Showing papers on "Operator (computer programming) published in 1971"
TL;DR: A unique optimal solution for an edge operator results, where the operator obtains the best fit of an ideal edge element to any empirically obtained edge element.
Abstract: Because of the fundamental importance of edges as primitives of pictures, automatic edge finding is set as goal. A set of requirements which should be met by a local edge recognizer is formulated. Their main concerns are fast and reliable recognition in the presence of noise. A unique optimal solution for an edge operator results. The operator obtains the best fit of an ideal edge element to any empirically obtained edge element. Proof of this is given. A reliability assessment accompanies every recognition process.
456 citations
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447 citations
TL;DR: In this article, the Wick and anti-Wick operator symbols are studied in connection with expansion into normal and antinormal series in terms of generation and annihilation operators, and a series of characteristic spectral properties are identified for.
Abstract: In this paper Wick and anti-Wick operator symbols are studied in connection with expansion into normal and antinormal series in terms of generation and annihilation operators. By the aid of the Wick and anti-Wick symbol of the operator a series of characteristic spectral properties are identified for . In particular, results are presented concerning necessary and sufficient conditions (separately) for to belong to the classes of bounded operators, completely continuous operators and nuclear operators, and also concerning bounds on the spectrum of , and the asymptotic behavior of the number of eigenvalues below ; and for positive selfadjoint operators a bound is obtained for the trace of the Green function: Bibliography: 14 titles.
107 citations
TL;DR: In this article, it was shown that the Liouville operator of the spin hamiltonian does not reflect any symmetry inherent in the spin system, whereas the vector space (Liouville space) comprising all operators of spin system does.
Abstract: It is shown in discussing problems involving magnetic relaxation in liquids that, whilst the usual Hilbert space spanned by all the eigenkets of the spin hamiltonian does not reflect any symmetry inherent in the spin system, the vector space (Liouville space) comprising all operators of the spin system does so. The transformation properties of the Liouville operator, as reflected by those of the high resolution spin hamiltonian and relaxation operators whose effects are introduced by means of Redfield relaxation theory, with respect to arbitrary rotations of the coordinate system are investigated. The use of irreducible tensor operators as a set of basis operators spanning Liouville space is stressed, since it is shown that their super-matrix elements of the Liouville operator are given by the Wigner-Eckart theorem provided that relaxation by anisotropy of the chemical shift or anisotropic random fields is absent. These arguments are independent of the fine details of molecular reorientation in the extrem...
104 citations
TL;DR: In this article, the expansion of products of local operators when their space-time distance approaches the light cone is motivated and discussed, and attempts to prove the expansion from Wilson's short distance expansion are analyzed.
92 citations
TL;DR: In this article, a factorization of the residual operator for nonorthogonal analysis of variance is given, interpreted geometrically in terms of the critical angles between the subspaces determined by the factors.
Abstract: SUMMARY A factorization is given of the residual operator for nonorthogonal analysis of variance. It is interpreted geometrically in terms of the critical angles between the subspaces determined by the factors. The factorization determines a recursive procedure for analysis as described by Wilkinson (1970). Canonical components are defined and a method of computing them is given together with formulae for their variances, since these would be required for combining information, as for instance, in the recovery of interblock information.
88 citations
TL;DR: In this paper, three direct integration schemes for the matrix equations of motion of structural dynamics, the Newmark generalized acceleration operator, the Wilson averaging variant of the linear acceleration operator and an averaging method based on a variational principle derived by Gurtin, are investigated for stability and approximation viscosity.
80 citations
TL;DR: In this paper, it is shown that the transformation properties of the Liouville operator can be expressed as a sum of super-operators describing the time evolution of the density operator caused by individual nuclear Zeeman interactions, scalar couplings between pairs of nuclei and individual relaxation processes.
Abstract: Recently introduced methods of discussing and simplifying problems concerning magnetic relaxation in liquids, which involve investigation of the transformation properties of the Liouville operator, are further developed. It is shown that the previous results can be obtained by a simpler method and that the Liouville operator can be expressed as a sum of super-operators describing the time evolution of the density operator caused by individual nuclear Zeeman interactions, scalar couplings between pairs of nuclei and individual relaxation processes whose effects are introduced by means of Redfield relaxation theory. These methods prove useful when dealing with multispin systems (being also applicable to single-spin systems) because the super-matrix elements of these Liouville operators between operators, which are irreducible tensor operators with respect to rotations in the Liouville space appropriate to the entire spin system, constructed by vector coupling the irreducible tensor operators pertaining to s...
63 citations
TL;DR: In this paper, a complete mathematical theory of two-body quantum mechanics for a class of potentials which is larger than the usual L2-classes and which includes potentials with singularities as bad as r−2+ǫ.
Abstract: We present a complete mathematical theory of two-body quantum mechanics for a class of potentials which is larger than the usualL2-classes and which includes potentials with singularities as bad asr−2+ɛ. The basic idea is to defineHo+V as a sum of quadratic forms rather than as an operator sum.
62 citations
TL;DR: In this article, a detailed analysis of Newton's method applied to operators with Holder continuous derivatives is given, and the analysis is shown to reduce the analysis of Lancaster (Num. Math.A.N. 1968) when the operator has a continuous second derivative.
Abstract: The concept of majorizing sequences introduced by Rheinboldt (SIAM J.N.A. 1968) is used to prove convergence for Newton's method for operator equations of the formT f=? when the operator satisfied the condition that the Frechet derivative is Holder continuous.
A detailed analysis of computational errors is given for Newton's method applied to operators with Holder continuous derivatives. This analysis is shown to reduce the analysis of Lancaster (Num. Math. 1968) when the operator has a continuous second derivative.
The above analysis is applied to an example of a second order differential equation.
61 citations
TL;DR: Theorem 3.1 of the Fejér-Riesz theorem on the factorization of nonnegative trigonometric polynomials and Ahiezer's version [l] of its generalization to entire functions of exponential type which are nonnegative on the real axis were studied in this article.
Abstract: Introduction. Let f be a function defined on the circle T = {e : 0 ̂ 6 < 2T } or line R = ( — <*>, <*> ) whose values are nonnegative operators on a separable complex Hubert space. We are concerned with the problem of finding conditions that F = G*G a.e. where G is the strong boundary value function of a suitable operator valued analytic function defined in the disk \\z\\ < 1 or half-plane y>0. Mainly we are interested in special classes of functions in which such a factorization is always possible. Our study is motivated by the Fejér-Riesz theorem on the factorization of nonnegative trigonometric polynomials, and Ahiezer's version [l ] of its generalization to entire functions of exponential type which are nonnegative on the real axis. Both results generalize to operator valued functions, and, in fact, both appear as special cases of a very general result (Theorem 3.1). More generally we present a unified treatment of the factorization problem, and thus much of §1 is expository. There we develop the theory of a corresponding abstract factorization problem for nonnegative Hubert space operators. Both the results and methods of §1 are purely operator theoretic. In §2 we show how the abstract theory relates to the theory of operator valued functions defined on the circle T or line R. The main applications to the factorization problem for nonnegative operator valued functions are deferred to §3. The factorization problem arises in the prediction theory of stationary stochastic processes. For this connection see Helson and Lowdenslager [ l l ] , Rozanov [27], and Wiener and Masani [28]. We wish to thank Professor Loren Pitt for calling our attention to the paper by E. Robinson [23]. We have extended Robinson's results in §2.
TL;DR: In this article, it is proved that if a rearrangement invariant function space X lies, in a certain sense, between the rearrange invariant spaces X 1 and X 2, then every operator of weak type on X i, i = 1, 2, is a bounded operator on X.
TL;DR: In this article, the form of density operator for unpolarized radiation was obtained by a simple method, and the density operator was then used to obtain the density of unpolarised radiation.
Abstract: The form of density operator for unpolarized radiation is obtained by a simple method.
Patent•
21 Jun 1971
TL;DR: In this paper, a system for addition to a conventional dispatched vehicle radio communication system to enable an operator to notify a central dispatcher of an emergency condition arising after the operator leaves the vehicle is presented.
Abstract: A system for addition to a conventional dispatched vehicle twoway radio communication system to enable an operator to notify a central dispatcher of an emergency condition arising after the operator leaves the vehicle. The system includes a unit which plugs directly into the microphone input of the conventional system and which is responsive to a signal transmitted from a portable transmitter carried by the operator for playing a prerecorded emergency message through the transmitter of the conventional radio system.
TL;DR: In this article, it was shown that the backward heat operator is not hypoelliptic everywhere, but is not locally solvable in any open set which intersects the linex 1 = 0.
Abstract: It is proved that the differential operatorD1 +ix1D22 is hypoelliptic everywhere, but is not locally solvable in any open set which intersects the linex1=0. Thus, this operator is not contained in the usual classes of hypoelliptic differential operators. The proofs involve certain properties of the characteristic Cauchy problem for the backward heat operator.
TL;DR: In this article, the graphical representation of angular momentum is used as the basis of a procedure for the complete evaluation of the matrix element of a Coulomb or multipole interaction operator between atomic states having any number of open shells.
Abstract: The graphical representation of angular momentum is used as the basis of a procedure for the complete evaluation of the matrix element of a Coulomb or multipole interaction operator between atomic states having any number of open shells. The method is presented in the form of a step-by-step procedure and is designed to permit straightforward extension to the evaluation of the matrix elements of other types of tensor operators and of sums of products of Coulomb matrix elements, such as occur in the perturbation theory of configuration interaction.
TL;DR: In this paper, the Bethe-Goldstone wave function in terms of solutions of the Schrodinger equation for two interacting particles in a harmonic-oscillator well is used to calculate the reaction matrix in a two-particle basis.
Abstract: A new, simple, and exact method is given for calculating the reaction matrix $G$ in a two-particle harmonic-oscillator basis. The method makes use of an expansion of the Bethe-Goldstone wave function in terms of solutions of the Schr\"odinger equation for two interacting particles in a harmonic-oscillator well. Since a two-particle basis is used, the Pauli operator $Q$ is diagonal and can be treated exactly. Reaction matrix elements based on the Hamada-Johnston potential are used in a shell-model calculation of $A=18$ nuclei. The results are compared with those of earlier calculations using approximate Pauli operators. The dependence of the reaction matrix on the starting energy is studied, and the relationship of this energy to the intermediate-state spectrum and to the Pauli operator $Q$ is discussed. In this same context the difference between using a Brueckner $Q$ and a shell-model $Q$ is also discussed.
TL;DR: In this paper, it was proved that the resolvents of the Dirac and Klein-Gordon operators have only a removable singularity atc = ∞, which implies the analyticity atc=∞ of the eigenvalues and eigenvectors corresponding to the bound states of the mentioned operators.
Abstract: The analytic functional calculus, relatively bounded and analytic perturbations of pseudoresolvents have been studied. As an application, the nonrelativistic limit of the Dirac and Klein-Gordon operator in the presence of an external static field has been considered. It has been proved that the resolvents of these operators have only a removable singularity atc=∞. This implies the analyticity atc=∞ of the eigenvalues and eigenvectors corresponding to the bound states of the mentioned operators.
TL;DR: In this paper, the authors studied the properties of duality and factorization of the generalization to N-particle scattering of the Virasoro model, and showed that the spectrum increases exponentially with the energy by a factor √ 2 more than in the generalized Veneziano model.
Abstract: We study the properties of duality and factorization of the generalization toN-particle scattering—recently given by Shapiro for α(0) = 2—of the Virasoro model. In particular we write this fully symmetric model (FSM) using the usual operator formalism with the addition of another infinite set of harmonic oscillatorsb n . The residue of each pole is shown to factorize in a finite number of terms independently of the number of external particles. The spectrum increases exponentially with the energy by a factor √2 more than in the generalized Veneziano model (GVM). Two infinite sets of Ward operators are shown to be present and the physical states on mass shell are defined as in the GVM.
TL;DR: In this paper, it was shown that dual-resonance amplitudes can be expressed in terms of rudimental amplitudes defined by functional integrals which correspond to transition amplitudes of quantum-mechanical systems of strings with imaginary time.
Abstract: It is shown that dual-resonance amplitudes can be expressed in terms of rudimental amplitudes defined by functional integrals which correspond to transition amplitudes of quantum-mechanical systems of strings with imaginary time. The equivalence between the path-integral and operator formulation of quantum mechanics is used to establish the connection between this approach and the usual operator approach. The factorization of rudimental amplitudes is studied to obtain the Feynman-like rules for dual-resonance amplitudes. This allows us to express $N$-Reggeon vertices in terms of rudimental amplitudes, and to determine the propagator, which is shown to be the usual spurious-free twisted propagator. $N$-loop orientable diagrams are calculated. In general, the functional integrals considered can be calculated by solving appropriate Neuman's boundary-value problems of corresponding bounded Riemann surfaces. This provides a generalization of the analog model to the case of external Reggeons which are described by extended momentum distributions on the boundaries.
TL;DR: For a multilinear differential operator which satisfies the necessary conditions, this paper established a method of constructing a smooth function which maps no points to the zero operator, and proved that the smooth function can be constructed in a smooth manner.
Abstract: For a multilinear differential operator which satisfies the necessary conditions, we establish a method of constructing a smooth function which maps no points to the zero operator.
TL;DR: In this paper, an operator formalism which exhibits factorization of the nonplanar dual model proposed first by Virasoro and generalized by Shapiro is presented, which is shown to contain sufficient gauge operators as well as a selection rule in order to eleminate all the ghosts.
TL;DR: In this paper, the masterequation is treated in Liouvillespace as Hilbertspace for a class of non-hermitean Liouvilleoperators describing thermal and nonthermal contact with reservoirs.
Abstract: The masterequation is treated in Liouvillespace as Hilbertspace for a class of non-hermitean Liouvilleoperators describing thermal and nonthermal contact with reservoirs. It is shown that these Liouvilleoperators are equivalent to normal operators; their eigenvectors and -values are given. For the solution of the resolvent equation the interaction-Liouvilleoperator is approximated by an operator of finite rank, which can be treated exactly.
TL;DR: It is shown, under the condition that C is semidefinite, that the determining function method leads to a simple characterization of the spectrum of the seminormal operator T + iV.
Abstract: With every pair of bounded self-adjoint operators {U,V} on Hilbert space such that VU - UV = (1/πi)C, where C is trace class, there is associated a certain function of two complex variables called the determining function of the pair. It was previously shown how the determining function can be obtained as the solution of a certain Riemann-Hilbert problem canonically associated with the pair, and how the complete spectral multiplicity theory for both U and V can be obtained from the determining function. We now show, under the condition that C is semidefinite, that the determining function method leads to a simple characterization of the spectrum of the seminormal operator T = U + iV.