Showing papers on "Operator (computer programming) published in 1980"
TL;DR: In this article, a class of random finite difference Schrodinger operators with a random potential was studied and the exact location of the spectrum was obtained with probability one, in various situations, and criterions for a given part in the spectrum to be pure point or purely continuous.
Abstract: We study a class of random finite difference operators, a typical example of which is the finite difference Schrodinger operator with a random potential which arises in solid state physics in the tight binding approximation. We obtain with probability one, in various situations, the exact location of the spectrum, and criterions for a given part in the spectrum to be pure point or purely continuous, or for the static electric conductivity to vanish. A general formalism is developped which transforms the study of these random operators into that of the asymptotics of a multiple integral constructed from a given recipe. Finally we apply our criterions and formalism to prove that, with probability one, the one-dimensional finite difference Schrodinger operator with a random potential has pure point spectrum and developps no static conductivity.
403 citations
01 Jan 1980-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: A checklist paradigm is given, by which entirely new light is thrown upon the semantics of these operators, connecting them, in a unified way, with measures which might be made upon more refined data.
Abstract: After a brief discussion of the need for fuzzy relation theory in practical systems work, the paper explains the new triangle products of relations and the sort of results to be expected from them, starting from a crisp situation. The asymmetry of these products, in contrast to correlation, is noted as essential to the investigation of hierarchial dependencies. The panoply of multi-valued implication operators, with which the fuzzification of these products can be accomplished, is presented, and a few of their properties noted. Then, most importantly, a checklist paradigm is given, by which entirely new light is thrown upon the semantics of these operators, connecting them, in a unified way, with measures which might be made upon more refined data. Using a well-known psychological test in an actual situation, so that the finer structure is in fact available, a comparison is made between a checklist measure and several of the operator values, showing the interrelationship concretely. Finally, some products and their interpretations are presented, using further real-world data.
330 citations
01 Jan 1980
TL;DR: This communication is a first step towards a general approach to fuzzy set-theoretic operators, i.e. algebraic operators which coincide with set-operators when membership values are crisp, which can be crucial in decision analysis, information retrieval, pattern recognition and more.
Abstract: This communication is a first step towards a general approach to fuzzy set-theoretic operators, i.e. algebraic operators which coincide with set-operators when membership values are crisp. Some properties of subclasses of such fuzzy set-theoretic operators are investigated. Specific examples are given. An attempt to discuss a possible interpretation of these operators is proposed. The choice of a good operator in a given practical situation can be crucial in decision analysis, information retrieval, pattern recognition for the purpose of aggregating several pieces of information.
162 citations
TL;DR: In this paper, the Radon transform R and its dual R' are defined as pseudodifferential operators and a necessary condition on the defining measures for R'R to be invertible by a differential operator is given.
Abstract: ABsmAcr. Guillemin proved that the generalized Radon transform R and its dual R' are Fourier integral operators and that R'R is an elliptic pseudodifferential operator. In this paper we investigate the dependence of the Radon transform on the defining measures. In the general case we calculate the symbol of R'R as a pseudodifferential operator in terms of the measures and give a necessary condition on the defining measures for R'R to be invertible by a differential operator. Then we examine the Radon transform on points and hyperplanes in RX with general measures and we calculate the symbol of R'R in terms of the defining measures. Finally, if R'R is a translation invariant operator on RI then we prove that R'R is invertible and that our condition is equivalent to (R'R)' being a differential operator.
118 citations
Book•
01 Jan 1980
TL;DR: In this paper generalized Kothe-to-eplitz duals are used to characterize matrix classes and provide consistency theorems for matrix classes, and operator Norlund means.
Abstract: Notation and terminology.- Generalized Kothe-Toeplitz duals.- Characterization of matrix classes.- Tauberian theorems.- Consistency theorems.- Operator Norlund means.
99 citations
TL;DR: In this article, the authors consider closed operator ideals, which mean operator ideals A whose components A(E, F) are closed subspaces of the space L(E and F).
85 citations
TL;DR: In this paper, a decomposition of an N-particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite oneparticle basis set, the decomposition is invariant under unitary transformations of the basis set.
Abstract: A decomposition of an N-particle operator as a sum of N + 1 components is defined such that, in the case of a model system employing a finite one-particle basis set, the decomposition is invariant under unitary transformations of the basis set. Applied to a two-particle Hamiltonian, this decomposition gives rise to the distinction between the independent-particle energy and the coupling energy defined in previous papers. Applied to the reduced density operator for a quantum state, the decomposition corresponds to partitioning the density into irreducible components. This partitioning is illustrated by graphs of electron density for the water molecule.
52 citations
TL;DR: In this paper, the Schrodinger equation cannot convert a pure state into a mixture, and the classical analog of such an operator cannot be measured, because to do so would violate classical irreversibility.
Abstract: The Schr\"odinger equation cannot convert a pure state into a mixture (just as Newton's equations cannot display irreversibility). However, to observe phase relationships between macroscopically distinguishable states, one has to measure very peculiar operators. An example, constructed explicitly, shows that the classical analog of such an operator cannot be measured, because to do so would violate classical irreversibility. This result justifies von Neumann's measurement theory, without any hypothesis on the role of the observer.
48 citations
TL;DR: In this article, a multiplier theorem for the Weyl transform is proved and sufficient conditions for the boundedness of a general operator on Lp(Rn) are derived for multipliers of the Hermite expansion.
48 citations
TL;DR: In this paper, a general operator-theoretic result from which the Pick-Nevanlinna theorem and the Loewner theorem on functions with positive imaginary part in the upper half plane can be deduced.
Abstract: In this paper we formulate a general operator-theoretic result from which we deduce some old and some new function-theoretic interpolation theorems. The theorems we are concerned with have as prototype the Pick-Nevanlinna theorem and the Loewner theorem on restrictions of functions with positive imaginary part in the upper half plane.
42 citations
TL;DR: In this paper, the Schrodinger hamiltonian was used to derive pseudopotential theories based on the relativistic effects, which incorporate relativism effects in the theory in which all the orbitals are treated to the lowest non-vanishing order (1/c 2).
Abstract: The fully relativistic Dirac-Fock generalizations of non-relativistic Phillips-Kleinman and generalized Phillips-Kleinman pseudopotentials are used to derive pseudopotential theories based on the Schrodinger hamiltonian which incorporate relativistic effects. In the theory in which all the orbitals are treated to the lowest non-vanishing order (1/c 2), the relativistic corrections to the energies are obtained by taking the expectation value of a perturbing operator over the non-relativistic wavefunctions. This perturbation consists of coulomb and exchange operators built from the relativistically induced changes in the charge distributions of other orbitals and two new operators arising from the pseudopotential, in addition to the standard mass-velocity, spin-orbit coupling and Darwin terms. The leading corrections to Hartree-Fock theory are obtained by omitting the pseudopotential operators and correct two expressions reported previously. The relative contributions of the standard operators and the coulo...
01 Jan 1980
Abstract: This report describes a study of human factors engineering aspects of the Three Mile Island-2 (TMI-2) accident on 28 March 1979 The objective of the study was to evaluate the causal contributions, if any, of operator performance and effects on operator performance of: control room design; operator training; and emergency procedures The topic of the current report is the degree to which operator errors were, in turn, caused by human factors engineering aspects of the control room design, operator training, and emergency procedures
TL;DR: In this paper, it was shown that time and entropy operators may exist as superoperators in the framework of the Liouville space provided that the Hamiltonian has an unbounded absolutely continuous spectrum.
Abstract: It is shown that time and entropy operators may exist as superoperators in the framework of the Liouville space provided that the Hamiltonian has an unbounded absolutely continuous spectrum. In this case the Liouville operator has uniform infinite multiplicity and thus the time operator may exist. A general proof of the Heisenberg uncertainty relation between time and energy is derived from the existence of this time operator.
TL;DR: In this paper, a formalism for expressing annihilation cross sections directly in terms of the vacuum expectation values of certain time-ordered products is developed, which is used to study qualitatively the effects of a dilute gas of instantons on weighted cross sections.
Patent•
21 Nov 1980
TL;DR: In this article, an apparatus for controlling a device such as a motor vehicle in which a signal representing a manually controlled function is compared with a function signal, and the manually controlled signal is then modified in accordance with the function signal is presented.
Abstract: An apparatus for controlling a device such as a motor vehicle in which a signal representing a manually controlled function is compared with a function signal, and the manually controlled signal is then modified in accordance with the function signal. The function signal is developed by analyzing human functions of the operator, environmental conditions, and vehicle conditions, etc.
Journal Article•
TL;DR: This work proposes an automated method based upon the cross-correlation between projections of the images that becomes computationally cheap with fast Fourier transforms.
Abstract: The computer comparison of two images of the same organ requires proper alignment of the images before further computer processing. This alignment can be achieved by (a) fixing patient position during the study, (b) alignment methods using analytical transformations, or (c) operator interaction. We propose an automated method based upon the cross-correlation between projections of the images. With fast Fourier transforms, the algorithm becomes computationally cheap.
TL;DR: In this paper, the existence of the evolution operator for the Klein-Gordon equation in the evolution form du/dt = T-1(t)u on Sobolev spaces was proved.
TL;DR: In this paper, the effect of correlation upon the interaction of the 2p electrons of this configuration is represented by effective two-body operators of the form ΣakTk(1) Tk(2).
Abstract: The effective-operator form of many-body theory is reviewed and applied to the calculation of the effective interaction of electrons in an open-shell atom. Numerical results are given for the 1s22s22p2 configuration of carbon. The effect of correlation upon the interaction of the 2p electrons of this configuration is represented by effective two-body operators of the form ΣakTk(1) Tk(2). These operators are evaluated using angular-momentum diagrams and solving numerically a two-particle equation for the linear combination of excited states which contribute to the Goldstone diagrams. The effect of the operators of even rank is to depress the values of the two-electron Slater integrals Fk(2p, 2p) below their Hartree-Fock values. The two-body operator of odd rank does not appear in the Hartree-Fock theory. Our second-order values of the Slater integrals agree quite well with experiment but the value which we obtain of the coefficient of odd rank is much too small. This is partly due to a large cancellation which occurs for the contribution of the outer 2s2, 2s2p, 2p2 pair excitations. In order to study the convergence properties of the theory and to obtain more accurate values of the interaction integrals, we consider the higher-order terms in the perturbation expansion. An important family of two-particle effects is included to all orders by solving the pair equations iteratively until self-consistency is achieved. A more accurate description of the electron-electron interaction is obtained in this way. There are three additional families of wave-operator diagrams which can have an important effect. One family has an additional open-shell line which polarizes a closed-, open-, or excited orbital. There are also the coupled-cluster diagrams and a family of diagrams involving two polarizing open-shell lines, which appears first in fourth order. All of these diagrams can be included in our iterative scheme and they include all possible two-particle effects to self-consistency.
TL;DR: In this paper, an exact steady-state density operator was obtained for a model describing the collective behaviour of a system of N two-level atoms, which yields a Fokker-Planck equation which does not satisfy detailed balance.
Abstract: An exact steady-state density operator is obtained for a model describing the collective behaviour of a system of N two-level atoms. The model yields a Fokker-Planck equation which does not satisfy detailed balance. The density operator is further employed to obtain exact analytical expressions for steady-state expectation values of the collective atomic operators both for finite N and in the thermodynamic limit N → ∞.
TL;DR: In this paper, the groundstate energies of Schrodinger operators with a discrete spectrum were determined with an absolute error smaller than 0.0022 cm−1, i.e.
Abstract: In connection with Temple's formula variance minimization yields accurate values especially for groundstate energies of Schrodinger operators with a discrete spectrum. The result in a.u. for the groundstate E
0 of the He-atom in the infinite nuclear mass approximation is −2.90372438655≤E
0≤−2.90372437696 i.e. E
0 is determined with an absolute error smaller than 0.0022 cm−1.
TL;DR: The existence of the light-cone expansion in renormalized perturbation theory is proved in this paper, which relies on the method of Anikin and Zavialov which applies new subtraction operators and allows the elimination of a remainder which is small for x 2 → 0.
TL;DR: Methods for interval iteration to include a solution of an operator equation is obtained by transforming the equation in iterative form a parameter is chosen appropriately, so that the convergence of the interval sequence becomes as fast as possible.
Abstract: For nonlinear operators in partially ordered spaces interval extensions will be defined by means of Lipschitz operators. Assumptions are made for the inclusion monotony of these interval extensions. In this manner we obtain methods for interval iteration to include a solution of an operator equation. By transforming the equation in iterative form a parameter is chosen appropriately, so that the convergence of the interval sequence becomes as fast as possible.
TL;DR: In this article, a trace for iterates of p-summing maps in Banach spaces is defined and a criterion for the completeness of the eigenvectors of the operator is defined.
Abstract: where A and 6 are (Xand C-valued) entire functions satisfying exponential growth estimates of the form exp(Tj21z), the coefficients of which can be expressed by determinants involving the trace of iterates of T. We prove corresponding results for the larger class of absolutely p-summing maps in Banach spaces where p > 2. To get convergence of the series and the product expansion of 3, A and 6 have to be modified ; the growth estimates for them take the form exp(~121P). To express the coefficients of the functions A and 6 as determinants and to derive recursive formulae to calculate them, we define a trace for iterates of p-summing maps. The growth estimates yield a criterion for the completeness of the eigenvectors of the operator. The results are applied to integral equations in Lr(~2)-spaces, 1 _< r < 0% defined by weakly singular kernels which are no longer square-integrable. They even hold for slightly more general kernels. We now mention a few definitions and notations. For the definition of a quasinormed operator ideal N with quasinorm A we refer to [12]. The operators mapping a Banach space X into another Y which belong to 9A are denoted by 2[(X, Y) ; we also write 9A(X) = qI(X, X). 5~ stands for all continuous linear maps, for all finite rank operators. If (9.1, A) is a quasinormed operator ideal, we denote by 9~ ('° the ideal of all operators factoring as a product of n operators between Banach spaces, each of
TL;DR: A linear recurrence is a linear operator which maps rn into rn-1, where (rn) is a (recursive) sequence of functions that can be stated for the initial and boundary value problem.
TL;DR: In this article, a model theory of the interior operator on product topologies with continuous functions is presented, and the main results are a completeness theorem, an axiomatization of topological groups and a proof of an interpolation and definability theorem.
Abstract: In this paper we present a model theory of the interior operator on product topologies with continuous functions. The main results are a completeness theorem, an axiomatization of topological groups, and a proof of an interpolation and definability theorem.
TL;DR: In this paper, the authors make use of the ''path sum'' function to prove that the family of stretched operator functions characterized by the operator irrep labels satisfy a pair of general difference equations.
TL;DR: In ADA [I], [~, operator names can be overloaded, which means they denote more than one operator (i.e. identifiers for subprograms, literals, and operator symbols) which has several semantic meanings depending on their context.
Abstract: In ADA [I], [~, operator names (i.e. identifiers for subprograms, literals, and operator symbols) can be overloaded. This means they denote more than one operator (i.e. subprogram, constant, or operation). (In addition, there are syntactic constructs (such as indexed components, e.g. a(il,...,ik) ) which have several semantic meanings (e.g. function call, indexing an array, qualifying an aggregate, ...) depending on their context.) For each expression, the ambiguities which arise with respect to types and operators have to be resolved according to the overloading rules in ADA. This process is called the operator identification process, and is distinguished from the name identification process which precedes it and associates all possible meanings with an operator name according to the visibility rules.
TL;DR: In this article, the problem of classifying blocks of matrices up to similarity is considered, and the notion of block similarity used here is a natural generalization of similarity for matrices.
Abstract: In the present paper the problem of classifying blocks of matrices up to similarity is considered. The notion of block similarity used here is a natural generalization of similarity for matrices. The invariants are described and canonical forms are given. This theory of block-similarity provides a general framework, which includes the state feedback theory for systems, the theory of Kronecker equivalence and a similarity theory for non-everywhere defined operators. New applications, in particular to factorization problems, are also obtained.
TL;DR: The symbol map of Gohberg and Krupnik as mentioned in this paper for the closed algebra generated by singular integral operators with piecewise continuous coefficients is extended to the case of curves with corners.
Abstract: The symbol map of Gohberg and Krupnik [6] for the closed algebra generated by singular integral operators with piecewise continuous coefficients is extended to the case of curves with corners. This algebra includes the operator of the double layer potential on such curves.