Showing papers on "Constant (mathematics) published in 1992"

Observability analysis of piece-wise constant systems. I. Theory

Abstract: For pt.II see ibid., vol.28, no.4, p.1068-75, Oct. 1992. A method for analyzing the observability of time-varying linear systems which can be modeled as piece-wise constant systems (PWCS) is presented. An observability matrix for such systems is developed for continuous and discrete time representations. A stripped observability matrix (SOM) is introduced which simplifies the analysis in cases where the use of this matrix is legitimate. The observability analysis is presented as a step-by-step procedure. >

An extended Kalman filter approach to rotor time constant measurement in PWM induction motor drives

Abstract: A rotor time constant estimation technique for the purpose of updating the control gains of an induction motor field-oriented controller is described. An extended Kalman filter is employed to estimate the inverse rotor time constant online only using measurements of the stator voltages and currents and rotor speed of an induction motor. The motor is driven by a pulsewidth modulated (PWM) inverter with or without current feedback loops. By utilizing the wideband harmonic contents inherent in conventional PWM voltage waveforms, no external random test signal is required for parameter estimation. Both computer simulation and experimental results show that the filter is capable of estimating the rotor time constant while the rotor speed is either constant or time varying. >

On adaptive friction compensation

Abstract: A method of compensating for friction in control systems is presented. The method entails the use of an observer to estimate the friction which is modeled as a constant times the sign of the velocity. The purpose of the observer is to estimate this constant. The observer model is selected to ensure that the error in estimation of the friction constant converges asymptotically to zero. Simulation results verify the theory and show that the method can significantly improve the performance of a control system in which it is used. Although based on the assumption of a constant friction magnitude, the observer displays the ability to 'track' friction whose magnitude depends on velocity. >

Liouvillian first integrals of differential equations

Abstract: Liouvillian functions are functions that are built up from rational functions using exponentiation, integration, and algebraic functions. We show that if a system of differential equations has a generic solution that satisfies a liouvillian relation, that is, there is a liouvillian function of several variables vanishing on the curve defined by this solution, then the system has a liouvillian first integral, that is a nonconstant liouvillian function that is constant on solution curves in some nonempty open set. We can refine this result in special cases to show that the first integral must be of a very special form

Performance of Phenological Models Under Variable Temperature Regimes: Consequences of the Kaufmann or Rate Summation Effect

Abstract: Published research concerning insect development rate or phenology models shows that the effect of fluctuating temperature and rate summation on nonlinear and linear model predictions is not well understood. Models of rates of development at constant temperatures of an example insect are compared graphically with predicted rates under artificial and naturally varying temperature regimes. Acceleration of insect development at low temperatures and retardation at high temperatures are shown to be implicit to the assumption of nonlinearity of development. The influence of the diurnal range of the temperature regime on the rate summation effect and the interaction between rate summation and the mathematical structure of a particular development rate model are clearly demonstrated. This study shows that the selection of a development rate function for prescriptive use, based on closeness of fit to developmental data from constant temperature experiments, is meaningless. Nor should selection be based on how well a model derived from constant temperature experiments predicts insect development measured under a narrow range of fluctuating temperatures. Reasons why a nonlinear model fitted directly to rates observed under variable temperature laboratory or field data is inappropriate for subsequent prediction (in theory at least), are clearly demonstrated. An appropriate technique that calculates instantaneous development rate functions from fluctuating temperature development time observations is tested with hypothetical data. This technique failed to give reasonable estimates of the parameters of the instantaneous development rate function that generated the hypothetical data.

The formation factor of reconstructed porous media

Abstract: The porosity and the autocorrelation function of the pore space are measured on thin sections of Fontainebleau sandstones. This information is used to generate artificial porous media which share these statistical properties. The Laplace equation is numerically solved to determine the formation factor, or equivalently the electrical conductivity. With no adjustable constant, the predicted formation factors were found to be in acceptable agreement with the experimental ones.

Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules

Abstract: Simulated annealing algorithms are time inhomogeneous controlled Markov chains used to search for the minima of energy functions defined on finite state spaces. The control parameters, the so-called cooling schedule, control the probability that the energy should increase during one step of the algorithm. Most of the studies on simulated annealing have dealt with limit theorems, such as characterizing convergence conditions on the cooling schedule, or giving an equivalent of the law of the process for one fixed cooling schedule. In this paper we derive finite time estimates. These estimates are uniform in the cooling schedule and in the energy function. With new technical tools, we gain a new insight into the algorithm. We give a sharp upper bound for the probability that the energy is close to its minimum value. Hence we characterize the optimal convergence rate. This involves a new constant, the "difficulty" of the energy landscape. We calculate two cooling schedules for which our bound is almost reached. In one case it is reached up to a multiplicative constant for one energy function. In the other case it is reached in the sense of logarithmic equivalence uniformly in the energy function. These two schedules are both triangular: There is one different schedule for each finite simulation time. For each fixed finite time the second schedule has the currently used but previously mathematically unjustified exponential form. Finally, the title is "Rough large deviation estimates" because we have computed sharper ones (i.e., with sharp multiplicative constants) in two other papers.

On the complexity of approximating the independent set problem

Abstract: We show that for some positive constant c it is not feasible to approximate Independent Set (for graphs of n nodes) within a factor of n c , provided Maximum 2-Satisfiability does not have a randomized polynomial time approximation scheme We also study reductions preserving the quality of approximations and exhibit complete problems

The best sobolev constant

Abstract: For an arbitrary positive integer m, N > 2m, and q = 2N/ (N - 2m), the smallest possible constant is obtained for the Sobolev embedding .Explicit radial functions which attain this constant are demonstrated.

Dynamic mathematical model to predict microbial growth and inactivation during food processing.

Abstract: Many sigmoidal functions to describe a bacterial growth curve as an explicit function of time have been reported in the literature. Furthermore, several expressions have been proposed to model the influence of temperature on the main characteristics of this growth curve: maximum specific growth rate, lag time, and asymptotic level. However, as the predictive value of such explicit models is most often guaranteed only at a constant temperature within the temperature range of microbial growth, they are less appropriate in optimization studies of a whole production and distribution chain. In this paper a dynamic mathematical model--a first-order differential equation--has been derived, describing the bacterial population as a function of both time and temperature. Furthermore, the inactivation of the population at temperatures above the maximum temperature for growth has been incorporated. In the special case of a constant temperature, the solution coincides exactly with the corresponding Gompertz model, which has been validated in several recent reports. However, the main advantage of this dynamic model is its ability to deal with time-varying temperatures, over the whole temperature range of growth and inactivation. As such, it is an essential building block in (time-saving) simulation studies to design, e.g., optimal temperature-time profiles with respect to microbial safety of a production and distribution chain of chilled foods.

Fixed-parameter intractability

Abstract: The authors consider the complexity behavior of parametrized problems that they term fixed-parameter tractability: for each fixed parameter value y the problem is solvable in time O(n/sup c/), where c is a constant independent of the parameter y. They introduce a structure theory with which to address the apparent intractability of some parameterized problems, and they obtain completeness, density, and separation/collapse results. The greatest appeal of the theory is in the wide range of natural problems to which it can be applied, and in the practical significance of fixed-parameter problem complexities. Technical aspects are also interesting. >

Feedback control of nonlinear systems

Abstract: This paper deals with the design of (memoryless) state-feedback laws for systems modelled by nonlinear differential equations which are affine in the inputs. The purpose of the design is to obtain a (locally) internally stable closed-loop system in which the effect of exogenous inputs on a prescribed error (or, more in general, on a penalty variable) is attenuated. Two standard setups are considered: in the first one, the ratio between the energy associated with the penalty variable and that associated with the exogenous input is required to be bounded by a constant 0 < γ this setup includes (to some extent) the standard H∞control problem of linear system theory. In the second one, the penalty variable is required to converge to 0 as t ∞; this setup generalizes the so-called servomechanism problem of linear system theory.

An analytical solution for one-dimensional transport in porous media with an exponential dispersion function

Abstract: An analytical solution describing the transport of dissolved substances in heterogeneous porous media with an asymptotic distance-dependent dispersion relationship has been developed. The solution has a dispersion function which is linear near the origin (i.e., for short travel distances) and approaches an asymptotic value as the travel distance becomes infinite. This solution can be used to characterize differences in the transport process relative to both the classical convection-dispersion equation which assumes that the hydrodynamic dispersion in the porous medium remains constant and a dispersion solution which has a strictly linear dispersion function. The form of the hydrodynamic dispersion function used in the analytical solution is , where α(x) = a L[1 − e−bx/L] and is the average pore water velocity. The proposed model may provide an alternate means for obtaining a description of the transport of solutes in heterogeneous porous media, when the scale dependence of the dispersion relationship follows the behavior given by α(x). The overall behavior of the model is illustrated by several examples for constant concentration and flux boundary conditions.

Improved scale-up strategies of bioreactors

Abstract: Effective scale-up is essential for successful bioprocessing While it is desirable to keep as many operating parameters constant as possible during the scale-up, the number of constant parameters realizable is limited by the degrees of freedom in designing the large-scale operation Scale-up of aerobic fermentations is often carried out on the basis of a constant oxygen transfer coefficient, k L a, to ensure the same oxygen supply rate to support normal growth and metabolism of the desired high cell populations In this paper, it is proposed to replace the scale-up criterion of constant k L by a more direct and meaningful criterion of equal oxygen transfer rate at a predetermined value of dissolved oxygen concentration This can be achieved by using different oxygen partial pressures in the influent gas streams for different scales of operation One more degree of freedom, ie, gas-phase oxygen partial pressure, is thus added to the process of scale-up Accordingly, one more operating factor can be maintained constant during scale-up It can be used to regulate the power consumption in large-scale fermentors for economical considerations or to describe the fluid mixing more precisely Examples are given to show that the results of optimization achieved in the bench-scale study can be translated to the production-scale fermentor more successfully with only a small change in the gas-phase oxygen partial pressure employed in the bench-scale operation

IMM algorithm for tracking targets that maneuver through coordinated turns

Abstract: The interacting multiple model (IMM) algorithm uses multiple models that interact through state mixing to track a target maneuvering through an arbitrary trajectory. However, when a target maneuvers through a coordinated turn, the acceleration vector of the target changes magnitude and direction, and the maneuvering target models commonly used in the IMM (e.g., constant acceleration) can exhibit considerable model error. To address this problem an IMM algorithm that includes a constant velocity model, a constant speed model with the kinematic constraint for constant speed targets, and the exponentially increasing acceleration (EIA) model for maneuver response is proposed. The constant speed model utilizes a turning rate in the state transition matrix to achieve constant speed prediction. The turning rate is calculated from the velocity and acceleration estimates of the constant speed model. The kinematic constraint for constant speed targets is utilized as a pseudomeasurement in the filtering process with the constant speed model. Simulation results that demonstrate the benefits of the EIA model and the kinematic constraint to the IMM algorithm are given. The tracking performance of the proposed IMM algorithm is compared with that of an IMM algorithm utilizing constant velocity and constant turn rate models.

Apparatus for performing multiply and accumulate instructions with reduced power and a method therefor

Abstract: An apparatus for performing multiplications with reduced power includes an arithmetic logic unit and a decode block for performing an equivalent of a multiply instruction. A frequently-encountered multiply instruction occurs between a variable and a known constant. If the known constant is positive or negative one, the decode block enables the arithmetic logic unit to either add the variable to zero, or subtract the variable from zero, in response to the sign bit of the known constant. In response to a multiply and accumulate instruction between a variable and a known constant of positive or negative one, the decode block enables the arithmetic logic unit to either add the variable to the prior accumulated result or to subtract it therefrom, in response to the sign bit of the known constant. In either case, the high-speed multiplier is disabled and its power saved.

A consistent co‐rotational formulation for shells using the constant stress/constant moment triangle

Abstract: The facet-shell formulation involves the combination of the constant-strain membrane triangle with a constant-curvature bending triangle. The paper describes a technique whereby this facet-formulation is extended to handle geometric non-linearity by means of a co-rotational procedure. Emphasis is placed on the derivation of a technique that is increment-independent with both the internal force vector and tangent stiffness matrix being derived from the «total strain measures» in a «consistent manner».

Kinetic Phase Diagram and Scaling Relations for Stationary Diffusional Growth

Abstract: We propose a phase diagram for the selection of growth patterns in systems with a conserved quantity which evolve at asymptotically constant growth rate The occurrence of different growth forms like fractal, compact or dendritic, and the various transitions between them are characterized by scaling relations

Adaptive control of a simple nonlinear system without a priori information on the plant parameters

Abstract: The authors present an adaptive control scheme for nonlinear systems of the form x=c*/sup T/f(x)+b*u, where f(x) is Lipschitz, c* is a constant vector, and b* is a constant scalar. The control scheme achieves asymptotical model matching without a priori knowledge of the sign of the b* gain. The adaptive scheme is free from singularities in the sense that the estimate of b*, entering in the denominator of the control law, is bounded away from zero. The singularity has been overcome through a suitable modification of the parameter estimates which is based on standard least squares covariance matrix properties. >

Constant-axial-intensity nondiffracting beam.

Abstract: Numerical solutions of the Fresnel diffraction integral with various apodizing filter functions are used to indicate that a so-called nondiffracting beam can be produced that maintains a constant spot size and constant axial intensity over a considerable range, approximately 30 m in our example.

Stable constant mean curvature tori and the isoperimetric problem in three space forms

Abstract: Introduction Let ψ : M → N be an immersion of an orientable surface into a three dimensional oriented Riemannian manifold. Then ψ has constant mean curvature if and only if it is a critical point of the area functional for any compactly supported variation that preserves the volume enclosed by the surface. In this context we say that the constant mean curvature immersion ψ is stable if the second variation formula of the area, which we call henceforth the index form of ψ, is non negative for all variations of the above type. Otherwise, ψ is stable if for any f ∈ C∞(M) with compact support such that ∫ M f dA = 0, we have

Mathematical modelling of the elastic properties of retina: A determination of Young's modulus

Abstract: The retina can be regarded as an elastic membrane or sheet which stretches and deforms when a force is applied to it. Isolated bovine retina was taken and a graded traction force applied to determine retinal profile as a function of force. The resulting profile can be modelled mathematically and the model then used to determine a value for the elastic constant. The value of the elastic constant obtained by this method is approximately 2 N/m. This value of the elastic constant, combined with the observed retinal thickness, yields a value of Young's modulus for retina of approximately 2 x 10(4) Pa, which is about 2 orders of magnitude weaker than typical rubber. This value can then be used in modelling retinal behaviour in vivo when forces are applied to detached retina.

Ergodic systems of n balls in a billiard table

Abstract: We consider the motion ofn balls in billiard tables of a special form and we prove that the resulting dynamical systems are ergodic on a constant energy surface; in fact, they enjoy theK-property. These are the first systems of interacting particles proven to be ergodic for an arbitrary number of particles.

On the frequency of Titchmarsh's phenomenon for ζ(s). II

Abstract: We obtain a lower bound for max |ζ(1/2+it)| ast varies overT⩽t⩽T+Y, where (logT)1/100⩽Y⩽T, as a function ofY(1/100 is unimportant). Our lower bound is exp {D(logY)1/2 (log logY)−1/2} whereD is a positive constant. (After submitting this paper for publication we came to know through a preprint of H L Montgomery that he had proved our result in the caseY=T. In his proof an essential assumption is Riemann hypothesis and our result is independent of any such unproved hypothesis. However he has other new results which are free from any hypothesis).