Showing papers on "Generalization published in 1968"

Control of large-scale dynamic systems by aggregation

Abstract: A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.

Asymptotically Optimal Bayes and Minimax Procedures in Sequential Estimation

Abstract: In [4] we introduced a general method for obtaining asymptotically pointwise optimal procedures in sequential analysis when the cost of observation is constant The validity of this method in both estimation and testing was established in [4] for Koopman-Darmois families, and in [5] for the general case Section 2 of this paper generalizes Theorem 21 of [4] to cover essentially the case of estimation with variable cost of observation In Section 3 we show that in estimation problems, under a very weak condition, for constant cost of observation, the asymptotically pointwise optimal rules we propose are optimal in the sense of Kiefer and Sacks [9] The condition given is further investigated in the context of Bayesian sequential estimation in Section 4 and is shown to be satisfied if reasonable estimates based on the method of moments exist In Section 5 we consider the robustness of our rules under a change of prior The main result of this section is given by Theorem 51 Finally Theorem 52 deals with a generalization of Wald's [12] theory of asymptotically minimax rules and an application of that theory to the Bayesian model

A generalization of the Popov criterion

Abstract: A criterion for the stability of control systems which contain an arbitrary finite number of memoryless nonlinearities is considered. The criterion is such that the degree of stability may be specified, and such that for the case when the absolute stability of a control system having one memoryless nonlinearity is considered, it reduces to the original Popov criterion.

A generalization of the chromatic number

Abstract: One of the most widely studied concepts in graph theory is that of the colouring of graphs. Much of the research in this area has dealt with the chromatic number χ(G) of a graph G, defined as the minimum number of colours which can be assigned to the points of G so that adjacent points are coloured differently. One can obtain a natural generalization of this concept as follows: we define the n-chromatic number χn (G) to be the smallest number of colours which one can associate with the points of G so that not all points on any path of length n are coloured the same. The 1-chromatic number is then simply the chromatic number.

Generalization of the ''Schwarzschild surface'' to arbitrary static and stationary metrics.

Abstract: A generalization of the r = 2m ``Schwarzschild surface'' is defined for static metrics which are not necessarily spherically symmetric. This surface exhibits simultaneously the properties of being a ``one‐way membrane'' for causal propagation and of being a surface of infinite red shift. The necessary and sufficient condition that these two phenomena take place on the same surface in an arbitrary stationary metric is also obtained. The distinctions between the static and stationary cases are shown to be essential by examples from the Kerr metric.

On the quadratic convergence of a generalization of the jacobi method to arbitrary matrices

Abstract: A method of diagonalizing a general matrix is proved to be ultimately quadratically convergent for all normalizable matrices. The method is a slight modification of a method due to P. J. Eberlein, and it brings the general matrix into a normal one by a combination of unitary plane transformations and plane shears (non-unitary). The method is a generalization of the Jacobi Method: in the case of normal matrices it is equivalent to the method given by Goldstine and Horwitz.

Linear relationships in growth and size studies.

Abstract: Linear relationships between sets of variates measured on organisms are discussed. The effect of assumptions about departures of observed values from hypothetical values according with the relationships are dealt with in detail for the bivariate case. In the multivariate case existence of more than one relationship is discussed, and attention is drawn to various ways relationships may arise in practice. Interpretation is considered, and a proposed multivariate generalization of the allometry concept is examined.

A generalization of esseen's inequality and its application in probabilistic number theory

Abstract: We prove a generalization of Esseen's inequality on the estimation of the difference between distribution functions in terms of the difference between their characteristic functions. The generalization holds without any restrictions on the distributions in question. The result is applied to the refinement of the limit theorems connected with the distribution of values of arithmetical functions.

A note on a general expansion of functions of binary variables

Abstract: In this note a general expansion of functions of binary variables is presented, which has been obtained from our study of pattern recognition. We show that this result may be taken as a generalization of some well-known expansions.

On Concatenative Decompositions of Regular Events

Abstract: —Finding simple or "canonical representations" for regular events is one of the important problems concerning finite automata. The present paper is an attempt to find concatenative canonical decompositions for regular events. Five different decomposition types of regular events are defined, imustrated by examples, and their properties investigated. The main tool in our investigations is the notion of a decomposition set; it is a generalization of the notion of a decomposition state, introduced by the authors in a previous paper.[7]Let A =(S, M, s 0 , F) be a finite automaton; a subset S⊂S is a decomposition set if A goes through a state of S whenever it accepts a tape. In order to determine whether a given subset S⊂S is a decomposition set one has to check only tapes whose length is not greater than |S|-|S|-1, where |S| and |S| are the number of states in S and S, respectively. Thus, one can deternine all decomposition sets of A. The knowledge of the decomposition sets of A enables one to determine whether and in what form T(A), the set of tapes accepted by A, is decomposable.

The Study of One-Speed Multiregion Transport Problems in Plane Geometry by the Method of Boundary Sources

Abstract: This paper presents a method for solving multiregion transport problems which is a generalization of integral transport theory as typified by the well-known Amouyal-Benoist-Horowitz method. The the...

Generalization of Tests for Certain Properties of Variable-Length Codes

Abstract: In a 1964 report, Riley had already indicated how to generalize the Sardinas/Patterson and Levenshtein theorems for per word errorless models to special per word substitution error models and it seemed obvious to Calabi that the same kind of theorems should hold for general per word substitution error models. This paper established such theorems; as usual, more ideas were introduced and more technical tools were created. The paper relies very heavily on the fact that our models insure the expandability of our code properties. Such expandability is essential for the tests.

On the linear conjecture in the deterministic and stochastic stability of discrete systems

Abstract: Some generalization of Aizerman's conjecture for deterministic and stochastic stability of discrete systems is considered in this correspondence. Presented theorems are concerned with the verification of this conjecture.