一类2阶边值问题的分歧点

本文考虑以下２阶边值问题：其中．在关于Ａ，Ｂ；Ｐ，Ｑ，ｆ的一定条件下，证明了以上问题存在分歧点．所用的主要工具是Ｋｒａｓｎｏｓｅｌｓｋｉｉ的局部分歧定理与ＫｒｅｉｎＲｕｔｍａｎ定理．     

关于一类连续最优控制问题的一种可实现的离散方法

本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法，此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象，文中给出这种做法的理论证明和实现方案。     

Deterministic optimal control,given only a partial observation of the initial state

The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex ₀. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx ₀ and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations.     

A characterization of the logistic distribution by a sample median

Summary A functional form of the characteristic function of the sample median of three variates is shown to characterize the logistic distribution. A consequence of this is a characterization of the logistic in terms of the Laplace distribution. Research sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant No. AFOSR-77-3360. The United States Govenment is authorized to reproduce and distribute reprints for governmental purposes notwith-standing any copyright notation hereon.     

On the monotonicity of the power functions of tests based on traces of multivariate beta matrices

It is shown that for the MANOVA problem the power function of the test based on the trace of a multivariate beta matrix is monotonically increasing in each noncentrality parameter provided that the cutoff point is not too large. This result is also true for the problem of testing independence of two sets of variates.     

A survey of multicriteria optimization or the vector maximum problem,part I: 1776–1960

In this survey, the history of the subject from 1776 until 1960 is presented. A brief biographical sketch of Vilfredo Pareto is given first. Then, the more or less simultaneous development of the concepts of utility, preference, and welfare theory follows, with results which go back to Hausdorff and Cantor. A brief discussion of the work of Borel and von Neumann as initiators of game theory is included. Each of these areas has developed enough to warrant its own survey; hence, they are reviewed here only insofar as they provide necessary foundations. Thereafter, the concepts of efficiency, vector maximum problem, and Pareto optimality are reviewed in connection with production theory, programming, and economics. The survey is presented within a unified mathematical framework, and the emphasis is on mathematical results, rather than psychological or socio-economic discussion. To enable the reader to draw conclusions without having to obtain each article himself, the results have been presented in somewhat more detail than usual.     

order and disorder lines in systems with competing interactions: II. The IRF model

Systems with competing interactions can be often exactly solved on a restricted subspace of the parameter space, called an order or disorder trajectory. A simple method introduced within the transfer matrix formalism allows for the calculation of the free energy and spin-spin correlation functions along the order and disorder lines of the Ising model with all possible interactions around a face of the square lattice (IRF model). The general eight-vertex model is thoroughly examined and shows full analogy with the quantum spin chain results of the previous paper.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, 1088 Budapest, Puskin U. 5–7, Hungary.     

Orientational deconvolution of two-dimensional static disorder by a Tikhonov regularized method for 2H solid state NMR of nano-tubular-oriented structures

A general trend of supramolecular chemistry is the building of mesoscopic-oriented nanotubes. When the typical radius of the channel almost fits the mean supramolecular cross-sectional radius, the guest supramolecule is ultraconfined in the channel. In that case, only rotational disorder around the channel axis is allowed. For sufficiently low temperatures, we expect this 2D disorder to be static on the NMR timescale, and it should reflect the local symmetry of the channels. In this article, we show that experiments performed with deuterium single crystal solid-state NMR as a function of rotation around the channel axis may lead to important information concerning the static orientational disorder of the confined supramolecules. Using an inversion method with Tikhonov regularization and a positivity constraint, that also takes into account of the nonideal pulse sequence response, the orientational probability density can be obtained from 1D experiments performed at different angles, even for significant disorder. As a first step, the method is validated on four different theoretical distributions. It is then applied to ²H NMR single crystal experiments performed on an archetype of parallel channels intergrowth compounds: selectively deuterated 1,10-decanedicarboxylic diacids in hydrogenated urea channels. The diacids form one-dimensional infinite hydrogen-bonded chains ultraconfined in urea linear channels.     

Stochastic methods for Dirichlet problems

Using an equivalent expression for solutions of second order Dirichlet problems in terms of Ito type stochastic differential equations, we develop a numerical solution method for Dirichlet boundary value problems. It is possible with this idea to solve for solution values of a partial differential equation at isolated points without having to construct any kind of mesh and without knowing approximations for the solution at any other points. Our method is similar to a recently published approach, but differs primarily in the handling of the boundary. Some numerical examples are presented, applying these techniques to model Laplace and Poisson equations on the unit disk. Visiting Professor, Universidad de Salamanca.