解非线性多点边值问题的一类拟牛顿法

(一)引言 考虑非线性多点边值问题 x=f(x,t) t_1≤t≤t_m (1.1) g(x(t_1),…,x(t_m)=0 t_1相似文献   

变系数线性系统的一种求解方法及若干可积类型

<正>对线性系统dx/dt=(?)(t)=A(t)x(t)=(a_(ij)(t))x(t)(x∈R~n,i,j=1,2,     

一类新的乘子法

一 增广Lagrange式和算法 本文考虑一般的非线性规划问题(P):min{f(x)|gi(x)≤0,i=1,2,…r;gi(x)=0,i=r+1,…,m}。假定其中函数f,gi:R~n→R~i,i=1,2,…,m,且是连续可微的。建立相应的增广Lagrange式:     

几类非光滑精确罚函数中控制参数的界的估计

精确罚函数方法是数学规划中求解带约束优化问题的一种重要方法,其本质在于利用精确罚函数的性质把原带约束优化问题转化成一个无约束优化问题或带简单约束优化问题求解.考虑一般的非线性规划问题:(?) f(x),(P)s.t.g_i(x)≤0,i=1,2,…,m,h_j(x)=0,j=1,2,…,l.其中 X 是 R~n 中的非空子集.     

互助-竞争型扩散反应方程解的渐近性质

含有n个物种的生态问题中,要研究如下形式的定解问题:其中ΩR~n是开区域,x=(x_1,…,x_n),a_i<0(i=1,…,m).[1]中讨论了m=2的竞争情形,即a_(ij)<0(i≠j,i,j=1,2)。[2]中讨论了m=3且是第二边     

变分流方程组初边值问题的Blow—up性质

§1 引言及主要结果设 Q 是 R~n 中具有光滑边界(?)Ω的有界区域,考虑抛物变分流方程组((?)u~i)/((?)t)=sum from α=1 to n (?)/((?)X_α) F_(?)(x,u,Du)-F_u~i(x,u,Du) (1)((x,t)∈Ω×[0,T),i=1,2,…,N)的第一初边值问题(?)以及第三初边值问题     

广义拟Newton法及其收敛性定理

1引言设R~n.R_+n.R_+~n分别表示Euclidean空间及R~n的非负和正子空间：符号┃·┃表示向量或矩阵的2-范数，非线性互补问题（NLCP）     

一类混合型时滞微分差分比较原理

在研究中立型系统解的性质时,遇到如下一类混合型时滞微分差分不等式:其中x∈R~m,y∈R~n,X(t)(?)_Sup x(t+θ)(常数r>0),y(t)的含意类似;f:R~+×R~M×R~m×R~n×R~n→R~m,g:R~+×R~m×R~m×R~n×R~n→R~n,并且f(t,α,β,γ,ξ)关于β,γ,ξ单调不减,关于α为非对角线不减(即对于a_1~(1)=α_i~(2),α_j~(1)≤a_j~(2),有f_i(t,a~(1),β,γ,ξ)≤f_i(t,a~(2),β,γ,ξ),i≠j(i,j=1,2,…,m)),g(t,α,β,γ,ξ)满足相同的条件。D(x)表示x(t)的Dini导数。     

The Dirichlet Problem for a Class of Quasilinear Elliptic Equations of Second Order

In this paper,we consider the Dirichlet problem for the quasilinear ellipticequation sum from i=1 to n D_i[a_i(x,Du)]+f(x,u)=0 in Ω, u=0 on Ω,where Ω R~n is a bounded domain. Let p_i>1(i=1,2,…,n),p~*=max p_i and let 1≤i≤n     

非线性互补问题的L1模算法

非线性互补问题(记作NCP(F))定义为求x∈R~n,满足X≥0,F(x)≥0且X~гF(x)=0。其中F:R~n→R~n。本文假设F(x)是一阶连续可微的。 引人映射H:R~n→R~n,其中H的第i个分量H_i(x)=min(x_i,F_i(x))及其L_1模函数 θ(x)=sum from i=1 to n |min(x_i,F_i(x)|设全集I={1,2,…,n},定义其子集: I_f(x)={i|F_i(x)0}, I(x)={i|F_i(x)=x_i},I_f(x)={i|F_i(x)相似文献   

A Characterization of the Fermat Point in Hilbert Spaces

This paper studies the Fermat point in Hilbert spaces for a system of n distinct points. We prove the existence of the Fermat point and we determine its location in the convex hull of the given system of points. A new concept of Fermat point for a non–discrete set of points is introduced and there are proved similar results to discrete case. In the second part of this paper we give close form formulas of Fermat point for a system of 3 and 4 distinct points. We also describe some iterative methods to find the Fermat point for a system of more than 4 distinct points.     

On “Pre-historic” Linear Programming and the Figure of the Earth

In this paper, we develop algorithms to solve generalized Fermat–Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.     

Exact Location of the Weighted Fermat–Torricelli Point on Flat Surfaces of Revolution

We find the exact location of the weighted Fermat–Torricelli point of a geodesic triangle on flat surfaces of revolution (circular cylinder and circular cone) in the three dimensional Euclidean space by applying a cosine law of three circular helixes which form a geodesic triangle on a circular cylinder, an explicit solution of the corresponding weighted Fermat–Torricelli point in the dimensional Euclidean space by calculating some lengths of geodesic arcs and angles and by using some lengths of straight lines on a circular cone which connect the vertices of the geodesic triangle with the vertex of the circular cone.     

Generalized Fermat, double Fermat and Newton sequences

In this paper, we discuss the relationship among the generalized Fermat, double Fermat, and Newton sequences. In particular, we show that every double Fermat sequence is a generalized Fermat sequence, and the set of generalized Fermat sequences, as well as the set of double Fermat sequences, is closed under term-by-term multiplication. We also prove that every Newton sequence is a generalized Fermat sequence and vice versa. Finally, we show that double Fermat sequences are Newton sequences generated by certain sequences of integers. An approach of symbolic dynamical systems is used to obtain congruence identities.     

Transport economies of scale and firm location

This paper studies the impact of economies of scale in transportation on a firm’s location decision. We relate the location problem to weighted Fermat problems and ramified optimal transportation problems and analyze how transport technologies affect the firm’s transportation and location choices. It is found that in general when the level of transport economies of scale is high, the firm locates its factory in the interior of the Weber triangle with a branching transport structure. Two examples are constructed to illustrate how interactions between transport technology and production technology would affect the firm’s input purchase and factory location.     

Prime witnesses in the Shor algorithm and the Miller-Rabin algorithm

We prove that prime witnesses in the Miller-Rabin algorithm coincide with those in the Shor algorithm which satisfy the condition of Fermat’s little theorem. We describe the set of natural numbers, whose prime witnesses in the Miller-Rabin algorithm coincide with those in the Shor algorithm. We find all such numbers less than 100,000,000 and experimentally study the rate of increase of the ratio of the quantity of such numbers to the quantity of Carmichael numbers.     

An interior proximal linearized method for DC programming based on Bregman distance or second-order homogeneous kernels

Abstract

We present an interior proximal method for solving constrained nonconvex optimization problems where the objective function is given by the difference of two convex function (DC function). To this end, we consider a linearized proximal method with a proximal distance as regularization. Convergence analysis of particular choices of the proximal distance as second-order homogeneous proximal distances and Bregman distances are considered. Finally, some academic numerical results are presented for a constrained DC problem and generalized Fermat–Weber location problems.     

Fermat Quotients over Function Fields

IfPis an irreducible element of a polynomial ring over a finite field, then one can define a Fermat quotient function associated toP. This is the direct analog of the traditional Fermat quotient function defined over the rational numbers using Fermat's “little” theorem. This paper provides answers for several of the central questions about the Fermat quotients over function fields.     

度量空间中有限点集的费马点

本文首先对紧致的度量拓扑空间证明了有限点集的费马点是存在的，其次，运用度量几何的经典方法考察了度量空间（包括双曲空间和Ｂａｎａｃｈ空间）中有限点集的费马点的唯一性，此外，还对ｎ维欧氏空间Ｅ＾ｎ中有限点集的费马作了进一步研究。     

Mathematical features of the Calculus

The fundamental theorems of the calculus describe the relationships between derivatives and integrals of functions. The value of any function at a particular location is the definite derivative of its integral and the definite integral of its derivative. Thus, any value is the magnitude of the slope of the tangent of its integral at that position, and any two subtracted values are the area under its derivative. The slope formula of secant lines actually is the mean value theorem for the derivative function in addition to representing the well-known Fermat definition of the derivative. The sine and other functions are discussed.