Showing papers on "Constant (mathematics) published in 1985"

A √N algorithm for mutual exclusion in decentralized systems

Abstract: An algorithm is presented that uses only c√N messages to create mutual exclusion in a computernetwork, where N is the number of nodes and c a constant between 3 and 5. The algorithm issymmetric and allows fully parallel operation.

Constant propagation with conditional branches

Abstract: Constant propagation is a well known global flow analysis problem. The goal of constant propagation is to discover values that are constant on all possible executions of a program and to propagate these constant values as far forward through the program as possible. Expressions that have all constant operands can be evaluated at compile time and the results further propagated. The use of the algorithms presented here can result in smaller and faster compiled programs.

Deterministic simulation of probabilistic constant depth circuits

Abstract: We explicitly construct, for every integer n and e ≫ 0, a family of functions (psuedo-random bit generators) fn,e:{0,1}ne → {0,1}n with the following property: for a random seed, the pseudorandom output "looks random" to any polynomial size, constant depth, unbounded fan-in circuit. Moreover, the functions fn,e themselves can be computed by uniform polynomial size, constant depth circuits. Some (interrelated) consequences of this result are given below. 1) Deterministic simulation of probabilistic algorithms. The constant depth analogues of the probabilistic complexity classes RP and BPP are contained in the deterministic complexity classes DSPACE(ne) and DTIME(2ne) for any e ≫ 0. 2) Making probabilistic constructions deterministic. Some probablistic constructions of structures that elude explicit constructions can be simulated in the above complexity classes. 3) Approximate counting. The number of satisfying assignments to a (CNF or DNF) formula, if not too small, can be arbitrarily approximated in DSPACE(ne) and DTIME(2ne), for any e ≫ 0. We also present two results for the special case of depth 2 circuits. They deal, respectively, with finding a satisfying assignment and approximately counting the number of assignments. For example, for 3-CNF formulas with a fixed fraction of satisfying assignmemts, both tasks can be performed in polynomial time!

Constant pressure-constant temperature molecular dynamics for rigid and partially rigid molecular systems

Abstract: The method of molecular dynamics at fixed pressure and/or temperature is adapted to rigid or partly rigid molecular systems with geometrical constraints using the cartesian coordinate approach. Both isotropic and anisotropic volume fluctuations, allowing for shape variation, are considered. The simulation of a benzene crystal at zero pressure and various temperatures is given as an illustration.

Type curves for finite radial and linear gas-flow systems: constant-terminal-pressure case

Abstract: This paper presents gas production rate results in type curve form for finite radial and linear flow systems produced at a constant terminal (bottomhole) pressure. These results can be utilized in the analysis of actual gas and oil rate-time data to estimate reservoir size and make some inference about reservoir shape. The type curves are based upon dimensionless variables that are a generalized form of those presented previously. In addition, a previously presented drawdown parameter is used. Example applications are given which demonstrate the applicability of the type curves to a variety of reservoir configurations. The Appendix contains derivations of the dimensionless variables and the drawdown parameter.

Asymptotic Score-Statistic Processes and Tests for Constant Hazard Against a Change-Point Alternative

Abstract: The problem of testing for a constant failure rate against alternatives with failure rates involving a single change-point is considered. The asymptotic significance level for tests based on maximal score statistics are shown to involve the solution to a first passage time problem for an Ornstein-Uhlenbeck process. An example illustrates the methodology.

On the sampling of a linear analytic control system

Abstract: In the present work we characterize the discrete time system which reproduces exactly the evolutions in the state of a given vector input linear analytic continuous time system driven by inputs which are constant on time intervals of fixed amplitude. This is achieved by comparing the Volterra series associated respectively to the sampled and continuous input state functionals. Moreover we give a compact Lie formula for the solution of a parametrized nonlinear differential equation which enables to characterize the nonlinear difference equation which solves the problem in terms of formal Lie series. On these bases, it becomes very natural to introduce a notion of approximated sampling of main efficiency in practical situations for computing purpose.

Simple criteria for stability of interval matrices

Abstract: In this paper, the simple sufficient conditions are presented for the stability of a constant real matrix whose elements are not known precisely but we know the upper and lower bounds of intervals in which the elements of matrix A are confined. These conditions are also applied in determining the stability and the degree of stability of a matrix.

Effective action on the hyperbolic plane in a constant external field

Abstract: Massive scalar and spin 1/2 fields are considered on a two‐dimensional space‐time with constant background curvature and in the presence of an external constant field. For each case, the Euler–Heisenberg effective action and the pair creation rate and their dependence on both the curvature and external field is determined exactly.

Liquid state quantum chemistry : A cavity model

Abstract: A cavity model for quantum chemical calculations on physically solvated molecules is described. The cavity is defined by a surface on which the electronic contribution to the electrostatic potential is constant and the value of this quantity is fixed by the volume of the cavity which is equal to the molecular volume in the liquid. The solvent is represented by its static dielectric constant. Although the thermodynamic quantities computed with this model are strongly dependent on the shape of the cavity, the electronic structure can be obtained with a good accuracy by approximating the surface by an ellipsoid which allows an analytical calculation of the electrostatic term and even the dispersion term of the interaction free energy. A general scheme is proposed for a liquid state quantum chemistry.

Analysis of Arbitrarily Oriented Microstrip Transmission Lines in Arbitrarily Shaped Dielectric Media Over a Finite Ground Plane

Abstract: A numerical analysis is presented for a multiconductor transmission line in multilayered Iossy, dielectric regions where the ground plane is of finite extent. The transmission fines are infinitely long and vary in cross section from finite to infinitesimally thin. The Green's function for such a two-dimensional transmission line involves an arbitrary constant. If the ground plane is infinite, the method of images could be used where this constant cancels out. However, in the case of a finite ground plane, the constant has to be evaluated. Here a numerical method is presented where the constant could be eliminated rather than evaluated by imposing the condition for the total charge to be zero. The transmission lines, dielectric regions, and the ground plane can have arbitrary cross sections.

Predictor laws for pictorial flight displays

Abstract: Two predictor laws are formulated and analyzed: (1) a circular path law based on constant accelerations perpendicular to the path and (2) a predictor law based on state transition matrix computations. It is shown that for both methods the predictor provides the essential lead zeros for the path-following task. However, in contrast to the circular path law, the state transition matrix law furnishes the system with additional zeros that entirely cancel out the higher-frequency poles of the vehicle dynamics. On the other hand, the circular path law yields a zero steady-state error in following a curved trajectory with a constant radius. A combined predictor law is suggested that utilizes the advantages of both methods. A simple analysis shows that the optimal prediction time mainly depends on the level of precision required in the path-following task, and guidelines for determining the optimal prediction time are given.

Stable and Semistable Low Order Finite Elements for Viscous Flows

Abstract: It is shown that i) the bilinear/constant and linear/constant “box” elements are not uniformly stable and ii) certain element pairs derived from those above by restricting the pressure spaces are stable. The notion of (div)-semistability is developed to study the behavior of the bilinear/constant and linear/constant “box” elements in detail.

Pole assignment of strictly proper and proper linear systems by constant output feedback

Abstract: A new unifying approach for the study of pole assignment by constant output feedback (CPAP) for strictly proper and proper linear systems is presented. The multilinear nature of CPAP is reduced to a linear problem and to the standard multilinear problem of decomposability of multivectors; the solvability of CPAP thus becomes a problem of finding real intersections of a linear variety with the Grassmann variety of a projective space. An alternative proof to the ml≥n(m, I, n are the numbers of outputs, inputs, states) necessary and sufficient condition for generic pole-assignability of strictly proper systems by complex output feedback is given; the above result is extended to the ml≥ n + 1 condition for the case of proper systems. Stronger necessary conditions for generic pole assignment by a real output feedback are obtained by using the recently introduced invariant, the Plucker matrix Pn such conditions are that Pn must have full rank and ml≥n (strictly proper case), or ml≥ n + 1 (proper case). It is sh...

Diffusion, mobility and the einstein relation

Abstract: We investigate the Einstein relation σ = βD between the diffusion constant D and the “mobility”, of a “test particle” interacting with its environment: β−1 is the temperature of the system where D is measured and σE is the drift in a constant external field E The relation is found to be satisfied for all model systems in which we can find a unique stationary non-equilibrium State of the environment, as seen from the test particle in the presence of the field For some systems, eg infinite systems of hard rods in one dimension, we find non unique stationary states which do not satisfy the Einstein relation For some models in a periodic box the Einstein relation is the most direct way of obtaining D A precise macroscopic formulation of the Einstein relation which makes it mathematically very plausible is given

Reliability analysis of a system in a randomly changing environment

Abstract: In reliability analysis of a repairable system, it is usually assumed that the system operates in, a constant environment. In fact, it needn't be so. For example, environment may have different stress levels, and the lifelength of a repairable system under these stresses might differ from each other, too.

Technical Note—On Normalizing Constants in Queueing Networks

Abstract: We present a method for deriving the normalizing constant for the state space probabilities in a closed Markovian queueing network with constant service rates. Our method produces a much simpler expression than any obtained previously. This expression takes the form of a sum of only M terms (if the visitation rate to service rate ratios are distinct), and is easily generalized to the degenerate case. The expression also yields a closed form solution for time delay distributions in cyclic networks of any length and with any number of customers.

Phase locked loop circuit

Abstract: PURPOSE:To obtain a phase locked loop PLL having an excellent loop stability by changing the converting gain of a phase comparator in response to the frequency dividing ratio. CONSTITUTION:Plural constant current sources of a phase comparator 2 are controlled by a frequency divider control input 6 via a current source control circuit 7 so as to nearly satisfy Equation, where N1, N2 denote the 1st and 2nd frequency dividing ratios of the frequency dividing ratio N, Kd is the converting gain of a constant current source 1, (a) is a comparison constant, and I2 is a current value of a constant current source 2 (not shown). Thus, the loop gain is made nearly constant by controlling the constant current source of the phase comparator 2 via the circuit 7 as to various N and the stability of the loop is improved. The phase locked loop PLL stable to secular change and temperature change is obtained for digital processing until the constant current source is changed over from the frequency divider control input 6.

Time variation of coupling constants in Kaluza-Klein cosmologies.

Abstract: We present a cosmological analysis of a six-dimensional Einstein-Yang-Mills-Higgs model with SO(3) invariance to which is added a matter term. An analytical expression for the time variation of the internal radius is obtained together with the predictions for the variations of the coupling ''constants'' involved. Their variation is limited to the very early stages of the cosmological evolution since the internal radius quickly becomes constant. It is shown that, once the asymptotic behavior sets in, the four-dimensional space-time expands linearly in time with a zero effective cosmological constant, after fine tuning.