10720150
Regularization of controllability problems and observability problems for distributed parameter systems of parabolic type
The purpose of this paper is to investigate the controllability problem and the observability problem for a distributed parameter system of parabolic type. For a distributed parameter system of parabolic type, both problems are not well-posed in general. A well-posed approximation method which regularizes the problems is presented. The method is analyzed under the assumption that the system is controllable at time T and observable at time T.
116446833
Design of Servomechanism for Distributed Parameter Systems
Abstract In this paper a servomechanism problem is investigated for a distributed parameter system of parabolic type. The servomechanism problem considered here is to design a feedback control system such that the controlled output will tend to a desired constant reference vector as t→∞. Under some assumptions with respect to a control operator and an output operator we present the sufficient conditions for the existence of a feedback controller which stabilizes and regulates the system. From a practical and applicable point of view, a design procedure of a servomechanism is presented which can be realized by "finite dimensional" theories and techniques for "infinite dimensional" systems. In the design procedure it is necessary to construct a finite dimensional state observer in order to estimate the system state from measurements.
121539902
Branching processes in the presence of random immigration and representations for time series
The statistics of branching processes of particles in a multiplicative medium are developed by taking account of a random non-stationary particle immigration. The probability distribution functions of the number of particles found in the medium at any fixed time and/or of particles counted in a time interval are given in closed form. Also given are conditional probabilities, conditioned on having a fixed number of particles at time t=0. These are applied to the case that exactly two particles are produced by branching.
116940747
A generalization of Dold-Thom's isomorphism theorem for the homotopy groups with coefficients.
121946651
Homotopy groups with coefficients and a generalization of Dold-thom's isomorphism theorem, I
121149837
A Theorem on Weak Homotopy Equivalences
118014139
Non-immersion theorems for lens spaces. II