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Showing papers in "Journal of The Korean Mathematical Society in 2005"


Journal ArticleDOI
TL;DR: In this paper, the authors studied the Ricci tensor invariance of the Riemannian curvature tensor of the Kenmotsu manifold, which is derived from the almost contact Ricci manifold with some special conditions.
Abstract: The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

90 citations


Journal ArticleDOI
TL;DR: In this article, the authors introduced the notion of pointwise 1-type Gauss map of the first and second kinds and studied surfaces of revolution with such Gauss maps, and proved that the right cone is the only rational surface of revolution having such a map.
Abstract: In this article, we introduce the notion of pointwise 1-type Gauss map of the first and second kinds and study surfaces of revolution with such Gauss map. Our main results state that surfaces of revolution with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only rational surfaces of revolution with pointwise 1-type Gauss map of the second kind.

84 citations


Journal ArticleDOI
TL;DR: In this article, the authors classify N(•)-contact metric manifolds which sat- isfy Z(»;X) ¢ Z = 0, Z( «;X] ¢ R = 0 or R(»,X) ǫ = 0.
Abstract: We classify N(•)-contact metric manifolds which sat- isfy Z(»;X) ¢ Z = 0, Z(»;X) ¢ R = 0 or R(»;X) ¢ Z = 0.

74 citations


Journal ArticleDOI
TL;DR: A discrete time is introduced to the model to describe the time between infection of a CD4 + T-cells, and the emission of viral particles on a cellular level to study the effect of the time delay on the stability of the endemically infected equi- librium.
Abstract: In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4 + T-cells, and the emission of viral particles on a cellular level. We study the efiect of the time delay on the stability of the endemically infected equi- librium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution. Mathematical modelling has proven to be valuable in understand- ing the dynamics of HIV-1 infection. By direct application of models to data obtained from experiments in which antiretroviral drugs were given to perturb the dynamical state of infection in HIV-1 infected pa- tients, minimal estimates of the death rate of productively infected cells, the rate of viral clearance and the viral production rate have been ob- tained (1{6). Those models gave so accurate depiction of the virus load which are almost consistent with the actual data. The research of math- ematical models is very helpful for the clinical treatment. Especially, the models of combination therapy provide very important meaning for the cure of HIV. However, infection by HIV-1 and HCV has many puzzling quantitative features. For example, there is an average 10 years between infection with the virus and the AIDS in adults. The reason for this time lag remains largely unknown, although it seems tied to changes in the number of circulating CD4 + T cells. The major target of HIV infection

71 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduced (, )-skew Armendariz rings, which are a generalization of -rigid rings and Armenderiz rings and investigated their properties.
Abstract: For a ring endomorphism and an -derivation , we introduce (, )-skew Armendariz rings which are a generalization of -rigid rings and Armendariz rings, and investigate their properties. A semi prime left Goldie ring is -weak Armendariz if and only if it is -rigid. Moreover, we study on the relationship between the Baerness and p.p. property of a ring R and these of the skew polynomial ring R[x; , ] in case R is (, )-skew Armendariz. As a consequence we obtain a generalization of [11], [14] and [16].

60 citations


Journal ArticleDOI
TL;DR: In this article, the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically im-mersed in Kenmotsu space forms.
Abstract: Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically im- mersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

48 citations


Journal ArticleDOI
TL;DR: This work proves the existence and uniqueness of the solution for fuzzy stochas- tic difierential equation under suitable Lipschitz condition and uses the maximal inequality for fuzzy Stochastic integrals.
Abstract: A fuzzy stochastic difierential equation contains a fuzzy valued difiusion term which is deflned by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochas- tic difierential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

39 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold $(M, π)$ canonically relates the action spectra of different normalized Hamiltonians on the manifold.
Abstract: In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold $(M,\omega)$ canonically relates the action spectra of different normalized Hamiltonians on {\it arbitrary} symplectic manifolds $(M,\omega)$. The natural class of normalized Hamiltonians consists of those whose mean value is zero for the closed manifold, and those which are compactly supported in $\text{Int} M$ for the open manifold. We also study the effect of the action spectrum under the $\pi_1$ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [Oh4].

37 citations


Journal ArticleDOI
TL;DR: In this article, the rank functions for matrices over semirings and their properties are surveyed, including factor rank, row and column rank, term rank, and zero-term rank.
Abstract: Inequalities on the rank of the sum and the product of two matrices over semirings are surveyed. Preferences are given to the factor rank, row and column ranks, term rank, and zero-term rank of matrices over antinegative semirings. During the past century a lot of literature has been devoted to in- vestigations of semirings. Brie∞y, a semiring is essentially a ring where only the zero element is required to have an additive inverse. Therefore, all rings are also semirings. Moreover, among semirings there are such combinatorially interesting systems as the Boolean algebra of subsets of a flnite set(with addition being union and multiplication being intersec- tion), nonnegative integers and reals(with the usual arithmetic), fuzzy scalars(with fuzzy arithmetic), etc. Matrix theory over semirings is an object of much study in the last decades, see for example (9). In particu- lar, many authors have investigated various rank functions for matrices over semirings and their properties, see (1, 3, 6, 7, 8, 12) and references there in. There are classical inequalities for the rank function ‰ of sums and products of matrices over flelds, see, for example (10, 11): The rank-sum inequalities:

37 citations


Journal ArticleDOI
TL;DR: In this paper, the hyponormality of Toeplitz operators on the Bergman space (D) with symbol in the class of functions f + g with polynomials f and g was studied.
Abstract: In this note we consider the hyponormality of Toeplitz operators on the Bergman space (D) with symbol in the class of functions f + g with polynomials f and g

36 citations


Journal ArticleDOI
TL;DR: For weighted sum of a sequence fX;Xn;n ‚ 1g of iden-tically distributed, negatively orthant dependent random variables such that jXj r ;r > 0, has a flnite moment generating function, a strong law of large numbers is established as mentioned in this paper.
Abstract: For weighted sum of a sequence fX;Xn;n ‚ 1g of iden- tically distributed, negatively orthant dependent random variables such that jXj r ;r > 0, has a flnite moment generating function, a strong law of large numbers is established.

Journal ArticleDOI
TL;DR: Cho and Kim as mentioned in this paper gave a sucient condition for a graph with one hole to have competition number one and showed that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial.
Abstract: Let D be an acyclic digraph. The competition graph of D has the same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that (u;x) and (v;x) are arcs of D. The competition number of a graph G, de- noted by k(G), is the smallest number k such that G together with k isolated vertices is the competition graph of an acyclic digraph. It is known to be di-cult to compute the competition number of a graph in general. Even characterizing the graphs with competi- tion number one looks hard. In this paper, we continue the work done by Cho and Kim(3) to characterize the graphs with one hole and competition number one. We give a su-cient condition for a graph with one hole to have competition number one. This gener- ates a huge class of graphs with one hole and competition number one. Then we completely characterize the graphs with one hole and competition number one that do not have a vertex adjacent to all the vertices of the hole. Also we show that deleting pendant vertices from a connected graph does not change the competition number of the original graph as long as the resulting graph is not trivial, and this allows us to construct inflnitely many graph having the same competition number. Finally we pose an interesting open problem.

Journal ArticleDOI
TL;DR: In this paper, the authors use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a (t)x(t) + c(t), x( t - g(t)) + q(t, x, t), x (t - g (t)) has a periodic solution.
Abstract: We use Krasnoselskii's fixed point theorem to show that the nonlinear neutral difference equation with delay x(t + 1) = a(t)x(t) + c(t)x(t - g(t)) + q(t, x(t), x(t - g(t)) has a periodic solution. To apply Krasnoselskii's fixed point theorem, one would need to construct two mappings; one is contraction and the other is compact. Also, by making use of the variation of parameters techniques we are able, using the contraction mapping principle, to show that the periodic solution is unique.

Journal ArticleDOI
TL;DR: In this paper, the authors show that all Sasakian 3-manifolds are pseudo-symmetric spaces of constant type, and that they are homogeneous 3-menifolds.
Abstract: Contact Homogeneous 3-manifolds are pseudo-symmetric spaces of constant type. All Sasakian 3-manifolds are pseudo-symmetric spaces of constant type.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the composition operator is metrically bounded on the holomorphic self-map of the unit ball and the unit sphere, if and only if for some constant C and if it is compact on the Hardy spaces.
Abstract: Let B and S be the unit ball and the unit sphere in , respectively. Let be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\; be a holomorphic self-map of B. Let denote the pull-back measure . In this paper, we prove that the composition operator is metrically bounded on (B) if and only if for some constant C and is metrically compact on if and only if as uniformly in . Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of on the Hardy spaces .

Journal ArticleDOI
TL;DR: In this paper, the authors obtained polynomial representations and formulas of the Fibonacci and Lucas sequences for q = 5 and q = 4, respectively, and showed that the Lucas sequence is a Lucas sequence.
Abstract: In this paper, we obtain some properties of the sequences introduced in [6]. We find polynomial representations and formulas of them. For q = 5, is the Fibonacci sequence is the Lucas sequence .

Journal ArticleDOI
TL;DR: In this article, Park et al. obtained a KKM type theorem, matching theorems, axed point theorem, and a coincidence theorem for open-valued multimaps.
Abstract: Let (X;D;) be a G-convex space and Y a Hausdor� space. Then A c (X;Y ) KO(X;Y ), where A c is an admissible class (due to Park) and KO denotes the class of multimaps having the KKM property for open-valued multimaps. This new result is used to obtain a KKM type theorem, matching theorems, axed point theorem, and a coincidence theorem.

Journal ArticleDOI
TL;DR: In this paper, the authors investigate properties of the entire function of the hyper order less than sharing one value with its k-th derivative, and they show that the properties of such a function can be reduced to
Abstract: In this paper, we investigate some properties of the entire function of the hyper order less than sharing one value CM with its k-th derivative.

Journal ArticleDOI
TL;DR: In this paper, the boundedness of weighted Bergman projection for 1 < p < 1 and non-orthogonal projections for 1 • p − 1 was shown on the upper half-space H of the Eu- clidean n-space.
Abstract: On the setting of the upper half-space H of the Eu- clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < 1 and nonorthogonal projections for 1 • p < 1. Using these results, we show that Bergman norm is equiva- lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we flnd the dual of b 1.

Journal ArticleDOI
TL;DR: In this article, the authors proved the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and studied the asymptotic behavior of the corresponding solutions.
Abstract: In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the TP and CTP operators satisfy Weyl's theorem type results for polynomial-time linear transformations on a Hilbert H into a Hilbert Hilbert H. If A 2 TP, if B ⁄ 2 CTP is isoloid, and if dAB 2 B(B(H) denotes either of the elementary op- erators -AB(X) = AX i XB and 4AB[X] = AXB i X
Abstract: An operator T belonging to the algebra B(H) of bound- ed linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator P 2 B(H) such that TT ⁄ = T ⁄ PT. A posinormal operator T is said to be condi- tionally totally posinormal (resp., totally posinormal), shortened to T 2 CTP (resp., T 2 TP), if to each complex number ‚ there corre- sponds a positive operator P‚ such that j(Ti‚I) ⁄ j 2 = jP 1 2 ‚ (Ti‚I)j 2 (resp., if there exists a positive operator P such that j(T i‚I) ⁄ j 2 = jP 1 2(T i ‚I)j 2 for all ‚). This paper proves Weyl's theorem type results for TP and CTP operators. If A 2 TP, if B ⁄ 2 CTP is isoloid and if dAB 2 B(B(H)) denotes either of the elementary op- erators -AB(X) = AX i XB and 4AB(X) = AXB i X, then it is proved that dAB satisfles Weyl's theorem and d ⁄ satisfles a-Weyl's theorem.

Journal ArticleDOI
TL;DR: In this article, a selection principle in the class of locally compact spaces and its relationship with game the-ory and a Ramseyan partition relation is studied. And a selective version of the game is considered.
Abstract: G. Gruenhage gave a characterization of paracompact- ness of locally compact spaces in terms of game theory ((6)). Start- ing from that result we give another such characterization using a selective version of that game, and study a selection principle in the class of locally compact spaces and its relationships with game the- ory and a Ramseyan partition relation. We also consider a selective version of paracompactness.


Journal ArticleDOI
TL;DR: In this article, it was shown that the ideal µ(M) = P m2M (Rm :R M) = \P2N(M)\V (annR(M))
Abstract: Let R be a commutative ring with identity and let M be an R-module. Then M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N = IM. Let M be a non-zero multiplication R-module. Then we prove the following: (1) there exists a bijection : N(M)\V (annR(M)) i! SpecR(M) and in particular, there exists a bijection : N(M) \ Max(R) i! MaxR(M); (2) N(M) \ V (annR(M)) = Supp(M) \ V (annR(M)), and (3) for every ideal I of R, ((( p I + annR(M))M) :R M) = \P2N(M)\V (annR(M))P: The ideal µ(M) = P m2M (Rm :R M) of R has proved useful in studying multiplication modules. We generalize this ideal to prove the following result: Let R be a commutative ring with identity, P 2 Spec(R), and M a non-zero R-module satisfying

Journal ArticleDOI
TL;DR: In this paper, the authors studied n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and gave conditions in order for such a submanifold to be a tube over a Quaternionic invariant submanivold.
Abstract: The purpose of this paper is to study n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and to give su-cient conditions in order for such a submanifold to be a tube over a quaternionic invariant submanifold.

Journal ArticleDOI
TL;DR: In this paper, the authors study free actions of abelian groups on 3-dimensional nilmanifolds and show that all such actions are completely classi- fled. But they do not consider conjugacy.
Abstract: We study free actions of flnite abelian groups on 3- dimensional nilmanifolds. By the works of Bieberbach and Wald- hausen, this classiflcation problem is reduced to classifying all nor- mal nilpotent subgroups of almost Bieberbach groups of flnite in- dex, up to a-ne conjugacy. All such actions are completely classi- fled.

Journal ArticleDOI
TL;DR: In this article, the disjoint (A 2,D 2 )-pair property of toroidal manifolds and Seifert flbered spaces was shown to hold on genus g 2 Heegaard splittings of compact orientable 3-manifolds.
Abstract: We consider interesting conditions, one of which will be called the disjoint (A 2 ;D 2 )-pair property, on genus g ‚ 2 Heegaard splittings of compact orientable 3-manifolds. Here a Heegaard split- ting (C1;C2;F) admits the disjoint (A 2 ;D 2 )-pair property if there are an essential annulus Ai normally embedded in Ci and an essen- tial disk Dj in Cj ((i;j) = (1;2) or (2;1)) such that @Ai is disjoint from @Dj. It is proved that all genus g ‚ 2 Heegaard splittings of toroidal manifolds and Seifert flbered spaces admit the disjoint (A 2 ;D 2 )-pair property.

Journal ArticleDOI
TL;DR: In this article, it was shown that a weakly one-sided Artinian ring R is weakly duo under each of the fol-lowing conditions: (1) R is semilocal with nil Jacobson radical; (2) R was shown to be locally flnite; and (3) the composition length of R was studied.
Abstract: Yu showed that every right (left) primitive factor ring of weakly right (left) duo rings is a division ring. It is not di-cult to show that each weakly right (left) duo ring is abelian and has the classical right (left) quotient ring. In this note we flrst pro- vide a left duo ring (but not weakly right duo) in spite of it being left Noetherian and local. Thus we observe conditions under which weakly one-sided duo rings may be two-sided. We prove that a weakly one-sided duo ring R is weakly duo under each of the fol- lowing conditions: (1) R is semilocal with nil Jacobson radical; (2) R is locally flnite. Based on the preceding case (1) we study a kind of composition length of a right or left Artinian weakly duo ring R, obtaining that i(R) is flnite and a i(R) R = Ra i(R) = Ra i(R) R for all a 2 R, where i(R) is the index (of nilpotency) of R. Note that one-sided Artinian rings and locally flnite rings are strongly …-regular. Thus we also observe connections between strongly …- regular weakly right duo rings and related rings, constructing avail- able examples.

Journal ArticleDOI
TL;DR: The mapping properties of the Marcinkiewicz integral!-to at some end spaces were studied in this article, where it was shown that!to is a bounded operator from H to H. The results in this note are the extensions of the results obtained by Lee and Rim recently.
Abstract: In this note we give the mapping properties of the Marcinkiewicz integral !-to. at some end spaces. More precisely, we first prove that !-to. is a bounded operator from H() to H (). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of , but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO() to BMO(). The results in this note are the extensions of the results obtained by Lee and Rim recently.