Showing papers in "International Journal of Mathematics and Mathematical Sciences in 2010"
TL;DR: The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group in the language of planar diagrams with local generators and local defining relations as mentioned in this paper.
Abstract: The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with local generators and local defining relations.
80Β citations
TL;DR: The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers based on interval difference that is compatible with existing distance measures and some numerical examples are considered for applying the proposed measure.
Abstract: The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.
54Β citations
TL;DR: The authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2πΉ1, Watson, Dixon and Whipple for theseries 3π¬2, and a few other hypergeometric identities.
Abstract: Motivated by the extension of classical Gauss's summation theorem for the series 2πΉ1 given in the literature, the authors aim at presenting the extensions of various other classical summation theorems such as those of Kummer, Gauss's second, and Bailey for the series 2πΉ1, Watson, Dixon and Whipple for the series 3πΉ2, and a few other hypergeometric identities for the series 3πΉ2 and 4πΉ3. As applications, certain very interesting summations due to Ramanujan have been generalized. The results derived in this paper are simple, interesting, easily established, and may be useful.
49Β citations
TL;DR: In this paper, the authors introduced the concept of almost paracontact manifold, and in particular, of ''para-Sasakian'' manifolds, and showed that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an''para'' Sasakian structure.
Abstract: We introduce the concept of ()-almost paracontact manifolds, and in particular, of ()-para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of ()-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an ()-para Sasakian structure. We show that, for an ()-para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp., timelike) ()-para Sasakian manifold is locally isometric to a pseudohyperbolic space (resp., pseudosphere ). At last, it is proved that for an ()-para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric, and Einstein are all identical.
40Β citations
TL;DR: A systemic study of some families of π-Genocchi numbers and families of polynomials of NΓΆrlund type is presented by using the multivariate fermionic π-adic integral on β€π.
Abstract: A systemic study of some families of π-Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic π-adic integral on β€π. The study of these higher-order π-Genocchi numbers and polynomials yields an interesting π-analog of identities for Stirling numbers.
36Β citations
TL;DR: It is proved that an additive derivation of a linearly ordered MV-algebral is an isotone and some characterizations of a derivations of an MV- algebra are given.
Abstract: We introduce the notion of derivation for
an MV-algebra and discuss some related properties. Using the notion of an
isotone derivation, we give some characterizations of a derivation of an
MV-algebra. Moreover, we define an additive derivation of an MV-algebra and
investigate some of its properties. Also, we prove that an additive
derivation of a linearly ordered MV-algebral is an isotone.
34Β citations
TL;DR: It is proved that if for all or for all, then the semiprime ring must contains a nonzero central ideal, provided the ring must be commutative.
Abstract: Let be a ring with center and a nonzero ideal of . An additive mapping is called a generalized derivation of if there exists a derivation such that for all . In the present paper, we prove that if for all or for all , then the semiprime ring must contains a nonzero central ideal, provided . In case is prime ring, must be commutative, provided . The cases (i) and (ii) for all are also studied.
32Β citations
TL;DR: A fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers.
Abstract: This paper presents a fuzzy goal programming FGP procedure for solving bilevel multiobjective
linear fractional programming BL-MOLFP problems. It makes an extension work of Moitra
and Pal 2002 and Pal et al. 2003. In the proposed procedure, the membership functions for
the defined fuzzy goals of the decision makers DMs objective functions at both levels as well
as the membership functions for vector of fuzzy goals of the decision variables controlled by
first-level decision maker are developed first in the model formulation of the problem. Then a
fuzzy goal programming model to minimize the group regret of degree of satisfactions of both
the decision makers is developed to achieve the highest degree unity of each of the defined
membership function goals to the extent possible by minimizing their deviational variables and
thereby obtaining the most satisfactory solution for both decision makers. The method of variable
change on the under- and over-deviational variables of the membership goals associated with
the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal
programming LGP methodology. Illustrative numerical example is given to demonstrate the
procedure.
31Β citations
TL;DR: Using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem of nonlinear fractional differential equation are obtained.
Abstract: We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with -Laplacian operator , , , , , where , , , denotes the Caputo derivative, and is continuous function, , , . By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.
30Β citations
TL;DR: The notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset is introduced and fuzzy interior ideals of Abel Grassmann's groupoids are characterized in terms of these relations.
Abstract: Using the notion of a fuzzy point and its belongness to and quasicoincidence with a fuzzy subset, some new concepts of a fuzzy interior ideal in Abel Grassmann's groupoids are introduced and their interrelations and related properties are invesitigated. We also introduce the notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset and characterize fuzzy interior ideals of in terms of these relations.
25Β citations
TL;DR: The fixed-point theorem is generalized for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974) to prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive inequality of integral type.
Abstract: First we prove existence of a fixed point for mappings defined on a complete modular space satisfying a general contractive
inequality of integral type. Then we generalize fixed-point theorem for a quasicontraction mapping given by Khamsi (2008) and Ciric (1974).
TL;DR: Using the diagrammatic calculus for Soergel bimodules, as well as Rasmussen's spectral sequence, an integral version of HOMFLY-PT and sl(π)-link homology is constructed.
Abstract: Using the diagrammatic calculus for Soergel bimodules, developed by Elias and Khovanov, as well as Rasmussen's spectral sequence, we construct an integral version of HOMFLY-PT and sl(π)-link homology.
TL;DR: The initial-boundary value problem for Benjamin-Ono equation on a half-line is considered and traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to theInitial-boundaries value problem and the asymptotic behavior of solutions for large time are studied.
Abstract: We consider the initial-boundary value problem for Benjamin-Ono
equation on a half-line. We study traditionally important problems of the theory
of nonlinear partial differential equations, such as global in time existence
of solutions to the initial-boundary value problem and the asymptotic behavior
of solutions for large time.
TL;DR: In the setting of the Siegel threefold, it is proven that this Spezialschar of ππ(2π) is the Maass Spezialchar.
Abstract: Let ππ(π) be the space of Siegel modular forms of degree π and even weight π. In this paper firstly a certain subspace Spez(ππ(2π)), the Spezialschar of ππ(2π), is introduced. In the setting of the Siegel threefold, it is proven that this Spezialschar is the Maass Spezialschar. Secondly, an embedding of ππ(2) into a direct sum β¨βπ/10βπ=0 Sym2ππ
TL;DR: In this paper, a Rademacher-type convergent series formula which generalizes the Hardy-Ramanujan-Rademacher formula for the number of partitions of Η« and the Zuckerman model for the Fourier coefficients was presented.
Abstract: A Rademacher-type convergent series formula which generalizes the Hardy-Ramanujan-Rademacher formula for the number of partitions of π and the Zuckerman formula for the Fourier coefficients of π4(0β£π)β1 is presented.
TL;DR: The operational technique is used for the conventional right-sided Laplace transformation and its extension to generalized functions to describe a complete family of eigenfunctions and fundamental solutions of the operator in classes of functions represented by the left-sided fractional integral of a summable function or just admitting an summable fractional derivative.
Abstract: We deal with the following fractional generalization of the Laplace equation for rectangular domains , which is associated with the Riemann-Liouville fractional derivatives , , where , . Reducing the left-hand side of this equation to the sum of fractional integrals by and , we then use the operational technique for the conventional right-sided Laplace transformation and its extension to generalized functions to describe a complete family of eigenfunctions and fundamental solutions of the operator in classes of functions represented by the left-sided fractional integral of a summable function or just admitting a summable fractional derivative. A symbolic operational form of the solutions in terms of the Mittag-Leffler functions is exhibited. The case of the separation of variables is also considered. An analog of the fractional logarithmic solution is presented. Classical particular cases of solutions are demonstrated.
TL;DR: The notions of -subalgebras and -closed ideals in BCH-alge bras are introduced, and the relation between - Subalge Bras and-closed ideals is considered.
Abstract: The notions of -subalgebras and -closed ideals in BCH-algebras are introduced, and the relation between -subalgebras and -closed ideals is considered. Characterizations of -subalgebras and -closed ideals are provided. Using special subsets, -subalgebras and -closed ideals are constructed. A condition for an -subalgebra to be an -closed ideal is discussed. Given an -structure, the greatest -closed ideal which is contained in the -structure is established.
TL;DR: This paper investigates several interesting properties of the new generalised derivative operator introduced in πππ,π1,π2, which generalised many well-known operators studied earlier by many authors.
Abstract: A new generalised derivative operator πππ,π1,π2 is introduced. This operator generalised many well-known operators studied earlier by many authors. Using the technique of differential subordination, we will study some of the properties of differential subordination. In addition we investigate several interesting properties of the new generalised derivative operator.
TL;DR: A very new theorem on the degree of approximation of the generating function by (πΈ,1) means of its Fourier-Laguerre series at the frontier point π₯=0 is obtained.
Abstract: A very new theorem on the degree of approximation of the generating function by (πΈ,1) means of its Fourier-Laguerre series at the frontier point π₯=0 is obtained.
TL;DR: It is explained how the powers of which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules.
Abstract: The Misra-Miwa -deformed Fock space is a representation of the quantized affine algebra . It has a standard basis indexed by partitions, and the nonzero matrix entries of the action of the Chevalley generators with respect to this basis are powers of . Partitions also index the polynomial Weyl modules for as tends to infinity. We explain how the powers of which appear in the Misra-Miwa Fock space also appear naturally in the context of Weyl modules. The main tool we use is the Shapovalov determinant for a universal Verma module.
TL;DR: Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy and -trust maximin equilibrium strategy are defined and the technique of genetic algorithm is applied to find the equilibrium strategies.
Abstract: We concentrate on discussing a class of two-person zero-sum games with rough payoffs. Based on the expected value operator and the trust measure of rough variables, the expected equilibrium strategy and -trust maximin equilibrium strategy are defined. Five cases whether the game exists -trust maximin equilibrium strategy are discussed, and the technique of genetic algorithm is applied to find the equilibrium strategies. Finally, a numerical example is provided to illustrate the practicality and effectiveness of the proposed technique.
TL;DR: The structure of compact and countably compact primitive topological inverse semigroups are described and it is shown that any countably Compact primitive topology inverse semigroup embeds into a compact primitiveTopological inverseSemigroup.
Abstract: We study (countably) compact and (absolutely) π»-closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive topological inverse semigroup embeds into a compact primitive topological inverse semigroup.
TL;DR: The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact πΎ with respect to the set Ξ©π.
Abstract: The aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact πΎ with respect to the set Ξ©π={π§βππ;expππΎ(π§)β€π}, where ππΎ=sup{(1/π)ln|ππ|,ππpolynomialofdegreeβ€π,βππβπΎβ€1} is the Siciak extremal function of a πΏ-regular compact πΎ.
TL;DR: It is proved that every regular incline is a distributive lattice and characterizations of the set of all generalized inverses are presented as a generalization and development of regular elements in a β-regular ring.
Abstract: Inclines are additively idempotent semirings in which products are less than (or) equal to either factor. Necessary and sufficient conditions for an element in an incline to be regular are obtained. It is proved that every regular incline is a distributive lattice. The existence of the Moore-Penrose inverse of an element in an incline with involution is discussed. Characterizations of the set of all generalized inverses are presented as a generalization and development of regular elements in a β-regular ring.
TL;DR: The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group, and it is demonstrated how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra.
Abstract: The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also
given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra.
TL;DR: Making use of the generalized hypergeometric functions, a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients are defined and integral means inequalities are obtained for the function that belongs to the class in the unit disc.
Abstract: Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the class . In particular, we obtain integral means inequalities for the function that belongs to the class in the unit disc.
TL;DR: The Jungck-multistep iteration is introduced and it is shown that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space.
Abstract: We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized.
TL;DR: This paper introduces the concept of an approach merotopological space and studies its category-theoretic properties, and takes a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotipological spaces, and approach merots.
Abstract: This paper introduces the concept of an approach merotopological space and
studies its category-theoretic properties. Various topological categories are shown to be embedded into the category whose objects are approach merotopological spaces. The order structure of the family of all approach merotopologies on a nonempty set is discussed. Employing the theory of bunches, bunch completion of an approach merotopological space is constructed. The present study is a unified look at the completion of metric spaces, approach spaces, nearness spaces, merotopological spaces, and approach merotopological spaces.
TL;DR: Two functors from Elias and Khovanov's diagrammatic Soergel category are defined, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other targeting the category of (universal) sl(3) foams.
Abstract: We define two functors from Elias and Khovanov's diagrammatic Soergel category, one targeting Clark-Morrison-Walker's category of disoriented sl(2) cobordisms and the other targeting the category of (universal) sl(3) foams.
TL;DR: This paper considers certain invariance properties of quasinearly subharmonic functions and gives partial generalizations to Kojic's results by showing that in βπ, πβ₯2, these both classes are invariant under bi-Lipschitz mappings.
Abstract: After considering a variant of the generalized mean value inequality of quasinearly subharmonic functions, we consider certain invariance properties of quasinearly subharmonic functions. Kojic has shown that in the plane case both the class of quasinearly subharmonic functions and the class of regularly oscillating functions are invariant under conformal mappings. We give partial generalizations to her results by showing that in βπ, πβ₯2, these both classes are invariant under bi-Lipschitz mappings.