Showing papers on "Constant (mathematics) published in 1987"
TL;DR: A randomized algorithm that sorts on an N- node network with constant valence in O(log N) time with probability at least 1 - N - “α” - “ α” for all large enough items.
Abstract: A randomized algorithm that sorts on an N node network with constant valence in O(log N) time is given. More particularly, the algorithm sorts N items on an N-node cube-connected cycles graph, and, for some constant k, for all large enough a, it terminates within ka log N time with probability at least 1 - N-a.
242 citations
TL;DR: The existence of weak solutions of the Cauchy problem for the Navier-Stokes equations of compressible, isentropic flow of a polytropic gas in one space dimension was proved in this article.
Abstract: We prove the global existence of weak solutions of the Cauchy problem for the Navier-Stokes equations of compressible, isentropic flow of a polytropic gas in one space dimension. The initial velocity and density are assumed to be in L2 and L2 n BV respectively, modulo additive constants. In particular, no smallness assumptions are made about the intial data. In addition, we prove a result concerning the asymptotic decay of discontinuities in the solution when the adiabatic constant exceeds 3/2.
224 citations
TL;DR: In this paper, the authors considered the problem of determining if the sphere is the only compact hypersurface with constant higher order mean curvature Hr, for some r = 1,..., n.
Abstract: A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature Hr, for some r = 1, ..., n.
213 citations
TL;DR: In this article, the authors apply dislocation theory to the superposition of thermal-activation kinetics and phonondrag control, and show that at very high strain rates, the glide kinetics should be entirely controlled by drag under the applied stress, without any significant contribution from the obstacle strength.
196 citations
TL;DR: In this article, it was shown that To is most nearly constant in the sense of minimizing the coefficient of variation var(T0)/(ET0)2 over all transition matrices Pij and exponential delay parameters λi- in each state when Pii = 1, i = n, n- l, l, 1 and λ i, ≡ constant.
Abstract: Let Xt, t ≥ 0 be any continuous-time Markov process on states 0,1, …, n where Xo = n and To is the time to reach 0 which is absorbing. We prove that To is most nearly constant in the sense of minimizing the coefficient of variation var(T0)/(ET0)2 over all transition matrices Pij and exponential delay parameters λi- in each state when Pii = 1, i = n, n - l,…, 1 and λi, ≡ constant. The latter chain is Erlang's process on n fictitious states and has been used to show that an arbitrary semi-Markov process can be approximated by a Markov process. It has been a long-open problem since the work of Kendall, Cox, and others to try to improve on Erlang's scheme by generalizing the transition structure of X, i.e. adding loops, twists, and turns in order to make the overall waiting time have smaller coefficient of variation. We destroy this hope by showing at last that Erlang's original method is not improvable. Our proof is simple and elegant and is a nice example of the power of martingales; it seems intractible wi...
178 citations
TL;DR: In this article, the authors considered the problem of estimating the probability that a given initial surplus will lead to a catastrophic loss, and the corresponding density of the deficit at the time of ruin.
Abstract: In the usual model of the collective risk theory, we are interested in the severity of ruin, as well as its probability. As a quantitative measure, we propose G(u, y), the probability that for given initial surplus u ruin will occur and that the deficit at the time of ruin will be less than y, and the corresponding density g(u, y). First a general answer in terms of the transform is obtained. Then, assuming that the claim amount distribution is a combination of exponential distributions, we determine g; here the roots of the equation that defines the adjustment coefficient play a central role. An explicit answer is also given in the case in which all claims are of constant size.
159 citations
TL;DR: In this article, a theory is developed based on the model of random interactions between a large number of lattice defects and domain walls in ferroelectric materials, which gives the characteristic parameters of the hysteresis loop such as initial dielectric constant ei, Rayleigh constant ν, and coercive field Ec in terms of the microstructure of the domain walls and the number and interaction strength of the lattice defect.
Abstract: A theory is developed based on the model of random interactions between a large number of lattice defects and domain walls in ferroelectric materials. The theory gives the characteristic parameters of the hysteresis loop such as initial dielectric constant ei, Rayleigh constant ν, and coercive field Ec in terms of the microstructure of the domain walls and the number and interaction strength of the lattice defects. Results from large amplitude measurements on BaTiO3 doped with Fe show that a linear relationship exists between the dielectric constant and the ac field as required by Rayleigh’s law. In addition, the Rayleigh constant itself is inversely proportional to the Fe concentration as predicted by the model. Therefore, it is concluded that Fe as a dopant in BaTiO3 can act as obstacles to domain wall motion and control the characteristics of the hysteresis loop.
136 citations
TL;DR: In this paper, the surfaces of constant energy in integrable Hamiltonian systems which possess Bott integrals are classified and a complete topological classification of surgery of Liouville tori in general position is given.
Abstract: The surfaces of constant energy in integrable Hamiltonian systems which possess Bott integrals are classified. A complete topological classification is given of surgery of Liouville tori in general position in integrable Hamiltonian systems. Bibliography: 28 titles.
115 citations
108 citations
Patent•
Alza1
Abstract: An osmotic delivery system is disclosed for delivering a useful agent at a controlled and constant rate modulated by a pulsed delivery of the useful agent to an environment of use.
104 citations
TL;DR: In this paper, the phase angle exponent is related to the fractal dimension D of the surface by the relation η = (3-D), and the ac response of a fractal electrode has been shown to be of the constant phase angle type.
TL;DR: In this paper, the authors consider a family of two-stage stochastic control problems with nonclassical information patterns, and show that whenever the performance index does not contain a product term between the decision variables, the optimal solution is linear in the observation variables.
Abstract: In this note we consider a parameterized family of two-stage stochastic control problems with nonclassical information patterns, which includes the well-known 1968 counterexample of Witsenhausen. We show that whenever the performance index does not contain a product term between the decision variables, the optimal solution is linear in the observation variables. The parameter space can be partitioned into two regions in one of which the optimal solution is linear, whereas in the other it is inherently nonlinear. Extensive computations using two-point piecewise constant policies and linear plus piecewise constant policies provide numerical evidence that nonlinear policies may indeed outperform linear policies when the product term is present.
TL;DR: In this paper, the asymptotic efficiency of quasi-likelihood estimation is calculated under some particular distributions, and then more generally via an approximation for'small departures' from the corresponding natural exponential family.
Abstract: SUMMARY A quasi-likelihood method has been proposed by Wedderburn (1974) for the estimation of parameters in regression models when there is some assumed relationship between the mean and variance of each observation but not necessarily a fully specified likelihood. If the underlying distribution comes from a natural exponential family the quasi-likelihood estimates maximize the likelihood and so have full asymptotic efficiency; under more general distributions there is some loss of efficiency, which is investigated here. Three types of model are discussed in detail: models with constant variance, models with constant coefficient of variation and models with overdispersion relative to some exponential family. The asymptotic efficiency of quasi-likelihood estimation is calculated under some particular distributions, and then more generally via an approximation for 'small departures' from the corresponding natural exponential family. The possibility of refinement of the quasi-likelihood approach, to incorporate additional information about the underlying distribution, is considered.
TL;DR: In this paper, it was shown that the policy function obtained by optimizing a discounted infinite sum of stationary return functions is Lipschitz continuous when the instantaneous function is strongly concave.
01 Jan 1987
TL;DR: In this article, a congruence theorem for Riemannian hypersurfaces in a real space form was obtained for smooth and connected manifolds, where all geometrical objects are assumed to be smooth unless mentioned otherwise.
Abstract: For Riemannian hypersurfaces in a real space form, several authors investigated problems related to congruity under some assumptions. P. J. Ryan ([2], [3]) established a local congruence theorem in a real space form for Riemannian hypersurfaces whose shape operators have at most two mutually distinct constant eigenvalues. It is a natural question to consider this problem for semiRiemannian hypersurfaces in a semi-Riemannian real space form. The main purpose of this paper is obtain a congruence theorem for proper semi-Riemannian hypersurfaces analogous to that of Ryan. Throughout this paper, all manifolds are smooth and connected and geometrical objects are assumed to be smooth unless mentioned otherwise.
TL;DR: In this paper, the authors investigated the effect of the environmental history on the strength of random fiber reinforced polyester resin composite using three-point bend tests and showed that reduction of the strength due to hydrothermal effects is a rate process for which the temperature influences only the rate constant.
TL;DR: This work examines several methods for drawing a sequential random sample of n records from a file containing N records and recommends method D, which is on-line, has a small constant memory requirement, and is easy to program.
Abstract: We examine several methods for drawing a sequential random sample of n records from a file containing N records. Method D is recommended for general use. The algorithm is on-line (so that CPU time can be overlapped with I/O), has a small constant memory requirement, and is easy to program. An improved implementation is detailed in the Appendix.
TL;DR: In this article, the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N was established and the weights f were found to obtain constant curvatures on M X f N when M is compact.
Abstract: We establish the relationship between the scalar curvature of a warped product M Xf N of Riemann manifolds and those ones of M and N. Then we search for weights f to obtain constant scalar curvature on M Xf N when M is compact.
TL;DR: In this paper, a new expression for estimating the dielectric constant of a fluid mixture as a function of temperature, density and composition is presented for phase-equilibrium calculations, for systems containing electrolytes and nonelectrolytes.
Abstract: A new expression is presented for estimating the dielectric constant of a fluid mixture as a function of temperature, density and composition. The estimated dielectric constants (and their derivatives) are required for phase-equilibrium calculations, based on an equation of state, for systems containing electrolytes and nonelectrolytes. The new expression holds for the entire range of fluid densities, from zero to liquid-like densities. Mixing of components is performed on a volume-fraction basis at constant temperature and constant reduced density. For polar components where data are not available at the temperature and/or reduced density of interest, the well-characterized behavior of water is used to extrapolate the available pure-component data. The importance of using the correct density of the mixture is shown. Using one adjustable parameter for each nonideal binary subsystem, predicted results can be significantly improved.
TL;DR: In this paper, an analysis is given of the FDAF where the window function is generalized and the convergence behavior of FDAF's with various window functions is compared, and the analysis describes the influence of \beta on the convergence behaviour of the FD over the whole convergence range.
Abstract: One of the advantages of a Frequency-Domain Adaptive Filter (FDAF) is that one can achieve convergence at a constant rate over the whole frequency range by choosing the adaptation constant for each frequency bin l equal to the overall adaptation constant divided by an estimate of the input power at this frequency bin. A commonly used method, applied in this paper, to estimate the input power is to do an exponentially weighting with smoothing constant \beta on the magnitude squared of the input values at each frequency bin l . Furthermore, it is known that a correctly implemented FDAF, using the overlap-save method, contains five 2 N -points Fast Fourier Transforms (FFT). Two of these are used to force the last N points of the time-domain augmented impulse response to zero by applying a particular window function. In this paper, an analysis is given of the FDAF where the window function is generalized. Using these results, the convergence behavior of FDAF's with various window functions is compared. Furthermore, the analysis describes the influence of \beta on the convergence behavior of the FDAF over the whole convergence range.
TL;DR: A necessary condition for the existence of a global bounded continuous solution is given in this article, which is dictated by physics and is a source of essential difficulties in the mathematical treatment of this problem.
TL;DR: In an effort that has spanned more than a century to connect gravitation to the other forces of nature, over 200 experiments on G have been completed and reported; but many of them have not been reported in what would now be considered to be the open literature as mentioned in this paper.
Abstract: The Newtonian Gravitational Constant, G, has probably been measured more often but, interestingly, with less precision than any other physical constant of fundamental importance. In an effort that has spanned more than a century to connect gravitation to the other forces of nature, over 200 experiments on G have been completed and reported; but many of them have not been reported in what would now be considered to be the open literature. This paper is a third, more complete attempt to carry MacKenzie's and Poynting's bibliographies forward from the 1800's to the present; and thereby include as many as possible of the experimental results on G that have been obtained since 1900.
01 Jan 1987
TL;DR: In this article, an equivalent medium model is developed to relate the propagation constant y associated with propagation of the mean field through a vegetation canopy, to the geometrical and dielectric parameters of the canopy constituents.
Abstract: An equivalent-medium model is developed to relate the propagation constant y, associated with propagation of the mean field through a vegetation canopy, to the geometrical and dielectric parameters of the canopy constituents. The model is intended for media containing vertical cylinders, representing the stalks, and randomly oriented discs, representing the leaves. The formulation accounts for both absorption and scattering by the cylinders, but uses a quasi-static approximation with respect to the leaves. The model was found to be in good agreement with experimental results at 1.62 and 4.75 GHz, but underestimates the extinction loss at 10.2 GHz. The experimental component of the study included measurements of the attenuation loss for horizontally polarized and vertically polarized waves transmitted through a fully grown corn canopy, andof the phase difference between the two transmitted waves. The measurements were made at incidence angles of 20°, 40° , 60°, and 90° relative to normal incidence. The major conclusion of this study is that the proposed model is suitable for corn-like canopies, provided the leaves are smaller than ¿ in size.
01 Jan 1987
TL;DR: In an effort that has spanned more than a century to connect gravitation to the other forces of nature, over 200 experiments on G have been completed and reported; but many of them have not been reported in what would now be considered to be the open literature.
Abstract: The Newtonian Gravitational Constant, G, has probably been measured more often but, interestingly, with less precision than any other physical constant of fundamental importance. In an effort that has spanned more than a century to connect gravitation to the other forces of nature, over 200 experiments on G have been completed and reported; but many of them have not been reported in what would now be considered to be the open literature. This paper is a third, more complete attempt to carry MacKenzie's and Poynting's bibliographies forward from the 1800's to the present; and thereby include as many as possible of the experimental results on G that have been obtained since 1900.
TL;DR: The coverage dependent diffusion rate of CO on Ni(100) has been studied by laser-induced desorption methods as discussed by the authors, where the CO diffusion rate varies with the morphology of the adlayer.
Abstract: The coverage dependent diffusion rate of CO on Ni(100) has been studied by laser‐induced desorption methods. The CO diffusion rate varies with the morphology of the adlayer. At low coverages, where the CO is disordered, the rate is relatively low but constant. At high coverages where a c(5√2×√2)R45 structure is known to prevail, the rate is significantly faster but again constant with coverage. Between these two regions (0.3<θCO <0.5), where a c(2×2) structure develops, the rate is intermediate and tends to increase with coverage. The activation energy Ed decreases but the preexponential term D0 also decreases when the rate increases. This compensation effect between Ed and D0 is used to anticipate surface phase changes.
TL;DR: In this paper, it was shown that two-dimensional and timelike 'elementary' quasi-regular singularities provide a generalised version of the unusual cosmic strings. But the properties of such generalised cosmic strings are investigated and it is shown in particular that they are totally geodesic submanifolds on which the mass density mu is constant.
Abstract: It is shown that two-dimensional and timelike 'elementary' quasi-regular singularities provide a generalised version of the unusual cosmic strings. The properties of such generalised cosmic strings are investigated and it is shown in particular that they are totally geodesic submanifolds on which the mass density mu is constant.
Patent•
27 Aug 1987TL;DR: In this paper, a method for generating a plurality of points that lie on the surface of a blended solid model is presented, where the points are obtained from the unblended solid model by a numerical solution to a convolution integral, wherein the CNN includes a spherically symmetric blending function with a size responsive to the blend radius desired for each of one or more regions on the solid model.
Abstract: A method is provided for generating a plurality of points that lie on the surface of a blended solid model. These points are obtained from the unblended solid model by a numerical solution to a convolution integral, wherein the convolution integral includes a spherically symmetric blending function with a size responsive to the blend radius desired for each of one or more regions on the solid model. For example, the spherical blending function may possess a constant value everywhere inside a sphere of radius R, and a value of zero outside (here called a ''hard sphere''), or it may be represented by other functions of the radial direction, more specifically, the gaussian bell curve, in which case it will be called a ''gaussian sphere''. The numerical solution to the convolution integral is performed iteratively by placing the blending sphere at a plurality of locations along each of a set or rays that are defined substantially normal to and intersecting the solid model surface. The location on each ray at which the convolution integral is equal to a preselected value is stored. These stored locations may be used directly, or they may be used to define a set of surfaces that interpolate the blended solid model.
Patent•
20 Oct 1987
TL;DR: In this article, the authors proposed a method and a system of pumping a first and a second liquid in an artificial kidney in substantially equal quantities at a substantially constant flow. But they did not consider the effect of reciprocation of the pumps in both directions.
Abstract: A method and a system of pumping a first and a second liquid in an artificial kidney in substantially equal quantities at a substantially constant flow The system includes a main pump having complementary main chambers, and first and second auxiliary pumps each having complementary auxiliary chambers The pumps are reciprocated in unison and the system further includes a unique configuration of intake and discharge lines and associated control valves which provide a constant and equal flow of first and second liquid into and out of the artificial kidney during reciprocation of the pumps in both directions
TL;DR: In this article, a novel method of analysing serial production lines has been developed, which lets one compute the throughput rate of lines composed of dissimilar stations, as well as for a large class of distributions of station service times.
Abstract: A novel method of analysing serial production lines has been developed. This method lets one compute the throughput rate of lines composed of dissimilar stations, as well as for a large class of distributions of station service times. Several distribution-free models of 3-station lines are presented. These models are used to compute the throughput rate of unbalanced lines in which the sum of the mean service times is constant. Results are shown as contour plots of constant throughput rate. The bowl phenomenon is reviewed in the light of this capacity to model with a greater degree of freedom.