Showing papers on "Operator (computer programming) published in 1991"

Fast wavelet transforms and numerical algorithms I

Abstract: A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon-Zygmund and pseudo-differential operators. The algorithms of this paper require order O(N) or O(N log N) operations to apply an N × N matrix to a vector (depending on the particular operator and the version of the algorithm being used), and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here.

Spectra of Random and Almost-Periodic Operators

Abstract: I. Metrically Transitive Operators.- 1 Basic Definitions and Examples.- 1.A Random Variables, Functions and Fields.- 1.B Random Vectors and Operators.- l.C Metrically Transitive Random Fields.- l.D Metrically Transitive Operators.- 2 Simple Spectral Properties of Metrically Transitive Operators.- 2.A Deficiency Indices.- 2.B Nonrandomnessofthe Spectrum and of its Components.- 2.C Nonrandomness of Multiplicities.- Problems.- II. Asymptotic Properties of Metrically Transitive Matrix and Differential Operators.- 3 Review of Basic Results.- 4 Matrix Operators on ?2 (Zd).- 4.A Essential Self-Adjointness.- 4.B Existence of the Integrated Density of States and Other Ergodic Properties.- 4.C Simple Properties of the Integrated Density of States and of the Spectra of Metrically Transitive Matrix Operators.- 4.D Location of the Spectrum.- 5 Schrodinger Operators and Elliptic Differential Operators on L2(Rd).- 5.A Criteria for Essential Self-Adjointness.- 5.B Ergodic Properties.- 5.C Some Properties of the Integrated Density of States.- 5.D Location of the Spectrum of a Metrically Transitive Schrodinger Operator.- Problems.- III. Integrated Density of States in One-Dimensional Problems of Second Order.- 6 The Oscillation Theorem and the Integrated Density of States.- 6. A The Phase and the Existence of the Integrated Density of States.- 6.B Simplest Asymptotics of the Integrated Density of States at the Edges of the Spectrum.- 6.C Schrodinger Operator with Markov Potential.- 6.D The Brownian Motion Model.- 6.E Jacobi Matrices with Independent and Markov Coefficients.- 6.F Smoothness of N (?) Special Energies.- 7 Examples of Calculation of the Integrated Density of States.- 7.A The Kronig-Penny Stochastic Model.- 7.B Random Jacobi Matrices.- Problems.- IV. Asymptotic Behavior of the Integrated Density of States at Spectral Boundaries in Multidimensional Problems.- 8 Stable Boundaries.- 9 Fluctuation Boundaries: General Discussion and Classical Asymptotics.- 9.A Introduction and Heuristic Discussion.- 9.B Simplest Bounds. Gaussian and Negative Poisson Potentials.- 9.C Generalized Poisson Potential.- 10 Fluctuation Boundaries: Quantum Asymptotics.- 10.A The Lifshitz Exponent.- 10.B Generalized Poisson Potential with a Nonnegative, Rapidly Decreasing Function.- 10.C Smoothed Square of a Gaussian Random Field.- Problems.- V. Lyapunov Exponents and the Spectrum in One Dimension.- 11 Existence and Properties of Lyapunov Exponents.- 11.A The Multiplicative Ergodic Theorem and the Existence of Lyapunov Exponents.- 11.B The Lyapunov Exponent and the Integrated Density of States.- 11.C Simplest Asymptotic Formulas and Estimates for Lyapunov Exponents.- 12 Lyapunov Exponents and the Absolutely Continuous Spectrum.- 12.A Basic Facts About the Spectrum of One-Dimensional Operators of the Second Order.- 12.B Lyapunov Exponents and the Absolutely Continuous Spectrum.- 12.C Multiplicity of the Spectrum.- 12.D Deterministic Potentials.- 12.E Some Inverse Problems.- 13 Lyapunov Exponents and the Point Spectrum.- 13.A Heuristic Discussion.- 13.B Conditions for Positive Lyapunov Exponents to Imply a Pure Point Spectrum.- Problems.- VI. Random Operators.- 14 The Lyapunov Exponent of Random Operators in One Dimension.- 14.A Positiveness of the Lyapunov Exponent.- 14.B Asymptotic Formulas for the Lyapunov Exponent.- 15 The Point Spectrum of Random Operators.- 15.A The Pure Point Spectrum in One Dimension.- 15.B Other One-Dimensional Results.- 15.C The Point Spectrum in Multidimensional Problems.- Problems.- VII. Almost-Periodic Operators.- 16 Smooth Quasi-Periodic Potentials.- 16.A The Integrated Density of States and the Gap Labeling Theorem.- 16.B Absolutely Continuous Spectrum.- 16.C Lower Bounds of Solutions and Absence of a Point Spectrum.- 16.D Lower Bounds for the Lyapunov Exponent and Absence of an Absolutely Continuous Spectrum in the Discrete Case.- 16.E Point Spectrum of Almost-Periodic Operators.- 16.F The Almost-Mathieu Operator.- 17 Limit-Periodic Potentials.- 17.A Basic Results.- 17.B Spectral Data for Periodic Potentials of Increasing Period.- 17.C Proof of the Main Theorems.- 18 Unbounded Quasiperiodic Potentials.- 18.A General Results and the Integrated Density of States.- 18.B The Case of Strongly Incommensurate Frequencies.- 18.C The One-Dimensional Case.- 18.D The Schrodinger Operator with a Nonlocal Quasiperiodic Potential.- Problems.- Appendix A: Nevanlinna Functions.- Appendix B: Distribution of Eigenvalues of Large Random Matrices.- List of Symbols.

pseudodifferential-operators-and-nonlinear-pde

Abstract: The theory of pseudodifferential operators has played an important role in many investigations into linear PDE. This book is devoted to a summary and reconsideration of some uses of pseudodifferential operator techniques in nonlinear PDE.

The Schrödinger Equation

Abstract: 1. General Concepts of Quantum Mechanics.- 1.1. Formulation of Basic Postulates.- 1.2. Some Corollaries of the Basic Postulates.- 1.3. Time Differentiation of Observables.- 1.4. Quantization.- 1.5. The Uncertainty Relations and Simultaneous Measurability of Physical Quantities.- 1.6. The Free Particle in Three-Dimensional Space.- 1.7. Particles with Spin.- 1.8. Harmonic Oscillator.- 1.9. Identical Particles.- 1.10. Second Quantization.- 2. The One-Dimensional Schrodinger Equation.- 2.1. Self-Adjointness.- 2.2. An Estimate of the Growth of Generalized Eigenfunctions.- 2.3. The Schrodinger Operator with Increasing Potential.- 1. Discreteness of spectrum.- 2. Comparison theorems and the behaviour of eigenfunctions as x ??..- 3. Theorems on zeros of eigenfunctions.- 2.4. On the Asymptotic Behaviour of Solutions of Certain Second-Order Differential Equations as x ??.- 1. The case of integrable potential.- 2. Liouville's transformation and operators with non-integrable potential.- 2.5. On Discrete Energy Levels of an Operator with Semi-Bounded Potential.- 1 The operator in a half-axis with Dirichlet's boundary condition.- 2. The case of an operator on the half-axis with the Neumann boundary condition.- 3. The case of an operator on the whole axis.- 2.6. Eigenfunction Expansion for Operators with Decaying Potentials...- 1. Preliminary remarks.- 2. Formulation of the main theorem.- 3. Two proofs of Theorem 6.1..- 4. One-dimensional oper-ator obtained from the radially symmetric three-dimensional operator.- 5. The case of an operator on the whole axis.- 2.7. The Inverse Problem of Scattering Theory.- 1. Inverse problem on the half-axis.- 2. Inverse problem on the whole axis.- 2.8. Operator with Periodic Potential.- 1. Bloch functions and the band structure of the spectrum.- 2. Expansion into Bloch eigenfunctions.- 3. The density of states.- 3. The Multidimensional Schrodinger Equation.- 3.1. Self-Adjointness.- 3.2. An Estimate of the Generalized Eigenfunctions.- 3.3. Discrete Spectrum and Decay of Eigenfunctions.- 1. Discreteness of spectrum.- 2. Decay of eigenfunctions.- 3. Non-degeneracy of the ground state and positiveness of the first eigenfunction.- 4. On the zeros of eigenfunctions 180..- 3.4. The Schrodinger Operator with Decaying Potential: Essential Spectrum and Eigenvalues.- 1. Essential spectrum.- 2. Separation of variables in the case of spherically symmetric potential and the Laplace-Beltrami operator on a sphere.- 3. Estimation of the number of negative eigenvalues.- 4. Absence of positive eigenvalues.- 3.5. The Schrodinger Operator with Periodic Potential.- 1. Lattices.- 2. Bloch functions.- 3. Expansion in Bloch functions.- 4. Band functions and the band structure of the spectrum.- 5. Theorem on eigenfunction expansion.- 6. Non-triviality of band functions and the absence of a point spectrum.- 7. Density of states.- 4. Scattering Theory.- 4.1. The Wave Operators and the Scattering Operator.- 1. The basic definitions and the statement of the problem.- 2. Physical interpretation.- 3. Properties of the wave operators.- 4. The invariance principle and the abstract conditions for the existence and completeness of the wave operators.- 4.2. Existence and Completeness of the Wave Operators.- 1. The abstract scheme of Enss.- 2. The case of the Schrodinger operator.- 3. The scattering matrix.- 4. One-dimensional case.- 5. Spherically symmetric case.- 4.3. The Lippman-Schwinger Equations and the Asymptotics of Eigen-functions.- 1. A derivation of the Lippman-Schwinger equations.- 2. Another derivation of the Lippman-Schwinger equations.- 3. An outline of the proof of the completeness of wave operators by the stationary method.- 4. Discussion on the Lippman-Schwinger equation.- 5. Asymptotics of eigenfunctions.- 5. Symbols of Operators and Feynman Path Integrals.- 5.1. Symbols of Operators and Quantization: qp-and pq-Symbols and Weyl Symbols.- 1. The general concept of symbol and its connection with quantization.- 2. The qp-and pq-symbols.- 3. Symmetric or Weyl symbols.- 4. Weyl symbols and linear canonical transformations.- 5. Weyl symbols and reflections.- 5.2. Wick and Anti-Wick Symbols. Covariant and Contravariant Symbols.- 1. Annihilation and creation operators. Fock space.- 2. Definition and elementary properties of Wick and Anti-Wick symbols.- 3. Covariant and contravariant symbols.- 4. Convexity inequalities and Feynman-type inequalities.- 5.3. The General Concept of Feynman Path Integral in Phase Space. Symbols of the Evolution Operator.- 1. The method of Feynman Path integrals.- 2. Weyl symbol of the evolution operator.- 3. The Wick symbol of the evolution operator.- 4. pq-and qp-symbols of the evolution operator and the path integral for matrix elements.- 5.4. Path Integrals for the Symbol of the Scattering Operator and for the Partition Function.- 1. Path integral for the symbol of the scattering operator.- 2. The path integral for the partition function.- 5.5. The Connection between Quantum and Classical Mechanics. Semiclassical Asymptotics.- 1. The concept of a semiclassical asymptotic.- 2. The operator initial-value problem.- 3. Asymptotics of the Green's function.- 4. Asymptotic behaviour of eigenvalues.- 5. Bohr's formula 383..- Supplement 1. Spectral Theory of Operators in Hilbert Space.- S1.1. Operators in Hilbert Space. The Spectral Theorem.- 1. Preliminaries.- 2. Theorem on the spectral decomposition of a self-adjoint operator in a separable Hilbert space.- 3. Examples and exercises.- 4. Commuting self-adjoint operators in Hilbert space, operators with simple spectrum.- 5. Functions of self-adjoint operators.- 6. One-parameter groups of unitary operators.- 7. Operators with simple spectrum.- 8. The classification of spectra.- 9. Problems and exercises.- S1.2. Generalized Eigenfunctions.- 1. Preliminary remarks.- 2. Hilbert-Schmidt operators.- 3. Rigged Hilbert spaces.- 4. Generalized eigenfunctions.- 5. Statement and proof of main theorem.- 6. Appendix to the main theorem.- 7. Generalized eigenfunctions of differential operators.- S1.3. Variational Principles and Perturbation Theory for a Discrete Spectrum.- S1.4. Trace Class Operators and the Trace.- 1. Definition and main properties.- 2. Polar decomposition of an operator.- 3. Trace norm.- 4. Expressing the trace in terms of the kernel of the operator.- S1.5. Tensor Products of Hilbert Spaces.- Supplement 2. Sobolev Spaces and Elliptic Equations.- S2.1. Sobolev Spaces and Embedding Theorems.- S2.2. Regularity of Solutions of Elliptic Equations and a priori Estimates.- S2.3. Singularities of Green's Functions.- Supplement 3. Quantization and Supermanifolds.- S3.1.Supermanifolds:Recapitulations.- 1. Superspaces and supermanifolds.- 2. Classical Lie superalgebras.- 3. Lie supergroups and homogeneous superspaces in ternis of the point functor.- 4. Two types of mechanics on supermanifolds and Shander's time.- S3.2. Quantization: main procedures.- S3.3. Supersymmetry of the Ordinary Schrodinger Equation and of the Electron in the Non-Homogeneous Magnetic Field.- A Short Guide to the Bibliography.

Elliptic theory of differential edge operators I

Abstract: Examples of edge operators include Laplacians on asymptotically flat and asymptotically hyperbolic manifolds. Edge operators also arise in boundary problems around higher condimension boundaries. This paper is concerned with the analysis of general elliptic edge operators with constant indicide roots. We determine when such an operator has a distributional asymptotic expansion. Conditions are given to guarantee that the coefficients of this expansion are smooth. In Part I of this paper we only study the case when the operator is semi-Fredholm. Part II will examine edge operators with infinite dimensional kernel and cokernel, as well as develop the theory of Poisson edge operators.

A spatial operator algebra for manipulator modeling and control

Abstract: A recently developed spatial operator algebra for manipu lator modeling, control, and trajectory design is dis cussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high- level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced concep tual 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 mechanizat...

A Mathematica™ Package for Computing Operator Product Expansions

Abstract: A general purpose Mathematica™ package for computing Operator Product Expansions of composite operators in meromorphic conformal field theory is described. Given the OPEs for a set of “basic” fields, OPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. Two explicit examples are presented: the conformal anomaly for superstrings and a free field realization for the $\widehat{B_2}$ Kac-Moody-algebra.

Convergence estimates for product iterative methods with applications to domain decomposition

Abstract: In this paper, we consider iterative methods for the solution of symmetric positive definite problems on a space % which are defined in terms of products of operators defined with respect to a number of subspaces. The simplest algorithm of this sort has an error-reducing operator which is the product of orthogonal projections onto the complement of the subspaces. New normreduction estimates for these iterative techniques will be presented in an abstract setting. Applications are given for overlapping Schwarz algorithms with many subregions for finite element approximation of second-order elliptic problems.

Vehicle collision avoidance system

Abstract: The collision avoidance system includes structure mountable at the side mirror position of a vehicle. The system includes a rotatable mirror and an ultrasonic transmitting and receiving unit which is adaptable to scan a predetermined area about the vehicle to detect the presence of an object and to calculate its distance from the vehicle. If the distance and speed are determined to pose a threat, the distance is placed on a display and an alarm is sounded. Two displays are provided, one for the forward end of the vehicle and another for the rear end of the vehicle. The system operates when the vehicle is moving forwardly and rearwardly. Also, when the vehicle is not moving, the presence of a potential intruder is also monitored and the system can actuate an anti-theft alarm of the vehicle. Further, the system can be programmed by a plurality of operators to particular distances, with the system discerning which operator is driving and automatically using that operator's input.

The automated solution of second quantization equations with applications to the coupled cluster approach

Abstract: Theoretical methods in chemistry frequently involve the tedious solution of complex algebraic equations. Then the solutions, sometimes still quite complex, are usually hand-coded by a programmer into an efficient computer language. During this procedure it is all too easy to make an error which will go undetected. A better approach would be to introduce the computer at an even earlier stage in the development of the theory by programming it to first solve the set of equations and then compile the solution into an efficient computer language. In this research a program has been written in the C programming language which can efficiently compute the quasivacuum expectation value of a product of creation and annihilation operators and scalar arrays. The terms in the resulting expressions are then transformed into a canonical form so that all equivalent terms can be combined. Finally, the equations are compiled into a simple representation which can be rapidly interpreted by a Fortran program. This symbol manipulator has been applied to open-shell coupled cluster theory. Two coupled cluster methods using high-spin open-shell references are presented. In one of these methods, the cluster operator contains the unitary group generators, and products thereof, which generate all single and double excitations with respect to the reference. The other uses a simplified cluster operator which generates equations that must be spin-projected. These methods are compared to other descriptions of electron correlation for the CH2 singlet-triplet splitting and the NH2 potential energy surface.

The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems

Abstract: The bi-Hamiltonian structure of integrable supersymmetric extensions of the Korteweg-de Vries (KdV) equation related to theN=1 and theN=2 superconformal algebras is found. It turns out that some of these extensions admit inverse Hamiltonian formulations in terms of presymplectic operators rather than in terms of Poisson tensors. For one extension related to theN=2 case additional symmtries are found with bosonic parts that cannot be reduced to symmetries of the classical KdV. They can be explained by a factorization of the corresponding Lax operator. All the bi-Hamiltonian formulations are derived in a systematic way from the Lax operators.

System for managing a hold queue

Abstract: A system for electronically managing calls in a hold queue wherein the hold queue is prioritized into a number of priority categories according to user selectable priority criteria. As an operator becomes available, the system selectively assigns the calls on hold to an available operator in a sequential manner according to the priority category of the calls and the type of hold queue utilized.

Strategic behavior, workload, and performance in task scheduling

Abstract: Scheduling theory is proposed as a normative model for strategic behavior when operators are confronted by several tasks, all of which should be completed within a fixed time span, and when they are free to choose the order in which the tasks should be done. Three experiments are described to investigate the effect of knowing the correct scheduling rule on the efficiency of performance, subjective workload, and choice of strategy under different conditions of time pressure. The most potent effects are from time pressure. The reasons for the weak effect of knowing the rules are discussed, and implications for strategic behavior, displays, and decision aids are indicated.

Scale-Space: Its Natural Operators and Differential Invariants

Abstract: Why and how one should study a scale-space is prescribed by the universal physical law of scale invariance, expressed by the so-called Pi-theorem. The fact that any image is a physical observable with an inner and outer scale bound, necessarily gives rise to a ‘scale-space representation’, in which a given image is represented by a one-dimensional family of images representing that image on various levels of inner spatial scale. An early vision system is completely ignorant of the geometry of its input. Its primary task is to establish this geometry at any available scale. The absence of geometrical knowledge poses additional constraints on the construction of a scale-space, notably linearity, spatial shift invariance and isotropy, thereby defining a complete hierarchical family of scaled partial differential operators: the Gaussian kernel (the lowest order, rescaling operator) and its linear partial derivatives. They enable local image analysis in a robust way, while at the same time capturing global features through the extra scale degree of freedom. The operations of scaling and differentiation cannot be separated. This framework permits us to construct in a systematic way multiscale, orthogonal differential invariants, i.e. true image descriptors that exhibit manifest invariance with respect to a change of cartesian coordinates. The scale-space operators closely resemble the receptive field profiles in the mammalian front-end visual system.

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

Abstract: A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Two conjectures on the admissibility of control operators

Abstract: We are searching for necessary and/or sufficient conditions for the admissibility of unbounded control operators for semigroups on Hilbert spaces, with respect to input functions of class L 2. Our first conjecture is that admissibility of an unbounded input element 6 for a semigroup with generator A is equivalent to a certain decay rate of ∥(sI - A)-1 b∥ as Re s → ∞. The second conjecture states that a control operator B defined on a Hilbert space U is admissible if and only if, for any v ∈ U, Bv is an admissible input element. It is proved that both conjectures hold in many important particular cases (e.g., the first conjecture is true if the semigroup is normal).

Weighted Sobolev-Poincaré inequalities and pointwise estimates for a class of degenerate elliptic equations

Abstract: In this paper we prove a Sobolev-Poincare inequality for a class of function spaces associated with some degenerate elliptic equations. These estimates provide us with the basic tool to prove an invariant Harnack inequality for weak positive solutions. In addition, Holder regularity of the weak solutions follows in a standard way. Let y = Z,7 ai(aij9 a ) be a second-order degenerate elliptic operator in divergence form with measurable coefficients. In this paper we shall obtain pointwise estimates for the weak solutions of Su = 0 (H61der continuity of the weak solutions and Harnack inequality for nonnegative solutions). Let us recall that the original results for elliptic operators were obtained by De Giorgi, Nash, and Moser. An extensive bibliography about the degenerate case can be found in [FLI, FL2, FS]. To introduce the results of the present paper, let us recall some recent results. In [FL1, FL2] a suitable metric d is associated with the differential operator Y in such a way that we obtain a new geometry which is natural for the degenerate operator as the Euclidean geometry is natural for the Laplace operator (or, more precisely, as a suitable Riemannian geometry is natural for a secondorder elliptic operator). In the smooth case, this idea is contained in many papers: we refer to [FP, NSW]. The basic results in [FL 1, FL2] are obtained via a precise description of this geometry under suitable technical hypotheses on the coefficients whose aim is to give a nonsmooth formulation of the Hormander hypoellipticity condition for sum-of-squares operators. We note that the same idea is used in [NSW, S, J, V] to obtain pointwise estimates for sum-of-squares operators. On the other hand, a different class of degenerate elliptic operators is considered in [FKS]: instead of a geometrical degeneracy, a measure degeneracy is allowed. A typical example of this class is given by Yu = div(wo(x)Vu), where cl is a weight function belonging to the A2-class of Muckenhoupt. Unified results for a class containing both the operators in [FL 1] and in [FKS] have Received by the editors August 1, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 46E35, 35J70. Partially supported by G.N.A.F.A. of C.N.R. and M.U.R.S.T., Italy. ( 1991 American Mathematical Society 0002-9947/91 $1.00 + $.25 per page

Weighted norm inequalities for averaging operators of monotone functions

Abstract: We prove weighted norm inequalities for the averaging operator Af(x) = 1/x ?0x f of monotone functions.

Commitment strategies in planning: a comparative analysis

Abstract: In this paper we compare the utility of different commitment strategies in planning. Under a "least commitment strategy", plans are represented as partial orders and operators are ordered only when interactions are detected. We investigate claims of the inherent advantages of planning with partial orders, as compared to planning with total orders. By focusing our analysis on the issue of operator ordering commitment, we are able to carry out a rigorous comparative analysis of two planners. We show that partial-order planning can be more efficient than total-order planning, but we also show that this is not necessarily so.

Printing system with automatic statistical compilation and billing

Abstract: An electronic reprographic printing system which is capable of scanning a set of documents, electronically storing in memory images of the scan documents, and printing the electronic images in accordance with operator specified reprographic system functions for the print job. Customer accounts are set up within the reprographic printing system, and billing rates for the various system functions are specified within each account. When a print job is to be performed, the system operator of the reprographic system can allocate the cost of the system functions of the print job to a default account, or to a particular customer account. The billing rates for the various accounts can be changed by the system operator, and statistical and billing reports can be generated covering many different time frames.

A generalized relational model for indefinite and maybe information

Abstract: A generalized relational model which is capable of representing and manipulating disjunctive and maybe kinds of information is presented. A data structure, called M-table, is defined, and the information contained in the M-table is precisely stated. Redundant information in M-tables is characterized, and an operator to remove this redundant information is presented. The relational algebra is suitably generalized to deal with M-tables. Additional operators, R-projection and merge, are presented. Queries can be expressed as a combination of the various generalized relational algebraic operators. The M-table accurately models the two bounds on the external interpretation of a query. The sure component of an M-table corresponds to one of the bounds which is the set of objects which belong to the external interpretation of the query. The maybe component of an M-table corresponds to the other bound which is the set of objects for which the possibility of belonging to the external interpretation of the query cannot be ruled out. >

Prototype image constraints for set-theoretic image restoration

Abstract: Constraints based on prototype images are developed and used in set-theoretic image restoration. A prototype can be obtained as a result of applying a predetermined operator to the observed image. In this case, the operator and the bound, which limits the variation of the restored image from the prototype, are the two defining quantities of a prototype constraint. General guidelines for rigorously estimating the defining bound of a prototype constraint under certain simplifying conditions are discussed. The authors provide two examples of prototype constraints where the prototypes are obtained by the Wiener filtering operator and a local averaging operator. The projection onto convex sets algorithm using the prototype constraints is applied to both monochrome and color images degraded by out-of-focus blur at different noise levels. The results show significant improvement over the Wiener restoration in reducing the restoration artifacts. >