Showing papers on "Constant (mathematics) published in 1978"
TL;DR: These procedures nearly achieve recently established lower bounds on the amount of space inherently required to solve the covering and boundedness problems for vector addition systems, and so are much more efficient than previously known non-primitive-recursive decision procedures.
426 citations
TL;DR: In this paper, a second-order turbulence model is used to study the stable boundary layer (SBL) over a horizontal surface, a constant surface cooling rate drives the SBL to a steady state within a few hours.
Abstract: A second-order turbulence model is used to study the stable boundary layer (SBL). Over a horizontal surface, a constant surface cooling rate drives the SBL to a steady state within a few hours. Parameterizations are developed for eddy diffusivities, the kinetic energy dissipation rate and the geostrophic drag law in this idealized case. Over a sloped surface, a constant cooling rate produces a quasi-steady-state SBL in which some flow properties continue to vary but h(|f|/u*L)½ becomes constant; however, this constant is a function of the wind direction relative to the slope and the baroclinity, as measured by the cooling rate times the slope. Calculated eddy diffusivity profiles in the baroclinic (sloping terrain) case compare well with recent data from Antarctica. If a surface energy budget is used rather than a constant cooling rate, the SBL does not reach a steady state even over a horizontal surface; the nondimensional height slowly decays. We conclude that equilibrium models of the SBL are ...
370 citations
PARC1
TL;DR: In this paper, a sum-mand an is given and the goal is to find those S(n) with the property [Formula: see text] with respect to a given an.
Abstract: Given a summand an, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given an, finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text] and we can also conclude that [Formula: see text] is inexpressible as S(m) - S(0), for any S(n) satisfying Eq. 2.
367 citations
TL;DR: In this paper, a necessary and sufficient condition on weight functions u and v such that for l ≤ p≤q≤∞ there exists a constant C for which a corresponding dual result is also given is given.
Abstract: We give a necessary and sufficient condition on weight functions u and v such that for l≤p≤q≤∞ there exists a constant C for which A corresponding dual result is also given. This extends a result of B. Muckenhoupt which appeared in Studia Math., 34 (1972).
228 citations
TL;DR: In this paper, the authors consider the case of many exhaustible resources and derive results on substitution among resources and on the nature of paths of development, and show the existence of paths for production functions not of the Cobb-Douglas form.
Abstract: In Hartwick [3], it was shown that implicit in Solow's [10] model of intergenerational equity and exhaustible resources was the savings-investment rule: society should invest in reproducible capital precisely the current returns from the use of flows of exhaustible resources in order to maintain per capita consumption constant. Population was assumed to remain constant. In Solow [10] and Hartwick [3] it was assumed that there was only one exhaustible resource. Beckmann [1] & [2] has investigated optimal growth in models with many exhaustible resources. In this paper we consider the case of many exhaustible resources and derive results on substitution among resources and on the nature of paths of development. One of Beckrmann's results on substitution is analysed. Our approach is first to analyse efficient paths under the assumption of general savings functions and then to analyse efficient paths under the assumption of the special savings function referred to above. Our results indicate the Solow's existence theorem remains valid for the case of many exhaustible resources and some light is shed on the existence of paths for production functions not of the Cobb-Douglas form.
227 citations
TL;DR: In this paper, the trace relation of the flow is calculated and is used to determine the spectrum of the dynamical system, leading among other things to a description of the behaviour of powers of the shift homeomorphism on the system arising from any substitution.
Abstract: Minimal flows and dynamical systems arising from substitutions are considered. In the case of substitutions of constant length the trace relation of the flow is calculated and is used to determine the spectrum of the dynamical system. Several methods are indicated to obtain new substitutions from given ones, leading among other things to a description of the behaviour of powers of the shift homeomorphism on the system arising from any substitution.
209 citations
TL;DR: In this paper, it was shown that a magnetic field being force-free, i.e. satisfying ▽ × B = αB, with α = constant (α ≠ 0) in the whole exterior of the Sun cannot have a finite energy content and cannot be determined uniquely from only one magnetic field component given at the photosphere.
Abstract: At first it is shown that a magnetic field being force-free, i.e. satisfying ▽ × B = αB, with α = constant (α ≠ 0) in the whole exterior of the Sun cannot have a finite energy content and cannot be determined uniquely from only one magnetic field component given at the photosphere. Then the boundary value problem for a semi-infinite column of arbitrary cross section is solved by a Green's function method.
192 citations
TL;DR: In this paper, four methods are proposed for estimating the dominant time constant and dead time of a given process from a knowledge of its moments, s-plane, frequency or transient response data, which are faster and simpler and, in terms of accuracy and reliabiltiy, are comparable to the time domain least squares procedure for parameter estimation.
Abstract: Four methods are proposed for estimating the dominant time constant and dead time of a given process from a knowledge of its moments, s-plane, frequency or transient response data. The methods are faster and simpler and, in terms of accuracy and reliabiltiy, are comparable to the time domain least squares procedure for parameter estimation. Applications of the methods are illustrated with the aid of a dispersion model. A comparison is also made with other known techniques to demonstrate the superiority of the suggested methods.
152 citations
TL;DR: In this article, a simulation of a fluid n-butane system has been carried out using a straight-chain skeletal model, involving fluid densities from 288.80 to 721.99 kg/m3 at several distinct temperatures.
Abstract: A simulation of a fluid n‐butane system has been carried out using a straight‐chain skeletal model. The calculations reported here involve fluid densities from 288.80 to 721.99 kg/m3 at several distinct temperatures. In the course of this investigation the linear self‐diffusion constant, the rate of torsional gauche/trans relaxation and rotational tumbling of the fluid have been studied. This model shows a high degree of cooperativity between the molecular vibration and rotation, and the bulk fluid motion.
121 citations
TL;DR: In this article, the change of variable method introduced by Landau for the one-dimensional problem is extended to the multi-dimensional using an independent variable which takes constant values at the boundary and the freezing front.
Abstract: This paper presents a simple numerical method for solving two and three-dimensional freezing problems with arbitrary geometries. The change of variable method introduced by Landau for the one-dimensional problem is extended to the multi-dimensional using an independent variable which takes constant values at the boundary and the freezing front. Example calculations were performed for the Stefan type freezing problem in regular squares, triangles, and ellipses. Then some of the results were compared with the experimental ones that were obtained for the constant cooling rate.
108 citations
TL;DR: This reply takes the position that the term set point, which refers to an input Variable in a control system, should be used only as an input variable and then only when there is evidence that such a reference variable exists.
01 Jan 1978
TL;DR: In this paper, a differential equation that incorporates time of recruitment (t = body size) and body size on rate of constant minimum (L,,,) is given, giving an improved description (d~ld~ = L!,,,,) when body size is minimal.
Abstract: (2), giving a differential equation that incorporates 1. time of recruitment (t = body size is some effects of both time (season) and body size on rate of constant minimum (L,,,). 2. ~~~~~h rate is maximal growth. Its solution should give an improved description (d~ld~ = L!,,,,) when body size is minimal. 3. ~h~~~ of changing body size for those animals exhibiting seasonal growth.
TL;DR: In this article, the second-order sensitivity of natural frequencies is analyzed for the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses, and the web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.
Abstract: The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.
TL;DR: In this article, a perfect capital market model is developed and solved explicitly for a constant absolute risk aversion utility function, where low replacement rates (less than 50%) are optimal for realistic parameter values and if there is no lending or borrowing the optimal rates rise to about 75%.
01 Jan 1978
TL;DR: In this paper, a model for which an existence and continuation theorem leads to a proof of blowup for certain solutions is presented, and the concavity method is adapted to show that for suitable initial conditions and pressures, no weak solution can exist for all time and that the L norm of the solution possesses a lower bound which blows up in finite time.
Abstract: Publisher Summary This chapter discusses the finite time blow-up in nonlinear problems. It highlights an initial boundary value problem for a nonlinear elastic body subjected to constant pressures applied to its surface. The boundary conditions are, for example, appropriate to the case of inflation of a hollow shell under a maintained internal pressure. The stored-energy function of the elastic material is assumed to satisfy a special case of the concavity inequality of Knops, Levine, and Payne. This assumption is interpreted as a precise statement about the weakness of the material for large strains. The concavity method is adapted to show that for suitable initial conditions and pressures, no weak solution can exist for all time and that the L norm of the solution possesses a lower bound which blows up in finite time. The chapter presents a model problem for which an existence and continuation theorem leads to a proof of blowup for certain solutions.
TL;DR: In this article, an Ashby-type deformation mechanism map is simplified by plotting in the form of normalized stress versus the reciprocal of the homologous temperature, and the boundaries separating the various fields appear as straight lines.
Abstract: An Ashby-type deformation mechanism map may be considerably simplified by plotting in the form of normalized stress versus the reciprocal of the homologous temperature. In this form, the boundaries separating the various fields appear as straight lines and the constant strain rate contours may be approximated as straight lines. Representative maps are presented for conditions of high temperature creep, and a simple procedure is outlined for constructing several maps for the same material at different grain sizes.
TL;DR: In this paper, the effect of heating rate and sample mass on the first two stages of thermal decomposition of calcium oxalate monohydrate in a nitrogen atmosphere has been evaluated in detail using non-isothermal thermogravimetry.
TL;DR: In this article, the authors proposed a block replacement policy to eliminate this kind of waste, under which items are replaced at constant intervals of time and at failure, is wasteful because sometimes almost new items are also replaced.
Abstract: Block replacement policy, under which items are replaced at constant intervals of time and at failure, is wasteful because sometimes almost new items are also replaced. In order to eliminate this kind of waste, the following replacement policy is suggested.
TL;DR: In this article, three alternative methods for estimating individual probabilities of brand choice: a multi-attribute attitude model, a dollar-metric model, and a constant sum scale model.
Abstract: This paper investigates three alternative methods for estimating individual probabilities of brand choice: a multi-attribute attitude model, a dollar-metric model, and a constant sum scale. These approaches are compared to actual choice behavior in a controlled experimental setting, with the constant sum scale being the dominant method.
TL;DR: A new method for generating random variables from the gamma distribution with nonintegral shape parameter α is proposed, which is similar to two other methods recently given by Wallace and Fishman and is compared with Fishman's and Ahrens and Dieter's methods.
Abstract: A rejection method is proposed for generating gamma variates with nonintegral shape parameter a, a > 1. This method is similar to other methods given by Fishman, Wallace, and Tadikamalla and is faster than these methods for a > 2. The core storage requirements and the programming effort for the proposed method are similar to those of Wallace's or Tadikamalla's methods. The computational times for the proposed method remain fairly constant for medium and large values of a and are superior to times obtained by Arhens and Dieter's method for all values of a. The proposed method is simpler than Ahrens and Dieter's method.
TL;DR: In this article, the general invariance group of the unsteady, two-dimensional, stream-function equation was derived for the case where the kinematic viscosity v is equal to a constant and the case when v = 0.
Abstract: The methods described by Bluman & Cole (1974) are used to derive the infinitesimals of the general invariance group of the unsteady, two-dimensional, stream-function equation for the case where the kinematic viscosity v is equal to a constant and the case where v = 0. The infinitesimals in each case involve ten independent parameters, seven of which appear explicitly and three of which are contained implicitly in three arbitrary functions of time. The various finite groups and similarity transformations which may be derived from the infinitesimals are discussed through examples. Two of the arbitrary functions of time are non-trivial and represent invariance of the stream-function equation under a transformation to a co-ordinate system which moves in a non-uniform irrotational fashion. A general similarity form is derived for which the equations dx/dt = u(x, y, t) and dy/dt = v(x, y, t) for the particle paths may be reduced to an autonomous system. This form is general enough to suggest the hypothesis that, under certain restrictions, the entrainment processes of unsteady flows dominated by two-dimensional large-scale motions may be displayed diagrammatically on a phase-plane plot of particle trajectories.
TL;DR: Under conditions where the background frequencies were fixed and the pattern frequencies were moved, thus combining the manipulation of embedding with that of transposition of the pattern, overlap of pattern and background frequencies was still the principal cause of deterioration in performance.
Abstract: Listeners identified one of six permutations of three frequencies, presented as brief three‐note melodies. Identification performance remained high in spite of transposition of the original three frequencies throughout a two‐octave range, so long as the musical intervals or frequency ratios between the adjacent pairs of frequencies remained constant. Even when those intervals were compressed or expanded, while remaining about equal to each other, identification was quite good for the range between the lowest and highest frequency of no more than approximately 1/3 octave. Performance decreased sharply when the span was much wider. Unequal intervals, where the low and middle frequencies were closer together or farther apart than the middle and high frequencies, did not retain good identification performance. When the three‐tone patterns were embedded in longer sequences of seven or eight tones, the identification performance was best when the pattern occurred at the beginning or the end of the sequence, and when the range of frequencies from which the irrelevant background tones were chosen lay outside the range of pattern frequencies. Under conditions where the background frequencies were fixed and the pattern frequencies were moved, thus combining the manipulation of embedding with that of transposition of the pattern, overlap of pattern and background frequencies was still the principal cause of deterioration in performance. The findings are related to some analogies to the perceptual rules of Gestalt theory, as well as to certain aspects of musical practice.
TL;DR: In this paper, a zonally averaged climate model of the energy-balance type is examined and the effect of variation of the solar constant is investigated in detail, showing that the model is much more stable with regard to variations in the solar input than has been assumed so far.
Abstract: A zonally averaged' climate model of the energy-balance type is examined. Recently published satellite measurements were used to improve existing parameterizations of planetary albedo and outgoing radiation in terms of surface and sea level temperature. A realistic constant for the diffusion of energy was found by tuning the model to the present climate.. For the actual solar constant both the present climate and an ice-covered earth are solutions of the model. They are extremely stable for temperature perturbations. The effect'of variation of the solar constant was investigated in detail. If the solar constant is decreased by 9-10% the warm solution (partial ice cover) jumps to the cold one (complete ice cover). Transition from the cold to the warm solution requires an increase of the solar constant to 109-110% of its present value. Therefore, we conclude that the model climate is much more stable with regard to variations in the solar input than has been assumed so far. This is caused mainly by our updated formulation of the outgoing radiation. Further experiments showed that our model is much more sensitive to changes in the outgoing radiation than to changes in the diffusivity for energy.
TL;DR: In this paper, the geometric nature of the infinite zeros of the root-loci of linear multivariate systems is investigated using the canonical form derived by Morse (1973), and it is shown that an invertible system S(A, B, C) has integer-order infinite zero in the generic case equal to the controllability indices of a pair (A + KC, B).
Abstract: The geometric nature of the infinite zeros of the root-loci of linear multivariate systems is investigated using the canonical form derived by Morse (1973). It is shown that an invertible system S(A, B, C) has integer-order infinite zeros in the generic case equal to the controllability indices of a pair (A + KC, B), that suitable choice of proportional output feedback guarantees the absence of other than integer-order zeros and that the orders and asymptotic directions of the infinite zeros are independent of constant state feedback and output injection.
Patent•
10 Mar 1978
TL;DR: In this article, the hydraulic buffer means, control valves and various sensors are combined such that an optimum spring constant is selected in accordance with various running conditions of the vehicle such as orad surface, revolution and acceleration or deceleration.
Abstract: PURPOSE:To provide a suspension for a vehicle, in which hydraulic buffer means, control valves and various sensors are combined such as to permit an optimum spring constant to be selected in accordance with various running conditions of the vehicle such as orad surface, revolution and acceleration or deceleration
TL;DR: In this paper, an approximate lower bound for the MIT bag constant B relative to the QCD coupling parameter Λ was derived, where Λp ⩽ 0.89 GeV when the propagator of the gluon is used to renormalize the coupling constant.
TL;DR: In this paper, high pressure neutron diffraction experiments showed that the angles of tilt of TCNQ and TTF molecules to the stacking axis do not change under pressure, and this result was used to derive the constant volume stacking axis resistivity of TTF-TCNQ.
Abstract: 2014 High pressure neutron diffraction experiments show that the angles of tilt of the TCNQ and TTF molecules to the stacking axis do not change under pressure. This result, together with measurements of the pressure dependence of the conductivity as a function of temperature, is used to derive the constant volume stacking axis resistivity of TTF-TCNQ. The temperature dependence is strongly reduced from the T2.3 law at constant pressure, and is better characterized by a linear T law. LE JOURNAL DE PHYSIQUE LETTRES TOME 39, 1 er MAI 1978,
TL;DR: In this paper, an expression for the mean thickness N 99 of vapour-deposited thin films at the moment t 99 of 99% substrate coverage was derived, characterizing the thickness at which thin films reach continuity, decreases with decreasing substrate temperature T and/or increasing deposition rate R.