Showing papers on "Constant (mathematics) published in 1981"

(T, S i ) Policy Inventory Model for Deteriorating Items with Time Proportional Demand

Abstract: An EOQ model is reconsidered here in which the demand rate is changing linearly with time and the deterioration is assumed to be a constant fraction of the onhand inventory The planning horizon is finite and known and the replenishment periods are assumed to be constant The problem is to find the optimal number of replenishments, which are instantaneous When there is no deterioration, the model developed is related to the corresponding model for nondeteriorating items An example followed by sensitivity analysis is given to illustrate the derived results

The steady state of deformation

Abstract: The steady state of deformation for any mass of particles is that state in which the mass is continuously deforming at constant volume, constant normal effective stress, constant shear stress, and constant velocity. The steady state of deformation is achieved only after all particle orientation has reached a statistically steady-state condition and after all particle breakage, if any, is complete, so that the shear stress needed to continue deformation and the velocity of deformation remain constant. The similarities and differences between steady-state deformation and the current use of the term critical state are described. A special undrained triaxial test on a sand is presented to demonstrate clearly that a special flow structure exists during steady-state deformation, which is quite different from the initial structure, and which is credited to a nonrandom, i.e., statistically oriented, arrangement of the sand grains.

The form of the near-bed velocity profile in a tidally accelerating flow

Abstract: In an accelerating tidal flow the near-bed velocity profile departs from the usual logarithmic form. The amount of the departure may not necessarily be large, but is nevertheless important when the profiles are used to calculate the bed roughness length and shear stress. A form for the accelerated profile is derived in terms of an ‘acceleration length’. Profiles measured off the SW coast of England are fitted to this expression, and give a value for a constant γ appearing in it. Published laboratory oscillatory flow profiles are also fitted; in this case the constant γ is larger due to the greater relative bed roughness. Von Karman's constant is obtained from the field data and found to be equal to 0.40, closer to laboratory values than to the now widely used atmospheric value of 0.35. Some evidence is found, however, to support a slow decrease in von Karman's constant with increasing boundary-layer thickness to roughness length ratio.

Time-Space-Optimal String Matching

Abstract: Any string-matching algorithm requires at least linear time and a constant number of local storage locations. We design and analyze an algorithm which realizes both asymptotic bounds simultaneously. This can be viewed as completely eliminating the need for the tabulated “failure function” in the linear-time algorithm of Knuth, Morris, and Pratt. It makes possible a completely general implementation as a Fortran subroutine or even as a six-head finite automaton.

An analysis of single item inventory systems with returns

Abstract: Inventory systems with returns are systems in which there are units returned in a repairable state, as well as demands for units in a serviceable state, where the return and demand processes are independent. We begin by examining the control of a single item at a single location in which the stationary return rate is less than the stationary demand rate. This necessitates an occasional procurement of units from an outside source. We present a cost model of this system, which we assume is managed under a continuous review procurement policy, and develop a solution method for finding the policy parameter values. The key to the analysis is the use of a normally distributed random variable to approximate the steady-state distribution of net inventory. Next, we study a single item, two echelon system in which a warehouse (the upper echelon) supports N(N ⩾ 1) retailers (the lower echelon). In this case, customers return units in a repairable state as well as demand units in a serviceable state at the retailer level only. We assume the constant system return rate is less than the constant system demand rate so that a procurement is required at certain times from an outside supplier. We develop a cost model of this two echelon system assuming that each location follows a continuous review procurement policy. We also present an algorithm for finding the policy parameter values at each location that is based on the method used to solve the single location problem.

Analysis and optimal control of time-varying linear systems via block-pulse functions

Abstract: Succinct and clear-sighted operational properties of block-pulse functions are fully applied to the analysis and optimal control of time-varying linear systems with quadratic performance index. Piecewise constant solutions equally distributed, which are simple in form and convenient for use or implementation, are consequently obtained. Another advantage of this method is that any positive integer can be chosen as the number of sub-intervals, whereas in the case of Walsh function approximation the choice can only be made from 2, 4, 8, 16, 32, and so on. The algorithms developed in the paper are illustrated by appropriate examples.

The optimal production of an exhaustible resource when price is exogenous and stochastic

Abstract: This paper examines the optimal production of a resource such as oil when its price is determined exogenously (e.g. by a cartel such as OPEC), and is subject to stochastic fluctuations away from an expected growth path. We first examine the dependence of production on extraction cost, and show that the conventional exponential decline curve is indeed optimal if marginal cost is constant with respect to the rate of extraction but is a hyperbolic function of the reserve level. We next show that uncertainty about future price affects the optimal production rate in two ways. First, if marginal cost is a convex (concave) function of the rate of production, stochastic fluctuations in price raise (lower) average cost over time, so that there is an incentive to speed up (slow down) production. Second, the “option” value of the reserve, i.e. the ability to withhold production indefinitely and never incur the cost of extraction, provides an incentive to slow down the rate of production.

Calculation of critical points from cubic two-constant equations of state

Abstract: A computational modification of the Heidemann-Khalil method for calculating the critical temperatures and pressures for general phase-equilibrium problems greatly reduced the computing time for simple two-constant cubic equations of state. For systems where the unlike binary interaction parameters can be derived from the pure-component parameters using the geometric mean values, a further simplification lowers the computing times to a few milliseconds, regardless of the number of components.

Totally real submanifolds in a 6-sphere

Abstract: A 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. We investigate 3-dimensional totally real submanifolds in 56 and classify 3-dimensional totally real submanifolds of constant sectional curvature.

Transient distortion and nth order filtering in deep level transient spectroscopy (DnLTS)

Abstract: Problems associated with intrinsic sensitivity and time constant selectivity of capacitive DLTS systems are discussed as well as intrinsic limitations in predominantly deep level doped semiconductors. A previously published figure of merit for the optimized exponential correlator for capacitive DLTS studies is shown to be too high because of improper consideration of effects of level restoration: when correctly compared, a filter with a 12% lower figure of merit can be constructed based purely on gating and a weighted phase inversion before the integrator and a phase sensitive detector has a 20% lower figure of merit. The exponential DLTS correlator is also inadequate for analysis of continuous spectra because of its slow drop off in response (∝ TS for TS shorter than the peak response time constant and ∝ TS−1 for longer times). Blanking is necessary to achieve more selectivity relative to short time constants. When performed on-line, D2LTS gives a response ∝ TS−2 for longer times. Still more selective filters of order n, or DnLTS, are considered based on weighted averages over time intervals in geometric progression that are suitable for DLTS and a system with ±1 weighting and suitably chosen time intervals for use with DDLTS. For these filters there is no penalty in figure of merit associated with choice of DDLTS which also appears to be easier to achieve than DLTS. On-line filters with long time constant responses ∝ TS−3 or higher order are shown to exact a large penalty in figure of merit. Equivalent filters can, however, be synthesized with much better figure of merit by a software compensation of multichannel data. The channels are then selected so that the responses of successive channels peak a factor of 2 away in TS and the number of pulses used is decreased by a factor of two. Relative to a multipoint averager, the software compensated analyzer requires a factor of 100 less in measurement time for comparable accuracy when a spectrum must cover a range of 1000:1 in relaxation times. There are also comparable improvements in the holding time specifications and the number of A/D conversions if the system is to be coupled to a computer. When the deep level concentration is comparable to the shallow doping concentration, the peak responses of both DLTS and DDLTS are broadened, the sensitivity increases, the response peaks are shifted to larger relaxation times, and the system becomes essentially nonlinear in response to the individual deep level constituents. This distortion can, in principle, be corrected by going to a constant capacitance mode of operation both during the initial driving pulse and during the recovery transient.

An analysis of a uniformly accurate difference method for a singular perturbation problem

Abstract: It will be proven that an exponential tridiagonal difference scheme, when applied with a uniform mesh of size h to: euXx + b(x)ux = f(x) for O O, b and f smooth, e in (0, 1], and u(O) and u(I) given, is uniformly second-order accurate (i.e., the maximum of the errors at the grid points is bounded by Ch2 with the constant C independent of h and e). This scheme was derived by El-Mistikawy and Werle by a C' patching of a pair of piecewise constant coefficient approximate differential equations across a common grid point. The behavior of the approximate solution in between the grid points will be analyzed, and some numerical results will also be given.

Trigonometric sums over primes I

Abstract: We write e(x) for e2πix and let ‖x‖ denote the distance of x from the nearest integer. The notation A ≪ B will mean |A| ≤ C|B| where C is a positive constant depending at most on an arbitrary positive number e, and on an integer k. The letter p always denotes a prime number. The main results of the present paper are as follows.

On the Distribution of Multidimensional Reflected Brownian Motion

Abstract: Let $Z = \{ Z(t),t > 0\} $ be a reflected Brownian motion on the K-dimensional nonnegative orthant, with the direction of reflection constant over each boundary surface. Such processes arise in heavy traffic theory for K-station networks of queues. This paper continues our study of the diffusion process Z,with attention restricted to the case $k = 2$ for simplicity. (Most of the results extend directly to higher dimensions; our notation and style of argument are designed to suggest appropriate generalizations for arbitrary K wherever possible.) The backward equation for the transition density function (with boundary and initial conditions), the corresponding forward equation and the equation for the steady-state distribution are all derived informally. Also presented are various calculations relating to steady-state distributions, including a moment formula and the derivation of a condition (involving the drifts and directions of reflection), that we conjecture to be necessary and sufficient for existence...

Lagrangian analysis and quantum mechanics : a mathematical structure related to asymptotic expansions and the Maslov index

Abstract: This work might have been entitled "The Introduction of Planck's Constant into Mathematics, "in that it introduces quantum conditions in a purely mathematical way in order to remove the singularities that arise in obtaining approximations to solutions of complex differential equations.The book's first chapter develops the necessary mathematical apparatus: Fourier transforms, metaplectic and symplectic groups, the Maslov index, and lagrangian varieties. The second chapter orders Maslov's conceptions in a manner that avoids contraditions and creates step by step an essentially new structure-the lagrangian ayalysis.Unexpectedly and strangely the last step requires the datum of a constant, which in applications to quantum mechanics is identified with Planck's constant. The final two chapters apply lagrangian analysis directly to the Schrodinger, the Klein-Gordon, and the Dirac equations. Magnetic field effects and even the Paschen-Back effect are taken into account.Jean Leray-who has been professor at the College de France for the past thirty years-has made fundamental contributions to theoretical hydrodynamics, to the study of elliptic, hyperbolic, and analytic linear and nonlinear equations, and to algebraic topology and its applications to analysis. His motivations always had their origin in physical problems, except during World War II: As a prisoner of war in Germany for five years, he concealed his interest in mathematical applications by making fruitful investigations in the field of pure algebraic topology.

Stable cycling in discrete-time genetic models.

Abstract: Examples of stable cycling are discussed for two-locus, two-allele, deterministic, discrete-time models with constant fitnesses. The cases that cycle were found by using numerical techniques to search for stable Hopf bifurcations. One consequence of the results is that apparent cases of directional selection may be due to stable cycling.

Memoryless stabilization of linear delay-differential systems

Abstract: Sufficient conditions for memoryless feedback stabilization of linear time-invariant delay-differential systems are derived for both constant and time-dependent delays.

Elementary first integrals of differential equations

Abstract: It is not always possible and sometimes not even advantageous to write the solutions of a system of differential equations explicitly in terms of elementary functions. Sometimes, though, it is possible to find elementary functions which are constant on solution curves, that is, elementary first integrals. These first integrals allow one to occasionally deduce properties that an explicit solution would not necessarily reveal.

Dilation analyticity in constant electric field. II. $N$-body problem, Borel summability

Abstract: We extend the analysis of Paper I from two body dilation analytic systems in constant electric field toN-body systems in constant electric field. Particular attention is paid to what happens to isolated eigenvalues of an atomic or molecular system in zero field when the field is turned on. We prove that the corresponding eigenvalue of the complex scaled Hamiltonian is stable and becomes a resonance. We study analyticity properties of the levels as a function of the field and also Borel summability.

Implications of constant risk aversion

Abstract: The assumption of constant risk aversion often leads to a considerable simplification of decision theoretic analyses. It is shown that this restriction on constant risk aversion permits the description of a wide range of risk averse patterns between the extreme cases of risk neutrality and the exclusive orientation on the pessimistic maxmin criterion. In particular, a new axiomatic foundation of the constant risk aversion is given and a series of properties for the certainty equivalent are derived. Possible applications are shown by the treatment of risk premiums, values of information, portfolio selection, capital market theory and syndicates.

Diffusion in a Bistable Potential: The Functional Integral Approach

Abstract: We study, with the help of the Onsager-Machlup functional integral approach, the distributionP of a single stochastic variable, the evolution of which is described by a Fokker-Planck equation with a first moment deriving from a bistable potential. We set up the approximation scheme appropriate, in this approach, to the limit of constant and small diffusion coefficient. Two regimes are to be distinguished: Very long times (Kramers regime) are treated within the frame of a free-instanton-molecule gas approximation, and at intermediate times (Suzuki regime) a standard semiclassical calculation is legitimate. We thus rederive exactly the results obtained from the mode expansion and WKB method.

The thermodynamics of characteristic defect parameters

Abstract: The authors discuss the distinction between defect parameters (energies and entropies) defined at constant pressure and those defined at constant lattice parameter or constant volume and draw attention to the relations which exist between these quantities. These relations are important for the comparison of theoretical and experimental values, since the latter are almost invariably obtained from experiment at constant pressure while the basic calculations are most conveniently done at constant volume. They illustrate this importance with detailed calculations for AgCl and in particular show that the enthalpy of Frenkel defect formation at constant pressure, hp, and the corresponding internal energy for defect formation at constant volume, uv, depend in opposite ways upon the temperature. In addition the authors calculate the free volume of defect formation, also as a function of temperature. The agreement between these calculations and experiment is excellent.

The origin of piezoelectricity in poly(vinylidene fluoride)

Abstract: Electrostriction constant (K31) and Poisson's ratio of a film (μ31, μ21) and that of a crystal (μ′) were measured for uniaxially drawn and rolled poly(vinylidene fluoride) films. The highly stretched films showed the large values of MH (∼0.8). μc(∼ 4.0) and K31(∼ 30). These values depend strongly on the structures of films such as crystal structure and molecular orientation. The induced piezoelectric stress constant e 31 by poling was interpreted fairly well by the theory proposed by Wada and Hayakawa in terms of three factors; μ31, μ′c and K31. Contribution of each factor to the piezoelectricity was evaluated. Among them, the Poisson's ratio of a film has the largest effect which amounts to 50% of the total piezoelectric activity.

Unsteady flow to a well produced at constant pressure in a fractured reservoir

Abstract: The objective of this study is to delineate the characteristics of a well flowing at a constant pressure in a naturally fractured reservoir. Methods are suggested to determine system parameters. Consideration is given to both pseudosteady state and unsteady state fluid transfer from the matrix system to the fracture system. If pseudo steady state flow governs the transfer of fluids, then the rate data exhibit an initial period of decline indicating the depletion of the fracture, followed by a period in which the rate is nearly constant and finally a rapid decline in rate. The period of constant rate reflects replenishment of the fracture by the matrix. If unsteady state flow in the matrix governs the well response, then the constant rate period does not exist. Instead, the rate vs. time graph is a straight line on log-log coordinates with slope equal to 0.5. 18 refs.