Showing papers in "Bulletin of The Korean Mathematical Society in 2009"
TL;DR: This work presents a scheme for multi-authority CP-ABE, proposes the first two constructions that fully implement the scheme, and proves their security against chosen plaintext attacks.
Abstract: In classical encryption schemes, data is encrypted under a single key that is associated with a user or group. In Ciphertext-Policy Attribute-Based Encryption(CP-ABE) keys are associated with attributes of users, given to them by a central trusted authority, and data is en- crypted under a logical formula over these attributes. We extend this idea to the case where an arbitrary number of independent parties can be present to maintain attributes and their corresponding secret keys. We present a scheme for multi-authority CP-ABE, propose the first two constructions that fully implement the scheme, and prove their security against chosen plaintext attacks.
106 citations
TL;DR: In this paper, it was shown that a semiprime right Goldie ring R is weak Armendariz if and only if Q is a direct product of division rings.
Abstract: In the present note we study the properties of weak Armen- dariz rings, and the connections among weak Armendariz rings, Armen- dariz rings, reduced rings and IFP rings. We prove that a right Ore ring R is weak Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result we can show that a semiprime right Goldie ring R is weak Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP if and only if Q is a nite direct product of division rings, obtaining a simpler proof of Lee and Wong's result. In the process we construct a semiprime ring extension that is innite dimensional, from given any semiprime ring. We next nd more examples of weak Armendariz rings.
56 citations
TL;DR: In this paper, the authors considered linear Weingarten hyper-surface in a sphere and obtained some rigidity theorems, which were extended by Cheng-Yau (3) and Li (7).
Abstract: In this paper, we have considered linear Weingarten hyper- surfaces in a sphere and obtained some rigidity theorems. The purpose of this paper is to give some extension of the results due to Cheng-Yau (3) and Li (7).
46 citations
TL;DR: In this paper, the authors developed the idea of a generalized upper set in a BE-algebra and considered these sets in the context of transitive and self-distributional BE algebras and their ideals.
Abstract: In this paper, we develop the idea of a generalized upper set in a BE-algebra. Furthermore, these sets are considered in the context of transitive and self distributive BE-algebras and their ideals, providing characterizations of one type, the generalized upper sets, in terms of the other type, ideals.
40 citations
TL;DR: In this paper, the authors consider the question of when the products of composition and differentiation are bounded and compact on Bloch and little Bloch spaces and show that they are bounded.
Abstract: We will consider the questions of when the products of composition and differentiation are bounded and compact on Bloch and little Bloch spaces.
31 citations
TL;DR: In this article, the authors give necessary and sucient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E.
Abstract: A matrix P 2C n◊n is called a generalized reflection matrix if P ⁄ = P and P 2 = I. An n◊n complex matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = iPAP). It is well-known that the reflexive and anti-reflexive matrices with respect to the generalized reflection matrix P have many special properties and widely used in engineering and sci- entific computations. In this paper, we give new necessary and sucient conditions for the existence of the reflexive (anti-reflexive) solutions to the linear matrix equation AXB + CY D = E and derive representation of the general reflexive (anti-reflexive) solutions to this matrix equation. By using the obtained results, we investigate the reflexive (anti-reflexive) solutions of some special cases of this matrix equation.
29 citations
TL;DR: In this article, the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation were analyzed and two critical exponents q1,q2 2 (0,+1) with q1 < q2 were revealed.
Abstract: This paper deals with the critical blow-up and extinction ex- ponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents q1,q2 2 (0,+1) with q1 < q2. In other words, when q belongs to dierent intervals (0,q1),(q1,q2),(q2,+1), the solution possesses complete dierent prop- erties. More precisely speaking, as far as the blow-up exponent is con- cerned, the global existence case consists of the interval (0,q2). However, when q 2 (q2,+1), there exist both global solutions and blow-up so- lutions. As for the extinction exponent, the extinction case happens to the interval (q1,+1), while for q 2 (0,q1), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = q1 is concerned, the other parameter ‚ will play an im- portant role. In other words, when ‚ belongs to dierent interval (0 ,‚1) or (‚1,+1), where ‚1 is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely dierent properties.
27 citations
TL;DR: In this paper, the authors studied surfaces of revolution without par- abolic points in a Euclidean 3-space whose Gauss map G satisfies the condition that h G = AG,A 2 Mat(3,R), where h denotes the Laplace op- erator of the second fundamental form h of the surface and Mat( 3,R) the set of 3-dimensional real matrices.
Abstract: In this article, we study surfaces of revolution without par- abolic points in a Euclidean 3-space whose Gauss map G satisfies the condition ¢ h G = AG,A 2 Mat(3,R), where ¢ h denotes the Laplace op- erator of the second fundamental form h of the surface and Mat(3,R) the set of 3◊3-real matrices, and also obtain the complete classification the- orem for those. In particular, we have a characterization of an ordinary sphere in terms of it.
26 citations
TL;DR: In this article, the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-archimedean normed spaces is studied.
Abstract: We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.
22 citations
19 citations
TL;DR: In this paper, the authors mainly discuss factorable surfaces in 3D Minkowski space and give classification of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
Abstract: In this paper, we mainly discuss factorable surfaces in 3dimensional Minkowski space and give classification of such surfaces whose mean curvature and Gauss curvature satisfy certain conditions.
TL;DR: In this article, the authors studied the hyperbolic cosine and sine laws in the extended de Sitter space, which is an analytic continuation of the original Hyperbolic Space.
Abstract: We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. And we also study the spherical cosine and sine laws in the extended de Sitter space which con- tains de Sitter space S n as a subset and is also an analytic continuation of de Sitter space. In fact, the extended hyperbolic space and extended de Sitter space are the same space only dier by i1 multiple in the met- ric. Hence these two extended spaces clearly show and apparently explain that why many corresponding formulas in hyperbolic and spherical space are very similar each other. From these extended trigonometry laws, we can give a coherent and geometrically simple explanation for the various relations between the lengths and angles of hyperbolic polygons, and rela- tions on de Sitter polygons which lie on S 2 1 , and tangent laws for various polyhedra.
TL;DR: In this article, a generalization of the rotation surface in a Minkowski space is studied and examples of new classes of helicoidal surfaces with constant mean curvature in a 3-space are provided.
Abstract: The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.
TL;DR: In this paper, the authors define a quarter symmetric metric connection in an al- most r-paracontact Riemannian manifold and consider invariant, non- invariant and anti-invariant hypersurfaces.
Abstract: We define a quarter symmetric metric connection in an al- most r-paracontact Riemannian manifold and we consider invariant, non- invariant and anti-invariant hypersurfaces of an almost r-paracontact Rie- mannian manifold endowed with a quarter symmetric metric connection.
TL;DR: In this paper, the ridgelet transform is extended to the space of square integrable Boehmians, and it is proved that the extended R is consistent with the classical R, linear, one-to-one, onto and both R,R i1 are continuous with respect to convergence and convergence.
Abstract: The ridgelet transform is extended to the space of square integrable Boehmians. It is proved that the extended ridgelet transform R is consistent with the classical ridgelet transform R, linear, one-to-one, onto and both R,R i1 are continuous with respect to --convergence as well as ¢-convergence.
TL;DR: Relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can been solved within a polynomial time is investigated.
Abstract: Cryptographic protocols depend on the hardness of some computational problems for their security. Joux brie∞y summarized kno- wn relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time (6). In this paper, we investigate additional relations between them. First- ly, we show that the computational Di-e-Hellman assumption implies the bilinear Di-e-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a flxed inversion of a bilinear map with homomor- phic property is impossible. Finally, we remark that a self-bilinear map proposed in (7) is not essentially self-bilinear.
TL;DR: The notion of generalized derivation was introduced by Chang and Lin this article, who considered the problem of finding a non-commutative Lie ideal of R for an associative ring with center Z(R).
Abstract: Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that u s H(u)u t = 0 for all u 2 L, where s ‚ 0,t ‚ 0 are fixed integers. Then H(x) = 0 for all x 2 R unless char R = 2 and R satisfies S4, the standard identity in four variables. Let R be an associative ring with center Z(R). For x,y 2 R, the commutator xyiyx will be denoted by (x,y). An additive mapping d from R to R is called a derivation if d(xy) = d(x)y + xd(y) holds for all x,y 2 R. A derivation d is inner if there exists a 2 R such that d(x) = (a,x) holds for all x 2 R. An additive subgroup L of R is said to be a Lie ideal of R if (u,r) 2 L for all u 2 L, r 2 R. The Lie ideal L is said to be noncommutative if (L,L) 6 0. Hvala (8) introduced the notion of generalized derivation in rings. An additive mapping H from R to R is called a generalized derivation if there exists a derivation d from R to R such that H(xy) = H(x)y+xd(y) holds for all x,y 2 R. Thus the generalized derivation covers both the concepts of derivation and left multiplier mapping. The left multiplier mapping means an additive mapping F from R to R satisfying F(xy) = F(x)y for all x,y 2 R. Throughout this paper R will always present a prime ring with center Z(R), extended centroid C and U its Utumi quotient ring. It is well known that if ‰ is a right ideal of R such that u n = 0 for all u 2 ‰, where n is a fixed positive integer, then ‰ = 0 (7, Lemma 1.1). In (2), Chang and Lin consider the situation when d(u)u n = 0 for all u 2 ‰ and u n d(u) = 0 for all u 2 ‰, where ‰ is a nonzero right ideal of R. More precisely, they proved the following: Let R be a prime ring, ‰ a nonzero right ideal of R, d a derivation of R and n a fixed positive integer. If d(u)u n = 0 for all u 2 ‰, then d(‰)‰ = 0 and if u n d(u) = 0 for all u 2 ‰, then d = 0 unless R » M2(F), the 2◊2 matrices over a field F of two elements.
TL;DR: In this paper, the authors prove the local existence of classical solutions of quasi-linear integrodifierential equations in Banach spaces by using fractional powers of operators and the Schauder flxed-point theorem.
Abstract: We prove the local existence of classical solutions of quasi- linear integrodifierential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder flxed- point theorem. An example is provided to illustrate the theory.
TL;DR: In this article, the regularity properties of a class of semilinear integrodierentia l functional dierential equations were analyzed and the Lipschitz continuity and uniform boundedness of the nonlinear term can be considerably weakened.
Abstract: This paper deals with the regularity properties for a class of semilinear integrodierentia l functional dierential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given. Let H and V be two complex Hilbert spaces such that V is a dense subspace of H. Identifying the antidual of H with H we may consider V ‰ H ‰ V ⁄ . In this paper we deal with the approximate controllability for the semilinear equation in H as follows. (SE) ( d dt x(t) = Ax(t) + R t 0 k(t i s)g(s,x(s),u(s))ds + Bu(t),
TL;DR: In this article, the univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained, and relevant connections of the results presented in this paper, with various other known results are also pointed out.
Abstract: In this paper, univalence of a certain integral operator and some interesting properties involving the integral operators on the classes of complex order are obtained. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.
TL;DR: In this paper, a generalized difierential operator is used to intro-duce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships.
Abstract: Making use of a generalized difierential operator we intro- duce some new subclasses of multivalent analytic functions in the open unit disk and investigate their inclusion relationships. Some integral pre- serving properties of these subclasses are also discussed.
TL;DR: In this article, it was shown that every generalized Jordan triple higher derivation on a 2-torsion free semiprime ring is a generalized Jordan derivation, which is a generalization of the original derivation.
Abstract: In this paper we prove that every generalized Jordan triple higher derivation on a 2-torsion free semiprime ring is a generalized higher derivation. This extend the main result of (9) to the case of a semiprime ring. 1. Introduction and preliminaries Let R be an associative ring not necessarily with identity element. A deriva- tion (resp. Jordan derivation) of R is an additive map d : R i! R such that d(xy) = d(x)y + xd(y) for all x,y 2 R (resp. d(x 2 ) = d(x)x + xd(x) for all x 2 R). Obviously, every derivation is a Jordan derivation. The converse is in general not true. Herstein (6) proved that the converse is true on a 2-torsion free prime ring. Subsequently, Cusack and Bresar independently extended this re- sult to the case of a 2-torsion free semiprime ring in (4) and (2), respectively. The following two definitions are corresponding to derivations and Jordan deriva- tions, respectively. One is a common extension of derivation, and another is a generalization of Jordan derivation. An additive map µ : R i! R is called a generalized derivation of R if there exists a derivation d of R such that µ(xy) = µ(x)y + xd(y) for all x,y 2 R. d is called an associated derivation of µ. An additive map µ : R i! R is called a generalized Jordan derivation of R if there exists a Jordan derivation d of R such that µ(x 2 ) = µ(x)x + xd(x) for all x 2 R. The map d is called an associated Jordan derivation of µ. When R is a 2-torsion free ring, this definition is equivalent to saying that there exists
TL;DR: In this paper, the authors considered semi-discrete Gauge-Uzawa finite element method (GU-FEM) to solve the Navier-Stokes equations.
Abstract: The Gauge-Uzawa finite element method (GU-FEM)[3] is a fully discrete projection type method to solve the evolution Navier-Stokes equations, which overcomes many shortcomings of projection methods and displays superior numerical performance. Since Gauge-Uzawa is consistent with Navier-Stokes equations, it can be applied easily to more complicate fluid problems [4,6] and the normal mode solution shows full accuracy without spurious boundary layer term for smooth solutions in contrast other projection type methods [7]. In addition, it is an unconditionally stable scheme [3]. However, we have only suboptimal accuracy via the energy estimate which has been proved in [3]. In this paper, we consider semi-discrete Gauge-Uzawa method to prove optimal convergence via energy estimate: ∥u(tⁿ?¹)-uⁿ?¹∥?≤C T and a distinctive result ∥u(tⁿ?¹)-uⁿ?¹∥₁+∥p(tⁿ?¹)-pⁿ?¹∥?≤C T .
TL;DR: In this article, the relations between ideals, filters, reg- ular congruences and normal congruence in inclines were studied and it was shown that for any incline, there are a one-to-one correspondence between all ideals and all regular con-gruences.
Abstract: This paper studies the relations between ideals, filters, reg- ular congruences and normal congruences in inclines. It is shown that for any incline, there are a one-to-one correspondence between all ideals and all regular congruences and a one-to-one correspondence between all filters and all normal congruences.
TL;DR: In this article, the authors studied the topological properties of a collection of prime ideals in 2-primal near-rings and showed that the spectrum of prime ideal ideals is a compact space and Max(N), the maximal ideal of N, forms a compact T1-subspace.
Abstract: In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact T1-subspace. We also study the zero-divisor graph iI(R) with respect to the completely semiprime ideal I of N. We show that iP(R), where P is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph iP(R).
TL;DR: In this article, a generalized Riemann problem of the first order hyperbolic conservation laws is considered and a unique piecewise smooth solution u = u(t, x) is presented.
Abstract: In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution u = u(t, x), and this solution has a structure similar to the similarity solution u = of the correspondin Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth.
TL;DR: In this article, the authors established generalizations of classical Dixon's theorem for the series 3F2, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan.
Abstract: The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series 3F2, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series 2F1 obtained earlier by Lavoie, Grondin, and Rathie.
TL;DR: In this article, two algorithms to determine the domain of attraction by using the moment matrices are presented. And as an application, they consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method.
Abstract: The domain of attraction of a nonlinear dierential equations is the region of initial points of solution tending to the equilibrium points of the systems as the time going. Determining the domain of attraction is one of the most important problems to investigate nonlinear dynamical systems. In this article, we first present two algorithms to determine the domain of attraction by using the moment matrices. In addition, as an application we consider a class of SIRS infection model and discuss asymptotical stability by Lyapunov method, and also estimate the domain of attraction by using the algorithms.
TL;DR: In this paper, it was shown that the first eigenvalue of Dirac operator can be improved via a well-chosen divergence-free symmetric tensor (DSS) tensor.
Abstract: We proved in (10) that Friedrich's estimate (5) for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.