A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

A generalization of Lagrange's method of undetermined multipliers using zero-zone functionals

A unifying zero-zone function concept extends the Lagrange method of undetermined multipliers to treat both equality and inequality subsidiary conditions. The mathematical formulation is general for restrained function extremization in algebra.     

Existence theorems for lagrange control problems with unbounded time domain

Existence theorems are proved for usual Lagrange control systems, in which the time domain is unbounded. As usual in Lagrange problems, the cost functional is an improper integral, the state equation is a system of ordinary differential equations, with assigned boundary conditions, and constraints may be imposed on the values of the state and control variables. It is shown that the boundary conditions at infinity require a particular analysis. Problems of this form can be found in econometrics (e.g., infinite-horizon economic models) and operations research (e.g., search problems).The author wishes to thank Professor L. Cesari for his many helpful comments and assistance in the preparation of this paper. This work was sponsored by the United States Air Force under Grants Nos. AF-AFOSR-69-1767-A and AFOSR-69-1662.     

Extremum principles for optimal control in normed linear spaces

Extremum principles intended for use in optimal control are derived in the form of necessary conditions and sufficient conditions, formulated in general normed linear spaces. The method of application is illustrated by several examples involving optimal control problems, mathematical programming problems, lumped-parameter systems, and distributed-parameter systems. The basic theorems provide a unified approach which is applicable to a wide variety of problems in open-loop optimal control.     

A second-order Lagrangian condition for restricted control problems

We derive a second-order condition for optimal control problems defined by ordinary differential equations with time-varyingconvex restrictions on controls and with endpoint constraints. This condition generalizes theaccessory minimum problem of the calculus of variations.This research was partially supported by Grant No. MCS 76-06756 of the National Science Foundation.     

On the properties of a periodic fluid

The Born-Green equation is used to clarify and estimate the error introduced into Monte Carlo and molecular dynamics simulations of dense fluids by the use of periodic boundary conditions. This theory is applied to the Lennard-Jones fluid and the theoretical predictions are found to be in reasonable agreement with experiment. The implications for size dependence of pressure, for anisotropy of the radial distribution function, for size dependence of the supercooling limit for crystal nucleation, and for the orientations of nucleated crystals are discussed.This research was supported under grants MPS73-04743 and MPS73-04922 of the National Science Foundation, Washington D.C.     

Synthesis of new nucleoside analogues comprising a methylenecyclobutane unit

Synthesis of eight nucleoside analogues 3-10 with a methylene cyclobutane unit is described. Wittig or Peterson reactions with protected 2-hydroxycyclobutanones 12 and 13 gave E- and Z-derivatives, respectively. After functional modifications the heterocyclic moieties were introduced via a Mitsunobu reaction either on the lateral chain or on the cycle. When adenine was used in this reaction only the N-9 substitution products were obtained. Removal of the protecting groups provided the target products.     

关于人才标准理论与实践的历史考察

从历史角度梳理人才标准的变化脉络,考察各个时代对人才的具体要求以及人才政策的变化,是有益的。不同历史发展阶段对人才素质的不同要求,又往往会产生是重德还是重才的议论和争执。“治平尚德行,有事尚功能”的实践活动标准以及历代选用人才的实践活动,则使德才关系在相互对立中统一起来。