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Articles 1201 - 1230 of 2595
Full-Text Articles in Mathematics
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 …
Quasinilpotents In Rings And Their Applications, Jian Cui
Quasinilpotents In Rings And Their Applications, Jian Cui
Turkish Journal of Mathematics
An element $a$ of an associative ring $R$ is said to be quasinilpotent if $1-ax$ is invertible for every $x\in R$ with $xa=ax$. Nilpotents and elements in the Jacobson radical of a ring are well-known examples of quasinilpotents. In this paper, properties and examples of quasinilpotents in a ring are provided, and the set of quasinilpotents is applied to characterize rings with some certain properties.
Natural Mates Of Frenet Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Azeb Alghanemi
Natural Mates Of Frenet Curves In Euclidean 3-Space, Sharief Deshmukh, Bang-Yen Chen, Azeb Alghanemi
Turkish Journal of Mathematics
For each Frenet curve $\alpha $ in the Euclidean 3-space $\mathbb{E}^{3}$, there exists a unique unit speed curve $\beta$ tangent to the principal normal vector field of $\alpha $. We simply call this curve $\beta $ the natural mate of $\alpha$. The main purpose of this paper is to prove some relationships between a Frenet curve and its natural mate. In particular, we obtain some necessary and sufficient conditions for the natural mate of a Frenet curve to be a helix, a spherical curve, or a curve of constant curvature. Several applications of our main results are also presented.
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.
Strongly $Cm$-Semicommutative Rings, Liang Zhao, Jiaqun Wei
Strongly $Cm$-Semicommutative Rings, Liang Zhao, Jiaqun Wei
Turkish Journal of Mathematics
We study the strongly semicommutative properties relative to a monoid crossed product. The concept of strongly $CM$-semicommutative rings is introduced and investigated. Many results related to semicommutative properties over polynomial rings, skew polynomial rings, monoid rings, and skew monoid rings are extended and unified.
On Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
On Biquaternion Algebras With Orthogonal Involution, Amir Hossein Nokhodkar
Turkish Journal of Mathematics
We investigate the Pfaffians of decomposable biquaternion algebras with involution of orthogonal type. In characteristic two, a classification of these algebras in terms of their Pfaffians and some other related invariants is studied. Also, in arbitrary characteristic, a criterion is obtained for an orthogonal involution on a biquaternion algebra to be metabolic.
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Turkish Journal of Mathematics
In this work, we consider two types of second-order neutral differential equations and we obtain sufficient conditions for the existence of positive $\om$-periodic solutions for these equations. We employ Krasnoselskii's fixed point theorem for the sum of a completely continuous and a contraction mapping. An example is included to illustrate our results.
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Characterizations Of *-Dmp Matrices Over Rings, Yuefeng Gao, Jianlong Chen
Turkish Journal of Mathematics
Let $R$ be a ring with involution $*$. $R^{m\times n}$ denotes the set of all $m\times n$ matrices over $R$. In this paper, we give a characterization of the pseudo core inverse of $A\in R^{n\times n}$ in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, where $N_l(A)=\{x\in R^{1\times m} xA=0\}$ and $N_r(A)=\{x\in R^{n\times 1}~ ~Ax=0\}.$ Then we obtain necessary and sufficient conditions for $A\in R^{n\times n}$, in the form of $A=GDH$, $N_r(G)=0$, $N_l(H)=0$, $D^2=D=D^*$, to be *-DMP. If $R$ is a principal ideal domain (resp. semisimple Artinian ring), then matrices expressed as that form include all $n\times n$ matrices over $R$.
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Stability Of Abstract Dynamic Equations On Time Scales By Lyapunov's Second Method, Alaa Hamza, Karima Oraby
Turkish Journal of Mathematics
In this paper, we use the Lyapunov's second method to obtain new sufficient conditions for many types of stability like exponential stability, uniform exponential stability, $h$-stability, and uniform $h$-stability of the nonlinear dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t,x),\;t\in \mathbb{T}^+_\tau:=[\tau,\infty)_{\mathbb T}, \end{equation*} on a time scale $\mathbb T$, where $A\in C_{rd}(\mathbb T,L(X))$ and $f:\mathbb T\times X\to X$ is rd-continuous in the first argument with $f(t,0)=0.$ Here $X$ is a Banach space. We also establish sufficient conditions for the nonhomogeneous particular dynamic equation \begin{equation*} x^{\Delta}(t)=A(t)x(t)+f(t),\,t\in\mathbb{T}^+_{\tau}, \end{equation*} to be uniformly exponentially stable or uniformly $h$-stable, where $f\in C_{rd}(\mathbb T,X)$, the space of rd-continuous functions from …
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
On The Hilbert Formulas And Of Change Of Integration Order For Some Singular Integrals In The Unit Circle, Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Perez De La Rosa, Baruch Schneider
Turkish Journal of Mathematics
We obtain some analogues of the Hilbert formulas on the unit circle for $\alpha$-hy\-per\-ho\-lo\-mor\-phic function theory when $\alpha$ is a complex number. Such formulas relate a pair of components of the boundary value of an $\alpha$-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincaré-Bertrand formula for the $\alpha$-hyperholomorphic singular integrals in the unit circle is presented.
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Connection Between Bi$^{S}$Nomial Coefficients And Their Analogs And Symmetric Functions, Abdelghafour Bazeniar, Moussa Ahmia, Hacene Belbachir
Turkish Journal of Mathematics
In this paper, on one hand, we propose a new type of symmetric function to interpret the bi$^{s}$nomial coefficients and their analogs. On other hand, according to this function, we give an interpretation of these coefficients by lattice paths and tiling. Some identities of these coefficients are also established. This work is an extension of the results of Belbachir and Benmezai's ''A $\mathit{q}$-analogue for bi$^{\mathit{s}}$nomial coefficients and generalized Fibonacci sequences".
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Iterative Roots Of Some Functions, Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan
Turkish Journal of Mathematics
The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Weyl- And Horn-Type Inequalities For Cyclically Compact Operators, Uğur Gönüllü
Turkish Journal of Mathematics
A variant of Weyl- and Horn-type inequalities for cyclically compact operators on Kaplansky-Hilbert modules is given.
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Three Binomial Sums Weighted By Falling And Rising Factorials, Emrah Kiliç
Turkish Journal of Mathematics
In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
On A New Identity For The H-Function With Applications To The Summation Of Hypergeometric Series, Arjun Kumar Rathie, Luan Carlos De Sena Monteiro Ozelim, Pushpa Narayan Rathie
Turkish Journal of Mathematics
Using generalized hypergeometric functions to perform symbolic manipulations of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, that function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new …
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
Continuous Dependence Of Solutions To The Strongly Damped Nonlinear Klein-Gordon Equation, Şevket Gür, Mesude Eli̇f Uysal
Turkish Journal of Mathematics
This article is devoted to the study of the initial-boundary value problem for the strongly damped nonlinear Klein-Gordon equation. It is proved that the solution depends continuously on changes in the damping terms, diffusion, mass, and nonlinearity effect term in the $H^1$ norm.
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
Nearly Kahler And Nearly Kenmotsu Manifolds, Nikrooz Heidari, Niloufar Hoseein Pour Kashani, Behzad Najafi
Turkish Journal of Mathematics
We study the class of strict nearly Kenmotsu manifolds and prove that there is no Einstein manifold or locally symmetric or locally $\phi$-symmetric in this class of manifolds. We describe strict nearly Kenmotsu manifolds in low dimensions. Finally, we obtain a relation between the curvature of nearly Kenmotsu manifolds and nearly Kahler manifolds.
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences, Takao Komatsu, Laszlo Szalay
A New Formula For Hyper-Fibonacci Numbers, And The Number Of Occurrences, Takao Komatsu, Laszlo Szalay
Turkish Journal of Mathematics
In this paper, we develop a new formula for hyper-Fibonacci numbers $F_n^{[k]}$, wherein the coefficients (related to Stirling numbers of the first kind) of the polynomial ingredient $p_k(n)$ are determined. As an application we investigate the number of occurrences of positive integers among $F_n^{[k]}$ and determine all the solutions in nonnegative integers $x$ and $y$ to the Diophantine equation $F_x^{[k]}=F_y^{[\ell]}$, where $0\le k
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Reflexivity Of Vector-Valued Köthe-Orlicz Sequence Spaces, Mohamed Ahmed Ould Sidaty
Turkish Journal of Mathematics
Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
On The Growth Of Meromorphic Solutions Of Some Higher Order Linear Differential Equations, Farid Mesbout, Tahar Zerzaihi
Turkish Journal of Mathematics
Let $k,m,n $ be integers such that $k\geq 1$, $n\geq 2$ and $1\leq m\leq n$. In this article we study the order $\rho(f)$ and the hyperorder $\rho_2(f)$ of nonzero meromorphic solutions $f$ of the differential equation $$\sum_{j=1,j\ne m}^{n}A_j(z)f^{(j)}(z)+A_m(z)e^{p_m(z)}f^{(m)}(z)+\left(A_0(z)e^{p(z)}+B_0(z)e^{q(z)}\right)f(z)=0,$$ where $B_0(z)$, $A_0(z), \cdots, A_n(z)$ are meromorphic functions such that $A_0A_mA_nB_0\not\equiv 0$, $\max\{\rho(B_0), \rho(A_0), \cdots,\rho(A_n)\}
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal, Kerem Uğurlu
Dynamic Optimal Contract Under Parameter Uncertainty With Risk-Averse Agent And Principal, Kerem Uğurlu
Turkish Journal of Mathematics
We consider a continuous-time principal--agent model on a finite time horizon, where we look for the existence of an optimal contract that both parties agreed on. Contrary to the mainstream, where the principal is modeled as risk-neutral, we assume that both the principal and the agent have exponential utility and are risk-averse with same risk awareness level. Moreover, the agent's quality is unknown and is modeled as a filtering term in the problem, which is revealed as time passes. The principal cannot observe the agent's real action, but can only recommend action levels to the agent. Hence, we have a …
On The Existence And Uniqueness Of Solutions To Dynamic Equations, Başak Karpuz
On The Existence And Uniqueness Of Solutions To Dynamic Equations, Başak Karpuz
Turkish Journal of Mathematics
In this paper, we prove the well-known Cauchy-Peano theorem for existence of solutions to dynamic equations on time scales. Some simple examples are given to show that there may exist more than a single solution for dynamic initial value problems. Under some certain conditions, it is also shown that there exists only one solution.
On The Monodromy Of Milnor Open Books, Selma Altinok Bhupal, Mohan Lal Bhupal
On The Monodromy Of Milnor Open Books, Selma Altinok Bhupal, Mohan Lal Bhupal
Turkish Journal of Mathematics
We present some techniques that can be used to factorize the monodromy of certain Milnor open books. We also describe a class of Milnor open books for which we can explicitly express the monodromy as a product of Dehn twists.
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
Generation Of Efficient And $\Epsilon$-Efficient Solutionsin Multiple Objective Linear Programming, Zohra Sabrina Delhoum, Sonia Radjef, Fatima Boudaoud
Turkish Journal of Mathematics
We develop an algorithm to solve a multiple objective linear programming problem with bounded variables. It is based on the scalarization theorem of optimal solutions of multiobjective linear programs and the single objective adaptive method. We suggest a process for the search for the first efficient solution without having to calculate a feasible solution, and we elaborate a method to generate efficient solutions, weakly efficient solutions, and $\epsilon$-efficient solutions. Supporting theoretical results are established and the method is demonstrated on a numerical example.
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
An Expansion Theorem For $Q$-Sturm-Liouville Operators On The Wholeline, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna
Turkish Journal of Mathematics
In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singular $q-$Sturm-Liouville operator on the whole line.
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
The United Stable Solution Set Of Interval Continuous-Time Algebraic Riccati Equation And Verified Numerical Computation Of Its Outer Estimation, Tayyebe Haqiri, Mahmoud Mohseni Moghadam, Azim Rivaz
Turkish Journal of Mathematics
This paper introduces the interval continuous-time algebraic Riccati equation $\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0$, where $\mathbf{A}, \mathbf{G}$, and $\mathbf{Q}$ are known $n \times n$ complex interval matrices, $\mathbf{G}$ and $\mathbf{Q}$ are Hermitian, and $X$ is an unknown matrix of the same size, and develops two approaches for enclosing the united stable solution set of this interval equation. We first discuss the united stable solution set and then derive a nonlinear programming method in order to find an enclosure for the united stable solution set. We also advance an efficient technique for enclosing the united stable solution …
Modified Objective Function Approach For Multitime Variational Problems, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
Modified Objective Function Approach For Multitime Variational Problems, Anurag Jayswal, Tadeusz Antczak, Shalini Jha
Turkish Journal of Mathematics
The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate …
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Fedja's Proof Of Deepti's Inequality, Sofiya Ostrovska, Mehmet Turan
Turkish Journal of Mathematics
The paper aims to present, in a systematic way, an elegant proof of Deepti's inequality. Both the inequality and various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none have appeared in the literature thus far. In this work, suggestions pertaining to users 'Deepti' and 'fedja' are traced, whence the title. The results or the paper are new, and the proof is divided into a series of statements, many of which are of interest in themselves.
Vertex Covers In Graphs With Loops, Maurizio Imbesi, Monica La Barbiera
Vertex Covers In Graphs With Loops, Maurizio Imbesi, Monica La Barbiera
Turkish Journal of Mathematics
We investigate ideals of vertex covers for the edge ideals associated to considerable classes of connected graphs with loops and exhibit algebraic information about them, such as the existence of linear quotients, the computation of invariant values, and the Cohen-Macaulay property. These algebraic procedures are good instruments for evaluating situations of minimal node coverings in networks.
On Spacelike Rectifying Slant Helices In Minkowski 3-Space, Bülent Altunkaya, Levent Kula
On Spacelike Rectifying Slant Helices In Minkowski 3-Space, Bülent Altunkaya, Levent Kula
Turkish Journal of Mathematics
In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in $E_1^3$. First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones.