Showing papers on "Computation published in 1970"

Outline of a Mathematical Theory of Computation

Abstract: However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be ignored because, as he points out, the machines that the programs of study run on are not capable of dealing with such an abstract level of understanding. That is, the computaional approach should not be abandoned because the machines that we build operate on that lower level.

The computation of chemical equilibria

Abstract: Foreword Preface 1. The foundations of chemical equilibrium computation 2. Mathematical structure of the chemical equilibrium problem 3. Methods based on optimization techniques 4. Methods based on the solution of non-linear equations 5. General considerations and conclusions Appendices Bibliography Indices.

On the computation of the spherical harmonic terms needed during the numerical integration of the orbital motion of an artificial satellite

Abstract: A method is presented for the accurate and efficient computation of the forces and their first derivatives arising from any number of zonal and tesseral terms in the Earth's gravitational potential. The basic formulae are recurrence relations between some solid spherical harmonics,V n,m, associated with the standard polynomial ones.

Universality in cellular automata

Abstract: Complex behavior by machines can be achieved by either having a large number of very simple machines or by having a complex machine with which to start Our primary interest in this paper was with the former By considering the global behavior of a large number of the simplest of machines, the following results were shown: 1 An array of identical square cells each of which can exist in only four states and communicates with its four nearest neighbors (forming a neighborhood of five cells) can a) perform any computation which is computable and b) construct (almost) any configuration--in particular, it can be self-reproducing Cells capable of the first behavior are called universal computers; the second behavior characterizes the universal constructor 2 A three state, five neighbor cell is capable of universal computation when configured in a finite initial area 3 Two states and five neighbors are sufficient for universal computation, but require an infinite initial configuration Being parallel machines, these cellular automata can serve as a good theoretical basis for parallel computation and should be useful mathematically in many of the same areas as the Turing Machine Practical physical applications were also indicated

A Computer Program for Approximating System Reliability

Abstract: A computer program, which provides bounds for system reliability, is described. The algorithms are based on the concepts of success paths and cut sets. A listing of the elements in the system, their predecessors, and the probability of successful operation of each element are the inputs. The outputs are the success paths, the cut sets, and a series of upper and lower reliability bounds; these bounds converge to the reliability which would be calculated if all the terms in the model were evaluated. The algorithm for determining the cuts from the success paths is based on Boolean logic and is relatively simple to understand. Two examples are described, one of which is very simple and the computation can be done by hand, and a second for which there are 55 success paths and 10 cuts and thus machine computation is desirable.

Computation of rate and volume of stream depletion by wells

Abstract: When field conditions approach certain assumed conditions, the depletion in flow of a nearby stream caused by pumping a well can be calculated readily by using dimensionless curves and tables. Computations can be made of (1) the rate of stream depletion at any time during the pumping period or the following nonpumping period, (2) the volume of water induced from the stream during any period, pumping or nonpumping, and (3) the effects, both in rate and volume of stream depletion, of any selected pattern of intermittent pumping. Sample computations illustrate the use of the curves and tables. An example shows that intermittent pumping may have a pattern of stream depletion not greatly different from a pattern for steady pumping of an equal volume. The residual effects of pumping, that is, effects after pumping stops, on streamflow may often be greater than the effects during the pumping period. Adequate advance planning that includes consideration of residual effects thus is essential to effective management of a stream-aquifer system.

Stress fields produced by dislocations in anisotropic media

Abstract: Representations of the displacements and distortions produced by dislocation loops are given as Fourier integrals. These integrals are then reduced, to obtain solutions which are more explicit than any obtained previously, for the fields produced by infinite straight dislocations, a finite straight segment of a dislocation line and an elliptical dislocation loop, all in generally anisotropic media. The results should reduce the solution of many dislocation problems in which anisotropy cannot reasonably be ignored to fairly simple problems of routine computation.

A note on fast computation of Rayleigh wave dispersion in the multilayered elastic half-space

Abstract: Matrix formulas for modal solutions in the layered, elastic half-space are modified to give faster machine computation. Accuracy at high frequencies is also included. Computing time is reduced by 30 per cent from the fastest program previously reported.

Estimation of Pareto's Law from Grouped Observations

Abstract: The problem of estimating the scale parameter in the Pareto distribution from grouped observations is considered. Several estimators—the maximum likelihood estimator and four variants of least squares—are evaluated. Most of these have identical BAN properties but require nonlinear computations. A linearized BAN estimator is constructed, and numerical illustrations are provided.

A boundary technique for calculation of distributed resistance

Abstract: A numerical technique is presented for calculating the resistance of two-terminal distributed resistors and the resistance matrix for multiterminal regions in integrated circuit layers. The technique, useful for computer-aided design of multiterminal resistors, makes use of Cauchy's integral formula which facilitates coordination of conformal transformations at Singular boundary points. Results for a simple test structure (16 boundary points, 0.07 percent error in conductance calculation, 1.8 seconds computation time on a GE 635 computer) indicate this technique to be faster than various published techniques on computation time versus accuracy basis. The technique is applicable to structures with boundaries consisting of straight lines and circular arcs, multiply-connected, multiterminal, and open structures.

Integral equation method for computer evaluation of electron optics

Abstract: A Green's function technique for the computation of electric potentials in electrostatic systems of arbitrary configuration, especially with cylindrical symmetry, is developed. The system may include open boundaries and dielectric media. The integral equation is numerically solved by iteration. Its convergence is very fast. Computer calculated field and potential values are of high accuracy (usually better than 10-4). Errors in electron optical data, derived from trajectory computation, were found to be within fabrication tolerances of experimental systems. The computerized method proved to be an excellent tool for the design of electron optical systems, as electron image intensifiers.

Computation of optimal control for time-delay systems

Abstract: A numerical technique is presented for the computation of control for linear time-delay systems subject to a quadratic performance measure.

Angle-of-attack computer

Abstract: An angle-of-attack computer using closed loop computation techniques wherein various on-board sensor outputs are combined to determine a first or initial measure of angle-of-attack which is then used to derive a measure of the mass of the vehicle, which mass measure is then used to determine true airframe angleof-attack.

Computer-program description. Computation of rotationally symmetric laplacian potentioals

Abstract: A method of computing Laplacian potentials for rotationally symmetric Dirichlet boundary-value problems is developed. The algorithm is valid for N surfaces of revolution of arbitrary cross-section, and gives the potentials both inside the surfaces of revolution. The solution is obtained by solving the integral equation formulation using a step approximation to the source and point matching for testing. Sample computations are given, and a general computer program is available.

Computation of Sensitivities for Optimal Design of Microwave Networks

Abstract: In recent contributions, Director and Rohrer discussed the concept of the adjoint network and its relevance to automated design of networks in the frequency and time domains. Employing Tellegen's theorem they demonstrated how the gradient vector for a least squares type of response objective function with respect to all existing (and nonexisting, if desired) elements could be evaluated from only two complete analyses, one of the given network and one of its topologicalIy equivalent adjoint network. In the frequency domain they considered both reciprocal and nonreciprocal lumped, linear and time invariant elements. More recently, it was shown how their approach could be implemented for least pth and minimax response objective functions.

Nonlinear filtering techniques with application to strapdown computation

Abstract: Applying nonlinear filtering techniques to the attitude computation in a strapdown inertial navigation system is discussed. A special class of nonlinear filtering problems is formulated to accommodate the physical problem involving the attitude computation. Recursive filtering algorithms which take advantage of the special characteristics of this mathematical model are derived. Numerical works based on the Monte Carlo simulation are given and comparisons are made with a commonly used algorithm.

Exact computation of group delay and its sensitivities using adjoint-network concept

Abstract: The exact calculation of the group delay and its derivatives is described for active or passive lumped and/or distributed networks. Two simple examples are included to illustrate the application of the method.

A Dynamic Memory Allocation Algorithm

Abstract: A dynamic memory allocation algorithm is presented making use of a priori information about a computer program. A two- level storage system is assumed, and a replacement algorithm is developed based upon a priori knowledge of interaction factors between any two space-taking entities associated with a computation.

Synthesis of recursive digital filters using the FFT

Abstract: It has been shown that recursive digital filters can be synthesized using the fast Fourier transform. An algorithm for computer implementation has been developed and used in comparing the computation times and noise figures of filters synthesized in this manner with the computation times and noise figures of filters synthesized by recursion. A model has been proposed for analysis of noise in the two-pole filter. Predictions of this model have been found to be in good agreement with noise measurements.

Determining Optimum Reject Allowances for Multistage Job-Lot Manufacturing

Abstract: Since most manufacturing processes inevitably produce some defective items, it is common practice to produce a quantity larger than the actual order size. This excess is called a reject allowance. This article considers multistage job-lot manufacture where items are produced by a sequence of n stages (operations). It demonstrates that under appropriate conditions, the total expected cost function is uni-modal which establishes the existence of a smallest optimum reject allowance. Computation procedures are also discussed.

A technique for the computation of charged-particle trajectories in radio-frequency quadrupole devices

Abstract: A method of computing the trajectories of charged particles which would occur in a real quadrupole device is presented. A successive, over-relaxation procedure is used first to solve the Laplace equation for the specified electrode system. Subsequently a simple Runge-Kutta integration is used to compute the trajectory. A number of results are presented showing that the conditions necessary for stable trajectories in the particular system studied are more restrictive than those predicted by the hyperbolic solution.