Showing papers in "Journal of The Korean Mathematical Society in 2008"
TL;DR: In this article, by using q-deformed bosonic p-adic integral, the authors give -Bernoulli numbers and polynomials, and prove Witt's type formula of Bernoulli polynomorphisms and Gauss multiplicative formula for -Bernhoullomorphisms.
Abstract: In this paper, by using q-deformed bosonic p-adic integral, we give -Bernoulli numbers and polynomials, we prove Witt's type formula of -Bernoulli polynomials and Gauss multiplicative formula for -Bernoulli polynomials. By using derivative operator to the generating functions of -Bernoulli polynomials and generalized -Bernoulli numbers, we give Hurwitz type -zeta functions and Dirichlet's type -L-functions; which are interpolated -Bernoulli polynomials and generalized -Bernoulli numbers, respectively. We give generating function of -Bernoulli numbers with order r. By using Mellin transforms to their function, we prove relations between multiply zeta function and -Bernoulli polynomials and ordinary Bernoulli numbers of order r and -Bernoulli numbers, respectively. We also study on -Bernoulli numbers and polynomials in the space of locally constant. Moreover, we define -partial zeta function and interpolation function.
73 citations
TL;DR: In this article, a new method for solving a nonlinear two-point boundary value problem with finitely many singularities is presented, where the exact solution is represented in the form of series in the reproducing kernel space.
Abstract: In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities Its exact solution is represented in the form of series in the reproducing kernel space In the mean time, the n-term approximation un(x) to the exact solution u(x) is obtained and is proved to converge to the exact solution Some numerical examples are studied to demonstrate the accuracy of the present method Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other
45 citations
43 citations
TL;DR: In this paper, several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the classification of subspaces of Khalimsky n-dimensional space (Zn, T n).
Abstract: In this paper several continuities and homeomorphisms in computer topology are studied and their applications are investigated in relation to the classification of subspaces of Khalimsky n-dimensional space (Zn, T n). Precisely, the notions of K-(k0, k1)-,(k0, k1)-,KD-(k0, k1)continuities, and Khalimsky continuity as well as those of K-(k0, k1)-, (k0, k1)-, KD-(k0, k1)-homeomorphisms, and Khalimsky homeomorphism are studied and further, their applications are investigated.
41 citations
TL;DR: In this article, the signed count of the real J-holomorphic spheres passing through a generic real configuration of k points is independent of the choice of real configuration and choice of J, if the dimension of the Lagrangian submanifold L (fixed point set of involution) is two or three and also if L is orient able and relatively spin.
Abstract: We provide another proof that the signed count of the real J-holomorphic spheres (or J- holomorphic discs) passing through a generic real configuration of k points is independent of the choice of the real configuration and the choice of J, if the dimension of the Lagrangian submanifold L (fixed point set of involution) is two or three, and also if we assume L is orient able and relatively spin. We also assume that M is strongly semi-positive. This theorem was first proved by Welschinger in a more general setting, and we provide more natural approach using the signed degree of an evaluation map.
41 citations
TL;DR: In this paper, the Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain where the viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature.
Abstract: The Navier-Stokes system for heat-conducting incompressible fluids is studied in a domain . The viscosity, heat conduction coefficients and specific heat at constant volume are allowed to depend smoothly on density and temperature. We prove local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. For the strong regularity, we do not assume the positivity of initial density; it may vanish in an open subset (vacuum) of or decay at infinity when is unbounded.
40 citations
TL;DR: In this paper, for an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained for a class of random variables with respect to uniform integration.
Abstract: For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.
36 citations
TL;DR: In this article, a sequence of inequalities for superquadratic functions such as the convers and the reverse Jensentype inequalities, Giaccardi's nad Petrovic's inequality and Hermite-Hadamard inequality are given.
Abstract: Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the convers and the reverse Jensentype inequalities, Giaccardi's nad Petrovic's inequality and Hermite-Hadamard inequality. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.
35 citations
TL;DR: In this paper, the regularity problem for the Navier-Stokes equation in terms of the multiplier space has been studied in the context of weak solutions of Navier Stokes equations.
Abstract: Consider a weak solution u of the Navier-Stokes equations in the class . We establish a new approach to treat the regularity problem for the Navier-Stokes equation in term of the multiplier space .
30 citations
TL;DR: Biharmonic Legendre curves in a Sasakian space form are studied in this article, and a non-existence result in a 7-dimensional 3-Sasakian manifold is obtained.
Abstract: Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.
30 citations
TL;DR: In this article, a partial Cayley transform of the Siegel-Jacobi disk was presented, which gives a partial bounded realization of the Jacobi group on all complex matrices.
Abstract: Let and be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let be the Euclidean space of all complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk onto the Siegel-Jacobi space which gives a partial bounded realization of by . We prove that the natural actions of the Jacobi group on . and . are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel Jacobi disk . invariant under the natural action of the Jacobi group explicitly.
TL;DR: In this article, two classes of functions, involving a parameter and the classical Euler gamma function, were verified to be logarithmically completely monotonic in or ; some inequalities involving the Euler Gamma function were deduced and compared with those originating from certain problems of traffic flow, relating to the well known Stirling's formula.
Abstract: In this paper, two classes of functions, involving a parameter and the classical Euler gamma function, and two functions, involving the classical Euler gamma function, are verified to be logarithmically completely monotonic in or ; some inequalities involving the classical Euler gamma function are deduced and compared with those originating from certain problems of traffic flow, due to J. Wendel and A. Laforgia, and relating to the well known Stirling's formula.
TL;DR: The function [Γ(x+1)] 1/x x ( 1 + 1 x )x is strictly logarithmically completely monotonic in (0, ∞) as discussed by the authors.
Abstract: The function [Γ(x+1)]1/x x ( 1 + 1 x )x is strictly logarithmically completely monotonic in (0,∞) The function ψ′′(x + 2) + 1+x 2 x2(1+x)2 is strictly completely monotonic in (0,∞)
TL;DR: In this paper, the authors investigated connected conditions of the zero-divisor graph Γ(R) of a noncom-mutative ring R as follows: (1) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then X is connected and diam(Γ(r)) is equal to or less than 3.
Abstract: Let R be a ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. First, we investigate some connected conditions of the zero-divisor graph Γ(R) of a noncom- mutative ring R as follows: (1) if Γ(R) has no sources and no sinks, then Γ(R) is connected and diameter of Γ(R), denoted by diam(Γ(R)) (resp. girth of Γ(R), denoted by g(Γ(R))) is equal to or less than 3; (2) if X is a union of finite number of orbits under the left (resp. right) regular action on X by G, then Γ(R) is connected and diam(Γ(R)) (resp. g(Γ(R))) is equal to or less than 3, in addition, if R is local, then there is a vertex of Γ(R) which is adjacent to every other vertices in Γ(R); (3) if R is unit- regular, then Γ(R) is connected and diam(Γ(R)) (resp. g(Γ(R))) is equal to or less than 3. Next, we investigate the graph automorphisms group of Γ(Mat2(Zp)) where Mat2(Zp) is the ring of 2 by 2 matrices over the galois field Zp (p is any prime).
TL;DR: The main result of as mentioned in this paper is that every reciprocal Littlewood polynomial, one with {−1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots.
Abstract: The main result of this paper shows that every reciprocal Littlewood polynomial, one with {−1, 1} coefficients, of odd degree at least 7 has at least five unimodular roots, and every reciprocal Littlewood polynomial of even degree at least 14 has at least four unimodular roots, thus improving the result of Mukunda. We also give a sketch of alternative proof of the well-known theorem characterizing Pisot numbers whose minimal polynomials are in
TL;DR: In this article, the authors characterize the boundedness and compactness of the weighted composition operator from the general function space F(p, q, s) into the logarithmic Bloch space on the unit disk.
Abstract: We characterize the boundedness and compactness of the weighted composition operator from the general function space F(p, q, s) into the logarithmic Bloch space on the unit disk. Some necessary and sufficient conditions are given for which is a bounded or a compact operator from F(p,q,s), (p,q,s) into , respectively.
TL;DR: In this article, it was shown that if A ≥ 0 and T are two bounded linear operators on a complex Hilbert space satisfying the inequality T ∗AT ≤ A and the condition AT = A 1/2TA1/2, then there exists the maximum reducing subspace for A and T on which the equality T ∆AT = A is satisfied.
Abstract: It is shown that if A ≥ 0 and T are two bounded linear operators on a complex Hilbert space H satisfying the inequality T ∗AT ≤ A and the condition AT = A1/2TA1/2, then there exists the maximum reducing subspace for A and A1/2T on which the equality T ∗AT = A is satisfied. We concretely express this subspace in two ways, and as applications, we derive certain decompositions for quasinormal contractions. Also, some facts concerning the quasi-isometries are obtained.
TL;DR: In this article, the authors considered the hyponormality of Toeplitz operators Tφ on the Bergman space La(D) in the cases φ := f + g (f and g are polynomials).
Abstract: In this paper we consider the hyponormality of Toeplitz operators Tφ on the Bergman space La(D) in the cases, where φ := f + g (f and g are polynomials). We present some necessary or sufficient conditions for the hyponormality of Tφ under certain assumptions about the coefficients of φ.
TL;DR: In this article, the authors provide a criterion for Chow stability in terms of log canonical threshold of the Chow form in the Grassmannian, which is the same as the criterion in this paper.
Abstract: In this paper, we provide a criterion for Chow stability in terms of log canonical threshold of the Chow form in the Grassmannian.
TL;DR: In this article, the L∞-case of the Hofer norm on the group Hameo (M,ω) of Hamiltonian diffeomorphisms was studied.
Abstract: The group Hameo (M,ω) of Hamiltonian homeomorphisms of a connected symplectic manifold (M,ω) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the L(1,∞)-Hofer norm (and not the L∞-Hofer norm) on the space of Hamiltonian paths (see below for the definitions). A justification for this choice was given in [7]. In this article we study the L∞-case. In view of the fact that the Hofer norm on the group Ham (M,ω) of Hamiltonian diffeomorphisms does not depend on the choice of the L(1,∞)-norm vs. the L∞-norm [9], Y.-G. Oh and D. McDuff (private communications) asked whether the two notions of Hamiltonian homeomorphisms arising from the different norms coincide. We will give an affirmative answer to this question in this paper.
TL;DR: In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method.
Abstract: In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.
TL;DR: In this paper, the Lefschetz number and the Nielsen number of a self-map on the Klein bottle were computed by using the infra-nilmanifold structure of the Klein bottles.
Abstract: Let f : M → M be a self-map on the Klein bottle M . We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infranilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers NPn(f) and NΦn(f) of fn.
TL;DR: In this article, the authors derived some subordination and superordination results involving Carlson-Shaffer operator for certain normalized analytic functions in the open unit disk, with relevant connections of the results with various known results.
Abstract: The purpose of this present paper is to derive some subordination and superordination results involving Carlson–Shaffer operator for certain normalized analytic functions in the open unit disk.Relevant connections of the results, which are presented in the paper, with various known results are also considered.
TL;DR: In this article, some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian G2(Cm+2) with Lie parallel normal Jacobi operator were given.
Abstract: In this paper we give some non-existence theorems for Hopf hypersurfaces in the complex two-plane Grassmannian G2( Cm+2) with Lie parallel normal Jacobi operator � RN and totally geodesic D and D? components of the Reeb ow.
TL;DR: In this paper, the quantum Fourier-Gauss and quantum four-ier-mehler transforms are introduced and their properties and properties are studied, and the quantum Gross Laplacian and Beltrami Laplace are studied.
Abstract: Noncommutative extensions of the Gross and Beltrami Lapla- cians, called the quantum Gross Laplacian and the quantum Beltrami Laplacian, resp., are introduced and their basic properties are studied. As noncommutative extensions of the Fourier-Gauss and Fourier-Mehler transforms, we introduce the quantum Fourier-Gauss and quantum Four- ier-Mehler transforms. The infinitesimal generators of all differentiable one parameter groups induced by the quantum Fourier-Gauss transform are linear combinations of the quantum Gross Laplacian and quantum Beltrami Laplacian. A characterization of the quantum Fourier-Mehler transform is studied.
TL;DR: In this paper, it was shown that the strongly pseudocontractive mapping T converges strongly to a fixed point of T, which solves the variational inequality involving the mapping A. The existence of a path {xt} satisfying xt = tAxt + (1− t)Txt, t ∈ (0, 1) is shown.
Abstract: Let X be a real reflexive Banach space with a uniformly Gâteaux differentiable norm, C a nonempty closed convex subset of X, T : C → X a continuous pseudocontractive mapping, and A : C → C a continuous strongly pseudocontractive mapping. We show the existence of a path {xt} satisfying xt = tAxt +(1− t)Txt, t ∈ (0, 1) and prove that {xt} converges strongly to a fixed point of T , which solves the variational inequality involving the mapping A. As an application, we give strong convergence of the path {xt} defined by xt = tAxt + (1− t)(2I −T )xt to a fixed point of firmly pseudocontractive mapping T .
TL;DR: In this article, explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations.
Abstract: Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.
TL;DR: In this paper, a cross product algebra with N-generators is considered and the moments and cumulants of operators in the crossed product are computed for groups of all automorphisms.
Abstract: In this paper, we will consider certain amalgamated free product structure in crossed product algebras. Let M be a von Neumann algebra acting on a Hilbert space Hand G, a group and let : G AutM be an action of G on M, where AutM is the group of all automorphisms on M. Then the crossed product G of M and G with respect to is a von Neumann algebra acting on , generated by M and , where is the unitary representation of g on . We show that . We compute moments and cumulants of operators in . By doing that, we can verify that there is a close relation between Group Freeness and Amalgamated Freeness under the crossed product. As an application, we can show that if is the free group with N-generators, then the crossed product algebra satisfies that , whenerver .
TL;DR: In this article, the authors characterize self-analytic mappings and operator-valued analytic mappings which generate weighted composition operators and invertible weighted composition operator on the spaces (G, E) and the Banach algebra of all bounded linear operators on a Banach space E.
Abstract: Let V be an arbitrary system of weights on an open connected subset G of and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let (G, E) and (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings and operator-valued analytic mappings which generate weighted composition operators and invertible weighted composition operators on the spaces (G, E) and (G, E) for different systems of weights V on G. Also, we obtained compact weighted composition operators on these spaces for some nice classes of weights