MULTIPLE POINTS OF IMMERSIONS OF M~6■R~7

In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobordant to P 2 and 7-fold point manifold are odd number.     

The Noncommutative Residue about Witten Deformation

In this paper, we compute lower dimensional volumes Vol_4~((1,1)) and Vol_6~((2,2)) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.     

GENERIC WARPED PRODUCT SUBMANIFOLDS OF LOCALLY CONFORMAL KEAHLER MANIFOLDS

Warped product manifolds are known to have applications in physics. For instance, they provide an excellent setting to model space-time near a black hole or a massive star （cf. [9]）. The studies on warped product manifolds with extrinsic geometric point of view were intensified after the B.Y. Chen＇s work on CR-warped product submanifolds of Kaehler manifolds （cf. [6], [7]）. Later on, similar studies were carried out in the setting of 1.c.K. manifolds and nearly Kaehler manifolds （el. [3], [11]）. In the present article, we investigate a larger class of warped product submanifolds of 1.c.K. manifolds, ensure their existence by constructing an example of such manifolds and obtain some important properties of these submanifolds. With regard to the CR-warped product submanifold, a special case of generic warped product submanifolds, we obtain a characterization under which a CR-submanifold is reducesd to a CR-warped product submanifold.     

Modular Invariance and Anomaly Cancellation Formulas in Odd Dimension Ⅱ

By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.     

THE LIMIT SET OF A CONTINUOUS SELF-MAP OF THE TREE

Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.     

THE COMPUTATION OF CENTER MANIFOLDS AND HOPF TRAJECTORIES

In this paper, we use a kind of main part symmetry scheme to study the center manifolds and Hop f bifurcations for ODEs, and set up a kind of method for calculation them.     

Smoothness of invariant manifolds and foliations for infinite dimensional random dynamical systems Dedicated to Professor Shantao Liao

In this paper, we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces. We discuss on the effect of temperedness and the spectral gaps in the nonuniform pseudo-hyperbolicity so as to prove the existence of invariant manifolds and invariant foliations, which preserve the C~(N,τ(ω))Holder smoothness of the random system in the space variable and the measurability of the random system in the sample point. Moreover, we also prove that the stable foliation is C~(N-1,τ(ω))in the base point.     

EXPONENTIAL CONVERGENCE OF SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

In this paper,we propose a Sample Average Approximation(SAA)method for a class ofStochastic Mathematical Programs with Complementarity Constraints(SMPCC)recentlyconsidered by Birbil,Gürkan and Liste[3].We study the statistical properties of obtainedSAA estimators.In particular we show that under moderate conditions a sequence of weakstationary points of SAA programs converge to a weak stationary point of the true problemwith probability approaching one at exponential rate as the sample size tends to infinity.To implement the SAA method more efficiently,we incorporate the method with sometechniques such as Scholtes' regularization method and the well known smoothing NCPmethod.Some preliminary numerical results are reported.     

CONVERGENCE OF NEWTON＇S METHOD FOR A MINIMIZATION PROBLEM IN IMPULSE NOISE REMOVAL

Recently, two-phase schemes for removing salt-and-pepper and random-valued impulse noise are proposed in [6, 7]. The first phase uses decision-based median filters to locate those pixels which are likely to be corrupted by noise (noise candidates). In the second phase, these noise candidates are restored using a detail-preserving regularization method which allows edges and noise-free pixels to be preserved. As shown in [18], this phase is equivalent to solving a one-dimensional nonlinear equation for each noise candidate.One can solve these equations by using Newton‘s method. However, because of the edgepreserving term, the domain of convergence of Newton‘s method will be very narrow. In this paper, we determine the initial guesses for these equations such that Newton‘s method will always converge.     

On 1-connected 8-manifolds with the Same Homology as S~3×S~5

In this article, we classify 1-connected 8-dimensional Poincaré complexes, topological manifolds and smooth manifolds whose integral homology groups are isomorphic to those of S~3× S~5. A topic related to a paper of Escher and Ziller is also discussed.     

CONVERGENT AND DIVERGENT SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR DIFFERENCE SYSTEM

In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form (?)xn+1=anxn+bnf(yn), yn=cnyn-1+dng(xn). We classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can he applied to certain difference systems.     

RESEARCH ANNOUNCEMENTS ON “RIGIDITY OF THURSTON'S SPHERE PACKINGS ON3-DIMENSIONAL MANIFOLDS”

正1 Introduction and Main Results In the study of hyperbolic metrics on 3-dimensional manifolds,Thurston (see [9],Chapter 13) introduced Thurston's circle packing on surfaces,which allows the circles to intersects with non-obtuse angles and is a natural generalization of the tangential circle packing studied by Andreev [1,2] and Koebe [6].Thurston further proved the Andreev-Thurston theorem,     

EXACT SOLUTIONS OF (2+1)-DIMENSIONAL NONLINEAR SCHRöDINGER EQUATION BASED ON MODIFIED EXTENDED TANH METHOD

In this paper, the modified extended tanh method is used to construct more general exact solutions of a(2+1)-dimensional nonlinear Schr¨odinger equation.With the aid of Maple and Matlab software, we obtain exact explicit kink wave solutions, peakon wave solutions, periodic wave solutions and their 3D images.     

CHARACTER, DENSITY AND CELLULARITY OF L-FUZZY TOPOLOGICAL SPACES

In this paper we generalize the notions of weight,character, density and cellularity of topological spaces to L-fuzzy topogical spaces. We prove theorems corresponding to some of usual theorems. In particular we generalize Hewitt-Marczewski-Pondiczery theorem on the density of the product of topological spaces to the case of L-fuzzy topological spaces (Theorem 4. 4). We also discuss the relations between topological spaces and its induced fuzzy topological spaces for these cardinal functions.     

Orbit configuration spaces of small covers and quasi-toric manifolds

In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.     

某些缩影为棱锥的棱的图式流形同胚类的代表元

In this note, we reported some results of homeomorphic classification of graphlike manifolds of which contractions are edges of pyramids, and the number of vertexes of the base of a pyramid, equal to 6 or 7 or 8.     

A TAILORED FINITE POINT METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS IN HETEROGENEOUS MEDIUM

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm.     

Approximate Inertial Manifolds to the Generalized Symmetric Regularized Long Wave Equations with Damping Term

In the present paper, we construct two approximate inertial manifolds for the generalized symmetric regularized long wave equations with damping term. The orders of approximations of these manifolds to the global attractor are derived.     

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.     

On the bilinear and cubic forms of some symplectic connected sums

Let ( M1 , M2 , N ) be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1#NM2 . In this paper, we consider the bilinear and cubic forms of H* (M1#NM2 , Z) when dim M1#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1#NM2 and M1■M2 .