Showing papers on "Constant (mathematics) published in 1979"

Sharp conditions for oscillations caused by delays

Abstract: AMS (MOS) subject classification (1970): Primary 34K15; Secondary 34K25, 34E10. A sufficient condition under which all solutions of the delay differential equation , where p(t≤0 and continuous and τ>0 and constant, are oscillatory is presented. It is explained that the condition is the best possible for oscillations. When the coefficient p(t) in equation (1) is a positive constant, p, then the condition becomes pτe>0 which is necessary and sufficient for all solutions of the DDE to be oscillatory.

Another Algorithm for Bracket Abstraction

Abstract: Much of the notation used in logic and mathematics can be recast in the following uniform syntax. A term is either an atom (i.e. a constant or a variable) or else it is of the form A B where A and B are terms and their juxtaposition denotes the application of a monadic function (on the left) to its argument (on the right). We may use parentheses to resolve ambiguity together with the convention that, in the absence of parentheses, juxtaposition associates to the left. So in A B C the function A is being applied to B and the result, itself presumably a function, is being applied to C. Functions of several arguments are adapted to this uniformly monadic syntax by replacing them by appropriately defined higher order functions of one argument. So for example a first-order dyadic function, d say, is replaced by a second-order monadic function d' defined so that d' x y always has the same value as d(x, y). (Note. This transformation is called "currying" after the logician H. B. Curry', thus we would say that d' is here a curried version of d.) In addition to operations which can be construed as the application of a function to arguments, however, our customary notations also use constructions of an apparently very different character, namely those which introduce bound variables (e.g. the quantifiers, the integration sign, Church's A). These too can be reduced to the above form provided that we can give a positive solution to the following problem. Given a term, X say, containing zero or more occurrences of the variable x, can we write down a term denoting the funtionf with the property (1) below?

Pole assignment by piecewise constant output feedback

Abstract: The problem of polo assignment by piecewise constant output feedback is considered for linear time-invariant systems with infrequent observation. An algorithm for computing the output feedback gain is presented, together with necessary and sufficient conditions for pole assignment. The resultant output feedback gain is a periodic piecewise constant function of time.

On Parsimonious Explanations of Production Relations

Abstract: This paper examines three bodies of macroscopic evidence that are relevant to testing the classical theory of production. No one of these bodies of evidence offers any persuasive support for the classical theory. Fits to data of the Cobb-Douglas and ACMS functions appear to be artifactual, the data actually reflecting the accounting identity between values of inputs and outputs. Similarly, there is little or no support for the U-shaped long-run cost curve, the data on firm size distributions being better explained by the Gibrat hypothesis and constant costs. Finally, observed distributions of executive salaries are explainable in simple sociological terms, without recourse to classical theory.

The generalized Pareto law as a model for progressively censored survival data

Abstract: SUMMARY The generalized Pareto distribution as a model for survival data is considered. The three parameter model is general enough so as to include increasing, decreasing and constant failure rate distributions. Maximum likelihood estimation for the progressively censored case is discussed at length and conditions for existence and uniqueness of estimates are given. Examples are presented to illustrate its appropriateness for a variety of situations. We consider a population of items whose times to failure from a well-defined origin are being observed. Time to failure is assumed to be a random variable T having survivor function S(t) = pr (T > t), density f(t), and hazard rate h(t) = -d log S(t)/dt. Although the most widely used model for h(t) is constant hazard, giving rise to the exponential distribution, this may not be a realistic assumption when modelling chronic disease populations. Also, when the origin corresponds to an event which may dramatically influence survival, such as surgery, the objection to constant hazard may be especially strong. In situations where constant hazard is not a reasonable assumption, monotone hazard usually is. The Weibull and most other parametric families used to model survival data have monotone hazard rates. Another family of monotone hazard rates which forms the basis of this paper is given by

The Smithsonian Astrophysical Observatory Solar Constant Program

Abstract: The Astrophysical Observatory of the Smithsonian Institution (APO) made measurements of the solar constant at many locations on the earth's surface from 1902 to 1962. These measurements have been interpreted by various authors to show that the sun has both a long-term secular change in brightness and cyclic variations. The same data set has been used by other authors to show that the sun is constant in output. The APO solar constant data are reexamined in this review in order to clarify what the APO staff did and what their results say about the behavior of the sun. There are serious problems with the internal consistency of the APO solar constant measurements indicated by the general lack of a common signal between stations or between different measurement methods. If the overall data set is considered, there is no evidence for cyclic variations or any long-term trend in the solar constant greater than a few tenths of a percent. Overall the solar constant appears to be constant to within about 0.1% over the period 1923–1954. Most of the observed variations are explained by errors in the data reduction scheme which failed to remove all the effects of atmospheric extinction or by improper changes in the radiation scale. The solar constant values are independent of solar activity. Although this null conclusion based on the examination of this data set is not encouraging as an easy explanation for climatic change during the twentieth century, the conclusion is valuable in that it sets constraints on the required long-term accuracy and reproducibility needed in the upcoming satellite observations of the solar constant.

Transport equations for the Wigner distribution function

Abstract: Equations have been derived which describe the transport of the Wigner distribution function in homogeneous and inhomogeneous media. In a weakly inhomogeneous medium, the transport equation can be formulated in geometrical optical terms as follows: along a geometrical optical light ray, the Wigner distribution function has a constant value.

Constant Television: A Background to Daily Life.

Abstract: For over one-third of inner city families, the set is always on and provides a constant backdrop to the child's home life.

A note on the graphical analysis of survival data

Abstract: SUMMARY Two graphical procedures for analysing distributions of survival time are compared. One works with the survivor function, or with the order statistics, and the other is based on estimates of log hazard and is designed to give points with independent errors of constant known variance. The distribution of survival time, T, may be described equivalently by a probability density function f(t), by a survivor function F(t) = pr (T> t), and by a hazard function p(t) = f(t)/l(t). One advantage of p(.) is that often, although not always, it varies slowly over all or most of its range. Constant p(.) corresponds to an exponential distribution and, even when it is not intended to base the analysis on an assumption of exponential form, that distribution often gives a natural base against which to judge distributional shape. There are a lot of ways of comparing data graphically with the exponential distribution; for a cryptic list of ten such, see Cox (1978, Table 2). Most are transformations of one another so that choice is partly a matter of taste. The present note contrasts two simple graphical techniques.

On the finite time control of linear systems by piecewise constant output feedback

Abstract: The problem of finite time controllability of linear time invariant systems by piecewise constant output feedback is considered It is shown that complete controllability and complete observability are both necessary and sufficient conditions for output feedback controllability by piecewise constant gain Dead-beat output feedback controllers that drives the system to the origin in at most (μd × vd) steps, are also presented, where μd and vg are the indices of controllability and observability

Diagrammatic theory of transition of pendulum like systems

Abstract: Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

Elongational behaviour of polymer melts in constant elongation-rate, constant tensile stress, and constant tensile force experiments

Abstract: The extensibility of polymer melts is of great practical importance for polymer processing. On the basis of a single-integral constitutive equation with a straindepent memory functional verified for two similar well-characterized LDPE melts, predictions are made on material behaviour in uniaxial extension under constant strain-rate, tensile stress, and tensile force conditions. It is found that experiments at constant tensile force are more adequately described by assuming purely viscous response of the polymer melts than by assuming Maxwell-model type of behaviour.

Divergences Among the Born and Classical Stability Criteria for Cubic Crystals under Hydrostatic Loading

Abstract: The classical criterion for the stability of cubic crystals under constant hydrostatic pressure is distinguished from the notional criterion of stability introduced by Born. Although the latter has been widely used in the literature, theoretical computations demonstrate appreciable quantitative and qualitative divergences between the criteria. The computations are made within the framework of a crystal model that is both mathematically tractable and sufficiently realistic for the intended purpose.

Polynomial maps with constant Jacobian

Abstract: It has been long conjectured that ifn polynomialsf 1, …,f n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf 1, …,f n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically.

Measured and Approximate Flux-Concentration Relations for Absorption of Water by Soil1

Abstract: The flux-concentration relation of Philip (1973) is calculated using moisture profiles measured during absorption of water by a fine sand when water was supplied at both constant hydraulic potential and constant rate. The general behavior of the measured flux-concentration relations was found to be consistent with those of the model soils calculated by Philip. Within the accuracy of the measurements, no significant time-dependence of the relation was found for the constant flux boundary condition over a large time span. Measurements of the time-averaged flux-concentration relation, however, suggest some significant time-dependence for short times. Simple approximations for the flux-concentration relation, based on these observations, are suggested. These approximations enable easily evaluated predictions to be made of the salient features of constant rate application of water to soil, which are sufficiently accurate for most practical purposes.