Showing papers on "Operator (computer programming) published in 1987"

Methods and applications of interval analysis

Abstract: Finite representations Finite evaluation Finite convergence Computable sufficient conditions for existence and convergence Safe starting regions for iterative methods Applications to mathematical programming Applications to operator equations An application in finance Internal rates-of-return.

Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena*

Abstract: Conventional finite-difference operators for numerical differentiation become progressively inaccurate at higher frequencies and therefore require very fine computational grids. This problem is avoided when the derivatives are computed by multiplication in the Fourier domain. However, because matrix transpositions are involved, efficient application of this method is restricted to computational environments where the complete data volume required by each computational step can be kept in random access memory. To circumvent these problems a generalized numerical dispersion analysis for wave equation computations is developed. Operators for spatial differentiation can then be designed by minimizing the corresponding peak relative error in group velocity within a spatial frequency band. For specified levels of maximum relative error in group velocity ranging from 0.03% to 3%, differentiators have been designed that have the largest possible bandwidth for a given operator length. The relation between operator length and the required number of grid points per shortest wavelength, for a required accuracy, provides a useful starting point for the design of cost-effective numerical schemes. To illustrate this, different alternatives for numerical simulation of the time evolution of acoustic waves in three-dimensional inhomogeneous media are investigated. It is demonstrated that algorithms can be implemented that require fewer arithmetic and I/O operations by orders of magnitude compared to conventional second-order finite-difference schemes to yield results with a specified minimum accuracy.

New approach for calculating the normally ordered form of squeeze operators.

Abstract: A new method for directly obtaining the normally ordered form of single- and two-mode squeeze operators is presented. This method is based on the technique of ``integration within an ordered product.'' The operator expressions are derived using the coherent-state representation as well as the coordinate and the momentum representations. The method is very simple, and the approach has an intuitive basis that makes the squeezing property manifest at the outset.

Resolvent Positive Operators

Abstract: Resolvent positive operators on an ordered Banach space (with generating and normal positive cone) are by definition linear (possibly unbounded) operators whose resolvent exists and is positive on a right half-line. Even though these operators are defined by a simple (purely algebraic) condition, analogues of the basic results of the theory of Q-semigroups can be proved for them. In fact, if A is resolvent positive and has a dense domain, then the Cauchy problem associated with A has a unique solution for every initial value in the domain of A, and the solution is positive if the initial value is positive. Also the converse is true (if we assume that A has a non-empty resolvent set and D(A) n E+ is dense in £+). Moreover, every positive resolvent is a Laplace-Stieltjes transform of a so-called integrated semigroup; and conversely every such (increasing, non-degenerate) integrated semigroup defines a unique resolvent positive operator.

Gaussian-Wigner distributions in quantum mechanics and optics

Abstract: Gaussian kernels representing operators on the Hilbert space scrH=L2(openRn) are studied. Necessary and sufficient conditions on such a kernel in order that the corresponding operator be positive semidefinite, corresponding to a density matrix (cross-spectral density) in quantum mechanics (optics), are derived. The Wigner distribution method is shown to be a convenient framework for characterizing Gaussian kernels and their unitary evolution under Sp(2n,openR) action. The nontrivial role played by a phase term in the kernel is brought out. The entire analysis is presented in a form which is directly applicable to n-dimensional oscillator systems in quantum mechanics and to Gaussian Schell-model partially coherent fields in optics.

Short characteristic solution of the non-LTE line transfer problem by operator perturbation—II. The two-dimensional planar slab

Abstract: We present the formal solution of the transfer problem in terms of the exponential short characteristic method and derive approximate operators that allow for the iterative solution of the non-LTE two-level atom problem. An eigenvalue analysis for the convergence rate of these operators and several approximate operators proposed by other authors is presented. The family of operators presented for the short characteristic approach range from local diagonal approximations to tridiagonal and pentadiagonal operators. The extension to multidimensions of the several proposed approximate operators is discussed.

A generalized restricted open-shell Fock operator

Abstract: We reexamine the open shell restricted Hartree-Fock theory and develop Fock-like operators that are quite general and easy to implement on a computer. We present a table of ‘vector coupling coefficients’ that define this operator for most of the cases that commonly arise. We compare the form of this operator with that suggested by others, and discuss the orbitals obtained by this procedure with respect to the generalised Brillouin's theorem, and the orbital energies with respect to Koopmans' approximation.

Null operator constructions

Abstract: Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1987.

An architecture for intelligent interfaces: outline of an approach to supporting operators of complex systems

Abstract: The conceptual design of a comprehensive support system for operators of complex systems is presented. Key functions within the support system architecture include information management, error monitoring, and adaptive aiding. One of the central knowledge sources underlying this functionality is an operator model that involves a combination of algorithmic and symbolic models for assessing and predicting an operator's activities, awareness, intentions, resources, and performance. Functional block diagrams are presented for the overall architecture as well as the key elements within this architecture. A variety of difficult design issues are discussed, and ongoing efforts aimed at resolving these issues are noted.

Operator mental condition detector

Abstract: An information processing apparatus includes a processor for performing various information processing operations in accordance with an instruction from an operator, a bioinformation sensor for detecting a mental condition of the operator, and an output unit for outputting corresponding information to the operator based on the detected mental condition The operator is relaxed by the information output from the output unit

Numerical radiative transfer

Abstract: Preface Introduction Part I. Operator Perturbation: 1. Survey of operator perturbation methods W. Kalkofen 2. Line formation in expanding atmospheres: multilevel calculations using approximate lambda operators W. R. Hamann 3. Stellar atmospheres in non-LTE: model construction and line formation calculations using approximate lambda operators K. Werner 4. Acceleration of convergence L. H. Auer 5. Line formation in a time-dependent atmosphere W. Kalkofen 6. Iterative solution of multilevel transfer problems Eugene H. Avrett and Rudolf Loeser 7. An algorithm for the simultaneous solution of thousands of transfer equations under global constraints Lawrence S. Anderson 8. Operator perturbation for differential equations W. Kalkofen Part II. Polarised Radiation: 9. A gentle introduction to polarised radiative transfer David E. Rees 10. Non-LTE polarised radiative transfer in special lines David E. Rees and Graham A. Murphy 11. Transfer of polarised radiation using 4x4 matrices E. Landi Degli'Innocenti 12. Radiative transfer in the presence of strong magnetic fields A. A. van Ballegooijen 13. An integral operator technique of radiative transfer in spherical symmetry A. Peraiah 14. Discrete ordinate matrix method M. Schmidt and R. Wehrse.

Difference Schemes: An Introduction to the Underlying Theory

Abstract: Ordinary Difference Equations. Difference Equations of First and Second Order. Examples of Difference Schemes. Boundary-Value Problems for Equations of Second Order. Basis of the FEBS Method. Difference Schemes for Ordinary Differential Equations. Elementary Examples of Difference Schemes. Convergence of the Solutions of Difference Equations as a Consequence of Approximation and Stability. Widely-Used Difference Schemes. Difference Schemes for Partial Differential Equations. Basic Concepts. Simplest Examples of the Construction and Study of Difference Schemes. Some Basic Methods for the Study of Stability. Difference Scheme Concepts in the Computation of Generalized Solutions. Problems with Two Space Variable. The Concept of Difference Schemes with Splitting. Elliptic Problems. Concept of Variational-Difference and Projection-Difference Schemes. Stability of Evolutional Boundary-Value Problems Viewed as the Boundedness of Norms of Powers of a Certain Operator. Construction of the Transition Operator. Spectral Criterion for the Stability of Nonselfadjoint Evolutional Boundary-Value Problems. Appendix: Method of Internal Boundary Conditions. Bibliographical Commentaries. Bibliography. Index.

Electro-optical sensors for manual control

Abstract: Novel method and apparatus are disclosed which assist in utilization of ranging type non-contact sensors with coordinate measurement machines (CMM's ) and other machines. Various visual and/or audible indicators are provided to assist the operator in using the machine.

Fresnel's reflection and transmission operators for stratified gyroanisotropic media

Abstract: For the general case of an inhomogeneous anisotropic and gyrotropic medium a differential tensor equation, expressing the evolution of the tangential component of the field vectors of an electromagnetic wave is obtained. A fundamental solution of this equation is given by a multiplicative integral. A plane-stratified system of anisotropic and gyrotropic layers is considered. By means of the characteristic matrix of such a medium Fresnel's reflection and transmission operators are derived. These operators have wide utility because they describe exactly the interaction of light with any plane-stratified gyroanisotropic structure. The conservation of the normal component of the Poynting vector in such a structure allows the authors to find a correlation between the operators of reflection and transmission. The operator dispersion equation of the multilayer gyroanisotropic waveguide is presented. All the calculations in this paper are based on the direct manipulation of tensors and their invariants, eliminating the use of coordinate systems. This facilitates solutions and provides results of great generality which are suitable for computer use.

Connected‐diagram expansions of effective Hamiltonians in incomplete model spaces. I. Quasicomplete and isolated incomplete model spaces

Abstract: In this and the following paper, we formulate a Fock space theory for incomplete model spaces (IMS) that applies both to coupled‐cluster expansions and to perturbation theory. We stress in this paper that the concept of the ‘‘connected’’ nature of extensive quantities like an effective Hamiltonian Heff is more fundamental than the ‘‘linkedness’’ that is conventionally used in many‐body perturbation theory. The ‘‘connectedness’’ of Heff follows when the wave operator W is multiplicatively separable into noninteracting subsystems. This is ensured by writing W as an exponential Fock space operator with the exponent connected. It is demonstrated in particular that the connectedness of the exponent in W requires that the normalization condition of W be separable as well. Unlike the situation in a complete model space, the definition of ‘‘diagonal’’ or ‘‘nondiagonal’’ operators depends generally on the particular m‐valence IMS. There are, however, special categories of IMS, the ‘‘quasicomplete’’ and the ‘‘isola...

Inverse scattering for the heat operator and evolutions in $2+1$ variables

Abstract: The asymptotic behavior of functions in the kernel of the perturbed heat operator δ12−δ2−u(x) suffice to determineu(x). An explicit formula is derived using the\(\bar \partial \) method of inverse scattering, complete with estimates for small and moderately regular potentialsu. Ifu evolves so as to satisfy the Kadomtsev-Petviashvili (KP II) equation, the asymptotic data evolve linearly and boundedly. Thus the KP II equation has solutions bounded for all time. A method for calculating nonlinear evolutions related to KP II is presented. The related evolutions include the so-called “KP II Hierarchy” and many others.

Continuously varying exponents and the value of the central charge

Abstract: The author shows that the conformal field theories describing two-dimensional critical behaviour with continuously varying exponents must have central charge c=1 if (a) there are no conserved spin-2 currents other than the stress tensor and (b) the marginal operator responsible for the line of fixed points does not mix with other operators. In such cases one may show the existence of a fixed line knowing only the four-point function of the marginal operator. The author applies this to the Ashkin-Teller model and the XY model with fourfold symmetry breaking.

Connected‐diagram expansions of effective Hamiltonians in incomplete model spaces. II. The general incomplete model space

Abstract: We generalize here the formalism of the preceeding paper to encompass the case of the general incomplete model space. The classification of operators as diagonal or nondiagonal depends in this case upon the specific m‐valence model space. It is stressed that even then one has to work in Fock space in order to get connected‐diagram expansions, since connectedness is a Fock space property. Two choices of separable normalization of the wave operator W leading to a connected Heff are discussed. It is shown that the intermediate normalization is not separable in general and hence not compatible with a connected‐diagram expansion. We also discuss how to generate ‘‘subduced’’ incomplete model spaces of lower particle rank such that Heff remains a valid effective Hamiltonian for these subduced model spaces as well. We discuss the nature of the various disconnected diagrams encountered in many‐body formalisms and point out which of these are really worth worrying about. We finally comment on the question of the se...

Index of a family of Dirac operators on loop space

Abstract: We use methods of constructive field theory to generalize index theory to an infinite-dimensional setting. We study a family of Dirac operatorsQ on loop space. These operators arise in the context of supersymmetric nonlinear quantum field models with HamiltoniansH=Q2. In these modelsQ is self-adjoint and Fredholm. A natural grading operator Γ exists such that ΓQ+QΓ=0. We studyQ+=P−QP+, whereP±=1/2 (1±Γ) are the orthogonal projections onto the eigenspaces of Γ. We calculate the indexi(Q+) for Wess-Zumino models defined by a superpotentialV(ω). HereV is a polynomial of degreen≧2. We establish thati(Q+)=n−1=degδV. In particular, the field theory models have unbroken supersymmetry, and (forn≧3) they have degenerate vacua. We believe that this is the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.

Machine assisted execution of process operating procedures

Abstract: A computer based system aids an operator in proceeding step-by-step through procedures for a complex process facility. At each step, monitored plant parameter values are used to evaluate relevant plant status and recommend action to be taken. The status and recommended action are presented to the operator on a display device together with prompts for generating appropriate responses. The step logic is carried out repetitively to provide the operator with feedback and to verify operator actions. The complete display picture including operator responses, and other plant conditions monitored in parallel with the current step, is logged for later review. An online review feature permits review of plant conditions and operator actions while the operator continues to execute the procedure. High-level textual statements of all steps of a current procedure can be reviewed and prior steps can be executed or re-executed.

Dynamic optical interconnects: volume holograms as optical two-port operators

Abstract: We view a real-time volume holographic medium as a programmable two-port device that operates on an optical electric field. A photorefractive two-port operator can be used to establish the interconnects required by neural network models. The index grating that forms in the medium serves to fully interconnect two layers of processing units and at the same time sums the input signals to the output layer. The dynamics of grating formation in photorefractive media are used to indicate the time evolution of the two-port operator when the diffraction efficiency of the medium is small. We experimentally demonstrate a projection operator whereby we store and recall, in iron-doped lithium niobate, seven 1-D images. The image storage is done without the usual angle or spatial encoding of reference beams. A projection operator is used to recognize what features of an input belong to a space defined by a set of stored vectors. The two-port operator can also be used to perform the complementary function: to recognize what features of an input do not belong to this space.

Integrated Directional Derivative Gradient Operator

Abstract: Accurate edge direction information is required in many image processing applications. A variety of operators for computing local edge direction have been proposed, many of them estimating a kind of gradient. These operators face two major problems. One problem is the inherent bias in their estimate of edge direction. The bias itself is a function of edge direction. Another problem is their sensitivity to the presence of noise in the image data. The second problem can be alleviated by an increase in the processing neighborhood size but usually at the expense of an increase in estimate bias and also inefrors in the processing of small or thin objects. An operator based on the cubic facet model is discussed, which reduces sharply both estimate bias and noise sensitivity with no increase in computational complexity. The measure of gradient strength is the maximum value of the integral of the first directional derivative taken over a rectangular or square neighborhood, the maximum being taken over all possible directions for the directional derivative. The line direction which maximizes the integral defines the new estimate of gradient direction. Experimental results show the superiority of this operator to others such as the Roberts operator, the Prewitt operator, the Sobel operator, and the standard cubic facet gradient operator for step edges and ramp edges. Under zero-noise conditions the 7× 7 integrated directional derivative gradient operator has a worst bias of less than 0.

Polynomial operator in galois fields and a digital signal processor comprising an operator of this type

Abstract: The polynomial operator in the Galois field of the invention is organized at three levels: a multiplexer level to select and transmit the operands to be used for the successive stage of the calculation to a second level; a so-called pipeline level comprising 3 flip-flop registers to memorize the operands selected at the first level; a third level for calculation, comprising a multiplier-adder which has its inputs X, Y and Z connected to the outputs of the registers, and which gives the coefficients of the resultant polynomials in the Galois field while always performing the same calculation by repetition of the same control instruction. This operator can be applied to digital telecommunications for the encoding and decoding of BCH or RS (REED SOLOMON) error-correcting codes, and can be used to make an integrated processor capable of processing digital data in the form of octets.

Quasi-associative operations in the combination of evidence

Abstract: Quasi‐associative operators are defined and suggested as a general structure useful for representing a class of operators used to combine various pieces of evidence. We show that both averaging operators and Dempster‐Shafer combining operators can be represented in this new framework.