C-cosine Operator Functions and the Second Order Abstract Cauchy Problem

Ｃ－ｃｏｓｉｎｅＯｐｅｒａｔｏｒＦｕｎｃｔｉｏｎｓａｎｄｔｈｅＳｅｃｏｎｄＯｒｄｅｒ　ＡｂｓｔｒａｃｔＣａｕｃｈｙＰｒｏｂｌｅｍＷａｎｇＨａｉｙａｎ（王海燕）（ＤｅｐａｒｔｍｅｔｎｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ，Ｓｏｕｔｈｅａｓｔ...     

On an Error Term Related to the r-th Power of the Euler Totient Function

ＯｎａｎＥｒｒｏｒＴｅｒｍＲｅｌａｔｅｄｔｏｔｈｅｒ－ｔｈＰｏｗｅｒｏｆｔｈｅＥｕｌｅｒＴｏｔｉｅｎｔＦｕｎｃｔｉｏｎＬｉｕＪｉａｎｙａ（刘建亚）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ，２５...     

Stream function finite element solution of Stokes flow with penalties

A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C⁰) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.     

Adjacency on polymatroids

This paper characterizes adjacency for extreme points of a polymatroid. Two extreme points of a polymatroid are adjacent if and only if they either differ in exactly one component or differ in exactly two components with the two components satisfying a certain ordering relation. A polynomial algorithm generates and lists all extreme points adjacent to a given extreme point of a polymatroid. Similar results hold for the core of a convex game.     

Selective lumping finite element method for nearshore current

A finite element method for the analysis of nearshore current, which is one of the principal currents in coastal seas, is presented in this paper. Because the nearshore current is induced by the variable distribution of the surface waves, it is necessary to analyse two main characteristics of the wave, i.e. direction and height. The current can be computed using the resulting wave characteristics. The present method makes it possible to employ procedures for which the same methods of solution are applicable for all basic equations of wave direction, height and current flow. The linear interpolation function is used for the discretization of spatial variables and a selective lumping two step explicit scheme is employed for the numerical integration in time. The numerical solutions obtained are compared with analytical, experimental and observed ones. From these comparative studies, it is concluded that the present finite element method provide a useful tool for the analysis of nearshore current.     

Feigenbaum函数方程的C~∞偶解

本文对Feigenbaum函数方程的一般偶连续解作了一些构造性的研究,进而对任意的 0<λ<1给出了C~∞偶解.     

Controllability of delay systems with restrained controls

Using a geometric growth condition, we characterize both the function space and Euclidean controllability of a nonlinear delay system which has a compact and convex control set. This extends analogous results for ordinary differential systems, and it yields conditions under which perturbed nonlinear delay controllable systems are controllable.This research was supported by the National Aeronautics and Space Administration under Contract No. NSG 1445Now on leave of absence as Professor, Department of Mathematics, University of Jos, Jos, Nigeria.     

Solving the subproblem in the lagrangian dual of separable discrete programs with linear constraints

This note presents an efficient method for the routine solution of the subproblem associated with the Lagrangian dual of discrete programming problems having separable non-linear objective function and linear constraints. An additional advantage for subgradient methods is described.     

Optimum design of four-bar function generators with minimum variance criterion

The closure equation of a four-bar linkage generally gives a nonzero result, which may be taken as an index of the error in the output for a given input. The actual output can be brought close to the desired value by specifying the mean error permissible in the entire range of operation and by minimizing the variance (standard deviation). The present method differs from the closed-form synthesis (i.e., precision-point synthesis), in the sense that it does not limit the number of precision points. The results show that the present method compares well with other methods.