Showing papers in "Journal of The Korean Mathematical Society in 2016"

Fractional calculus operators and their image formulas

Abstract: Abstract. During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.

Local convergence for some third-order iterative methods under weak conditions

Abstract: The solutions of equations are usually found using iterative methods whose convergence order is determined by Taylor expansions. In particular, the local convergence of the method we study in this paper is shown under hypotheses reaching the third derivative of the operator involved. These hypotheses limit the applicability of the method. In our study we show convergence of the method using only the first derivative. This way we expand the applicability of the method. Numerical examples show the applicability of our results in cases earlier results cannot.

Asymptotic behaviors of fundamental solution and its derivatives to fractional diffusion-wave equations

Abstract: Let p(t;x) be the fundamental solution to the problem @ t u = ( ) u; 2 (0; 2); 2 (0;1): If ; 2 (0; 1), then the kernel p(t;x) becomes the transition density of a L evy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t;x) and its space and time fractional derivatives D n ( x) D t I tp(t;x); 8 n2 Z+; 2 (0; ); ; 2 (0;1); where D n x is a partial derivative of order n with respect to x, ( x) is a fractional Laplace operator and D t and I t are Riemann-Liouville fractional derivative and integral respectively.

Computations of spaces of paramodular forms of general level

Abstract: This article gives upper bounds on the number of Fourier- Jacobi coecients that determine a paramodular cusp form in degree two. The level N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.

Asymptotic behaviors of solutions for an aerotaxis model coupled to fluid equations

Abstract: We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.

Automorphisms of the zero-divisor graph over 2 × 2 matrices

Abstract: The zero-divisor graph of a noncommutative ring R, denoted by ( R), is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let R = M2(Fq) be the 2×2 matrix ring over a finite field Fq. In this article, we investigate the automorphism group of ( R).

Classification of order sixteen non-symplectic automorphisms on k3 surfaces

Abstract: In the paper we classify K3 surfaces with non-symplectic automorphism of order 16 in full generality. We show that the fixed locus contains only rational curves and points and we completely classify the seven possible configurations. If the Neron-Severi group has rank 6, there are two possibilities and if its rank is 14, there are five possibilities. In particular if the action of the automorphism is trivial on the Neron-Severi group, then we show that its rank is six.

On graphs associated with modules over commutative rings

Abstract: Let M be an R-module, where R is a commutative ring with identity 1 and let G(V, E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs annf (Γ(MR)), anns(Γ(MR)) and annt(Γ(MR)) to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in annf (Γ(MR)), anns(Γ(MR)) and annt(Γ(MR)). We show that M over R is finite if and only if the metric dimension of the graph annf (Γ(MR)) is finite. We further show that the graphs annf (Γ(MR)), anns(Γ(MR)) and annt(Γ(MR)) are empty if and only if M is a prime-multiplicationlike R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs annf (Γ(MR)), anns(Γ(MR)) and annt(Γ(MR)) are empty if and only if M = R. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

Long paths in the distance graph over large subsets of vector spaces over finite fields

Abstract: Let , the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:

Smoothly embedded rational homology balls

Abstract: In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth $2$-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.

Common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in hilbert space

Abstract: In this paper, we introduce and study an explicit hybrid re- laxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solu- tion is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.

On annihilations of ideals in skew monoid rings

Abstract: According to Jacobson (31), a right ideal is bounded if it con- tains a non-zero ideal, and Faith (15) called a ring strongly right bounded if every non-zero right ideal is bounded. From (30), a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which sat- isfy Property (A) and the conditions asked by Nielsen (42). It is shown that for a u.p.-monoid M and � : M ! End(R) a compatible monoid homomorphism, if R is reversible, then the skew monoid ring RM is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and � : M ! End(R) is a weakly rigid monoid homomorphism, then the skew monoid ring RM has right Property (A).

Gauss maps of ruled submanifolds and applications i

Abstract: As a generalizing certain geometric property occurred on the helicoid of 3-dimensional Euclidean space regarding the Gauss map, we study ruled submanifolds in a Euclidean space with pointwise 1-type Gauss map of the first kind. In this paper, as new examples of cylindrical ruled submanifolds in Euclidean space, we construct generalized circular cylinders and characterize such ruled submanifolds and minimal ruled submanifolds of Euclidean space with pointwise 1-type Gauss map of the first kind.

Deformation rigidity of odd lagrangian grassmannians

Abstract: . In this paper, we study the rigidity under Kahler deforma-tion of the complex structure of odd Lagrangian Grassmannians, i.e., theLagrangian case Gr ω (n,2n+1) of odd symplectic Grassmannians. To ob-tain the global deformation rigidity of the odd Lagrangian Grassmannian,we use results about the automorphism group of this manifold, the Liealgebra of infinitesimal automorphisms of the affine cone of the variety ofminimal rational tangents and its prolongations. 1. IntroductionThe study on deformations of the complex structure of complex manifoldsoriginates with Riemann. One hundred years after Riemann, Kodaira andSpencer developed the deformation theory of higher dimensional compact com-plex manifolds. Kodaira and Spencer showed that an infinitesimal deformationof a compact complex manifold should be represented by the Kodaira-Spencerclass, which is an element of the first cohomology group with coefficients in thesheaf of germs of holomorphic vector fields (see [11] and [12]).Let Sbe a rational homogeneous manifold G/P for a complex simple Liegroup Gand a parabolic subgroup P⊂ G. As a consequence of the Bott-Borel-Weil theorem, H

THE INCOMPLETE GENERALIZED τ-HYPERGEOMETRIC AND SECOND τ-APPELL FUNCTIONS

Abstract: Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols and , we introduce here the family of the incomplete generalized -hypergeometric functions and . The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second -Appell hypergeometric functions and of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

Smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties

Abstract: We construct projective embeddings of horospherical varieties of Picard number one by means of Fano varieties of cones over rational homogeneous varieties. Then we use them to give embeddings of smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties.

Deforming pinched hypersurfaces of the hyperbolic space by powers of the mean curvature into spheres

Abstract: Abstract. This paper concerns closed hypersurfaces of dimension n ≥ 2 in the hyperbolic space H κ of constant sectional curvature κ evolving in direction of its normal vector, where the speed equals a power β ≥ 1 of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and β, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in H κ

Determination of the Fricke families

Abstract: For a positive integer $N$ divisible by $4$, let $\mathcal{O}^1_N(\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $\Gamma^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring $\mathcal{O}^1_N(\mathbb{Q})$ over $\mathbb{Q}$, from which we are able to classify all Fricke families of such level $N$.

On jacobson and nil radicals related to polynomial rings

Abstract: . This note is concerned with examining nilradicals and Jacob-son radicals of polynomial rings when related factor rings are Armendariz.Especially we elaborate upon a well-known structural property of Armen-dariz rings, bringing into focus the Armendariz property of factor rings byJacobson radicals. We show that J(R[x]) = J(R)[x] if and only if J(R) isnil when a given ring R is Armendariz, where J(A) means the Jacobsonradical of a ring A. A ring will be called feckly Armendariz if the factorring by the Jacobson radical is an Armendariz ring. It is shown that thepolynomial ring over an Armendariz ring is feckly Armendariz, in spiteof Armendariz rings being not feckly Armendariz in general. It is alsoshown that the feckly Armendariz property does not go up to polynomialrings. 1. On radicals whenfactor rings are ArmendarizThroughout this note every ring is associative with identity unless other-wise stated. For a ring R, J(R), N ∗ (R), N ∗ (R), N 0 (R) and N(R) denotethe Jacobson radical, the prime radical, the upper nilradical (i.e., sum of allnil ideals), the Wedderburn radical (i.e., the sum of all nilpotent ideals), andthe set of all nilpotent elements in R, respectively. Following [1, p. 130], asubset of R is said to be locally nilpotent if its finitely generated subringsare nilpotent. Also due to [1, p. 130], the Levitzki radical of R, written bysσ(R), means the sum of all locally nilpotent ideals of R. It is well-knownthat N

L 2 harmonic 1-forms on submanifolds with weighted poincaré inequality

Abstract: . In the present note, we deal with L 2 harmonic 1-forms oncomplete submanifolds with weighted Poincar´e inequality. By supposingsubmanifold is stable or has sufficiently small total curvature, we estab-lish two vanishing theorems for L 2 harmonic 1-forms, which are someextension of the results of Kim and Yun, Sang and Thanh, CavalcanteMirandola and Vitorio. 1. IntroductionIt is an interesting problem in geometry and topology to find sufficient con-ditions on the manifold for the space of harmonic k-forms to be trivial.In case of complete orientable stable minimal hypersurfaces, several resultson the nonexistence of L 2 harmonic forms are well-known. Recall that a min-imal hypersurface M in a Riemannian manifold N is said to be stable, if forany η ∈ C ∞0 (M),Z M |∇η| 2 ≥Z M (Ric(ν,ν) +|A| 2 )η 2 , η ∈ C ∞ (1.1) 0 (M),where ν is a unite normal vector field of M, A is the second fundamentalform of M, Ric is the Ricci curvature of N. On the other hand, let M be animmersed hypersurface in Riemannian manifold N, if M satisfies (1.1), we sayM has stability condition. In this case, Palmer [17] proved that the space ofL

Multiplicity results for nonlinear schrödinger-poisson systems with subcritical or critical growth

Abstract: In this paper, we consider the following Schrodinger-Poisson system: 8 < : −△u + u + ��u = µf(u) + |u|p−2u, in , −△� = u2, in , � = u = 0, on @, where is a smooth and bounded domain in R 3 , p ∈ (1,6), �,µ are two parameters and f : R → R is a continuous function. Using some critical point theorems and truncation technique, we obtain three multiplicity results for such a problem with subcritical or critical growth.

Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditions

Abstract: This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirich- let boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determin- ing not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.

On solutions to some nonlinear difference and differential equations

Abstract: . In this paper, we study entire solutions of some nonlineardifference equations and transcendental meromorphic solutons of somenonlinear differential equations. Our results generalize the results due to[11], [17]. 1. Introduction and mainresultWe assume that the reader is familiar with the standard notations and fun-damental results in Nevanlinna theory. For example, we use the followingnotations in value distribution such as T(r,f), m(r,f), N(r,f), S(r,f), whereas usual S(r,f) denotes any quantity satisfying S(r,f) = o{T(r,f)} as r → ∞outside a possible exceptional set of finite logarithmic measure. We refer thereader to the books [3, 6], and [7]. For an element η in complex plane C, we willuse f(z +η) and ∆ η f(z) := f(z +η) −f(z) to denote the shift and differenceof f(z) respectively.As we know, Nevanlinna theory is an efficient tool in the research of complexdifferential theory. It is interesting to use the Nevanlinna theory to studycomplex equation of various types. Many results about complex differenceequations (cf. [1, 2, 4, 5]), complex differential equations (cf. [14]) or complexdifferential-difference equations (cf. [10], [12] and [15]) were rapidly obtained,respectively.In 2004, Yang and Li [15] studied some certain types of nonlinear equations,and proved the following results.TheoremA([15]). Take a positive integer n. Let a,b

A CONVERSE THEOREM ON h-STABILITY VIA IMPULSIVE VARIATIONAL SYSTEMS

Abstract: In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse h-stability theorem of Massera’s type for the nonlinear impulsive systems by employing the t∞-similarity of the associated impulsive variational systems and relations.

Normal eigenvalues in evolutionary process

Abstract: Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a -semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on associated with the -periodic evolutionary process on a Banach space X, where stands for the space of all -periodic continuous functions mapping to X.