Authors:Ayman Shehata Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. The aim of the present work is to develop a pair of Lommel matrix functions of two variables suggested by the Bessel matrix functions and some of their properties are studied to be special cases of our results. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:01:25Z DOI: 10.1142/S1793557118500419

Authors:G. Lakshmi Devi, K. Jayalakshmi Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, we describe the reductive pair [math] with fixed decomposition [math] and construct a reductive Vinberg [math] ring relative to [math] which is based on the construction of nonassociative algebras with specified simple Lie algebra [math] of derivations. As a special case, we construct a class of Vinberg [math] algebras ([math], [math] of dimension 8 with [math] [math] and determine its associated reductive Lie algebra [math] [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:01:20Z DOI: 10.1142/S1793557118500377

Authors:Viachaslau I. Murashka Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, the widely supersoluble hypercenter of finite groups was studied and a new criterion of widely supersolubility of finite groups was obtained. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:01:14Z DOI: 10.1142/S1793557118500432

Authors:Neşe Ömür, Sibel Koparal Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, we define two [math] matrices [math] and [math] with [math] and [math] respectively, where [math] are a generalized hyperharmonic numbers of order [math]. We give some new factorizations and determinants of the matrices [math] and [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:01:08Z DOI: 10.1142/S1793557118500456

Authors:Akbar Ali Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. A recently proposed conjecture by Cheng and Wang [A lower bound for the harmonic index of a graph with minimum degree at least three, Filomat 30(8) (2016) 2249–2260] about the harmonic index is disproved. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:01:03Z DOI: 10.1142/S1793557118500353

Authors:Meena Sahai, Bhagwat Sharan Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. For a group algebra [math] of a group [math] over a field [math] of characteristic [math], it is well known that [math] is the minimal upper as well as the minimal lower Lie nilpotency index. Group algebras of upper Lie nilpotency index upto [math] have already been characterized completely. In this paper, we classify the modular group algebra [math] having upper Lie nilpotency index [math] which is the possible next higher Lie nilpotency index. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:52Z DOI: 10.1142/S1793557118500390

Authors:A. H. Abdel Kader, M. S. Abdel Latif, F. El Bialy, A. Elsaid Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, we obtained some new exact solutions of some nonlinear KdV-like equations using Lie point symmetry and [math]-symmetry methods. The obtained solutions are in the form of doubly periodic, bright and dark soliton solutions. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:46Z DOI: 10.1142/S1793557118500407

Authors:Sergey Davidov, Aleksandar Krapež, Yuri Movsisyan Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. Functional equations are equations in which the unknown (or unknowns) are functions. We consider equations of generalized associativity, mediality (bisymmetry, entropy), paramediality, transitivity as well as the generalized Kolmogoroff equation. Their usefulness was proved in applications both in mathematics and in other disciplines, particularly in economics and social sciences (see J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392–400; J. Aczél, Remarques algebriques sur la solution donner par M. Frechet a l’equation de Kolmogoroff, Pupl. Math. Debrecen 4 (1955) 33–42; J. Aczél, A Short Course on Functional Equations Based Upon Recent Applications to the Social and Behavioral Sciences, Theory and decision library, Series B: Mathematical and statistical methods (D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1987); J. Aczél, Lectures on Functional Equations and Their Applications (Supplemented by the author, ed. H. Oser) (Dover Publications, Mineola, New York, 2006); J. Aczél, V. D. Belousov and M. Hosszu, Generalized associativity and bisymmetry on quasigroups, Acta Math. Acad. Sci. Hungar. 11 (1960) 127–136; J. Aczél and J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, New York, 1991); J. Aczél and T. L. Saaty, Procedures for synthesizing ratio judgements, J. Math. Psych. 27(1) (1983) 93–102). We use unifying approach to solve these equations for division and regular operations generalizing the classical quasigroup case. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:39Z DOI: 10.1142/S179355711850033X

Authors:S. G. Latpate Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. The aim of this paper is to generalize some integral inequalities of Gronwall–Bellman type. We generalize the results presented by Pachpatte in [Inequalities for Differential and Integral Equations (Academic Press, New York, 1998)] and Abdeldaim in [On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation, J. Egypt. Math. Sci. Lett. 23 (2015) 470–475] and also establish some new forms. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:34Z DOI: 10.1142/S1793557118500328

Authors:Bekkai Messirdi, Sofiane Messirdi, Miloud Messirdi Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. Unbounded complex symmetric operators on Hilbert space are discussed and various spectral results on these operators are presented in this paper. In addition, we show that the technique of complex scaling allows one to identify the quantum resonances of complex self-adjoint Schrödinger Hamiltonians. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:29Z DOI: 10.1142/S1793557118500444

Authors:Abderrahim Frih, Zakaria Chalh, Mostafa Mrabti Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, a new methodology is proposed to determinate the controllability and the observability matrices of linear time varying systems modeled by bond graph. As the bond graph model can be viewed as a state space representation and as a module (algebraic approach), the determination of controllability and observability matrices is presented with the graphical approach. The equivalence between the two approaches (Graphic, Mathematical) is proposed and a graphical methodology is pointed out directly on the bond graph representation. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:23Z DOI: 10.1142/S1793557118500389

Authors:Denis Chee Keong Wong, Kuan Wai Wong, Wun-She Yap Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. Let [math] be the dihedral group of order [math], where [math] is an odd prime. A nonempty subset [math] of [math] is said to be exhaustive if there exists a positive integer [math] such that [math] covers all elements in [math]. The smallest such [math] is called the exhaustion number of [math]. In general, finding [math] for an arbitrary subset [math] of [math] is an interesting but difficult task. In this paper, we classify all possible exhaustion 2-subsets in [math] by considering a 2-subset [math] of [math] with either [math] or [math] and [math]. Some explicit formulas for [math] are identified and hence some bounds are derived to prove the existence for certain families of exhaustive sets. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:17Z DOI: 10.1142/S179355711850047X

Authors:Alireza Ansari, Mohammad Rasool Masomi Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, using the integral identities of Bessel functions, we obtain new integral identities for the products of Airy functions. We get various integrals involving the Widder potential, the Fourier sine and cosine transforms of the products of Airy functions in terms of some special functions. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:12Z DOI: 10.1142/S1793557118500468

Authors:J. Amjadi, M. Soroudi Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. Let [math] be a finite simple digraph with vertex set [math] and arc set [math]. A twin signed total Roman dominating function (TSTRDF) on the digraph [math] is a function [math] satisfying the conditions that (i) [math] and [math] for each [math], where [math] (respectively [math]) consists of all in-neighbors (respectively out-neighbors) of [math], and (ii) every vertex [math] for which [math] has an in-neighbor [math] and an out-neighbor [math] with [math]. The weight of an TSTRDF [math] is [math]. The twin signed total Roman domination number [math] of [math] is the minimum weight of an TSTRDF on [math]. In this paper, we initiate the study of twin signed total Roman domination in digraphs and we present some sharp bounds on [math]. In addition, we determine the twin signed Roman domination number of some classes of digraphs. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T09:00:06Z DOI: 10.1142/S1793557118500341

Authors:Andrej V. Plotnikov, Tatyana A. Komleva, Irina V. Molchanyuk Abstract: Asian-European Journal of Mathematics, Volume 11, Issue 03, June 2018. In this paper, we consider two types of set-valued Volterra–Hammerstein integral equations and prove the existence and uniqueness theorem. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-03T08:59:56Z DOI: 10.1142/S1793557118500365

Authors:Marius Tărnăuceanu Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this short note, we give a characterization of ZM-groups that uses the functions defined and studied in [M. Tărnăuceanu, A generalization of the Euler’s totient function, Asian-Eur. J. Math. 8(4) (2015) 1550087; M. Tărnăuceanu, On a generalization of the Gauss formula, Asian-Eur. J. Math. 10(1) (2017) 1750008]. This leads to a proof of Conjecture 6 in [M. Tărnăuceanu, On a generalization of the Gauss formula, Asian-Eur. J. Math. 10(1) (2017) 1750008]. Citation: Asian-European Journal of Mathematics PubDate: 2018-05-14T09:15:23Z DOI: 10.1142/S1793557118910011

Authors:Daniel A. Romano Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we introduce and discuss a concept of co-quasiordered residuated relational systems. The setting of this research is Bishop’s constructive mathematics — a mathematics based on the Intuitionisic logic and particular principle-philosophical orientation of this attitude. Moreover, we introduce the concept of co-filters in such relational system. Additionally, some of the fundamentals properties of these substructures we have been shown. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-24T09:35:51Z DOI: 10.1142/S1793557119500736

Authors:Indah Emilia Wijayanti, Dian Ariesta Yuwaningsih, Salmah Abstract: Asian-European Journal of Mathematics, Ahead of Print. We introduce the dual notions of [math]-weakly prime submodules, that is, [math]-weakly second submodules in a commutative ring with identity. We investigate the properties of [math]-weakly second submodules and obtain some related useful characterizations of this dualization. Moreover, we also prove some properties of [math]-weakly second submodules related to multiplication and comultiplication modules. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-23T09:24:57Z DOI: 10.1142/S1793557119500724

Authors:Ritika, Safeer Hussain Khan Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we introduce a new four-step iterative process and name it as RK-iterative process and prove some [math]-convergence and strong convergence results using this process for generalized nonexpansive mappings in CAT(0) spaces. Our results generalize the corresponding results of many authors in different directions. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-23T09:24:55Z DOI: 10.1142/S1793557119500773

Authors:Y. L. T. Jeufack, L. Diekouam, E. R. A. Temgoua Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] and [math] be two central relations on a finite set [math]. It is known from Rosenberg’s classification theorem (1965) that the clones [math] and [math] which consist of all operations on [math] that preserve [math], respectively, [math] are among the maximal clones on [math]. In this paper, we find all central relations [math] such that the clone [math] is a maximal subclone of [math], where [math] is a fixed central relation. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:29Z DOI: 10.1142/S1793557119500645

Authors:S. C. Shiralashetti, L. M. Angadi, A. B. Deshi Abstract: Asian-European Journal of Mathematics, Ahead of Print. This paper presents biorthogonal wavelet-based multigrid (BWMG) and full approximation scheme (FAS) for the numerical solution of parabolic partial differential equations (PPDEs), which are working horse behind many commercial applications like finger print image compression. Performance of the proposed schemes is better than the existing ones in terms of super convergence with less computational time. Some of the test problems are taken to demonstrate the applicability and validity of the method. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:28Z DOI: 10.1142/S1793557119500542

Authors:Ronnason Chinram, Samruam Baupradist Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a semigroup of all transformations on a set [math] Let [math] be a fixed nonempty subset of [math] and [math] Then [math] is a subsemigroup of [math] which leaves a subset [math] of [math] invariant. If [math] then [math] In this paper, we give necessary and sufficient conditions for elements in [math] to be left or right magnifying. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:28Z DOI: 10.1142/S1793557119500566

Authors:Hetal Patel, Ajay Gor Abstract: Asian-European Journal of Mathematics, Ahead of Print. Existing study gives ordering policy for non-instantaneous deteriorating items having three-variable Weibull distribution deterioration rate. Demand rate varies in different time interval. Before deterioration starts, demand is constant and after that it decreases exponentially with respect to time. The study considers total cost function as objective function including salvage value. Shortages are not allowed to stay in time-based competition. Results are proved theoretically and numerically. Sensitivity analysis is performed with respect to salvage value, scale parameter, shape parameter and location parameter including in deterioration rate function to show the liability of the model. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:28Z DOI: 10.1142/S1793557119500700

Authors:S. K. Nimbhorkar, U. R. Borsarkar Abstract: Asian-European Journal of Mathematics, Ahead of Print. Some properties of the weak product of graphs on lattices are studied. We consider the weak product of the atom-based graphs, the incomparability graphs and the zero-divisor graphs of lattices. The number of edges in the weak product of such graphs is found. It is shown that the weak direct product of the atom-based graphs of two lattices [math] and [math] cannot be an induced subgraph of the atom-based graph of [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:27Z DOI: 10.1142/S1793557119500529

Authors:Arnold A. Eniego, I. J. L. Garces Abstract: Asian-European Journal of Mathematics, Ahead of Print. For positive integer [math], a graph [math] is said to be [math]-magic if the edges of [math] can be labeled with the nonzero elements of Abelian group [math], where [math] (the set of integers) and [math] is the group of integers mod [math], so that the sum of the labels of the edges incident to any vertex of [math] is the same. When this constant sum is [math], we say that [math] is a zero-sum [math]-magic graph. The set of all [math] for which [math] is a zero-sum [math]-magic graph is the null set of [math]. In this paper, we will completely determine the null set of the join of a finite number of paths. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:27Z DOI: 10.1142/S1793557119500608

Authors:Kais Smaoui Abstract: Asian-European Journal of Mathematics, Ahead of Print. We establish analogues of Heisenberg uncertainty inequality for some classes of Lie groups, such as connected and simply connected nilpotent Lie groups, diamond Lie groups and Heisenberg motion groups. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:26Z DOI: 10.1142/S1793557119500657

Authors:F. Mohammadi, L. Moradi Abstract: Asian-European Journal of Mathematics, Ahead of Print. This paper presents a fractional-order nonlinear system of delay integro-differential equations which is used to model biological species living together. A numerical scheme based on the Chelyshkov polynomials is implemented to solve this fractional order system of integro-differential equations. The main advantages of the presented method is that it reduces under consideration problem to a system of nonlinear algebraic equations. Some test problems are considered to confirm validity and accuracy of the presented method. Moreover, the obtained numerical results are compared with those existing in the literature. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:26Z DOI: 10.1142/S1793557119500682

Authors:R. Rohila, R. C. Mittal Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, a new approach and methodology is developed by incorporating differential quadrature technique with Bernstein polynomials. In differential quadrature method, approximations are done in a way that the derivatives of the function are replaced by a linear sum of functional values at the grid points of the given domain. In Bernstein differential quadrature method (BDQM), Bernstein polynomials are employed for spatial discretization so that a system of ordinary differential equations (ODE’s) is obtained which is solved by SSPRK-43 method. The stability of the method is also studied. The accuracy of the present method is checked by performing numerical experiments on two-dimensional coupled Burgers’ and Brusselator systems and fourth-order extended Fisher Kolmogorov (EFK) equation. Implementation of the method is very easy, efficient and capable of reducing the size of computational efforts. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:26Z DOI: 10.1142/S1793557119500712

Authors:Majid Erfanian, Hamed Zeidabadi Abstract: Asian-European Journal of Mathematics, Ahead of Print. Everyone knows about the complicated solution of the nonlinear Fredholm integro-differential equation in general. Hence, often, authors attempt to obtain the approximate solution. In this paper, a numerical method for the solutions of the nonlinear Fredholm integro-differential equation (NFIDE) of the second kind in the complex plane is presented. In fact, by using the properties of Rationalized Haar (RH) wavelet, we try to give the solution of the problem. So far, as we know, no study has yet been attempted for solving the NFIDE in the complex plane. For this purpose, we introduce the continuous integral operator and real valued function. The Banach fixed point theorem guarantees that, under certain assumptions, the integral operator has a unique solution. Furthermore, we give an upper bound for the error analysis. An algorithm is presented to compute and illustrate the solutions for some numerical examples. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:25Z DOI: 10.1142/S1793557119500554

Authors:İsmet Altıntaş, Kemal Taşköprü Abstract: Asian-European Journal of Mathematics, Ahead of Print. The focus of this paper is to study the two-variable Kauffman polynomials [math] and [math], and the one-variable BLM/Ho polynomial [math] of [math]-torus link as the Fibonacci-type polynomials and to express the Kauffman polynomials in terms of the BLM/Ho polynomial. For this purpose, we prove that each of the examined polynomials of [math]-torus link can be determined by a third-order recurrence relation and give the recursive properties of them. We correlate these polynomials with the Fibonacci-type polynomials. By using the relations between the BLM/Ho polynomials and Fibonacci-type polynomials, we express the Kauffman polynomials in terms of the BLM/Ho polynomials. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:24Z DOI: 10.1142/S1793557119500530

Authors:Asuman Güven Aksoy, Monairah Al-Ansari, Qidi Peng Abstract: Asian-European Journal of Mathematics, Ahead of Print. We provide a new representation of an [math]-tree by using a special set of metric rays. We have captured the four-point condition from these metric rays and shown an equivalence between the [math]-trees with radial and river metrics, and these sets of metric rays. In stochastic analysis, these graphical representation theorems are of particular interest in identifying Brownian motions indexed by [math]-trees. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:24Z DOI: 10.1142/S1793557119500670

Authors:M. Rostamian Delavar, S. S. Dragomir Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, a condition which implies the continuity of an [math]-convex function is investigated. In fact, any [math]-convex function bounded from above is continuous if the function [math] satisfies a certain condition which is called pre-continuity condition. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-19T08:27:23Z DOI: 10.1142/S1793557119500591

Authors:Sassia Makhlouf, Lemnouar Noui Abstract: Asian-European Journal of Mathematics, Ahead of Print. Recently, several authors used linear codes to construct secret sharing schemes. It is known that if each nonzero codeword of a code [math] is minimal, then the dual code [math] is suitable for secret sharing. To seek such codes Ashikhmin–Barg give a sufficient condition from weights; in [math] code [math], let [math] and [math] be the minimum and maximum nonzero weights, respectively. If wmin wmax> q − 1 q(*) then all nonzero codewords of [math] are minimal. In this paper, a necessary and sufficient condition is given for self-dual codes and for MDS codes to verify the inequality (*). Special codes are examined and applied for secret sharing schemes. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:54Z DOI: 10.1142/S1793557119500268

Authors:Sadegh Abbaszadeh, Ali Ebadian, Mohsen Jaddi Abstract: Asian-European Journal of Mathematics, Ahead of Print. The theory of non-additive measures and relevant nonlinear integrals has recently been developed as a new branch of mathematics with various applications in other sciences. In this area, pseudo-additive measures and pseudo-integrals play important roles as new extensions of measures and integrals. The aim of this paper is to prove Hölder type integral inequalities with different pseudo-operations. Several examples are given to show the inequalities in more tangible forms. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:54Z DOI: 10.1142/S1793557119500323

Authors:M. J. Nikmehr, S. M. Hosseini Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a commutative ring with identity and [math] be the set of ideals of [math] with nonzero annihilator. The annihilator-ideal graph of [math], denoted by [math], is a simple graph with the vertex set [math], and two distinct vertices [math] and [math] are adjacent if and only if [math]. In this paper, we present some results on the bipartite, complete bipartite, outer planar and unicyclic of the annihilator-ideal graphs of a commutative ring. Among other results, bipartite annihilator-ideal graphs of rings are characterized. Also, we investigate planarity of the annihilator-ideal graph and classify rings whose annihilator-ideal graph is planar. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:53Z DOI: 10.1142/S1793557119500244

Authors:N. Annamalai, C. Durairajan Abstract: Asian-European Journal of Mathematics, Ahead of Print. This paper gives lower and upper bounds on the covering radius of codes over [math] with respect to Lee distance. We also determine the covering radius of various repetition codes over [math] Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:53Z DOI: 10.1142/S179355711950027X

Authors:Saroj Rani Abstract: Asian-European Journal of Mathematics, Ahead of Print. Constacyclic codes form an important class of linear codes which is remarkable generalization of cyclic and negacyclic codes. In this paper, we assume that [math] is the finite field of order [math] where [math] is a power of the prime [math] and [math] are distinct odd primes, and [math] are positive integers. We determine generator polynomials of all constacyclic codes of length [math] over the finite field [math] We also determine their dual codes. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:52Z DOI: 10.1142/S1793557119500505

Authors:Hojjat Afshari, Hassen Aydi Abstract: Asian-European Journal of Mathematics, Ahead of Print. The purpose of this paper is to present some new fixed point theorems for multifunctions, obtained by combining the methods of Suzuki and Samet and by using different conditions for generalized contractive multifunctions. Some examples are also considered. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:51Z DOI: 10.1142/S1793557119500220

Authors:M. H. Akhbari, F. Movahedi, M. Arslanov Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a simple graph. A set [math] is a doubly connected dominating set of [math] if it is a dominating set and both induced subgraphs [math] and [math] are connected. In this paper, we introduce the doubly connected domination polynomial of a graph. We investigate some properties of these polynomials for some specific graphs. Also, we compute the doubly connected domination polynomial for some families of graphs such as the friendship graphs and the cactus chains graphs. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:51Z DOI: 10.1142/S1793557119500360

Authors:Ali Taghavi, Mehran Razeghi, Mojtaba Nouri, Vahid Darvish Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] and [math] be two prime ∗-algebras. Let [math] be a bijective and satisfies Φ(A • B • C) = Φ(A) • Φ(B) • Φ(C), for all [math] where [math]. Then, [math] is additive. Moreover, if [math] is idempotent then we show that [math] is [math]-linear ∗-isomorphism. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:51Z DOI: 10.1142/S1793557119500384

Authors:Pavel Trojovský Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be the [math]th Fibonacci number and [math] be the [math]th Lucas number. The order of appearance [math] of a natural number [math] is defined as the smallest natural number [math] such that [math] divides [math]. For instance, [math], for all [math]. In this paper, among other things, we prove that [math] depends on [math], where [math] is the greatest common divisor of numbers [math] and [math], which fulfill the condition [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:51Z DOI: 10.1142/S1793557119500463

Authors:Azam K. Mousavi, Mohammad Reza R. Moghaddam, Mehdi Eshrati Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a pair of [math]-Lie algebras. Then, we introduce the concept of Schur multiplier of the pair [math], denoted by [math], and some inequalities for the dimension of [math] are given. We also determine a necessary and sufficient condition, for which the Schur multiplier of a pair of [math]-Lie algebras can be embedded into the Schur multipliers of their [math]-Lie algebra factors. Moreover, some inequalities for the Schur multiplier of a pair of finite-dimensional nilpotent [math]-Lie algebras are acquired. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:50Z DOI: 10.1142/S1793557119500281

Authors:Xiaohua Liu Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, the orbital stability of standing waves for nonlinear fractional Schrödinger equation is considered. By constructing the constrained functional extreme-value problem, the existence of standing waves is studied. With the help of the orbital stability theories presented by Grillakis, Shatah and Strauss, the orbital stability of standing waves is determined by the sign of a discriminant. To our knowledge, it is the first time that the abstract orbital stability theories presented by Grillakis, Shatah and Strauss are applied to study the stability of solutions for fractional evolution equation. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:50Z DOI: 10.1142/S1793557119500438

Authors:Tanmay Biswas Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a complete ultrametric algebraically closed field and [math] be the [math]-algebra of entire functions on [math]. For [math], [math], we wish to introduce the notions of relative order and relative lower order of [math] with respect to [math]. Hence, after proving some basic results, in this paper, we estimate some growth rates of composite [math]-adic entire functions on the basis of their relative orders and relative lower orders. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:50Z DOI: 10.1142/S179355711950044X

Authors:Ritu Agarwal, G. S. Paliwal, Parany Goswami Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [math]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:49Z DOI: 10.1142/S1793557119500359

Authors:Sayed Saber Abstract: Asian-European Journal of Mathematics, Ahead of Print. Let [math] be a complex manifold of dimension [math] and let [math]. Let [math] be a weakly [math]-convex and [math] be a weakly [math]-convex in [math] with smooth boundaries such that [math]. Assume that [math] and [math] satisfy property [math]. Then the compactness estimate for [math]-forms [math] holds for the [math]-Neumann problem on the annulus domain [math]. Furthermore, if [math] is [math]-closed [math]-form, which is [math] on [math] and which is cohomologous to zero on [math], the canonical solution [math] of the equation [math] is smooth on [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:49Z DOI: 10.1142/S1793557119500414

Authors:Maheshwar Pathak, Pankaj Srivastava Abstract: Asian-European Journal of Mathematics, Ahead of Print. In the present paper, certain new transformation formulae for basic hypergeometric series have been developed with the help of new WP-Bailey pair generated from old WP-Bailey pair. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:49Z DOI: 10.1142/S1793557119500499

Authors:Geena Joy, K. V. Thomas Abstract: Asian-European Journal of Mathematics, Ahead of Print. This paper introduces the concept of lattice vector space and establishes many important results. Also, this paper deals with linear transformations on lattice vector spaces and discusses their elementary properties. We prove that every finite dimensional lattice vector space is isomorphic to [math] and show that the set of all columns (or the set of all rows) of an invertible matrix over [math] is a basis for [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:48Z DOI: 10.1142/S1793557119500311

Authors:Camilo Sanabria Malagón Abstract: Asian-European Journal of Mathematics, Ahead of Print. The classical spectral theorem completely describes self-adjoint operators on finite-dimensional inner product vector spaces as linear combinations of orthogonal projections onto pairwise orthogonal subspaces. We prove a similar theorem for self-adjoint operators on finite-dimensional symplectic vector spaces over perfect fields. We show that these operators decompose according to a polarization, i.e. as the product of an operator on a Lagrangian subspace and its dual on a complementary Lagrangian. Moreover, if all the eigenvalues of the operator are in the base field, then there exists a Darboux basis such that the matrix representation of the operator is [math] blocks block-diagonal, where the first block is in Jordan normal form and the second block is the transpose of the first one. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:48Z DOI: 10.1142/S1793557119500335

Authors:Abdellah Gherbi, Bekkai Messirdi Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we extend the notion of quotient of linear operators to linear relations. We introduce for two given linear relations [math] and [math], the linear relation quotient [math] and we give a detailed treatment of some basic algebraic and topological properties of this new notion. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:48Z DOI: 10.1142/S1793557119500475

Authors:Ankur, Pramod Kumar Kewat Abstract: Asian-European Journal of Mathematics, Ahead of Print. We discuss self-dual codes over the ring [math]. We characterize the structure of self-dual, Type I codes and Type II codes over [math] with given generator matrix in terms of the structure of their Torsion and Residue codes. We construct self-dual, Type I and Type II codes over [math] for different lengths. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:47Z DOI: 10.1142/S1793557119500256

Authors:Kostaq Hila, Saleem Abdullah, Krisanthi Naka Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we are dealing with [math]-semihypergroups which are a generalization of a semigroup, [math]-semigroup and a semihypergroup. We introduce the notion of generalized quasi-[math]-hyperideal i.e. of [math]-quasi-[math]-hyperideal, [math]-right [math]-hyperideal and [math]-left [math]-hyperideal in [math]-semihypergroups and different properties of them and relations between them are studied. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:47Z DOI: 10.1142/S179355711950030X

Authors:Ivan Chajda, Helmut Länger Abstract: Asian-European Journal of Mathematics, Ahead of Print. We characterize those commutative rings [math] whose ideal lattice [math] endowed with the annihilation operation is an ortholattice. Moreover, we provide an analogous characterization for the annihilator lattice [math] endowed with the annihilation operation. Since the ideal lattice of [math] is modular, [math] is already an orthomodular lattice provided it is an ortholattice. However, there exist also commutative rings whose ideal lattices are complemented but the complementation differs from annihilation. We present an example of such a ring and develop a procedure producing infinitely many rings with this property. Finally, we provide a sufficient condition for double annihilation to be a homomorphism from [math] onto [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:46Z DOI: 10.1142/S1793557119500396

Authors:Jingqun Wang, Jing Li, Lixin Tian Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we investigate the two-component Camassa–Holm equation with fractional dissipation ut − utxx + k ∧γ(u − u xx) + 3uux − (2uxuxx + uuxxx) + ρρx = 0,t> 0,x ∈ R,ρt + ∧1 2ρ + (uρ)x = 0, t> 0,x ∈ R, where [math] denotes the fractional dissipative operator which is defined by the Fourier transform [math]. We prove the local-posedness of this equation via the Littlewood–Paley theory and the suitable iterative scheme. Furthermore, under appropriate discussions, we give the global well-posedness of the above equation. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:46Z DOI: 10.1142/S1793557119500517

Authors:Krishanu Dey, Sugato Gupta, Sujit Kumar Sardar Abstract: Asian-European Journal of Mathematics, Ahead of Print. The main purpose of the paper is to consider two Morita equivalent semirings [math] and [math] via Morita context [math] instead of considering them via the equivalence of the resulting semimodule categories and then to investigate various Morita invariants related to each of the pairs [math]; [math]; [math]; [math], etc. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:45Z DOI: 10.1142/S1793557119500232

Authors:Abdelaziz Tajmouati, Hamid Boua, Abdeslam El Bakkali Abstract: Asian-European Journal of Mathematics, Ahead of Print. A bounded operator [math] in a Banach space [math] is said to satisfy the descent spectrum equality, if the descent spectrum of [math] as an operator on [math] coincides with the descent spectrum of [math] as an element of the algebra [math] of all bounded linear operators on [math]. In this paper, we give some conditions under which the equality [math] holds for a single operator [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:45Z DOI: 10.1142/S1793557119500293

Authors:Zinovii Nytrebych, Oksana Malanchuk Abstract: Asian-European Journal of Mathematics, Ahead of Print. The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its characteristic determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-10T07:47:45Z DOI: 10.1142/S1793557119500372

Authors:Vivek Sahai, Ashish Verma Abstract: Asian-European Journal of Mathematics, Ahead of Print. This paper continues the study of finite summation formulas of multivariable hypergeometric functions. Earlier, Wang and Chen [Finite summation formulas of double hypergeometric functions, Int. Transf. Spec. Funct. 28(3) (2016) 239–253] established finite summation formulas of double hypergeometric functions by using some well-known summation theorems. We present here finite summation formulas for Srivastava’s general triple hypergeometric function. Certain particular cases leading to finite summation formulas for Lauricella functions and Srivastava’s triple hypergeometric functions are also presented. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-09T08:00:55Z DOI: 10.1142/S1793557119500207

Authors:Paula Catarino Abstract: Asian-European Journal of Mathematics, Ahead of Print. The aim of this work is to present the [math]-Pell, the [math]-Pell–Lucas and the Modified [math]-Pell sedenions and we give some properties involving these sequences, including the Binet-style formulae and the ordinary generating functions. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-09T08:00:54Z DOI: 10.1142/S1793557119500189

Authors:Chol-Hui Yun, Mi-Kyong Ri Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we present a construction of hidden variable bivariate fractal interpolation functions (HVBFIFs) with function vertical scaling factors and estimate errors of HVBFIFs on perturbation of the function vertical scaling factor. We construct HVBFIFs on the basis of the iterated function system (IFS) with function vertical scaling factors. The perturbation of the function vertical scaling factors in the IFS causes a change in the HVBFIF. An upper estimation of the errors between the original HVBFIF and the perturbed HVBFIF is given. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-09T08:00:54Z DOI: 10.1142/S1793557119500219

Authors:H. Orhan, N. Magesh, V. K. Balaji Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [math] of analytic bi-univalent function class [math] which is associated with Chebyshev polynomials in the open unit disk. Citation: Asian-European Journal of Mathematics PubDate: 2018-04-09T08:00:53Z DOI: 10.1142/S1793557119500177

Authors:Sami Segni, Mourad Ghiat, Hamza Guebbai Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this work, we build a new numerical method to approximate the solution of Volterra’s nonlinear integro-differential equation. This method needs fewer conditions to converge, compared to the direct Nytröm method. Numerical tests show its efficiency. This new method is more practical and compatible with the Volterra nonlinear integro-differential equation. Citation: Asian-European Journal of Mathematics PubDate: 2018-02-05T03:48:09Z DOI: 10.1142/S1793557119500165

Authors:S. F. Mohebian, S. Hosseini Abstract: Asian-European Journal of Mathematics, Ahead of Print. The concepts of autonilpotent groups were introduced by Parvaneh and Moghaddam in 2010. In this paper, we introduce the generalized version of lower n-autocenteral and upper n-autocenteral series. Using these concepts, the notion of n-autonilpotent groups will be defined and some of the well-known theorems on autonilpotent groups will be proved in the generalized version. Citation: Asian-European Journal of Mathematics PubDate: 2018-02-05T03:48:04Z DOI: 10.1142/S1793557119500141

Authors:Rabigul Tuniyaz, Abdukadir Obul Abstract: Asian-European Journal of Mathematics, Ahead of Print. In this paper, we establish Composition-Diamond lemma for multiple tensor products of commutative algebra [math], free associative algebras [math], Grassman algebras [math] and path algebras [math] over a field [math]. Citation: Asian-European Journal of Mathematics PubDate: 2018-02-05T03:47:59Z DOI: 10.1142/S1793557119500153