Showing papers in "Journal of The Korean Mathematical Society in 2003"
TL;DR: In this paper, the Finite Presentation Theorem was proved for singular data on an ambient algebraic scheme, which describes the total aggregate of the trees of infinitely near singular points, including all possible successions of permissible blowing-ups toward the reduction of singularities.
Abstract: The notion of infinitely near singular points, classical in the case of plane curves, has been generalized to higher dimen- sions in my earlier articles ((5), (6), (7)). There, some basic tech- niques were developed, notably the three technical theorems which were Dierentiation Theorem , Numerical Exponent Theorem and Ambient Reduction Theorem (7). In this paper, using those results, we will prove the Finite Presentation Theorem, which the auther believes is the first of the most important milestones in the gen- eral theory of infinitely near singular points. The presentation is in terms of a finitely generated graded algebra which describes the total aggregate of the trees of infinitely near singular points. The totality is a priori very complex and intricate, including all pos- sible successions of permissible blowing-ups toward the reduction of singularities. The theorem will be proven for singular data on an ambient algebraic shceme, regular and of finite type over any perfect field of any characteristics. Very interesting but not yet apparent connections are expected with many such works as ((1), (8)).
45 citations
TL;DR: In this article, the study of proper holomorphic rational mappings between balls in dierent dimen- sions relates to positivity conditions and isometric imbedding of holomorphic bundles.
Abstract: This article discusses in detail how the study of proper holomorphic rational mappings between balls in dierent dimen- sions relates to positivity conditions and to isometric imbedding of holomorphic bundles. The first chapter discusses rational proper mappings between balls; the second chapter discusses seven distinct positivity conditions for real-valued polynomials in several complex variables; the third chapter reveals how these issues relate to an iso- metric imbedding theorem for holomorphic vector bundles proved by the author and Catlin.
34 citations
TL;DR: In this paper, a density with integrability on the space (0, T; ) for some and T > 0 was assumed, and the supremum of the density is finite and the infimum of density is positive in the domain.
Abstract: In this paper, we assume a density with integrability on the space (0, T; ) for some and T > 0. Under the assumption on the density, we obtain a regularity result for the weak solutions to the compressible Navier-Stokes equations. That is, the supremum of the density is finite and the infimum of the density is positive in the domain (0, T). Moreover, Moser type iteration scheme is developed for norm estimate for the velocity.
33 citations
TL;DR: In this article, an approximation result was given for the case of almost complex manifolds, which is a generalization of the Poletsky theory of disc theory to complex manifold, and was shown to be equivalent to the result in this paper.
Abstract: We prove an approximation result, and we get a new proof of the main result in (7). I hope that this new proof may be a step towards a generalization of the Poletsky theory of discs to the case of almost complex manifolds. 1. A general question (to be made more precise) The general question, vaguely stated, is: Is every map from the unit disc into a complex manifold, with small @, close to a genuine holomor- phic map? In the study of Poletsky discs, and having possible generalizations in mind (see (8) and Section 7 below), the following question arises natu- rally. Let M be a complex manifold, equipped with some metric, and let › be a relatively compact region in M. For every † > 0, does there exist - > 0 such that if u is a map from the unit disc ¢ (in C) into ›, with j@uj • -, then there exists a homomorphic map h : ¢ ! › such that (abusing notations) jh i uj < †? For the application, it is absolutely essential that no bound be given on @u, and that no shrinking of the disc be allowed. If we added the hypothesis j@ujM, then the existence (but not an estimate!) of -, depending on ›;† and M, would result immediately from a normal family argument, arguing by contradiction. The answer to the above question is negative in general, as was shown to me by L. Lempert. His example is natural and embarrassingly simple. Take M any compact Riemann surface of genus ‚ 2, and › = M. See
29 citations
TL;DR: The Funk transform as discussed by the authors is defined by integrating a func- tion on the two-sphere over its great circles, and complex anal- ysis are used to invert this transform.
Abstract: The Funk transform is defined by integrating a func- tion on the two-sphere over its great circles. We use complex anal- ysis to invert this transform.
29 citations
TL;DR: In this paper, the authors introduce new notions of Ricci-like tensors and many kind of curvature-like (conformal) tensors such as concir-cular, projective, or conformal curvature tensors defined on semi-Riemannian manifolds.
Abstract: In this paper we introduce new notions of Ricci-like tensor and many kind of curvature-like tensors such that concir- cular, projective, or conformal curvature-like tensors defined on semi-Riemannian manifolds. Moreover, we give some geometric conditions which are equivalent to the Codazzi tensor, the Weyl tensor, or the second Bianchi identity concerned with such kind of curvature-like tensors respectively and also give a generalization of Weyl's Theorem given in (18) and (19).
27 citations
TL;DR: By forming completions of families of noncommuta-tive polynomials, a notion of non-commutative continuous functions and locally bounded Borel functions was defined in this article.
Abstract: By forming completions of families of noncommuta- tive polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncom- mutative analogue of the functional calculus for elements of com- mutative C*-algebras and von Neumann algebras. These notions give a precise meaning to C*-algebras defined by generator and re- lations and we show how they relate to many parts of operator and operator algebra theory.
22 citations
TL;DR: In this article, a twisted q-L-series which interpolates twisted qgeneralized Bernoulli numbers is presented. But the number of polynomials and numbers are not described explicitly.
Abstract: The aim of this work is to construct twisted q-L-series which interpolate twisted q-generalized Bernoulli numbers. By using generating function of q-Bernoulli numbers, twisted q-Bernoulli numbers and polynomials are defined. Some properties of this polynomials and numbers are described. The numbers is also given explicitly.
19 citations
TL;DR: In this article, it was shown that every domain in a separable Hilbert space, which has a C 2 smooth strongly pseudocon- vex boundary point at which an automorphism orbit accumulates, is biholomorphic to the unit ball of the domain.
Abstract: We show in this paper that every domain in a separable Hilbert space, say H, which has a C 2 smooth strongly pseudocon- vex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of H. This is the complete gener- alization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz (10) and subsequent improvement of Byun/Gaussier/Kim (3) in the infinite dimensions.
19 citations
TL;DR: In this paper, the continuity of the commutators of the Littlewood-Paley operators on Herzhardy spaces has been shown for certain Hardy and Herz-Hardy spaces.
Abstract: In this paper, the continuity for the commutators of Littlewood-Paley operators on certain Hardy and Herz-Hardy spaces are obtained.
19 citations
TL;DR: In this article, it was shown that the Mann iteration method with errors converges strongly to a unique fixed point of the smooth Banach space and is almost T-stable on K. The results presented in this paper generalize the results in [l]-[7], [20] and others.
Abstract: Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.
TL;DR: In this paper, the authors established a link between the study of completely integrable systems of partial differential equations and the work of generic submanifolds and provided the set of symmetries of such a system with a Lie group structure.
Abstract: We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in . Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.
TL;DR: In this article, strongly pseudoconvex handlebodies in whose center is a quadratic strongly pseudo-convex domain with an attached flat Lagrangian disc or plane were constructed.
Abstract: We construct strongly pseudoconvex handlebodies in whose center is a quadratic strongly pseudoconvex domain with an attached flat Lagrangian disc or plane.
TL;DR: In this article, the authors discuss how the dynamics of certain birational maps of the real plane can be studied using complex methods, such as complex methods of complex geometry and geometry.
Abstract: In this paper we discuss how the dynamics of certain birational maps of the real plane may be studied using complex methods.
TL;DR: In this paper, the Young type inequality is proved for a fixed function h, where h is a class of convolu- tion transforms f! f ⁄ h, and h = 1 2x Z R2 e i 1 2 x u 2+y2 uy + yu x f(u)h(y)dudy;x 2 R+ as integral operators.
Abstract: For a fixed function h we deal with a class of convolu- tion transforms f ! f ⁄ h, where (f ⁄ h)(x) = 1 2x Z R2 e i 1 2 x u 2+y2 uy + yu x f(u)h(y)dudy;x 2 R+ as integral operators Lp(R+;xdx) ! Lr(R+;xdx); p;r ‚ 1. The Young type inequality is proved. Boundedness properties are in- vestigated. Certain examples of these operators are considered and inversion formulas in L2(R+;xdx) are obtained.
TL;DR: In this article, the authors show that the Iwahori-Hecke algebra and the quantum superalgebra have commuting actions on the tensor product space, and determine the centralizer of each other.
Abstract: 【The Iwahori-Hecke algebra $H_{k}$ ( $q^2$ ) of type A acts on the k-fold tensor product space of the natural representation of the quantum superalgebra (equation omitted) $_{q}$ (gl(m, n)). We show the Hecke algebra $H_{k}$ ( $q^2$ ) and the quantum superalgebra (equation omitted) $_{q}$ (gl(m n)) have commuting actions on the tensor product space, and determine the centralizer of each other. Using this result together with Gyoja's q-analogue of the Young symmetrizers, we construct highest weight vectors of irreducible summands of the tensor product space.t space.】
TL;DR: In this paper, the authors introduce the general concepts of generalized multiobjective game, generalized weight Nash equi- libria and generalized Pareto equilibria, and prove the existence of generalized pareto equilibrium in non-compact generalized multi-objective games.
Abstract: In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equi- libria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik (5) and Kim-Tan (6), we shall prove the exis- tence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equi- libria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.
TL;DR: In this paper, a maximal commutative k-subalgebra of matrix algebra is constructed, which is neither a C1-construction nor a C2 -construction.
Abstract: Let (B;mB;k) be a maximal commutative k-subalgebra of Mm(k). Then, for some element z 2 Soc(B), a k-algebra R = B(X;Y )=I, where I = (mBX;mBY;X 2 i z;Y 2 i z;XY ) will cre- ate an interesting maximal commutative k-subalgebra of a matrix algebra which is neither a C1-construction nor a C2-construction. This construction will also be useful to embed a maximal commu- tative k-subalgebra of matrix algebra to a maximal commutative k-subalgebra of a larger size matrix algebra.
TL;DR: In this paper, the existence of solutions for over-determined PDE systems that admit prolongation to a complete system is studied, and the integrability conditions are expressed in terms of the coecients of the original system.
Abstract: We study the existence of solutions for overdetermined PDE systems that admit prolongation to a complete system. We reduce the problem to a Pfaan system on a submanifold of the jet space of unknown functions and then express the integrability conditions in terms of the coecients of the original system. As possible applications we present some local problems in CR ge- ometry: determining the CR embeddibility into spheres and the existence of infinitesimal CR automorphisms.
TL;DR: A vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds is established.
Abstract: We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.
TL;DR: A collection of similarly defined similarly defined such sequences which give rise to intriguingly different results are investigated.
Abstract: A number of variants of Hofstadter's original sequence have been investigated. Here we investigate a collection of similarly defined such sequences which give rise to intriguingly different results.
TL;DR: In this article, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism f 2 Aut(M)o ‰ Aut(m), o 2 M, is equal to the expression of a corresponding element of the homogeneous model.
Abstract: It is known that the CR geometries of Levi non-degen- erate hypersurfaces in C n and of the elliptic or hyperbolic CR sub- manifolds of codimension two in C 4 share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism f 2 Aut(M)o ‰ Aut(M), o 2 M, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this prop- erty, an extension theorem for CR maps is obtained.
TL;DR: All the conjugate points along the geodesics on N are characterized and the quaternionic Heisenberg group equipped with a left-invariant metric is characterized.
Abstract: Let N be the quaternionic Heisenberg group equipped with a left-invariant metric. We characterize all the conjugate points along the geodesics on N:
TL;DR: In this article, the authors describe changes of the structure of the holomorphic automorphism group of a bounded domain in C n under small perturbation of this domain in the Hausdorff metric.
Abstract: The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in C n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in C n does not exceed n.
TL;DR: In this article, the surface wave of an incompressible fluid passing over a small bump is studied and a forced KdV equation for surface wave is derived without assuming that flow is uniform at far upstream.
Abstract: We study the surface waves of an incompressible fluid passing over a small bump. A forced KdV equation for surface wave is derived without assuming that flow is uniform at far upstream. New types of steady solutions are discovered numerically. Two new cut o values of Froude number are found, above the larger of which two symmetric solutions exist and under the smaller of which two dierent symmetric solutions exist.
TL;DR: In this paper, it was shown that every order on every two-generator subgroup of a locally soluble orderable group G is central, and that G is locally nilpotent.
Abstract: G; 1: Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.
TL;DR: In this article, it was shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction and if one of Q or D is compact, then so is the other, and Q and D are strict contraction.
Abstract: It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T 2⁄ T 2 i 2T ⁄ T + I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict contraction.
TL;DR: In this article, some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given and applications for quadrature rules with values in Hilbert space are also pointed out.
Abstract: Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.
TL;DR: In this article, the authors studied the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4], and they were connected to the algebraic property of the Bergman kernel and the Szego kernel.
Abstract: In this paper we study the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szego kernel. We characterize the non-degenerate doubly connected canonical domains.
Journal Article•
TL;DR: In this article, the authors study the problem of finding projective structures on 3-manifolds and show that the 2-dimensional problem can be reduced to solving a system of homogeneous equations that are in product forms of scalar triple products of vectors.
Abstract: Geometric structures on 3-manifolds are often projectively flat structures. Projectively flat structures on 3-manifolds are given by atlases of charts to RP 3 with projective transition maps. Equivalently, they are given by projectively flat torsion-free connections. We study the question of putting projective structures on 3-manifolds. This is done by triangulating a given 3-manifold, and then reducing the question to a 2-dimensional classical projective geometry problem produced by the Haken diagram of the 3-manifold. Next, we show that the 2-dimensional problem can be reduced to solving a system of homogeneous equations that are in product forms of scalar triple products of vectors. Finally, we will compute the deformation spaces of projective structures on a small class of 3-orbifolds. Sullivan and Thurston [12] posed a question if every closed 3-manifold admits some analytic structures, in particular, projective structures. We aim to reduce the question of finding geometric structures on 3manifolds, in particular projective structures, to that of solving systems of polynomial equations, and finally to solve them. We succeed in the first part. The second part should be much harder. We may find obstructions to the existence of projective structures on 3-manifolds; however, we do not know of any obstructions to the existence presently. A projective structure on an n-manifold is given as a maximal atlas of charts to RP with projective transition maps between the charts. One can also think of a projective structure as a torsion-free projectively flat connection on a manifold. A projective structure on a manifold gives rise to notions of geodesics, totally geodesic submanifolds, and other projective local invariants as prescribed by the charts. Received July 29, 2002. 2000 Mathematics Subject Classification: Primary 57M50.