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Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu
Evaluating A Class Of Balanced $Q$-Series, Wenchang Chu
Turkish Journal of Mathematics
By means of the modified Abel lemma on summation by parts, we examine a class of terminating balanced $q$-series. Two transformation formulae are established that contain ten summation formulae as consequences.
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara
Corrigendum And Addendum To "Modules Whose $P$-Submodules Are Direct Summands", Yeli̇z Kara
Turkish Journal of Mathematics
This paper is written to correct the proof of Lemma 2.1$(i)$ in \cite{K} and to add some decomposition results for the class of $PD$-modules defined in \cite{K}.
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao
A Note On The Associated Primes Of Local Cohomology Modules For Regular Local Rings, Yubin Gao
Turkish Journal of Mathematics
Let $R$ be a regular local ring. In this note, we prove that $Ass_RH^2_I(R)$ is finite for any ideal $I$ of $R$. We also give a sufficient condition for $Ass_RH^3_{(x,y,z)}(R)$ to be finite for $x, y$ an $R$-regular sequence and $z\in R$, which would imply that Lyubeznik's conjecture is true in the regular local rings case.
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 …
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Suborbital Graphs For The Atkin-Lehner Group, Tuncay Köroğlu, Bahadir Özgür Güler, Zeynep Şanli
Turkish Journal of Mathematics
We investigate suborbital graphs for an imprimitive action of the Atkin-Lehner group on a maximal subset of extended rational numbers on which a transitive action is also satisfied. Obtaining edge and some circuit conditions, we examine some combinatorial properties of these graphs.
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
On The Volume Of The Indicatrix Of A Complex Finsler Space, Elena Popovici
Turkish Journal of Mathematics
Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Conditions under which the volume is constant are also determined and some classes of complex Finsler spaces with …
Nonpolynomial Spline Technique For The Solution Of Ninth Order Boundary Value Problems, Ghazala Akram, Zara Nadeem
Nonpolynomial Spline Technique For The Solution Of Ninth Order Boundary Value Problems, Ghazala Akram, Zara Nadeem
Turkish Journal of Mathematics
In this paper, a nonpolynomial spline technique is applied to solve the ninth order linear special case boundary value problems. The end conditions are derived to complete the definition of a spline. Three examples are numerically illustrated to check the efficiency of the method. The comparative analysis shows that the proposed technique gives better results than the homotopy perturbation method and the modified variational iteration method.
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Positive Solutions Of First Order Boundary Value Problems With Nonlinear Nonlocal Boundary Conditions, Smita Pati, Seshadev Padhi
Turkish Journal of Mathematics
We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by $x^{\prime}(t) = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), t \in [0,1]$ $\lambda x(0) = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\tau_j \in [0,1],$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous, the nonlocal points satisfy $0 \leq \tau_1 < \tau_2 < ... < \tau_n \leq 1$, the nonlinear functions $f_i$ and $\Lambda_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,...,m$ and $j = 1,2,...,n$ respectively, and $\lambda >1$ is a positive parameter. The Leray-Schauder theorem and Leggett--Williams fixed point theorem were used to prove our results.
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Some Results On The $\Mathcal{P}_{V,2n}$, $\Mathcal{K}_{V,N}$, And $\Mathcal{H}_{V,N}$-Integral Transforms, Ayşe Neşe Dernek, Fati̇h Aylikci
Turkish Journal of Mathematics
In this paper, the authors consider the $\mathcal{P}_{v,2n}$-transform, the $\mathcal{G}_n$-transform, and the $\mathcal{K}_{v,n}$-transform as generalizations of the Widder potential transform, the Glasser transform, and the $\mathcal{K}_v$-transform, respectively. Many identities involving these transforms are given. A number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are presented. Illustrative examples are given for the results.
Sufficient Conditions On Nonunitary Operators That Imply The Unitary Operators, Pabitra Kumar Jena
Sufficient Conditions On Nonunitary Operators That Imply The Unitary Operators, Pabitra Kumar Jena
Turkish Journal of Mathematics
In this paper, we give sufficient conditions on nonunitary operators on the Bergman space that imply the unitary operators.
On Certain Gbs-Durrmeyer Operators Based On $Q$-Integers, Dan Barbosu, Ana Maria Acu, Carmen Violeta Muraru
On Certain Gbs-Durrmeyer Operators Based On $Q$-Integers, Dan Barbosu, Ana Maria Acu, Carmen Violeta Muraru
Turkish Journal of Mathematics
In the present paper we introduce the $GBS$ (Generalized Boolean Sum) operators of Durrmeyer type based on $q$-integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms.
A Bivariate Sampling Series Involving Mixed Partial Derivatives, Rashad Mudhish Asharabi, Hamoud Al-Haddad
A Bivariate Sampling Series Involving Mixed Partial Derivatives, Rashad Mudhish Asharabi, Hamoud Al-Haddad
Turkish Journal of Mathematics
Recently Fang and Li established a sampling formula that involves only samples from the function and its first partial derivatives for functions from Bernstein space, $B^{p}_{\sigma}(\mathbb{R}^{2})$. In this paper, we derive a general bivariate sampling series for the entire function of two variables that satisfy certain growth conditions. This general bivariate sampling formula involves samples from the function and its mixed and nonmixed partial derivatives. Some known sampling series will be special cases of our formula, like the sampling series of Parzen, Peterson and Middleton, and Gosselin. The truncated series of this formula are used to approximate functions from the …
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
An Age-Structured Model For The Transmission Dynamics Of Hepatitis B: Asymptotic Analysis, Rodrigue Yves M'Pika Makoussou, Aboubakari Traore
Turkish Journal of Mathematics
In this paper, we consider the age-structured model for the transmission dynamics of Hepatitis B virus (HBV) proposed earlier in the article by Zou et al.: An age-structured model for transmission dynamics of hepatitis B. SIAM J Appl Math 2010; 70: 3121-3139, where a slight modification is made. We consider that the HBV infection processes act on a time scale different from that of the vital processes. Such a model becomes a multiple time scale model and thus it often can be significantly simplified by various asymptotic methods. We apply, as in the paper of Banasiak and M'pika Massoukou: A …
Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi
Characterization Of Substantially And Quasi-Substantially Efficient Solutions In Multiobjective Optimization Problems, Latif Pourkarimi, Masoud Karimi
Turkish Journal of Mathematics
In this paper, we study the notion of substantial efficiency for a given multiobjective optimization problem. We provide two characterizations for substantially efficient solutions: the first one is based on a scalar problem and the second one is in terms of a stability concept. Moreover, this paper introduces the notion of quasi-substantial efficiency. Similar to those of substantial efficiency, two characterizations for quasi-substantially efficient solutions are obtained.
Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat
Computation Of Conditional Expectation Based On The Multidimensional J-Process Using Malliavin Calculus Related To Pricing American Options, Mohamed Kharrat
Turkish Journal of Mathematics
In this work, we extend the uni-dimensional results, already found by Jerbi and Kharrat, for the multidimensional case: we compute the Malliavin weights related to the conditional expectation $\mathbb{E}(P_{t}(X_{t}) (X_{s}))$ for $0 \leq s \leq t$, where the only state variable follows a multidimensional J-process.
Approximation Of Analytic Functions Of Severalvariables By Linear K-Positive Operators, Tüli̇n Coşkun
Approximation Of Analytic Functions Of Severalvariables By Linear K-Positive Operators, Tüli̇n Coşkun
Turkish Journal of Mathematics
We investigate the approximation of analytic functions of several variables in polydiscs by the sequences of linear k-positive operators in the Gadjiev sense.
Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo
Regularity Of Solutions Of The Anisotropic Hyperbolic Heat Equation With Nonregular Heat Sources And Homogeneous Boundary Conditions, Juan Antonio López Molina, Macarena Trujillo
Turkish Journal of Mathematics
We study regularity properties for the solution of homogeneous boundary value problems for the anisotropic hyperbolic heat equation in the case of infinitely differentiable coefficients but irregular distributions as internal heat sources.
Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi
Factorization With Respect To A Divisor-Closed Multiplicative Submonoid Of A Ring, Ashkan Nikseresht, Abdulrasool Azizi
Turkish Journal of Mathematics
In this paper, we consider factorizations of elements of a divisor-closed multiplicative submonoid of a ring and also factorizations of elements of a module as a product of elements coming from a divisor-closed multiplicative submonoid of the ring and another element of the module. In particular, we study uniqueness and some other properties of such factorizations and investigate the behavior of these factorizations under direct sum and product of rings and modules.
Ranges And Kernels Of Derivations, Mohamed Ech Chad
Ranges And Kernels Of Derivations, Mohamed Ech Chad
Turkish Journal of Mathematics
In this paper we establish some properties concerning the class of operators $A\in {\cal L(H)}$ that satisfy $\overline{ { \cal R }(\delta_{A})}\cap\{A\}'=\{0\}$, where $\overline{ { \cal R }(\delta_{A})}$ is the norm closure of the range of the inner derivation $\delta_{A},$ defined on ${\cal L(H)}$ by $\delta_{A}(X)=AX-XA$. Here ${\cal H}$ stands for a Hilbert space; as a consequence, we show that the set $\{ A \in { \cal L(H)}\;\;/\;\;\overline{ { \cal R }(\delta_{A})}\cap\{A\}'=\{0\} \}$ is norm-dense. We also describe some classes of operators $A,\;B$ for which we have $\overline{ { \cal R }(\delta_{A,B})}\cap\ker(\delta_{A^{\ast},B^{\ast}})=\{0\}$ ($\ker(\delta_{A^{\ast},B^{\ast}})$ is the kernel of the generalized derivation …
A Note On The Generalized Matsumoto Relation, Eli̇f Dalyan, Eli̇f Medetoğullari, Mehmetci̇k Pamuk
A Note On The Generalized Matsumoto Relation, Eli̇f Dalyan, Eli̇f Medetoğullari, Mehmetci̇k Pamuk
Turkish Journal of Mathematics
~We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.
The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇
The Hahn-Banach Theorem For $A$-Linear Operators, Bahri̇ Turan, Fatma Bi̇li̇ci̇
Turkish Journal of Mathematics
In this short paper we present a generalization of the Hahn--Banach extensiontheorem for $A$-linear operators. Some theoretical applications andresults are given.
On The Rate Of $L_P$-Convergence Of Balakrishnan—Rubin-Type Hypersingular Integrals Associated To The Gauss-Weierstrass Semigroup, Meli̇h Eryi̇ği̇t, Seli̇m Çobanoğlu
On The Rate Of $L_P$-Convergence Of Balakrishnan—Rubin-Type Hypersingular Integrals Associated To The Gauss-Weierstrass Semigroup, Meli̇h Eryi̇ği̇t, Seli̇m Çobanoğlu
Turkish Journal of Mathematics
We introduce a family of Balakrishnan—Rubin-type hypersingular integrals depending ona parameter $\varepsilon$ and generated by the Gauss—Weierstrass semigroup. Then the connection between the order of $L_p$—smoothness of a $L_p$—function $\varphi$and the rate of $L_p$-convergence of these families to $\varphi$, as $\varepsilon$ tends to 0, is obtained.
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Generalized Drazin Invertibility Of The Product And Sum Of Two Elements In A Banach Algebra And Its Applications, Honglin Zou, Dijana Mosic, Jianlong Chen
Turkish Journal of Mathematics
Let $a,b$ be two commutative generalized Drazin invertible elements in a Banach algebra; the expressions for the generalized Drazin inverse of the product $ab$ and the sum $a+b$ were studied in some current literature on this subject. In this paper, we generalize these results under the weaker conditions $a^{2}b=aba$ and $b^{2}a=bab$. As an application of our results, we obtain some new representations for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra, extending some recent works.
Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly
Asymptotic Stability Of Solutions For A Certain Non-Autonomous Second-Order Stochastic Delay Differential Equation, Ahmed Mohamed Abou-El-Ela, Abdel-Rahiem Sadek, Ayman Mohammed Mahmoud, Eman Sayed Farghaly
Turkish Journal of Mathematics
In this paper, sufficient criteria that guarantee the existence of stochastic asymptotic stability of the zero solution of the nonautonomous second-order stochastic delay differential equation \eqref{3e1} were established with the aid of a suitable Lyapunov functional. Two examples are given in the last section to illustrate our main result.
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
$\Mathcal{Vw}$-Gorenstein Complexes, Renyu Zhao, Wei Ren
Turkish Journal of Mathematics
Let $\mathcal{V,W}$ be two classes of modules. In this paper, we introduce and study $\mathcal{VW}$-Gorenstein complexes as a common generalization of $\mathcal{W}$-complexes, Gorenstein projective (resp., Gorenstein injective) complexes, and $G_C$-projective (resp., $G_C$-injective) complexes. It is shown that under certain hypotheses a complex $X$ is $\mathcal{VW}$-Gorenstein if and only if each $X^n$ is a $\mathcal{VW}$-Gorenstein module. This result unifies the corresponding results of the aforementioned complexes. As an application, the stability of $\mathcal{VW}$-Gorenstein complexes is explored.
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Application Of A Generalised Function Method To The Infinitely Deep Square Well Problem, Basri̇ Ünal
Turkish Journal of Mathematics
The Schrödinger equation for the eigenvalues of the infinitely deep square well potential is solved within the class of generalised functions. It is found that the ground state consists of a step function like eigenfunction with the eigenvalue zero.
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
Turkish Journal of Mathematics
The intention of this article is to investigate the most important inequalities of $m$-convex functions without using their derivatives. The article also provides a brief survey of general properties of $m$-convex functions.
Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu
Dynamics Of A Predator-Prey System With A Mate-Finding Allee Effect On Prey, Ruiwen Wu, Xiuxaing Liu
Turkish Journal of Mathematics
We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.
Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici
Generalized Trial Equation Method And Its Applications Toduffing And Poisson-Boltzmann Equations, Ali̇ Özyapici
Turkish Journal of Mathematics
The trial equation method, which was proposed by Cheng-Shi Liu, is a very powerful method for solving nonlinear differential equations. After the original trial method, some modified versions of the trial equation method were introduced and applied to some famous nonlinear differential equations. Although each modified trial equation method provides a different perspective, they have some weaknesses according to the given differential equations. This is the main reason for introducing modified trial equation methods. This study aims to define a general representation of trial methods for solving nonlinear differential equations. The generalized trial equation method consists of the simple trial …
Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang
Stability Of Nonmonotone Critical Traveling Waves Forspatially Discrete Reaction-Diffusion Equations With Time Delay, Ge Tian, Guobao Zhang, Zhao-Xing Yang
Turkish Journal of Mathematics
This paper is concerned with the existence and stability of critical traveling waves (waves with minimal speed $c=c_*$) for a nonmonotone spatially discrete reaction-diffusion equation with time delay. We first show the existence of critical traveling waves by a limiting argument. Then, using the technical weighted energy method with some new variations, we prove that the critical traveling waves $\phi(x+c_{*}t)$ (monotone or nonmonotone) are time-asymptotically stable when the initial perturbations are small in a certain weighted Sobolev norm.