Showing papers on "Constant (mathematics) published in 1997"
TL;DR: It is shown that under some circumstances, finite-time blow-up of solutions is possible and in other circumstances, the solutions will decay to a spatially constant solution (collapse).
Abstract: We investigate the properties of solutions of a system of chemotaxis equations arising in the theory of reinforced random walks. We show that under some circumstances, finite-time blow-up of solutions is possible. In other circumstances, the solutions will decay to a spatially constant solution (collapse). We also give some intuitive arguments which demonstrate the possibility of the existence of aggregation (piecewise constant) solutions.
235 citations
TL;DR: In this paper, a polynomial approximation with respect to time is applied to the waveform of the transients in estimating the inertia constant, and a simple model based on the idea of average system frequency is assumed to estimate the capacity of the generators.
Abstract: A procedure for estimating the inertia constant M(=2H) of a power system and total on-line capacity of spinning-reserve support generators, using transients of the frequency measured at an event such as a generator load rejection test, is presented. A polynomial approximation with respect to time is applied to the waveform of the transients in estimating the inertia constant, and a simple model based on the idea of average system frequency is assumed in estimating the capacity of the generators. Results of the estimation using the transients at 10 events show that the inertia constant of the 60 Hz power system of Japan is around 14 to 18 seconds in the system load base, and the capacity of the spinning-reserve support generators is 20 to 40% of the system load. The proposed procedure is expected to be tested by Kansai Electric Power Company with increased number of events. This effort will contribute to estimate and evaluate the dynamic behavior of the system frequency in loss of generation or load.
224 citations
TL;DR: The solution of a tracking problem for a secondorder nonlinear system with uncertain dynamics and incomplete state measurement is obtained by means of a procedure directly inspired by the solution of the classical minimum-time optimal control problem.
215 citations
01 Jan 1997
TL;DR: In this paper, a quantum state can be stored intact for arbitrary long time at a constant decoherence rate with arbitrary small error probability, and fault tolerance is achieved by quantum error correction.
Abstract: Quantum error correction can be performed fault-tolerantly This allows to store a quantum state intact (with arbitrary small error probability) for arbitrary long time at a constant decoherence rate.
201 citations
TL;DR: In this paper, a second-order finite-difference algorithm for the numerical solution of diffusion problems in strongly heterogeneous and non-isotropic media is constructed, which is superior to all other algorithms compared it with.
196 citations
TL;DR: In this article, an analytical transport solution for non-equilibrium radiative transfer in an infinite and isotropically scattering medium is given, as a function of space and time and in the form of a double integral.
115 citations
TL;DR: In this article, a meta-algorithm was proposed to combine the use of variable steps with symplectic integrators, without destroying the favorable properties of long-time integrations.
111 citations
TL;DR: It is proved that for every constant δ>0 the chromatic number of the random graphG(n, p) withp=n−1/2−δ is asymptotically almost surely concentrated in two consecutive values.
Abstract: We prove that for every constant δ>0 the chromatic number of the random graphG(n, p) withp=n−1/2−δ is asymptotically almost surely concentrated in two consecutive values. This implies that for any β<1/2 and any integer valued functionr(n)≤O(nβ) there exists a functionp(n) such that the chromatic number ofG(n,p(n)) is preciselyr(n) asymptotically almost surely.
110 citations
TL;DR: Among all conformal classes of Riemannian metrics on the CP, the Fubini-Study metric has the largest Yamabe constant as discussed by the authors, which is proved by perturbations of the Seiberg-Witten equations, which yields new results on the total scalar curvature of almost Kahler 4-manifolds.
Abstract: Among all conformal classes of Riemannian metrics on ${\Bbb CP}_2$, that of the Fubini-Study metric is shown to have the largest Yamabe constant. The proof, which involves perturbations of the Seiberg-Witten equations, also yields new results on the total scalar curvature of almost-K\"ahler 4-manifolds.
105 citations
Posted Content•
01 Jan 1997TL;DR: In this paper the combined problem is formulated as a single-integer programming model and the LP-relaxation of this model is solved by column-generation techniques, and the results of an experimental evaluation show that the lower bounds are tight.
Abstract: This paper deals with two most important problems, from both practical and theoretical standpoints, arising in sequencing mixed-model assembly lines. Such lines have become core components of modern repetitive manufacturing, and just-in-time (JIT) manufacturing in particular. One problem is to keep the usage rate of all parts fed into the final assembly as constant as possible (the "level-scheduling problem"), while the other is to keep the line's workstation loads as constant as possible (the "car-sequencing problem"). In this paper the combined problem is formulated as a single-integer programming model. The LP-relaxation of this model is solved by column-generation techniques. The results of an experimental evaluation show that the lower bounds are tight.
104 citations
TL;DR: In this article, the impact of finite, though high, Pe on the transport of an inert solute in a heterogeneous aquifer is quantified by the Peclet numbers Peij=U/Ddij=I/αdij, which as a rule are much larger than unity.
Abstract: Transport of an inert solute in a heterogeneous aquifer is governed by two mechanisms: advection by the random velocity field V(x) and pore-scale dispersion of coefficients Ddij. The velocity field is assumed to be stationary and of constant mean U and of correlation scale I much larger than the pore-scale d. It is assumed that Ddij=αdijU are constant. The relative effect of the two mechanisms is quantified by the Peclet numbers Peij=U/Ddij=I/αdij, which as a rule are much larger than unity. The main aim of the study is to determine the impact of finite, though high, Pe on 〈C〉 and σC2, the concentration mean and variance, respectively. The solution, derived in the past, for Pe=∞ is reconsidered first. By assuming a normal X probability density function (p.d.f.), closed form solutions are obtained for 〈C〉 and σC2. Recasting the problem in an Eulerian framework leads to the same results if certain closure conditions are adopted. The concentration moments for a finite Pe are derived subsequently in a Lagrangean framework. The pore-scale dispersion is viewed as a Brownian motion type of displacement Xd of solute subparticles, of scale smaller than d, added to the advective displacements X. By adopting again a normal p.d.f. for the latter, explicit expressions for 〈C〉 and σC2 are obtained in terms of quadratures over the joint p.d.f. of advective two particles trajectories. While the influence of high Pe on 〈C〉 is generally small, it has a significant impact on σC2. Simple results are obtained for a small V0, for which trajectories are fully correlated. In particular, the concentration coefficient of variation at the center tends to a constant value for large time. Comparison of the present solution, obtained in terms of a quadrature, with the Monte Carlo simulations of Graham and McLaughlin [1989] shows a very good agreement.
TL;DR: In this article, a new class of exact solutions for FRW models was obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe, which is based on Lyra's geometry.
Abstract: FRW models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe.
TL;DR: In this paper, the authors investigated the behavior of solutions to the Cauchy problem with respect to the heat kernel and showed that if u is the solution to the linearized version, i.e. with ⊇, then u decays like a solution for the non-linear version.
Abstract: The aim of this paper is to investigate the behaviour as t→∞ of solutions to the Cauchy problem u t - Δu t - νΔu - (b,⊇u) =⊇.F(u), u(x, 0) = u o (x), where ν > 0 is a fixed constant, t ≥ 0, x ∈ R n . First, we prove that if u is the solution to the linearized equation, i.e. with ⊇.F (u) ≡ 0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u o .
TL;DR: In this paper, the authors used the Arrhenius law to estimate the compressive strength of a concrete mix subjected to a temperature history, based on a new definition of the rate of hydration linked to the concrete strength.
Abstract: This paper discusses the estimation, at early ages, of the compressive strength of a concrete mix subjected to a temperature history. The method of "equivalent age" based on the Arrhenius law is used. It involves a new definition of the rate of hydration linked to the concrete strength. This rate of hydration includes a model of a linear decrease of the long-term strength of concrete with increasing temperature. Tests at constant and variable temperatures were carried out. They enable, first, the proposed method applicable to the problem to be verified, and second, the accuracy of the new approach to be compared with that of the one currently used on construction sites.
09 Feb 1997
TL;DR: To measure the benefits of circuit specialization, a functional density metric is presented and will be used to justify runtime constant propagation as well as analyze the effects of reconfiguration time on run-time reconfigured systems.
Abstract: Circuit specialization techniques such as constant propagation are commonly used to reduce both the hardware resources and cycle time of digital circuits. When reconfigurable FPGAs are used, these advantages can be extended by dynamically specializing circuits using run-time reconfiguration (RTR). For systems exploiting constant propagation, hardware resources can be reduced by folding constants within the circuit and dynamically changing the constants using circuit reconfiguration. To measure the benefits of circuit specialization, a functional density metric is presented. This metric allows the analysis of both static and run-time reconfigured circuits by including the cost of circuit reconfiguration. This metric will be used to justify runtime constant propagation as well as analyze the effects of reconfiguration time on run-time reconfigured systems.
TL;DR: In this paper, it was shown that if a point p is a point of a Lorentzian manifold and p is spacelike Osserman at p, then p has constant sectional curvature at p ; similarly, if p is timelike OSS at p, then OSS has constant curvatures at p.
Abstract: Let p be a point of a Lorentzian manifold M
We show that if M is spacelike Osserman at p , then M has constant sectional curvature at p ; similarly, if M is timelike Osserman at p , then M has constant sectional curvature at p The reverse implications are immediate
The timelike case and 4-dimensional spacelike case were first studied in [ 3 ]; we use a different approach to this case
TL;DR: A method is introduced to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L 1 error of the corresponding kernel estimate is not larger than three times theerror of the estimate with the optimal smoothing factors plus a constant times √log n/n.
Abstract: We introduce a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the $L_1$ error of the corresponding kernel estimate is not larger than three times the error of the estimate with the optimal smoothing factor plus a constant times $\sqrt{\log n/n}$, where n is the sample size, and the constant depends only on the complexity of the kernel used in the estimate. The result is nonasymptotic, that is, the bound is valid for each n. The estimate uses ideas from the minimum distance estimation work of Yatracos. As the inequality is uniform with respect to all densities, the estimate is asymptotically minimax optimal (modulo a constant) over many function classes.
TL;DR: In this paper, the one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation.
Abstract: The one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the Cauchy and Signalling problems are expressed in terms of entire functions (of Wright type) in the similarity variable and their behaviours turn out to be intermediate between those for the limiting cases of a perfectly viscous fluid and a perfectly elastic solid. In view of the small dissipation exhibited by the seismic pulses, the nearly elastic limit is considered. Furthermore, the fundamental solutions for the Cauchy and Signalling problems are shown to be related to stable probability distributions with an index of stability determined by the order of the fractional time derivative in the evolution equation.
TL;DR: The existence of global constant mean curvature (CMC) foliations of 3-dimensional maximal hyperbolic Lorentzian manifolds with genus(Σ> 1) is proved in this paper.
TL;DR: In this paper, it is shown that for inclusions of constant eigenstrain and eigenstress, the shape of the inclusion is restricted and any part of a plane (i.e., polyhedral inclusion) is prohibited.
Abstract: It is shown, based on properties of analytic functions, that for inclusions of constant eigenstrain and eigenstress that the shape of the inclusion is restricted and any part of a plane (i.e. polyhedral inclusion) is prohibited.
Proceedings Article•
01 Dec 1997TL;DR: It is shown that the Aggregating Algorithm attains the optimal constant in the authors' bound, whereas the constant attained by the ridge regression procedure in general can be 4 times worse.
Abstract: We apply a general algorithm for merging prediction strategies (the Aggregating Algorithm) to the problem of linear regression with the square loss; our main assumption is that the response variable is bounded. It turns out that for this particular problem the Aggregating Algorithm resembles, but is slightly different from, the well-known ridge estimation procedure. From general results about the Aggregating Algorithm we deduce a guaranteed bound on the difference between our algorithm's performance and the best, in some sense, linear regression function's performance. We show that the AA attains the optimal constant in our bound, whereas the constant attained by the ridge regression procedure in general can be 4 times worse.
TL;DR: This work investigated a control strategy using constant C w instead of constant transmembrane pressure for ultrafiltration processes and explored three different strategies for such control and evaluated the theoretical and industrial implications for single solute systems.
TL;DR: In this article, the largest gap between consecutive primes below a given threshold was shown to be G(X)⩾(2e γ +o(1)) log Xlog 2 Xlog 4 X(log 3 X) −2, where γ is Euler's constant.
Patent•
24 Jan 1997TL;DR: In this article, a method for designing a constant multiplier system comprises identifying a repeated pattern in a minimal signed digit expression of a multiplier, designing a first accumulator stage to compute the product of a multiplicand by an instance of the pattern, and designing a second accumulators stage for accumulating shifted replicas of the patterns to yield a final product.
Abstract: A method for designing a constant multiplier system comprises identifying a repeated pattern in a minimal signed digit expression of a multiplier, designing a first accumulator stage to compute the product of a multiplicand by an instance of the pattern, and designing a second accumulator stage for accumulating shifted replicas of the pattern to yield a final product. Remainder terms, for example corresponding to non-zero digit positions not included in any instance of the pattern, are also accumulated at the second stage. By limiting the method to patterns with at least two non-zero values, the result tends to reduce the number of operations that must be performed to determine a final product. Thus, the size, complexity and speed of a constant multiplier system can be optimized.
TL;DR: In this article, a lower bound of the logarithmic Sobolev constant for diffusion processes on a compact Riemannian manifold with negative Ricci curvature is presented.
Abstract: This paper presents some explicit lower bound estimates of logarithmic Sobolev constant for diffusion processes on a compact Riemannian manifold with negative Ricci curvature. Let Ric≧−K for some K>0 and d, D be respectively the dimension and the diameter of the manifold. If the boundary of the manifold is either empty or convex, then the logarithmic Sobolev constant for Brownian motion is not less than
TL;DR: Examination of evidence for constant and decreasing timing aversion with respect to saving lives suggests that there is substantial evidence for decrease timing aversion and against the constant timing aversion hypothesis.
TL;DR: In this paper, the authors studied the infinite time ruin probability in a compound Poisson process with a constant premium rate and a constant interest force and showed that under appropriate conditions the ruin probability is exponentially bounded.
Abstract: We continue our discussion of infinite time ruin probabilities in continuous time in a compound Poisson process with a constant premium rate and a constant interest force. Under appropriate conditions the ruin probability is exponentially bounded. The usual adjustment coefficient is replaced by an adjustment function depending in an intricate way on the initial reserve, the interest force and all ingredients of the compound Poisson process. After deriving general bounds we also give expansions for the case where the interest force is small.
TL;DR: In this article, the stability and accuracy of the advection phase calculation of the Cubic Interpolated Propagation scheme, which solves the universal hyperbolic equation, were examined using Fourier analysis.