R~n上一类半线性椭圆方程解的存在唯一性和渐近性质

用上下解方法和位势估计，研究Rn上具有次线性项加超线性项半线性椭圆方程给出了其有界正解的存在性、唯一性和渐近性质，其中为常数，参数．     

牛顿对光与颜色的研究

详细叙述了牛顿在１６６５－１６７５年间对光和颜色的研究过程，阐明牛顿从原来看到光谱带有五种颜色到认为光谱带有七种颜色的转变，论述了这种转变的原因     

A dynamical strategy for approximation methodsUne stratégie dynamique pour les méthodes d'approximation

The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one. To cite this article: F. Jézéquel, C. R. Mecanique 334 (2006).     

风险企业的委托-代理模型

传统的委托—代理理论在解释风险企业家的行为时遇到了困难。通过对传统的委托—代理理论进行重新构造和拓展，本提出逆反努力法则，验证了隐藏行动的道德风险的存在，并通过Newton迭代法和图形学方法对风险企业家的长期努力水平进行计算，发现努力水平对努力效应指数n表现出协同效应。     

Inexact primal-dual interior point iteration for linear programs in function spaces

Motivated by a simple optimal control problem with state constraints, we consider an inexact implementation of the primal-dual interior point algorithm of Zhang, Tapia, and Dennis. We show how the control problem can be formulated as a linear program in an infinite dimensional space in two different ways and prove convergence results.The research of this author was supported by an Overseas Research Scholarship of the Ministry of Education, Science and Culture of Japan.The research of this author was supported by National Science Foundation grants #DMS-9024622 and #DMS-9321938, North Atlantic Treaty Organization grant #CRG 920067, and an allocation of computing resources from the North Carolina Supercomputing Program.The research of this author was supported by North Atlantic Treaty Organization grant #CRG 920067.     

Inexact Interior-Point Method

In this paper, we introduce an inexact interior-point algorithm for a constrained system of equations. The formulation of the problem is quite general and includes nonlinear complementarity problems of various kinds. In our convergence theory, we interpret the inexact interior-point method as an inexact Newton method. This enables us to establish a global convergence theory for the proposed algorithm. Under the additional assumption of the invertibility of the Jacobian at the solution, the superlinear convergence of the iteration sequence is proved.     

The Newton Polygon and Elliptic Problems with Parameter

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].     

A Global Optimization Algorithm using Lagrangian Underestimates and the Interval Newton Method

Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure.     

A PARALLEL COMPUTATION SCHEME FOR IMPLICIT RUNGE-KUTTA METHODS AND THE ITERATIVELY B-CONVERGENCE OF ITS NEWTON ITERATIVE PROCESS

In this paper, based on the implicit Runge-Kutta(IRK) methods, we derive a class of parallel scheme that can be implemented on the parallel computers with Ns(N is a positive even number) processors efficiently, and discuss the iteratively B-convergence of the Newton iterative process for solving the algebraic equations of the scheme, secondly we present a strategy providing initial values parallelly for the iterative process. Finally, some numerical results show that our parallel scheme is higher efficient as N is not so large.     

On the existence of <Emphasis Type="Italic">F</Emphasis>-crystals

Let (N,F) be an F-isocrystal, with associated Newton vector ν in . To any lattice M in N (an F-crystal) is associated its Hodge vector in . By Mazur's inequality we have . We show that, conversely, for any with , there exists a lattice M in N such that . We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains. Received: March 1, 2002