Showing papers on "Maxima and minima published in 1980"

Decentralized extrema-finding in circular configurations of processors

Abstract: This note presents an efficient algorithm, requiring O(n log n) message passes, for finding the largest (or smallest) of a set of n uniquely numbered processors arranged in a circle, in which no central controller exists and the number of processors is not known a priori.

Some results on finiteness in Plateau's problem, part II

Abstract: In this paper we attack the problem, whether any Jordan curve in R 3 may bound infinitely many surfaces (of the topological type of the disk) which furnish relative minima of the area functional. In Part I, we have reduced this problem to the study of certain one-parameter families of minimal surfaces, terminating in a minimal surface with a branch point; and in Part I, we dealt with the case of an interior branch point. In this paper, we take up the study of the boundary branch point case. We make several computations based on the eigenvalue problem associated with the second variation of the area functional. The result of these computations is that a one-parameter family of the sort described must satisfy certain conditions. If these conditions were contradictory, we would show that no real-analytic Jordan curve can bound infintely many relative minima of area; but instead, our computations led to the discovery of some one-parameter families that do satisfy these conditions, although they are bounded by a straight line instead of a Jordan curve. We are able to obtain a partial result formulated in geometric terms, showing that under certain conditions on a real-analytic Jordan curve F, F cannot bound infinitely many relative minima of area. Namely, this is so if every plane which contains a point not on the convex hull of F, meets F in at most 8 points. Note that this generalizes the result of Part I, where F was required to lie on the boundary of a convex body. If it is indeed true that no real-analytic Jordan curve bounds infinitely many relative minima of area, it must be proved by some method which (unlike those used here) would not apply to the examples mentioned (with straight-line boundaries). We now give a more general discussion of the context of this problem. If F is a Jordan curve in R 3, the classical problem of Plateau calls for a minimal surface (of the type of the disk) bounded by F. These minimal surfaces may be relative minima of area (in some suitable class of surfaces bounded by F and some suitable topology on this class of surfaces), or they may be unstable, i.e. not relative minima. Those minimal surfaces which are the mathematical

Problems with residual and additive elements and their control through specifications

Abstract: Circumstances responsible for a specification approach to the control of residual elements are reviewed. For deleterious elements, response varies from insistence on 100 % use of virgin materials to setting maximum limits on a large number of residual elements, to specifying the relative quantities of two or more interactive species. For beneficial elements, minima must be set and testing techniques must assure that the desired element is present not only in the proper amount but also in a state and location where its meliorating effects can be realized. Examples from both the alloy and ceramic fields are discussed.

The microstructure of quiet and masked thresholds

Abstract: Kemp [Scand. Audiol. Suppl. 9, 35–47 (1979)] showed that local maxima and minima in auditory thresholds are reflected in low level suprathreshold measurementsuch as loudness and frequency discrimination. While studying masking with tones and broad‐band noise, the author found that these maxima and minima (in earphone voltage) also affect masked thresholds. As masking levels and masked thresholds increase, the threshold differences decrease until the masked thresholds reach 40–50 dB SPL where no maxima and minima can be seen. The shape of psychophysical tuning curves can also be influenced by these maxima and minima leading to curves with more than one best frequency, with a flat tip or with the best frequency displaced away from the probe to the frequency of an adjacent minimum. [Work supported by NINCDS Grant NS 03856.]

Applications of Coherent States in Thermodynamics and Dynamics

Abstract: Coherent states for an arbitrary Lie group G are defined and their properties enumerated. These properties lead to a simple algorithm for studying the thermodynamic critical properties of Hamiltonians constructed from the generators of G. The algorithm is: 1. Replace H by its “classical limit” and add an entropy term — kTs(r). 2. Determine how the minima of the resulting function change as a function of T.

Information exchange between independent stochastic systems

Abstract: We considerN independent, linear, Gaussian stochastic systems, each controlled by a decision maker having independent measurements on his own system. The decision makers agree to cooperate in order to minimize a weighted sum of their own independent quadratic performance indices. For this, they may or may not exchange their measurements on line. If further constraints (such as the restriction to memoryless feedbacks) are imposed, an example shows that the best solution is not always decentralized; that is, exchanging information really improves the overall performance. Moreover, some properties of the best decentralized feedbacks are investigated; they are local minima in a more general class and even absolute minima in particular situations.

The Solution to the General Problem of Spectral Analysis Illustrated with Examples from NMR

Abstract: A general iterative method for locating the global minimum of an error functional ф = (s-ŝ)T (s-ŝ) in the presence of a multitude of local minima is presented It relies on the introduction of a square matrix W in data space whose off-diagonal elements can be exploited for inducing continuously adjustable correlation between the residuals by way of ф’ = (s-ŝ)T W(s-ŝ) The general structure of W is derived from symmetry, boundary and continuity requirements In spectroscopic applications the vector s in data space consists of n digitized signal intensities si and the theoretical model is expressed as a function ŝ = f (p, ω)) of a discrete vector p in parameter space and a continuous frequency variable ω The solution has been fully worked out for NMR spectra (high-resolution isotropic; anisotropic; exchange-broadened), including practical aspects such as automated data acquisition, data format conversion, pretruncation, baseline flattening, smoothing and posttruncation, and will be illustrated by a variety of examples

Stability regions and spectra of discrete third-order autoregressive time-series

Abstract: This paper presents an analysis of third order autoregressive time-series. The parameter regions, in the three dimensional parameter space, that produce the six separate types of power spectral density are analyzed. The study reveals that when a particular two dimensional cross section of the three dimensional parameter space is taken, the region of stability is always triangular. Within each triangular stability region in this two dimensional space, subregions which produce the six possible types of spectral shape are indicated. From these subregions it is possible to approximately choose the parameters necessary to model a process whose power spectral density contains at most two critical frequencies (maxima and minima).

Real time measurement of tone content of noise - averaging successive maxima and minima to derive tone amplitude and frequency

Abstract: The noise to be analysed is received by microphone, amplified and fed to two circuits. One circuit detects the successive maxima and minima of the fine structure and generates corres. timing pulses. The second circuit uses these pulses to sample the signal and convert the samples to digital form. Each successive pair of samples is averaged and placed in a store at a position corres. to the time of occurrence. The store is scanned to locate the positions of maxima and minima. The difference between max. and min. stored values gives the amplitude, and the number of store cells between them gives the frequency, of a tone component of the noise. The method may also be used as the basis of a computer program.

Aurorae, Sunspots and Weather, Mainly Since A.D. 1200

Abstract: Auroral records received for the Spectrum of Time project were used in 1955 to estimate sunspot activity and the dates maxima and minima back to 649 B.C. An additional set of rules has been developed (Schove 1979a) (especially the so-called X + 2 and X + 3 rules) and has made possible further improvements utilizing the separate auroral maxima associated with flares and coronal holes on the sun. A further set can now be given. 1) the time between sunspot maxima depends especially on the ratio of the amplitudes: the time between minima is high if the next cycle is very weak and low when the two consecutive cycles are both strong. 2) The time of rise is usually dependent on the strength of the next maxima, and the time of fall is low when a moderate cycle is followed by a strong one.

Optimalitätskriterien und Lokale Stetigkeit des Tschebyscheff-Operators

Abstract: Let A ⊂ ℝn, B ⊂ ℝm be nonempty sets, B compact and f: B → ℝ, F: A × B → ℝ continuous functions. The Chebyshev-approximation problem consists of the minimization of the distance-function ρf(a) = || F (a,.) — f(.)|| ∞. Let af∈ A be a strict local minimum for the function ρf. We present structures for the sets A, B and conditions on the functions f, F which lead-from a two-stage (optimization) point of view — in a natural way to the continuous dependence of the local optimal parameter af (w.r.t. (C-2) variations of f). These structures and conditions framework for the approximation of the function f. On the other hand the awill be interpreted geometrically. On one hand this approach leads to a stable pplicability of finite dimensional nonlinear optimization techniques for the search of local minima for ρfwill be guaranteed (e.g. Newton-Methods).

Globally convergent newton methods for constrained optimization using differentiable exact penalty functions.

Abstract: In this paper we consider Newton's method for solving the system of necessary optimality conditions of optimization problems with equality and inequality constraints. The principal drawbacks of the method are the need for a good starting point, the inability to distinguish between local maxima and local minima, and, when inequality constraints are present, the necessity to solve a quadratic programming problem at each interation. We show that all these drawbacks can be overcome to a great extent without sacrificing the superlinear convergence rate by making use of exact differentiable penalty functions introduced by Di Pillo and Grippo [1]. We also demonstrate a close relationship between the class of penalty functions of Di Pillo and Grippo and the class of Fletcher [12].