Showing papers on "Operator (computer programming) published in 1977"

Methods of algebraic geometry in the theory of non-linear equations

Abstract: CONTENTSIntroduction § 1. The Akhiezer function and the Zakharov-Shabat equations § 2. Commutative rings of differential operators § 3. The two-dimensional Schrodinger operator and the algebras associated with it § 4. The problem of multi-dimensional -algebraic operators Appendix 1. The Hamiltonian formalism in equations of Lax and Novikov types Appendix 2. Elliptic and rational solutions of the K-dV equations and systems of many particles Concluding Remarks References

Estimates of singular numbers of integral operators

Abstract: ContentsIntroduction § 1. Operator spaces and function spaces § 2. Estimates of singular numbers based on the method of piecewise-polynomial approximation § 3. Interpolation methods § 4. General results on estimates (statements) § 5. Proof of the main results on estimates § 6. Operators with a difference kernel § 7. Tests for nuclearity § 8. Multipliers in classes of kernels of integral operators § 9. Analytical results for the multiplier problem § 10. Operators with a homogeneous difference kernel § 11. Some special casesAppendix. M. Z. Solomyak, The Interpolation of bilinear maps from function spaces into operator spacesReferences

On generalized resolvents and Q-functions of symmetric linear relations (subspaces) in Hilbert space

Abstract: In some problems related to the spectral theory in Hubert space it is more natural and at the same time often less restrictive to use symmetric linear relations (in the terminology of [1], subspaces in the terminology of [2-4]) instead of symmetric operators. Hence the question arises if the theory of generalized resolvents of symmetric operators can be extended to symmetric linear relations. In [4] a description of all generalized resolvents of a symmetric linear relation was given, following the lines of A. V. Straus [5] in the operator case. It is the aim of this paper to generalize M. G. Kreϊn's formula for the generalized resolvents of a symmetric operator (see [6, 7]) to the symmetric linear relation case. This can be done rather easily by means of the Gayley transformation, using the results of [8]. However, in this connection there arise natural problems and questions: To introduce and to study the Q-function of a linear relation, to prove criteria for the selfadjoint extension of the given symmetric linear relation being an operator, to study the special case of a bounded nondensely defined operator etc. After the necessary definitions and their simple consequences in §1, the §2 is devoted to a study of the Q-f unction. From arguments similar to those in [9, 10] it follows that every function Q, whose values are bounded operators in a Hubert space and which is holomorphic in the upper half plane and has the property

An algorithm for reduction of operator strength

Abstract: A simple algorithm which uses an indexed temporary table to perform reduction of operator strength in strongly connected regions is presented. Several extensions, including linear function test replacement, are discussed. These algorithms should fit well into an integrated package of local optimization algorithms.

Control Theory Measures of Tracking as Indices of Attention Allocation Strategies

Abstract: In an intelligent man-machine control system, control theory measures describing the operator's tracking performance can provide useful information concerning an operator's attentional slate. This ...

The role of preprocessing in problem solving systems: An ounce of reflection is worth a pound of backtracking

Abstract: We describe REFLECT, a problem solver in simulated robot worlds. REFLECT has successfully solved a variety of non-linear problems described as a conjunction of subtasks, including most of those found in the literature. First, during a preprocessing phase, the system explores its capabilities in the environment it is presented with. Various intrinsic properties of the given operators are inferred, such as the unattainability of certain conjunctive tasks. Macro operators are built, again considering only the given operators. REFLECT is then ready to accept problems, and proceeds by conducting backward heuristic search on a variation of a regular state-space graph termed a Goal-Kernel graph. Attention is not focused on any one sub task in particular, so that a global view of the problem is always maintained.

Multi-lingual input keyboard and display

Abstract: A data entry device with a keyboard for use with a data processing system. A first data set of input keys are arranged in a standard typewriter configuration. A second set of keys comprises additional rows of data input keys that enable the operator to enter various special characters or symbols that are encountered in different languages. One row of keys in the first set constitutes a variable row. A legend corresponding to a selectable set of symbols is juxtaposed to the variable row. An operator can select a set of characters so that each input key in the variable row thereafter functions to identify the character designated in a corresponding position of the juxtaposed legend.

On algebras of pseudo differential operators In

Abstract: We discuss a sub-algebra ¸ of Pseudo Differential Operators of which is Fredholm-closed and commutative modulo the ideal of compact operators. The algebra ¸ contains in particular all LP - Fourier-multipliers of Mihlin type. is shown to be an algebra with symbol, and its symbol space is determined. As an application we get simple criteria for an operator in ¸to be Fredholm. Furthermore, we regard algebras ¸ on Sobolev spaces , which are isometrically isomorphic to ¸ and have equivalent properties. Finally we conclude Fredholm criteria for mroe general Differential and Pseudo Differential Operators.

Handle bar hand guards

Abstract: Rigid protective coverings for the hands when operating a handle bar controlled vehicle that are attached securely to the vehicle and allow convenient access for the operator.

Motor vehicle speed control system

Abstract: A digital speed control system including a processor performing arithmetical and logic operations in response to command inputs from the operator to maintain the present vehicle speed, to accelerate at a substantially constant rate to a new cruising speed or to a previously established cruising speed is disclosed. Certain processor operations are phased to speed sensor pulses to permit rate of change of speed computations to be performed with minimum hardware.

Display analysis with the optimal control model of the human operator

Abstract: Application of the optimal control model of the human operator to problems in display analysis is discussed Those aspects of the model pertaining to the operator-display interface and to operator information processing are reviewed and discussed The techniques are then applied to the analysis of advanced display/control systems for a Terminal Configured Vehicle Model results are compared with those obtained in a large, fixed-base simulation

Controllability of nonlinear systems

Abstract: Some sufficient conditions are presented for the controllability of general nonlinear systems. First, the controllability problem is transformed into the problem of existence of fixed points for some operator; using Schauder's theorem, it is derived that a sufficient condition for controllability is the existence of a subsetS inCn+m (T) which is invariant for a derived operator. Secondly, with the aid of the notion of comparison principle, the existence of the subsetS is guaranteed by the existence of solutions for some nonlinear integral inequality or equality equations. For example, one solution for such nonlinear integral equations is obtained under the assumption of the uniform boundedness for a nonlinear term of the differential equation.

Operator Siegel Domains

Abstract: A unified description and treatment is given for a large and important class of homogeneous Siegel domains in finite and infinite dimensions. These domains are shown to be linearly equivalent to generalized upper half-planes in spaces of operators having a kind of triple product structure.

Method and apparatus for fastening a door panel to a door operator mounted on an elevator car

Abstract: An elevator system including an elevator car, an elevator door, and a door operator for operating the door to open and close an entranceway to the car. The door has integral hanger brackets which are fastened to a hanger plate associated with the door operator. The door may be easily mounted, oriented and aligned in the field by a fastening arrangement and method which includes clamping bolts and jacking bolts. The clamping bolts are adjusted to initially support the weight of the door. Jacking bolts are then coupled between the hanger bracket and hanger plate, and the jacking bolts are actuated to align the door and set the sill gap. The clamping bolts are then tightened to maintain the selected alignment and sill gap. The clamping bolts, jacking bolts and the frictional area contact between the clamped surfaces all co-operate to support the weight of the door, and the clamped surfaces additionally function to add structural stiffness to the door and its support.

Control systems with delays: Areas of applications and present status of the linear theory

Abstract: This paper surveys several areas of applications of models of hereditary type and summarizes the present status of linear control theory in the autonomous case. By treating hereditary differential systems (HDS) in the Hilbert space M2 using evolution equations, we show that most system theoretic concepts can be put together in a unified framework. There an important role is played by a certain "hereditary operator" F which permits to achieve substantial simplifications of the existing theory. By using this operator, the spectral theory along with controllability and observability related concepts are reviewed. It is shown that the use of that operator permits to construct notions of controllability and observability which are directly related to feedback stabilization and solvability of the algebraic operator Riccati equation, thus making the whole theory complete.

Excitation operators and the extended random-phase approximation. I. Theory

Abstract: An analysis of extended random-phase approximations is made with emphasis on the justification of the simplifying assumptions used in applications. It is demonstrated that in a complete operator space, the equations of motion in expectation value form, supplemented by the ground-state annihilation condition, yield the exact result for excitation operators and are equivalent to the operator equation of motion. Certain operators that are normally neglected have to be included to obtain the exact solution; some of these additional operators are shown to be important while others are expected to have small effects. The random-phase approximation and its self-consistent variants are analyzed, and a number of improvements that can be introduced without increasing the difficulty of the calculations are suggested.

Δ plus a bad potential

Abstract: The purpose of this paper is to associate with −Δ+V (x) a self‐adjoint operator in case V is nonnegative. This has been done in many ways by previous authors under a variety of conditions. The point of the present work is to do this under conditions applying to, e.g., any many‐body potential, the only requirements being that V:R3n→[0,∞] be continuous and that V−1(∞) be not too large in the sense of volume and/or capacity; especially, no conditions of growth are imposed upon V. The method of proof is probabilistic, being based upon familiar properties of the Brownian motion.

On a Concept of a Derivative Among Functions Defined on the Dyadic Field

Abstract: In papers [10], [11], P. L. Butzer, H. J. Wagner and F. Pichler examined the concept of a dyadic derivative for functions defined on $(0,\infty ]$. In this paper, a corresponding inverse operator is defined for such functions, namely, the dyadic integral operator, and a dyadic calculus is developed. It is shown that the analogue of the fundamental theorems of the calculus holds for dyadic differentiation and integration.

On the extensions to the bidual of a maximal monotone operator

Abstract: An example is given which shows that a maximal monotone operator from a Banach space X to its dual X* may have several extensions into a maximal monotone operator from X** to X*. Introduction. Let X be a real Banach space with dual X* and let T: X 2x be a maximal monotone operator. Identifying as usual X to a subspace of X**, we look at T as a monotone operator from X** to 2X*; by Zorn's lemma, this operator can be extended into a maximal monotone operator from X** to 2x*. We are interested here in the question whether this extension is unique. There are a number of cases where it is so. Denote by T: X** -* 2x the (monotone) operator whose graph is the closure of the graph of T with respect to the weakest topology on X** x X* which is stronger than u(X**,X*) x u(X*,X**) and such that (x**,x*) * is upper semicontinuous. Since any maximal monotone extension of T to X ** contains T, we see that if T is maximal monotone, then T has a unique maximal monotone extension to X**. An operator T such that T is maximal monotone is called of dense type (a terminology slightly different from that of [2]). This kind of condition arises in the study of monotone operators in nonreflexive Banach spaces (cf. [2], [1], [7]). It is known, for instance, that the subdifferential of a convex function or the monotone operator associated with a saddle function are of dense type (cf. [6], [2], [5], [4]). On the other hand, there are maximal monotone operators which are not of dense type but which have a unique maximal monotone extension to the bidual (cf. the example in [3]: the uniqueness assertion is contained in Proposition I of [3] and the fact that the operator considered there is not of dense type follows easily from relation (1) of [3]). It is our purpose in this note to construct a maximal monotone operator which admits several (actually an infinity) maximal monotone extensions to the bidual. Our construction is based on a refinement of the method used in [3]. Received by the editors February 5, 1976. AMS (MOS) subject classifications (1970). Primary 47H05; Secondary 46B10, 35J60. ? American Mathematical Society 1977

Rigorous information-theoretic derivation of quantum-statistical thermodynamics. II

Abstract: Part I of the present work outlined the rigorous application of information theory to a quantum mechanical system in a thermodynamic equilibrium state The general formula developed there for the best-guess density operator\(\hat \rho\) was indeterminate because it involved in an essential way an unspecified prior probability distribution over the continuumDH of strong equilibrium density operators In Part II mathematical evaluation of\(\hat \rho\) is completed after an epistemological analysis which leads first to the discretization ofDH and then to the adoption of a suitable indifference axiom to delimit the set of admissible prior distributions Finally, quantal formulas for information-theoretic and thermodynamic entropies are contrasted, and the entire work is summarized

Convolution and H-equations for operator-valued functions with applications to neutron transport theory

Abstract: The Wiener–Hopf factorization of certain‐valued functions is related to operator‐valued generalizations of Chandrasekhar’s H‐functions. These functions satisfy a nonlinear system and may be computed by an iterative scheme. A general transport equation is solved in terms of these functions. The equation for steady‐state transport in one space dimension with isotropic scattering and continuous energy dependence is discussed as an application.

Operator Solutions in Terms of Asymptotic Fields in the Thirring and Schwinger Models

Abstract: The Thirring model and the Schwinger model (including non-Landau-gauge cases) are described in terms of asymptotic fields. In both models, operator solutions are found explicitly and it is shown that they possess the correct gauge-transformation property, the correct Lorentz-transformation property, locality with right statistics and canonical equal-time commutators. It is also found that, contrary to what is widely believed, gauge invariance is spontaneously broken and the Goldstone boson does exist in the Thirring model. Results of the preceding paper on a free massless scalar field are made use of extensively. The Thirring model and the Schwinger model are the celebrated exactly solvable examples of quantum field theory in two-dimensional space-time. They have a long history and there have appeared too many papers to quote all of them here. It is well known that formal solutions of both models can be very easily written down but they possess serious mathematical troubles.') Johnson2J was the first to give a consistent solution (in the form of Green's functions) of the Thirring model, but he gave up finding an operator solution. A thorough analysis of the Thirring model was made by Klaiber in his excellent lecture note. 3J He restored an operator solution in a modified form but used it only as a calculational tool. His primary. intention of using an operator solution was to guarantee a positivity condition for the solution given in the form of vacuum expectation values. There­ fore his operator solution was constructed in quite an artificial way. As for the Schwinger model, a detailed analysis was carried out by Lowenstein and Swieca.4J In all previous work, operator solutions are expressed in terms of a free massless spin or field *J that is, the spinor I-Ieisenberg operators have no corresponding asymptotic field.***> On the other *J Though there exists no spinor representation in two-dimensional space-time, it is customary to call a two-component half-vector a spinor. **l The singularity at p'=O is a branch point but not a simple pole. ***J This fact leads Casher, Kogut and Susskind'l to the use of the Schwinger model as a model of quark confinement.