Abstract: This article is concerned with a generalization of the problem of estimation of median effective dose in bioassay with a normal quantal response curve. A new kind of Bayesian motivated procedure is introduced which leads to a strongly consistent estimator. The convergence is robust in that it holds for a bundle of sequences of design vectors—an important feature in a mental testing context where a specified design vector cannot be produced on demand.

Abstract: Discussion is made of calculational reconstruction of refractive index distribution from "multidirectional interferograms." Two approximate calculation formulae are given for two-dimensional case. One is derived using the Born approximation and corresponds to a generalization of the formula in X-ray structure analysis. The other is obtained using Rytov's approximation and a generalization of straight path approximation.

Abstract: The full transformation semigroup F(X) is extremely important. As far back as 1952, Malcev (1952) showed that its automorphism group consisted of mappings of the form g-1 · g, g ∈ G(X). The present work is devoted to a generalization of this result.

Abstract: A class of bilinear estimation problems involving single-degree-of-freedom rotation is formulated and resolved. Continuous-time problems are considered here, and discrete-time analogs will be studied in a second paper. Error criteria, probability densities, and optimal estimates on the circle are studied. An effective synthesis procedure for continuous-time estimation is provided, and a generalization to estimation on arbitrary Abelian Lie groups is included. Applications of these results to a number of practical problems including frequency demodulation will be considered in a third paper.

Abstract: A response surface criterion for design selection is developed in this paper for the case of estimation of a set of parametric functions rather than a single response. A specific application is emphasized, that in which interest, centers on the partial derivat. ives of the response function. Both bias and variance of the parametric functions are taken into consideration. For the case of the slope of the response function two situations are given special emphasis; the fitting of a first order model in the presence of a true second order structure, and the fitting of a second order function in the presence of a third order alternative. The traditional response surface bias and variance criteria arise as a special case for the situation in which a single parametric function is merely the ordinary response surface.

Abstract: We consider a generalization, which we call the Shannon switching game on vertices, of a familiar board game called HEX. We show that determining who wins such a game if each player plays perfectly is very hard; in fact, it is as hard as carrying out any polynomial-space-bounded computation. This result suggests that the theory of combinatorial games is difficult.

Abstract: Reports of the use of behavior modification in the classroom are reviewed, with special attention given to the question of whether or not generalization of the effects of the behavior modification programs was obtained. Those programs in which generalization across time, settings, or behaviors was observed were found to differ from other programs in several important ways. These differences were utilized in formulating a set of 15 proposed “rules” for obtaining generalization of the effects of behavior modification procedures. It is suggested that these “rules” be used to make behavior modification more effective, both clinically and practically.

Abstract: 1. The Concept of Objectives.- 1.1. The Decision Situation under Consideration.- 1.2. The Concept of Objectives under Certainty.- 1.2.1. "Aspects" and "Points of View".- 1.2.2. The Category of Ordered Topological Spaces. The Ordinal and the Cardinal Category.- 1.2.3. The Definition of an Objective Under Certainty.- 1.2.4. An Illustration of the Introduced Concepts.- 1.2.5. Side Conditions under Certainty.- 1.3. The Concept of Objectives under Uncertainty.- 1.3.1. Excursus: Axiomatical Treatment of the Bernoulli-Principle. Some Results on Continuity and Integrability of Utility Functions.- 1.3.1.1. The Natural ?-Algebra and the Interval Topology.- 1.3.1.1.1. Measurable Structures.- 1.3.1.1.2. Topological Structures.- 1.3.1.1.3. Connections between the Measurable and the Topological Structures of Preference Ordered Sets.- 1.3.1.2. The Expected-Utility-Theorem.- 1.3.1.3. A Special Case: The Utility Function as an Algebraic Homomorphism.- 1.3.2. Substantiation of the Information Requirements of the Objective-Concept4l.- 1.3.3. An Example46 1.4. Partial Objectives and Managerial Decisions.- 2. Formal Statement of the Problem.- 2.1. Complete Systems of Objectives.- 2.2. Criteria Vectors.- 2.3. The Treatment of the Problem on Principle.- 2.4. Excursus: The Vector Maximum Problem.- 2.4.1. The Concept of a Solution.- 2.4.2. The Treatment of the Vector Maximum Problem in the Literature.- 2.4.3. The 2-dimensional Vector Maximum Problem.- 2.4.3.1. Abstract Treatment of the Problem.- 2.4.3.2. The Algorithm for the Case of Two Dimensions.- 2.4.4. Linear Preference Structures and the Determination of Weights.- 2.4.5. Hyperbolic Preferences and. the Determination of the Exponential Weights.- 2.4.6. Generalization.- 2.4.7. Sketch of an Algorithm to the n-dimensional Vector Maximum Problem.- 3. Solution Approaches to the Problem of Multi-Objective Decision Making under Uncertainty.- 3.1. The Linear Model.- 3.2. The Quadratic Model.- 3.3. The Hyperbolic Model.- 3.3.1. An Axiomatical Treatment of Hyperbolic Preferences.- 3.3.2. On the Uniqueness of the Utility Function.- 3.4. A Collection of Models.- 4. Application.- References.

Abstract: (1975). A Generalization of Krasnoselski's Theorem on the Real Line. Mathematics Magazine: Vol. 48, No. 3, pp. 167-168.

Abstract: Sufficient conditions for global relative controllability of certain types of nonlinear time-varying systems with time-variable delay in control are given. The results are obtained by using Schauder's fixed-point theorem. The results obtained are a generalization of Davison [3].

Abstract: A constructive and simple proof is given of a generalization of a result of Lyapunov on the convexity of the range of vector measure.

Abstract: Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that such states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces.

Abstract: This paper presents a numerical procedure for computing Bayes confidence intervals for the availability of a series or parallel system consisting of several statistically independent 2-state subsystems each having exponential distributions of life and repair time. The present results 1) provide a useful generalization of a previous result in which test data were limited to ``snap-shot'' observations on the subsystems operating states; 2) allow conventional life-test data for estimating the exponential parameters. The methods are suited to numerical evaluation using electronic computers as shown by particular examples.

Abstract: Canonical forms for m-valued functions referred to as m-Reed–Muller canonical (m-RMC) forms that are a generalization of RMC forms of two-valued functions are proposed. m-RMC forms are based on the operations ⊕m (addition mod m) and .m (multiplication mod m) and do not, as in the cases of the generalizations proposed in the literature, require an m-valued function for m not a power of a prime, to be expressed by a canonical form for M-valued functions, where M > m is a power of a prime. Methods of obtaining the m-RMC forms from the truth vector or the sum of products representation of an m-valued function are discussed. Using a generalization of the Boolean difference to m-valued logic, series expansions for m-valued functions are derived.

Abstract: A review of the fundamental ideas and methods of the optimal reception and processing of quantum signals is given Estimation via an operator based on the usual and generalized measurements (eg,

Abstract: The model of statistical-causal analysis developed by Stegmuller (1973) with reference to Salmon (1970, 1971) is applied to the diagnostic process and suggested as a replacement for the model of inductive-statistical systematization in the context of normative diagnostics (Westmeyer, 1972). For a generalization of the model with respect to discrete random variables, an algorithmic construction of the diagnostic process is given generally and then elucidated by a simple example. It becomes apparent that this model avoids important problems which confront normative diagnostics relying on the model of inductive-statistical systematization.

Abstract: This paper deals with a generalization of a class of optimal stopping problems often referred to as the secretary problem. In the secretary problem, a decision maker views a group ofN candidates sequentially, each of which can be ranked according to some quality, although he does not know any distribution for the quality being measured. Generalizations pursued in this paper include randomN and a more elaborate payoff structure. Conditions on the payoff structure are given which result in a special subclass of stopping rules.

Abstract: Using a generalization of a variational theorem due to Leighton, the authors obtain sufficient conditions for the second order nonlinear differential equation (a(t)xI)' + q(t)f(x) = r(t) to be nonoscillatory. Examples showing the necessity of certain hypotheses are also given.

Abstract: A class of bilinear stochastic control problems involving single-degree-of-freedom rotation is formulated and resolved. Both synchronization control and orientation control are considered. In each case, the measurement data is first processed through a nonlinear transformation. The transformed process then goes through an ordinary estimator, such as a Kalman–Busy filter. After another nonlinear processing of the output of the ordinary estimator, the desired optimal control is yielded. A generalization of the approach illustrated by these results to control problems on arbitrary Abelian Lie groups is included.

Abstract: This letter discusses a fast digital technique for decomposing signals which are linear superpositions of components having the same form but different widths. This technique, based on the work of Titschmarsh, is a generalization of a method used by Gardner et al. to analyze multicomponent exponential decays.

Abstract: The purpose of this note is to discuss certain features of population growth models carlier proposed and to construct an alternative diffusion model for regulated growth in random environment. This model is shown to be the analogue of the Malthusian one, although it is a generalization of the latter due to the presence of regulation.