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 cobor...     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

A Constrained Optimization Approach for LCP

In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x,y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K-T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem. In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point, However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions: M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method.     

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.     

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.     

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.     

ON EQUILIBRIA AND PERIODIC ORBITS OF COOPERATIVE SYSTEMS IN R~3

In the paper we present new criteria for existence of equilibria and periodic orbits for 3-dimensional systems which are cooperative. Particular attention is given to the relations of equilibria, cycle K and stable manifold of K. Meanwhile, the results of Hirsch [1, Theorem 9] and Jiang [2] are improved.     

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.     

AVERAGE σ-WIDTHS OF THE UNIT BALL OF I_1~∞(R)IN I_2~∞(R)

In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l_1~x (R) inl_2~α (R). The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor (for the σ- linear width) are identified.     

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.     

Existence and bifurcation of integral manifolds with applications

In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved.