Showing papers on "Operator (computer programming) published in 1988"

On ordered weighted averaging aggregation operators in multicriteria decisionmaking

Abstract: The author is primarily concerned with the problem of aggregating multicriteria to form an overall decision function. He introduces a type of operator for aggregation called an ordered weighted aggregation (OWA) operator and investigates the properties of this operator. The OWA's performance is found to be between those obtained using the AND operator, which requires all criteria to be satisfied, and the OR operator, which requires at least one criteria to be satisfied. >

Three-dimensional numerical integration for electronic structure calculations

Abstract: Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.

Time-frequency localization operators: a geometric phase space approach

Abstract: The author defines a set of operators which localize in both time and frequency. These operators are similar to but different from the low-pass time-limiting operator, the singular functions of which are the prolate spheroidal wave functions. The author's construction differs from the usual approach in that she treats the time-frequency plane as one geometric whole (phase space) rather than as two separate spaces. For disk-shaped or ellipse-shaped domains in time-frequency plane, the associated localization operators are remarkably simple. Their eigenfunctions are Hermite functions, and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions. >

Theory and application of radiation boundary operators

Abstract: A succinct unified review is provided of the theory of radiation boundary operators. With the recent introduction of the on-surface radiation condition (OSRC) method and the continued growth of finite-difference and finite-element techniques for modeling electromagnetic wave scattering problems, the understanding and use of radiation boundary operators has become increasingly important. Results are presented to illustrate the application of radiation boundary operators in both these areas. Recent OSRC results include analysis of the scattering behavior of both electrically small and large cylinders, a reactively loaded acoustic sphere, and a simple reentrant duct. Radiation boundary operator results include the demonstration of the effectiveness of higher-order operators in truncating finite-difference time-domain grids. >

On the Fokker-Planck-Boltzmann equation

Abstract: We consider the Boltzmann equation perturbed by Fokker-Planck type operator. To overcome the lack of strong a priori estimates and to define a meaningful collision operator, we introduce a notion of renormalized solution which enables us to establish stability results for sequences of solutions and global existence for the Cauchy problem with large data. The proof of stability and existence combines renormalization with an analysis of a defect measure.

Towards optimum one‐way wave propagation1

Abstract: Numerical wavefield extrapolation represents the backbone of any algorithm for depth migration pre- or post-stack. For such depth imaging techniques to yield reliable and interpretable results, the underlying wavefield extrapolation algorithm must propagate the waves through inhomogeneous media with a minimum of numerically induced distortion, over a range of frequencies and angles of propagation. A review of finite-difference (FD) approximations to the acoustic one-way wave equation in the space-frequency domain is presented. A straightforward generalization of the conventional FD formulation leads to an algorithm where the wavefield is continued downwards with space-variant symmetric convolutional operators. The operators can be precomputed and made accessible in tables such that the ratio between the temporal frequency and the local velocity is used to determine the correct operator at each grid point during the downward continuation. Convolutional operators are designed to fit the desired dispersion relation over a range of frequencies and angles of propagation such that the resulting numerical distortion is minimized. The optimization is constrained to ensure that evanescent energy and waves propagating at angles higher than the maximum design angle are attenuated in each extrapolation step. The resulting operators may be viewed as optimally truncated and bandlimited spatial versions of the familiar phase shift operator. They are unconditionally stable and can be applied explicitly. This results in a simple wave propagation algorithm, eminently suited for implementation on pipelined computers and on large parallel computing systems.

Video system and method for controlled viewing and videotaping

Abstract: A satellite TV or cable video receiver includes a decoder for decoding information embedded in a broadcasted TV program which can be utilized to permit an operator to select the program for viewing only, or viewing and the preparation of a copy of the program. In an alternate embodiment, the operator may also select and the receiver permit the preparation of a copy inhibited tape. With this receiver, first run movies may be displayed on a tape or view basis without destroying the after-market for the film.

Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics

Abstract: The purpose of this paper is to present a summary of new methods employing Lie algebraic tools for characterizing beam dynamics in charged- particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics by a certain operator. The operators can then be concatenated following well defined rules to obtain a resultant operator that characterizes the entire system. (AIP)

Kernels of trace class operators

Abstract: Let X C Rn and let K be a trace class operator on L2(X) with corresponding kernel K(x, y) E L2(X x X). An integral formula for tr K, proven by Duflo for continuous kernels, is generalized for arbitrary trace class kernels. This formula is shown to be equivalent to one involving the factorization of K into a product of Hilbert-Schmidt operators. The formula and its derivation yield two new necessary conditions for traceability of a Hilbert-Schmidt kernel, and these conditions are also shown to be sufficient for positive operators. The proofs make use of the boundedness of the HardyLittlewood maximal function on L2(Rn).

Two-dimensional “inverse scattering problem” for negative energies and generalized-analytic functions. I. Energies below the ground state

Abstract: The two-dimensional inverse problem of reconstructing the general (without the hypothesis of continuous symemetry) Schrodinger operator L = − ∑ α(∂α−iAα)+ u on the basis of data, “collected” from the family of eigenfunctions of one energy level LΨ = e0Ψ, was first considered in 1976 in [1] for the periodic case. From [2] the idea arose of a profound connection of this problem with integrable problems of the theory of solitons in dimension 2+ 1. [3]–[5] are devoted to the development of this approach in the periodic case and later [6, 7] in the rapidly decreasing one. The contemporary stage of research began with [3, 4] in 1984, where, in the periodic case, the group of reductions Z2×Z2 was explicitly found, singling out those data of the inverse problem from which one gets purely potential self-adjoint operators (1)

Light-front dynamics of elastic electron-deuteron scattering

Abstract: Measurements of the deuteron form factors over a wide range of momentum transfer can provide important clues to the role of subnucleon degrees of freedom in nuclear dynamics. For a meaningful calculation of the form factors it is essential that the current density operators and the deuteron wave function transform under Lorentz transformations in a mutually consistent manner. Standard nucleon-nucleon interactions can be used to construct unitary representations of the Poincare group on the two-nucleon Hilbert space. Deuteron wave functions represent eigenstates of the four-momentum operator. Existing parameterizations of measured single-nucleon form factors are used to construct a conserved covariant electromagnetic current operator. The light-front symmetry of the representation allows a clean separation of the effects of one- and two-body currents for arbitrary momentum transfers. Comparison with data indicates that for Q/sup 2/ < GeV/sup 2/ the elastic cross sections are not dominated by two-body currents.

Global renaming operators in concrete process algebra

Abstract: Renaming operators are introduced in concrete process algebra (concrete means that abstraction and silent moves are not considered) Examples of renaming operators are given: encapsulation, pre-abstraction, and localization We show that renamings enhance the defining power of concrete process algebra by using the example of a queue We give a definition of the trace set of a process, see when equality of trace sets implies equality of processes, and use trace sets to define the restriction of a process Finally, we describe processes with actions that have a side effect on a state space and show how to use this for a translation of computer programs into process algebra

The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator

Abstract: The authors present a method for finding the evolution operator for the Schrodinger equation for the Hamiltonian expressible as H(t)=a1(t)J4+a2(t)J0+a3(t) J- where J+, J0 and J- are the SU(2) group generators. Such a method is applied to the disentangling technique for exponential operators which are not necessarily unitary. As a demonstration of our general approach, they solved the problem of a harmonic oscillator with a varying mass.

Fixed points vs. infinite generation

Abstract: The author characterizes Rabin definability (see M.O. Rabin, 1969) of properties of infinite trees of fixed-point definitions based on the basic operations of a standard powerset algebra of trees and involving the least and greatest fixed-point operators as well as the finite union operator and functional composition. A strict connection is established between a hierarchy resulting from alternating the least and greatest fixed-point operators and the hierarchy induced by Rabin indices of automata. The characterization result is actually proved on a more general level, namely, for arbitrary powerset algebra, where the concept of Rabin automaton is replaced by the more general concept of infinite grammar. >

A spatial operator algebra for manipulator modeling and control

Abstract: A recently developed spatial operator algebra for modeling, control and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The operators themselves are elements in the algebra of linear bounded operators. The effect of these operators when operating on elements in the domain is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of spatially recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for the corresponding control and trajectory design algorithms. Expressions interpreted within the algebraic framework lead to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanization of specific algorithms is greatly simplified. This paper discusses the analytical formulation of the operator algebra, as well as its implementation in the Ada programming language.

A counterexample to the nodal domain conjecture and a related semilinear equation

Abstract: In this paper we first establish a nonuniqueness result for a semilinear Dirichlet problem of which the nonlinearity is of super-critical growth. We then apply this result to construct a Schr6dinger operator on a domain Q such that the second eigenfunctions of this operator (with zero Dirichlet boundary data) have their nodal sets completely contained in the interior of the domain 0.

Virtual pivot handcontroller

Abstract: A movable handcontroller that permits control while requiring low force-displacement gradient. The handcontroller may be used in a side-arm configuration in that it allows the operator's arm to remain essentially motionless in an armrest while control inputs are made about the fulcrum of the wrist.

Input device for digital processor based apparatus

Abstract: An input device is provided with an operating member to be freely moved within a predetermined area by an external input force, such as a force exerted through an operator's finger or hand, for inputting given information by operating the operating member.

One-center expansion for pseudopotential matrix elements

Abstract: Semilocal pseudopotential operators can be expressed as a linear combination of nonlocal (projection) operators. Pseudopotential operator integrals over a molecular basis set are therefore reduced to linear combinations of overlap integrals products. Molecular calculations indicate that sufficient precision can be achieved with a limited number of nonlocal operators. Analytic derivatives of pseudopotential integrals are easily deduced and implemented in a standard quantum chemistry program.

Choice of implicit and explicit operators for the upwind differencing method

Abstract: The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Product integration-collocation methods for noncompact integral operator equations

Abstract: We discuss the numerical solution of a class of second-kind integral equations in which the integral operator is not compact Such equations arise, for example, when boundary integral methods are applied to potential problems in a two-dimensional domain with corners in the boundary We are able to prove the optimal orders of convergence for the usual collocation and product integration methods on graded meshes, provided some simple modifications are made to the underlying basis functions These are sufficient to ensure stability, but do not damage the rate of convergence Numerical experiments show that such modifications are necessary in certain circumstances

Non-Deterministic Choice in Datalog

Abstract: Logic programming languages for database applications, such as LDL, and NAIL! [5] generate all solutions for a given query and fail to recognize multiple equivalent, i.e., redundant, solutions. The Prolog solution is to use the cut operator. Ideally, one would like to syntactically identify programs in which redundant solutions may be pruned but one faces undecidability results in this direction. In order to circumvent the recognition problem we provide an explicit construct, called choice, to choose subsets of relations. We show that choice has clean bottom-up semantics and subsumes the Prolog cut and existential queries.

Dimensions of Operator Workload

Abstract: Multiple measures of operator workload may dissociate, or fail to agree, for a given task. The goal of this study was to determine how workload as indexed by processing resource demand could explai...

Renormalizability and infrared finiteness of non-linear σ-models: A regularization-independent analysis for compact coset spaces

Abstract: The non-linearσ models in two space-time dimensions corresponding to compact homogeneous coset spacesG/H are studied with particular attention to three problems: first, independence of coordinate choice and regularization, second, the physical content of the theory, and finally the regularity of the “physics” in the infrared limit. Concerning in particular the physical content of the theory, we construct a set of local observables whose correlation functions depend on a finite number of parameters identified among those defining the metric tensor of the coset space. For these models, we give a general proof of renormalizability based on the introduction of a nilpotent BRS operator which describes the non-linear isometries and a classical action which contains a mass term for all quantized fields. The mass term belongs to a finite dimensional representation of the groupG, which allows us to prove the conjecture that the correlation functions of local observables, i.e., the local operators invariant underG, are regular in the infrared limit.

Exactly Solvable Models and New Link Polynomials. V. Yang-Baxter Operator and Braid-Monoid Algebra

Abstract: Yang-Baxter operator is shown to be a fundamental object which relates theory of solvable models to theory of knots and links. First, general properties of Yang-Baxter operators are investigated. Second, a method to construct composite Yang-Baxter operators is explicitly shown. Lastly, from Yang-Baxter operators with crossing symmetry, braid-monoid algebras are derived. It is emphasized that the factorized S -matrices and their graphical illustrations link two approaches, algebraic and combinatorial, in the knot theory.

Method of rapid entering of text into computer equipment

Abstract: A method and apparatus for rapidly entering text into a computing machine is described. An operator may enter text in abbreviated form using several simple rules to predict which abbreviated word forms will be correctly recognized. In the event of conflicts (where one abbreviated word matches more than one full text work), the operator selects the preferred resolution either on an individual or global basis.