Global convergence of slanting filter methods for nonlinear programming

In this paper, we present a general algorithm for nonlinear programming which uses a slanting filter criterion for accepting the new iterates. Independently of how these iterates are computed, we prove that all accumulation points of the sequence generated by the algorithm are feasible. Computing the new iterates by the inexact restoration method, we prove stationarity of all accumulation points of the sequence.     

Resolvents of cone pseudodifferential operators,asymptotic expansions and applications

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.      

The periodic risk model with investment

We consider a periodic risk model with the possibility of investing into a risky asset, given by a geometrical Brownian motion. The aim is to maximize the adjustment coefficient of the risk process. It is shown that the optimal investment strategy only depends on the averaged data of the model and is constant over time. Thus maximizing the adjustment coefficient is a very weak optimization criterion.     

Optimal superconvergent one step quadratic spline collocation methods

We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject classification (2000)  65N35, 65N22     

A partial order in the knot table II

A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.     

X射线光刻胶的研究

合成了甲基丙烯酸缩水甘油酯与甲基丙烯酸氯乙酯和甲基丙烯酸氯乙酯与甲基丙烯酸甲酯共聚物,并研究了该共聚物的分子量分布、结构和热稳定性能。研究了甲基丙烯酸缩水甘油酯与甲基丙烯酸氯乙酯正性X射线光刻胶。该光刻胶具有热稳定性和高分辨率性。最低线幅宽度为0.1μm。     

LONG-TIME CONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR NAVIER-STOKES EQUATIONS

1　IntroductionIn this paper,we firstprovide a generalized difference method for the two-dimension-al Navier-Stokes equations by combining the ideas of staggered scheme[6] and generalizedupwind scheme [4 ] in space,and by backward Euler time-stepping.Then we apply theabstractframework of[7] to prove its long-time convergence.The outline of this paper is as follows:In§ 2 we state the generalized differencemethod.In§ 3 we provide some lemmas.In§ 4 we study the one-sided Lipschitz condi-tio…     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

Limit theorems for random processes with random time substitution

In this paper we prove a theorem on sufficient conditions for the convergence in the Skorokhod space D[0, 1] of a sequence of random processes with random time substitution. We obtain almost sure versions of this theorem.     

A fundamental solution to the Cauchy problem for a fourth-order pseudoparabolic equation

The Cauchy problem for a fourth-order pseudoparabolic equation describing liquid filtration problems in fissured media, moisture transfer in soil, etc., is studied. Under certain summability and boundedness conditions imposed on the coefficients, the operator of this problem and its adjoint operator are proved to be homeomorphism between certain pairs of Banach spaces. Introduced under the same conditions, the concept of a θ-fundamental solution is introduced, which naturally generalizes the concept of the Riemann function to the equations with discontinuous coefficients; the new concept makes it possible to find an integral form of the solution to a nonhomogeneous problem.