb(T)$ in the strong operator topology. We discuss some properties of $J$-reflexive operators. We also give and prove some necessary and sufficient conditions under which an operator is $J$-reflexive. We show that isomorphisms preserve $J$-reflexivity and some examples are considered. Finally, we extend the $J$-reflexive property in terms of subsets.
Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh
Approximation By Integral Functions Of Finite Degree In Variable Exponentlebesgue Spaces On The Real Axis, Ramazan Akgün, Arash Ghorbanalizadeh
Turkish Journal of Mathematics
We obtain several inequalities of approximation by integral functions of finite degree in generalized Lebesgue spaces with variable exponent defined on the real axis. Among them are direct, inverse, and simultaneous estimates of approximation by integral functions of finite degree in $L^{p\left( \cdot \right)}.$ An equivalence of modulus of continuity with Peetre's $K$ -functional is established. A constructive characterization of Lipschitz class is also obtained.
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Regularity Of Semigroups Of Transformations With Restricted Range Preserving An Alternating Orientation Order, Somphong Jitman, Rattana Srithus, Chalermpong Worawannotai
Turkish Journal of Mathematics
It is well known that the transformation semigroup on a nonempty set $X$, which is denoted by $T(X)$, is regular, but its subsemigroups do not need to be. Consider a finite ordered set $X=(X;\leq)$ whose order forms a path with alternating orientation. For a nonempty subset $Y$ of $X$, two subsemigroups of $T(X)$ are studied. Namely, the semigroup $OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}$ and the semigroup $OS(X,Y)=\{\alpha\in T(X)\mid\alpha$ is order-preserving and $Y\alpha \subseteq Y\}$. In this paper, we characterize ordered sets having a coregular semigroup $OT(X,Y)$ and a coregular semigroup $OS(X,Y)$, respectively. Some characterizations of regular semigroups $OT(X,Y)$ …
Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu
Second Hankel Determinant For Certain Subclasses Of Bi-Univalent Functions Involving Chebyshev Polynomials, Hali̇t Orhan, Evri̇m Toklu, Ekrem Kadioğlu
Turkish Journal of Mathematics
In this paper our purpose is to find the upper bound estimate for the second Hankel determinant $ a_{2}a_{4}-a_{3}^{2} $ for functions defined by convolution belonging to the class $\mathcal{N}_{\sigma}^{\mu,\delta}(\lambda,t)$ by using Chebyshev polynomials.
A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör
A New Approach To $H$-Supplemented Modules Via Homomorphisms, Ali Reza Moniri Hamzekolaee, Abdullah Harmanci, Yahya Talebi, Burcu Üngör
Turkish Journal of Mathematics
The class of $H$-supplemented modules, which is a nice generalization of that of lifting modules, has been studied extensively in the last decade. As the concept of homomorphisms plays an important role in module theory, we are interested in $H$-supplemented modules relative to homomorphisms. Let $R$ be a ring, $M$ a right $R$-module, and $S=$ End$_{R}(M)$. We say that $M$ is endomorphism $H$-supplemented (briefly, $E$-$H$-supplemented) provided that for every $f\in S$ there exists a direct summand $D$ of $M$ such that $Imf+X=M$ if and only if $D+X=M$ for every submodule $X$ of $M$. In this paper, we deal with the …
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Solutions Of The Björling Problem For Timelike Surfaces In The Lorentz-Minkowski Space, Seher Kaya, Rafael Lopez
Turkish Journal of Mathematics
We give a number of new examples of timelike minimal surfaces in the Lorentz-Minkowski space. Our method consists of solving the Björling problem by prescribing a circle or a helix as the core curve $\alpha$ and rotating with constant angular speed the unit normal vector field in the normal plane to $\alpha$. As particular cases, we exhibit new examples of timelike minimal surfaces invariant by a uniparametric group of helicoidal motions.
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum
Existence And Uniqueness Of Solution Fordifferential Equation Of Fractional Order $2, Ghazala Akram, Fareeha Anjum
Turkish Journal of Mathematics
This paper is devoted to the study of nonlinear fractional differential equation involving Caputo fractional derivative of order $2
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Normality And Quotient In Crossed Modules Over Groupoids And Double Groupoids, Osman Mucuk, Serap Demi̇r
Turkish Journal of Mathematics
We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Olsen-Type Inequalities For The Generalized Commutator Of Multilinear Fractional Integrals, Xiao Yu, Shanzhen Lu
Turkish Journal of Mathematics
In this paper, we study certain multilinear operators of fractional integral type defined by \[ I^{\vec{A}}_{\alpha}\vec{f}(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion (\mathbb{R} %EndExpansion ^{n})^m}\frac{f_1(y_1)\cdots f_m(y_m)}{ (x-y_1,\cdots,x-y_m) ^{mn-\alpha+\sum\limits_{i=1}^m(N_i-1)}}\prod\limits_{i=1}^mR_{N_i}(A_i;x,y_i)d\vec{y}, \] where $0< \alpha
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Positive Solutions Of Neumann Problems For A Discrete System Coming From Models Of House Burglary, Tianlan Chen, Ruyun Ma, Yongwen Liang
Turkish Journal of Mathematics
We show existence results of positive solutions of Neumann problems for a discrete system: $$\aligned &\eta\Delta^2(A_{k-1}-A^0_{k-1})-A_{k}+A^0_{k}+N_kA_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta\big(\Delta N_{k-1}-2N_k\frac{\Delta A_{k-1}}{A_{k}}\big)-N_kA_{k}+A^1_{k}-A^0_{k}=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned $$ where the assumptions on $\eta,\ A_k^0$, and $A_k^1$ are motivated by some mathematics models for house burglary. Our results are based on the topological degree theory.
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
The Density Theorem For Hermitian K-Theory, Mohamed Elamine Talbi
Turkish Journal of Mathematics
Karoubi's density theorem was first proved in Benayat's thesis and then cited and used in several books and articles. As K-theory is a special case of hermitian $_{\varepsilon }L$-theory, a natural question is whether such a theorem is still true in the latter theory. The purpose of this article is to show that it is indeed the case.
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
A Further Extension Of The Extended Riemann-Liouville Fractional Derivative Operator, Martin Bohner, Gauhar Rahman, Shahid Mubeen, Kottakkaran Nisar
Turkish Journal of Mathematics
The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani
On The Higher Derivatives Of The Inverse Tangent Function, Mohamed Amine Boutiche, Mourad Rahmani
Turkish Journal of Mathematics
In this paper, we find explicit formulas for higher-order derivatives of the inverse tangent function. More precisely, we study polynomials that are induced from the higher-order derivatives of $\arctan(x)$. Successively, we give generating functions, recurrence relations, and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas, and matching polynomials are established.
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System, Jinjing Liu, Hanchun Yang
Delta-Shocks And Vacuums As Limits Of Flux Approximation For The Pressureless Type System, Jinjing Liu, Hanchun Yang
Turkish Journal of Mathematics
In this paper, we investigate the phenomena of concentration and cavitation and the formation of delta-shocks and vacuum states in solutions of the pressureless type system with flux approximation. First, the Riemann problem of the pressureless type system with a flux perturbation is considered. A parameterized delta-shock and generalized constant density solution are obtained. Then we rigorously prove that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state of the pressureless type system, respectively. Secondly, by adding an artificial pressure term in the pressureless type system, we solve the Riemann problem of the system with a …
$\Mathbb{Q}$-Korselt Numbers, Nejib Ghanmi
$\Mathbb{Q}$-Korselt Numbers, Nejib Ghanmi
Turkish Journal of Mathematics
Let $\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{Q}\setminus \{0\}$; a positive integer $N$ is said to be an \emph{$\alpha$-Korselt number} (\emph{$K_{\alpha}$-number}, for short) if $N\neq \alpha$ and $\alpha_{2}p-\alpha_{1}$ divides $\alpha_{2}N-\alpha_{1}$ for every prime divisor $p$ of $N$. In this paper we prove that for each squarefree composite number $N$ there exist finitely many rational numbers $\alpha$ such that $N$ is a $K_{\alpha}$-number and if $\alpha\leq1$ then $N$ has at least three prime factors. Moreover, we prove that for each $\alpha\in \mathbb{Q}\setminus \{0\}$ there exist only finitely many squarefree composite numbers $N$ with two prime factors such that $N$ is a $K_{\alpha}$-number.
On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer
On $3$-Dimensional $\Jt$-Tangent Centro-Affine Hypersurfaces And $\Jt$-Tangent Affine Hyperspheres With Some Null-Directions, Zuzanna Szancer
Turkish Journal of Mathematics
Let $\Jt$ be the canonical para-complex structure on $\R^4$. In this paper we study $3$-dimensional centro-affine hypersurfaces with a $\Jt$-tangent centro-affine vector field (sometimes called $\Jt$-tangent centro-affine hypersurfaces) as well as $3$-dimensional $\Jt$-tangent affine hyperspheres with the property that at least one null-direction of the second fundamental form coincides with either $\DD^+$ or $\DD^-$. The main purpose of this paper is to give a full local classification of the above-mentioned hypersurfaces. In particular, we prove that every nondegenerate centro-affine hypersurface of dimension $3$ with a $\Jt$-tangent centro-affine vector field that has two null-directions $\DD^+$ and $\DD^-$ must be both an …
On A New Subclass Of Bi-Univalent Functions Defined By Using Salagean Operator, Bi̇lal Şeker
On A New Subclass Of Bi-Univalent Functions Defined By Using Salagean Operator, Bi̇lal Şeker
Turkish Journal of Mathematics
In this manuscript, by using the Salagean operator, new subclasses of bi-univalent functions in the open unit disk are defined. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found.
Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife
Existence Of Solution For Some Two-Point Boundary Value Fractional Differential Equations, Kenneth Ifeanyi Isife
Turkish Journal of Mathematics
Using a fixed point theorem, we establish the existence of a solution for a class of boundary value fractional differential equation. Secondly, we will adopt the method of successive approximations to obtain an approximate solution to our problem. Furthermore, using the Laplace transform technique, an explicit solution to a particular case of our problem is obtained. Finally, some examples are given to illustrate our results.
When Is A Permutation Of The Set $\Z^N$ (Resp. $\Z_P^N$, $P$ Prime) An Automorphism Of The Group $\Z^N$ (Resp. $\Z_P^N$)?, Ben-Eben De Klerk, Johan H. Meyer
When Is A Permutation Of The Set $\Z^N$ (Resp. $\Z_P^N$, $P$ Prime) An Automorphism Of The Group $\Z^N$ (Resp. $\Z_P^N$)?, Ben-Eben De Klerk, Johan H. Meyer
Turkish Journal of Mathematics
For a given positive integer $n$, the structure, i.e. the number of cycles of various lengths, as well as possible chains, of the automorphisms of the groups $(\Z^n, +)$ and $(\Z_p^n,+)$, \ $p$ prime, is studied. In other words, necessary and sufficient conditions on a bijection $f : A \ra A$, where $ A $ is countably infinite (alternatively, of order $p^n$), are determined so that $A$ can be endowed with a binary operation $*$ such that $(A,*)$ is a group isomorphic to $(\Z^n,+)$ (alternatively, $(\Z_p^n,+)$) and such that $f\in \Aut(A)$.
Generalized Metric $N$-Leibniz Algebras And Generalized Orthogonal Representation Of Metric Lie Algebras, Rong Tang, Lina Song
Generalized Metric $N$-Leibniz Algebras And Generalized Orthogonal Representation Of Metric Lie Algebras, Rong Tang, Lina Song
Turkish Journal of Mathematics
We introduce the notion of a generalized metric $n$-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric $n$-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple datas). We further show that there is also a one-to-one correspondence between generalized orthogonal derivations (resp. generalized orthogonal automorphisms) on generalized metric $n$-Leibniz algebras and Lie triple data.
Some Characterizations Of Right $C$-Regularity And $(B,C)$-Inverse, Ruju Zhao, Hua Yao, Long Wang, Junchao Wei
Some Characterizations Of Right $C$-Regularity And $(B,C)$-Inverse, Ruju Zhao, Hua Yao, Long Wang, Junchao Wei
Turkish Journal of Mathematics
Let $R$ be a ring and $a,b,c\in R$. We give a novel characterization of group inverses (resp. EP elements) by the properties of right (resp. left ) $c$-regular inverses of $a$ and discuss the relation among the strongly left $(b,c)$-invertibility of $a$, the right $ca$-regularity of $b$, and the $(b,c)$-invertibility of $a$. Finally, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of the $(b,c)$-inverse of $a$.
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
On The Solution Of An Inverse Sturm-Liouville Problem With A Delay And Eigenparameter-Dependent Boundary Conditions, Seyfollah Mosazadeh
Turkish Journal of Mathematics
In this paper, a boundary value problem consisting of a delay differential equation of the Sturm-Liouville type with eigenparameter-dependent boundary conditions is investigated. The asymptotic behavior of eigenvalues is studied and the parameter of delay is determined by eigenvalues. Then we obtain the connection between the potential function and the canonical form of the characteristic function.
Closed Range Properties Of Li-Steviç Integral-Type Operators Between Bloch-Type Spaces And Their Essential Norms, Maryam Mohammadi Pirasteh, Nasrin Eghbali, Amir Hossein Sanatpour
Closed Range Properties Of Li-Steviç Integral-Type Operators Between Bloch-Type Spaces And Their Essential Norms, Maryam Mohammadi Pirasteh, Nasrin Eghbali, Amir Hossein Sanatpour
Turkish Journal of Mathematics
We investigate closed range properties of certain integral-type operators introduced by Li and Steviç. The operators are considered between Bloch-type spaces. We also give the essential norm of such operators. Our results are given in a general setting and we also give the essential norm of Li-Steviç integral-type operators between other well-known spaces of analytic functions.
Conditional Expectation Type Operators And Modular Inequalities, Dah-Chin Luor
Conditional Expectation Type Operators And Modular Inequalities, Dah-Chin Luor
Turkish Journal of Mathematics
In this paper we discuss the connection between conditional expectation type operators and integral operators. A variant of Schur's lemma is established and we obtain modular inequalities for a class of conditional expectation type operators.
Curves Whose Pseudo Spherical Indicatrices Are Elastic, Ahmet Yücesan, Gözde Özkan Tükel, Tunahan Turhan
Curves Whose Pseudo Spherical Indicatrices Are Elastic, Ahmet Yücesan, Gözde Özkan Tükel, Tunahan Turhan
Turkish Journal of Mathematics
The pseudo spherical indicatrix of a curve in Minkowski $3$-space emerges as three types: the pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve. The pseudo spherical tangent, principal normal, and binormal indicatrix of a regular curve may be positioned on De Sitter $2$-space (pseudo sphere), pseudo hyperbolic 2-space, and two-dimensional null cone in terms of causal character of the curve. In this paper, we separately derive Euler-Lagrange equations of all pseudo spherical indicatrix elastic curves in terms of the causal character of a curve in Minkowski $3$-space. Then we give some results of solutions of …
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
A Taylor Operation Method For Solutions Of Generalized Pantograph Type Delay Differential Equations, Şuayi̇p Yüzbaşi, Nurbol Ismailov
Turkish Journal of Mathematics
In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is that the method does not require collocation points. By using the proposed method, the generalized pantograph equation problem is reduced to a system of linear algebraic equations. The solving of this system gives the coefficients of our solution. Numerical examples are given …
Modules Whose $P$-Submodules Are Direct Summands, Yeli̇z Kara
Modules Whose $P$-Submodules Are Direct Summands, Yeli̇z Kara
Turkish Journal of Mathematics
In this article we deal with modules with the property that all $p$-submodules are direct summands. In contrast to $CLS$-modules, it is shown that the former property is closed under finite direct sums, but it is not inherited by direct summands. Hence we focus on when the direct summands of aforementioned modules enjoy the property. Moreover, we characterize the forenamed class of modules in terms of lifting homomorphisms.
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
The Local And Semilocal Convergence Analysis Of New Newton-Like Iteration Methods, Vatan Karakaya, Kadri̇ Doğan, Yunus Atalan, Nour El Houda Bouzara
Turkish Journal of Mathematics
The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.