Showing papers on "Linear approximation published in 1981"

Finite dimensional approximation of nonlinear problems

Abstract: In the first two papers of this series [4, 5], we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a Banach space. We derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point. The abstract theory is applied to the Galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von Karman equations.

Exchange and correlation potentials for finite temperature quantum calculations at intermediate degeneracies

Abstract: The exchange and correlation potentials which are needed in the study of electron systems (atoms, plasmas) at finite temperatures and finite degeneracies have been calculated and presented in a parametrised form convenient for use in Thomas-Fermi, Hartree-Fock, density-functional type effective single-particle models. The exchange corrected single-particle energies and chemical potential are calculated self-consistently and in the linear approximation. The natural generalisation of the Debye-Huckel screening length is used to extract a static model valid at intermediate degeneracies. The higher-order corrections (i.e., beyond Hartree-Fock) are evaluated from the ring sum and the second-order screened contributions to the thermodynamic grand potential. The ring sum is calculated via an approximation to the polarisation function which is known to be satisfactory at 0K and exact in the Debye-Huckel limit. The numerical results show that the correlation potential at finite temperatures consists of a static contribution and a dynamic part which goes to zero at high temperatures.

A state-space formulation for optimal Hankel-norm approximations

Abstract: The optimal Hankel-norm approximation problem studied in [1] is reformulated in a state-space setting. The crucial extension theorem is reestablished in this framework. The minimal degree optimal approximation is then derived in terms of state-space parameters

Optimal linear approximation in project compression

Abstract: When the cost of reducing the duration of activities is convex and nonlinear, it may be advisable (to reduce the computing burden) to seek a “satisficing” answer, in which the project is compressed to a desired completion time with a prespecified tolerable relative error. We treat the problem of constructing the optimal first degree interpolating linear spline that guarantees such maximal error and consider various possible refinements.

Method and apparatus for aligning an optical system

Abstract: A complex optical system may be aligned by means of a technique in which an analytical model of the system is utilized which is assumed to be capable of essentially optimal performance. A physical example of the same system design is then assembled and a plurality of performance characteristics measured. A plurality of specific adjustments are then calculated which would have the effect of degrading the performance of the analytical model to equal that measured for the physical example, whereupon compensating physical adjustments are made to the physical example. For many applications, the performance measurements may relate to aberrations to the wavefront of the point source image quantified by means of a Hartmann mask or the like. In that event, the estimation technique may be a straight-forward linear approximation technique including possible damping and/or weighting factors. The performance measurements may also be related to the intensity function associated with the image of a point source, in which case a second order estimation technique is required.

Study of a complex water resources system with screening and simulation models

Abstract: A sequential iterative modeling process for a complex water resources system is described. Two types of analytical models are used to find a reasonably small set of possible systems optimal design alternatives for a complex river basin. These models are a linear programing deterministic continuous (LPDC) model and a linear programing deterministic discontinuous (LPDD) model. Linear programing has been used with linear approximation of the nonlinear functions. A simulation program has been developed which continues screening on the basis of the information obtained from the linear programing model. The models are developed in the context of analysis of the Narmada River, a large river basin in India, for which in the first instance alternative combinations and capacities of six major dams have to be decided.

Linear approximation in a new theory of gravity

Abstract: A weak-field expansion is developed for a new theory of gravity, based on a Hermitian nonsymmetric gmu nu . Plane wave solutions exist for both the symmetric and skew parts of gmu nu . The symmetric part of gmu nu is associated with the spin-2 graviton, while the skew part is related to a massless spin-0 boson called the 'skewon'. In the linear approximation the Eotvos experiments is not violated. The one-boson exchange graph is calculated. Only quadrupole and higher poles contribute to gravitational radiation.

Powerlike decreasing solutions of the Boltzmann equation for a Maxwell gas

Abstract: We study the homogeneous, isotropic, nonlinear Boltzmann equation for a Maxwellian interaction We show that solutions decreasing like inverse powers of the energy are physically acceptable both in the linearized and the quadratic problem Because all moments may not exist, we introduce a generalized generating function and a finite differential system for generalized Sonine moments is derived These new solutions may lead to small relaxation rates and justify in most cases the linear approximation

Improved linear trial function finite element model of soil moisture transport

Abstract: Two methods of modeling a higher-order approximation function of soil moisture transport by an improved linear trial function approximation are presented. The first approach considered is based upon use of the alternation theorem and a finite element capacitance matrix that incorporates the Galerkin finite element, subdomain, finite difference, and proposed nodal domain integration methods. The second approach extends the first approach by developing a temporal relationship for element matrices such that a higher-order approximation function can be modeled by a linear approximation function. Comparison of model results produced from a nodal domain integration model incorporating these improved linear trial function approximations to the finite element, subdomain, and finite difference methods indicates that this approach may lead to a generalized modeling method for soil moisture transport problems.

An Extension of Yokota’s Diffusion Theory on Mixed Conduction to Larger Applied Voltages

Abstract: In Yokota's diffusion theory on mixed conduction, he has considered the case of small current density and obtained a solution in the linear approximation. In the present paper we consider larger current densities and look for an improved approximation over the linear one. The obtained approximate solution for larger applied voltages shows a better agreement with the numerical solution of the non-linear diffusion equation than the linear approximation. The comparison between the experiment and the calculation is done for βCu 2 S and α'Ag 2 Te.

Monolithic Crystal Filter Design Using a Variational Coupling Approximation

Abstract: where E and W are the energy and bandwidth of the input signal, respectively. In contrast, System C is based on the chirp and inverse ch rp transforms systems, which are a good representation of the Fourier and inverse Fourier transforms on a certain time interval. In conclusion we have demonstrated both experimentally and theoretically that by using SAW dispersive delay lines, speedup, slowdown, and time inversion can be obtained using three different systems. Time scaling of the input waveform can be adjusted also during time inversion. System A is the simplest system since the number of chirp filters required for its implementation is only two, but the distortion of the outvariable time scaling system simply by adjusting the sweep slope, whereas in the other systems a change in the sweep slope requires a change in the slope of the dispersive device.

A Simple Technique for Determining The Maximum Ground Level Concentration of An Elevated Gaseous Release

Abstract: A screening technique has been developed to determine the maximum one-hour ground level concentration of a gaseous emission from a stack located In flat terrain. The method does not require the use of a computer and eliminates the usual trial and error calculations. An infinite mixing height is assumed. It involves a linear or quadratic solution of the gaussian plume diffusion as a function of the effective stack height and a linear approximation of the Briggs plume rise equation. The linear approximation of the former gives results that are within 5 % of the gaussian plume results for stability criteria A, B, and C. For stability criteria D, the difference can be as great as 80%. If a quadratic estimation Is used, the differences are less than 3% for stability criteria A, B, and C, and are within 18% for stability criteria D. A linear approximation is used for the Briggs plume rise equation. This gives results within 4% of the Briggs equation. Overall, this is a simple straightforward approximation which...

Optimality conditions using sum-convex approximations

Abstract: The purpose of this paper is to give necessary and sufficient conditions of optimality for a general mathematical programming problem, using not a linear approximation to the constraint function but an approximation possessing certain convexity properties. Such approximations are called sum-convex. Theorems of the alternative involving sum-convex functions are also presented as part of the proof.

Measuring device of gas density

Abstract: PURPOSE:To perform an easy and high-accuracy measurement of the gas density, by giving an operation to the quantity of information by which the oscillation frequency of the Ys-cut quartz oscillator is obtained in the form of the function of temperature along with the oscillation frequency of the AT-cut quartz oscillator obtained as the function of pressure respectively CONSTITUTION:The Ys-cut quartz oscillator 1, which is cut in such an angle as to secure an approximation as a straight line between the change of temperature and the change of natural frequency, is incorporated into the oscillating circuit 4 for measurement of the temperature Then the natural frequency is extracted, and the total frequency is counted in a prescribed time Thus the temperature T of measurement is obtained by the arithmetic control device 20 At the same time, the At-cut quartz oscillator 2, which is cut in such an angle as to secure a linear approximation between the change of pressure and the change of natural frequency, is incorporated into the oscillating circuit 5 for measurement of the pressure Then the total frequency is counted in a prescribed time, and thus the pressure P of measurement is obtained by the device 20 Based on the temperature T and pressure P, the density of gas can be obtained by the device 20 and in an easy and high-accuracy way

Rational linear approximation to the wave equation with bottom interaction

Abstract: A rational linear approximation is used to derive a range‐dependent full‐wave propagation model, much like the parabolic equation, which can handle the dual problem of high angle propagation and bottom interaction. It uses an inexpensive tridiagonal implicit range step for economical calculation in the presence of large gradients, where range steps are necessarily very short. The use of matched cubic splines gives an accurate treatment of reflection and refraction at density and sound‐speed discontinuities. It gives an accurate treatment of propagation from 0° to 45° grazing angle. [Work supported by ONR 486.]

Error estimates for the finite element solutions of

Abstract: For plecewise linear approximation of variational inequalities asso- ciated with the mildly nonlinear elliptic boundary value problems having auxiliary constraint conditions, we prove that the error estimate for u-u h in the W 1'2- norm

Stochastic control of randomly varying systems

Abstract: In this paper we consider the linear quadratic regulator problem for a class of linear, randomly varying systems based on partial observation. The novelty, in part, of the solution is that the state estimator is non-linear and the separation principle does not hold (not in the usual sense, at any rate). Using a linear approximation, we indicate a procedure for constructing a class of approximately optimal controls.