On Incomplete Huyghens's Phenomenon for Hyperbolic Equations

Definition For a linear partial differential equation of hyperbolic type,when a set of Cauchy dataυ_1,υ_2,…,υ_n is given on a manifold,if the value of the solution of the Cauchy problem at any point P° bdepends on the valucs υ_(i1),υ(i2),… υ_(ik) only at points in a neighborhood of the intersection of bicharactertic curves passing through P°and the manifold,and if 0<κ相似文献   

Generalized Einstein tensor for a Weyl manifold and its applications

It is well known that the Einstein tensor G for a Riemannian manifold defined by G βα = R βα 1/2 Rδβα , R βα = g βγ R γα where R γα and R are respectively the Ricci tensor and the scalar curvature of the manifold, plays an important part in Einstein's theory of gravitation as well as in proving some theorems in Riemannian geometry. In this work, we first obtain the generalized Einstein tensor for a Weyl manifold. Then, after studying some properties of generalized Einstein tensor, we prove that the conformal invariance of the generalized Einstein tensor implies the conformal invariance of the curvature tensor of the Weyl manifold and conversely. Moreover, we show that such Weyl manifolds admit a one-parameter family of hypersurfaces the orthogonal trajectories of which are geodesics. Finally, a necessary and sufficient condition in order that the generalized circles of a Weyl manifold be preserved by a conformal mapping is stated in terms of generalized Einstein tensors at corresponding points.     

Laplacians and Spectrum for Singular Foliations

The author surveys Connes＇ results on the longitudinal Laplace operator along a （regular） foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator （unbounded） and has the same spectrum in every （faithful） representation, in particular, in L2 of the manifold and L2 of a leaf. The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.     

A GENERALIZED TRANSVERSALITY IN GLOBAL ANALYSIS

E. Zeidler in [10] mentions that transversality is certainly one of the most important concepts of modern mathematics, which provided an answer to the question: when is the preimage of a manifold a manifold. This is the celebrated transversality theorem, which has been applied widely to differential topology and dynamic system in [1,2] and [3].     

SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD

In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds in a Riemannian product manifold.     

半群的模糊内理想

Abstract The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.     

Canonical Foliations of Certain Classes of Almost Contact Metric Structures

The purpose of this paper is to study the canonical foliations of an almost cosymplectic or almost Kenmotsu manifold M in a unified way. We prove that the canonical foliation F defined by the contact distribution is Riemannian and tangentially almost Kahler of codimension 1 and that F is tangentially Kahler if the manifold M is normal. Furthermore, we show that a semi-invariant submanifold N of such a manifold M admits a canonical foliation FN which is defined by the antiinvariant distribution and a canonical cohomology class c（N） generated by a transversal volume form for FN. In addition, we investigate the conditions when the even-dimensional cohomology classes of N are non-trivial. Finally, we compute the Godbillon Vey class for FN.     

ON THE INVARIANT SUBMANIFOLDS OF RIEMANNIAN PRODUCT MANIFOLD

In this paper, the vertical and horizontal distributions of an invariant submanifold of a Riemannian product manifold are discussed. An invariant real space form in a Riemannian product manifold is researched. Finally, necessary and sufficient conditions are given on an invariant submanifold of a Riemannian product manifold to be a locally symmetric and real space form.     

A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

In this paper, a new approach to analyze synchronization of linearly coupled map lattices (LCMLs) is presented. A reference vector x(t) is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue "0" of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s(t) satisfying s(t 1) = f(s(t)) but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each xi(t) for i = 1, ... ,m, but not a solution s(t) satisfying s(t 1) = f(s(t)).     

Harmonic L~p-functions on Complete Riemannian Manifolds

This survey paper concerns some existence theorems of harmonic functions belonging to LP (M), M being a complete Riemannian manifold. It is well known that a function which is analytic and bounded on the whole complex plane must reduce to a constant.This classical result, known as Liouville's theorem, is also true on a higher-dimensional Euclidean spaces. The generalization of this theorem to other Riemannian manifolds is very interesting. Besides its beauty, the proof usally requires sharp estimates which provide deeper understanding of the Laplacian and hence give broad applications to problems in global analysis.The basic problem in this paper is to study how the geometric conditions of a complete Riemannian manifold affect the validity of the Liouville theorem. The paper consists of two parts. Part I describes the results systematically and Part I will be more technical and will contain the detailed proofs of the results given in the first part.     

AN ITERATED-SUBSPACE MINIMIZATION METHODS WITH SYMMETRIC RANK-ONE UPDATING

We consider an Iterated-Subspace Minimization(ISM) method for solving large-scale unconstrained minimization problems.At each major iteration of the method, a two-dimensional manifold, the iterated subspace, is constructed and an approximate minimizer of the objective function in this manifold then determined, and a symmetric rank-one updating is used to solve the inner minimization problem.     

GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered.In fact,this is a generalization of quasi-coincidence of a fuzzy point With a fuzzy set.By using this new idea,the notion of interval valued(∈,∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras,is defined,and related properties are investigated.In particular,the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.     

高维单形的等距共轭点性质初探(英文)

In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.     

A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection

The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition ■(ξ,Y)·■,where ■,■ are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed.     

Hopf Bifurcation of Delayed Predator-prey System with Reserve Area for Prey and in the Presence of Toxicity

A kind of three species delayed predator-prey system with reserve area for prey and in the presence of toxicity is proposed in this paper.Local stability of the coexistence equilibrium of the system and the existence of a Hopf bifurcation is established by choosing the time delay as the bifurcation parameter.Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained by means of the normal form theory and the center manifold theorem.Finally,we give a numerical example to illustrate the obtained results.     

Boundability of Open Manifolds

An open manifold in question is assumed to bea noncompact manifold with compact boundary (probably empty). Let M be a connected open n-dimensional smooth manifold. Take the one-point-compactification of M, it will be denoted by M=M∪{*}, where * is the infinite point. Since M has countable basis, M is metrizable and {*} is a closed subset and a G_δset. By Urysohn lemma, there exists a continuous function f:→[O,1] with f~-1(O)=M and f~-1(1)=*.Choose a sui-     

Global Classical Solutions of the Cauchy Problems for Nonlinear Vorticity Equations and Its Applications

In this paper, the definition of a vortieity equation on a compact Riemannian manifold without boundary is given. Some accurate a priori estimates are obtained with the use of the peculiarity of the equation. Then, the existence and “uniqueness” of global classical solution of the Cauchy problem for the equation is proved. As its application, the existence and “uniqueness” of Cauchy problem for barotropic nondivergent model is obtained. The model is a fundamental one in atmospheric dynamics.     

Projection on Segre varieties and determination of holomorphic mappings between real submanifolds Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.     

REGULARITY OF HARMONIC MAPS INTO POSITIVELY CURVED MANIFOLDS

Let M be a compact Riemannian manifold of dimension m, N a complete Amply connected δ-pinched Riemannian manifold of dimension n. There exists a constant d(n). It is proved that if m≤d(n), then every minimizing map from M into N is smooth in the interior of M. If m=d(n)+1, such a map has at most diserete singular set and in general the Hausdorff dimension of the singular set is at most m-d(n)-1.