Abstract: The high order maximal principle (HMP) which was announced in [11] is a generalization of the familiar Pontryagin maximal principle. By using the higher derivatives of a large class of control vari...

Abstract: Gibbs’ concept of dividing surfaces is supplemented explicitly by the concepts of dividing lines and dividing points. The general forms of the fundamental equations for dividing surfaces and lines are established by considering the proper extensive geometric properties, in addition to area and length. The detailed description of the fluid part of a capillary system by these fundamental equations is used to obtain the general conditions of equilibrium. Proper generalizations of the Laplace equation, the Neumann relation, and the Young equation are derived.

Abstract: A simple proof of the generalization of the theorem of Israel concerning the uniqueness of the Schwarzschild black hole is presented.

Abstract: A generalization of the Buneman variant of cyclic odd–even reduction algorithm for solving finite difference approximations to Poisson’s equations is presented. This generalization places no restriction on the block size, n, of the system and computes the solution in $O(n^2 \log _2 n)$ operations.

Abstract: Relational productions provide a mathematically tractable formal model for operators in discrete systems. Two paradigms for the inductive learning of such operators are considered: before-and-after situation pairs and situation sequences. An operational theory for the generalization of productions for these paradigms is then developed, based on previous work in concept induction. This theory has been computer implemented. In examples three "blocks world" operators are learned from six before-and-after pairs and also from a sequence of fifteen blocks world situations. A transformational grammar learning example of Hayes-Roth is repeated with an improvement in speed of two orders of magnitude.

Abstract: This paper is concerned with constructing observers for linear feedback control laws. Two types of observers (Kalman-type and Luenberger-type) are considered concurrently. Geometric theory of dynamic covers is developed for evaluating the minimal orders of observers. New lower and upper bounds are obtained for the minimal order of function observers possessing an arbitrarily prescribed set of poles. They are expressed simply in terms of observability indices of an augmented system and give a new light on the structural properties of observers. They also suggest the possibility of significant order reduction compared with observers estimating the whole state. A new geometric concept of generator, a natural generalization of cyclic generator, plays a key role in their derivation. A frequency domain characterization of observers is derived which reveals an interesting algebraic property of observers. It is used for devising a design algorithm in the frequency domain; in which the problem is reduced to pole assignment by dynamic compensator of a restricted type. Another design algorithm is presented in the time domain. Some illustrative examples are shown.

Abstract: The first half of this paper describes and contrasts two well known measures of power in voting systems. The second half develops an explanatory model for a generalization of the Shapley-Shubik measure.

Abstract: A generalization of the Ramsey theorem is stated. This solves a problem of P. Erdös and others. The result has recent applications in the theory of ultrafilters and model theory. The Ramsey theorem [3] states: For all positive integers k,m,p there exists an n such that for every coloring c: [n] —• k, there exists a homogeneous m set, I Ç n , \\M\\ = m, with \\c([M]P)\\= 1. This can be generalized to set systems of a given type and to set systems without forbidden subsystems. The purpose of this note is to announce this result. A family A = (Ô,.; i E I), 8, > 1, is called a type. (X, M) = (X, (M,; i E ƒ)) is a set system of type A if MzÇ [X] * and X is a finite ordered set. ƒ: (X, M) + (Y9 N) = (Y, (fy; / E ƒ)) is called an embedding if f: X * Y is a monotone 1-1 mapping and f(M) E Ut *=* M E M,for every i E I. (X, M) is a subsystem of (Y, M) if the inclusion X ÇY is an embedding. Denote by Emb (A, B) the set of all embeddings A —•> B and by Set (A) the category of all set systems of type A and all embeddings. The following holds: THEOREM. Let a type A be fixed. Let k be a positive integer and A E Set(A). Then for every B E Set(A) there exists C E Set(A) such that the following holds: for every coloring c: Emb (A, C) —• k there exists a subsystem B' of C which is isomorphic to B such that \\c(Emb(A9B'))\\ = 1. Moreover, if B does not contain a fundamental set system D, then C may be chosen with the same property. Here D = (X, M) is fundamental if for every i EI either M/ = 0 or Mt=[X} . This generalizes the Ramsey theorem and has the following consequences: COROLLARY 1. For every graph G = (V, E) without a complete graph with k-vertices, there exists a graph H = (W, F) without a complete subgraph AMS (MOS) subject classifications (1970). Primary 05A99; Secondary 04A20, 02H05.

Abstract: The usual bivariate Kendall's tau estimates the probability of concordance of point pairs minus the probability of discordance. This paper presents a multivariate generalization of this idea. The multivariate versions can be used to investigate dimensions (in the multicollinearity spirit) in the data. Examples are given.

Abstract: In this paper we consider an inflation model for a small open economy. \"Smallness\" is defined by the assumption that the economy meets an infinitely elastic demand and supply function for its tradable commodities, i.e., the country is assumed to be a price-taker in the world market. This implies that the rate of inflation of a small open economy depends upon the world rate of inflation. On the other hand, we observe a remarkable difference in the rates of inflation among various countries. Some Scandinavian authors like Odd Aukrust [1] and the group of authors Gtista Edgren, Kafl-Olof Faxen and ClasErik Odhner [7] have proposed a simple model which links the rate of inflation of a small open economy with international price developments and which also allows for differences in the rates of inflation among countries. The Scandinavian model of inflation received recently an increasing attention by European economists analysing its theoretical underpinnings and its empirical content [4, 5, I0, 12, 14, 15, 17]. Crucial for the model is the division of the economy into two sectors. The exposed sector (E-sector) produces \"tradables,\" i.e., commodities that compete on the world market, the sheltered sector (S-sector) produces \"non-tradables,\" i.e., commodities which are not traded internationally. The model assumes further fLxed exchange rates and explains the domestic rate of inflation through the world rate of inflation and a structural component which depends on domestic parameters.

Abstract: Subjects were given 12 training problems based on four primary bidimensional rules, the problems mixed so that the rule changed after every problem (to facilitate adoption of a truth-table strategy; condition M) or systematically blocked by rule (condition S). Their next tasks were to learn an unpracticed complementary rule, to discover a tridimensional rule, and to identify a rule based on novel and meaningful stimuli. The findings show that condition M facilitated the subjects' ability to abstract, generalize, and extend a higherorder strategy. They suggest the importance of the sequence as well as the variety of rules and imply a hierarchical model of concept learning.

Abstract: The ideal-theoretic concept of the Hermite interpolation was presented in [9]. Some of its results are summarized in this paper. By consideration of special ideals a n-dimensional generalization of Max Noether's theorem is obtained. This generalization enables us to answer questions arising in the constructive theory of functions as it is shown by three examples.

Abstract: This paper addresses the problem of defining the notion 'linguistically significant generalization'; it separates the notion of 'generalization' from that of 'significance', and proposes a rigorous objective method for determining the significance of a generalization, based on probability theory. The proposal is illustrated by applying it to examples central to theorizing in generative grammar. Precisely formulated versions of claims made by Chomsky on the use of certain abbreviatory notations (e.g. parentheses) and by Halle on certain 'natural classes' are investigated and shown to be not significant; i.e., they tell us nothing interestinrg about the nature of language. Other generalizations-on active/passive selectional restrictions, word-order universals, and noun phrase accessibility-are shown to be highly significant.*

Abstract: The note by Herath and Sharp (see ibid., vol.21, p.442, 1976), in which they use receiver operating characteristic (ROC) analysis to evaluate the effect of matched filter smoothing on simulated radioisotope scintigraphs is discussed. The authors' reply is included.