Operator (computer programming)

About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.

Virtual image display management system with head-up display

Abstract: A virtual image display management system using a head-up display that improves the ability of an operator of an automobile, or other equipment, to focus on primary functions, such as vehicle operation, while providing secondary information within the operator's primary visual field without requiring the operator to refocus. The present virtual image display management system integrates one or more secondary function displays into one reconfigurable virtual image head-up display. Several secondary functions are displayed sequentially using analog/digital symbology, icon representation, alphanumeric text or static/motion picture format. The operator may select secondary functions to be monitored, the display format, and the data acquisition intervals. A reconfigurable virtual image display processor accommodates more sophisticated sensor and communication functionality without penalizing efficiency and safety of the operator's primary functions. The present system integrates, interprets, selects and displays data derived from multiple sensors and communications systems at an optimum visual location within the operator's primary field of view. By displaying data in this fashion, an operator can vigilantly perform critical system functions while being kept well-informed of vehicle performance data, communication data and other useful functions and information.

CR invariant powers of the sub-Laplacian

Abstract: CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ``conformally invariant powers of the Laplacian'' via the Fefferman metric; the powers which arise for these operators are bounded in terms of the dimension. A second family is derived from a CR tractor calculus which is developed here; this family includes operators for every positive power of the sub-Laplacian. This result together with work of Cap, Slovak and Soucek imply in three dimensions the existence of a curved analogue of each such operator in flat space.

Random linear operators

Abstract: 1. Random Operators in Hilbert Space.- 1. Basic Definitions.- 1.1 Strong Random Operator.- 1.2 Weak Random Operator.- 1.3 Product of Random Operators.- 2. Characteristic Functions of Random Operators.- 2.1 Definition.- 2.2 Characteristic Functions of Strong and Bounded Operators.- 2.3 Gaussian Random Operators.- 3. Convergence of Random Operators.- 3.1 Weak Convergence of Random Operators.- 3.2 Strong Convergence of Random Operators.- 3.3 Convergence of Distributions corresponding to Random Operators.- 2. Functions of Random Operators.- 4. Spectral Representation for Symmetric Random Operators.- 4.1 Symmetric Random Operators and Selfadjoint Extensions.- 4.2 Spectral Representation of a Selfadjoint Random Operator.- 4.3 Spectral Representation of a Strong Symmetric Operator.- 5. Equations with Symmetric Random Operators.- 5.1 Evolution Equations.- 5.2 Schrodinger-type Equations.- 5.3 Spectral Moment Functions.- 5.4 Equation of Fredholm Type.- 6. Equations with Semi-Bounded Random Operators.- 6.1 Nonnegative Closed Random Operators.- 6.2 Resolvent of a Nonnegative Operator.- 6.3 Resolvent of a Nonnegative Random Operator.- 6.4 Equations of Fredholm Type.- 6.5 Equations of Evolution Type.- 3. Operator-Valued Martingales.- 7. Operator-Valued Martingale Sequences.- 7.1 Weak Operator-valued Martingale.- 7.2 Strong Operator-valued Martingales.- 7.3 Operator-valued Martingale.- 8. Convergence of Infinite Products of Independent Random Operators.- 8.1 Infinite Products as Martingales.- 8.2 Convergence of Infinite Products given the Existence of Two Moments.- 8.3 Convergence of Infinite Products in Absolute Norm.- 9. Continuous Operator-Valued Martingales.- 9.1 Some Properties of Continuous Real-valued Local Martingales.- 9.2 Continuous Martingales with values in X.- 9.3 Operator-valued Continuous Martingales.- 9.4 Strong Operator-valued Wiener Processes.- 4. Stochastic Integrals and Equations.- 10. Stochastic Integrals with Respect to an X-Valued Martingale.- 10.1 Definition.- 10.2 Integrals for Processes with Regular Characteristics.- 10.3 Stochastic Integral with respect to a Wiener Process.- 11. Stochastic Integral with Respect to an Operator-Valued Martingale.- 11.1 Integrals of X-valued Functions.- 11.2 Integrals of Operator-valued Functions.- 12. Stochastic Operator Equations.- 12.1 Operator-valued Functions of Random Operators.- 12.2 Stochastic Equations Involving I(Z, Y)t.- 12.3 Stochastic Equations Involving I*(Z, Y)t.- 12.4 Some Generalizations.- 5. Linear Stochastic Operator Equations.- 13. Generalization of the Stochastic Operator Integral.- 13.1 General Form of the Linear Equation.- 13.2 A Generalization of the Stochastic Integral.- 14. Linear Differential Operator Equations.- 14.1 Definition of a Linear Equation.- 14.2 Existence of Uniqueness of Solution.- 14.3 Linear Transformations of Solutions.- 14.4 Equations for Moments of the Solution of a Stochastic Equation.- 15. Continuous Stochastic Semigroups.- 15.1 Solutions of Simple Linear Equations -Stochastic Semigroups.- 15.2 Time Reversal in Stochastic Differential Equations.- 15.3 Definition of Stochastic Semigroups.- 15.4 Semigroups which are Martingales.

Collective fields, Calogero-Sutherland model and generalized matrix models

Abstract: On the basis of the collective field method, we analyze the Calogero--Sutherland model (CSM) and the Selberg--Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indicate relations with the CSM operators. Similar results are presented for the $q$--deformed case (the Macdonald operator and polynomials), which gives the generating functional of infinitely many conserved charges in the CSM.

Hyponormal operators and spectral density

Abstract: Introduction. We say an operator T on a Hilbert space H is hyponormal if Tx || > || T*x || for xeH, or equivalently T*T-TT* > 0. In this paperwe will first examine some general properties of hyponormal operators. Then we restrict our interest to hyponormal operators with "thin" spectra. The importance of the topological nature of the spectrum is evident in our main result (Theorem 4) which states that a hyponormal operator whose spectrum lies on a smooth Jordan arc is normal. We continue with a general discussion of a certain growth condition on the resolvent which obtains for hyponormal operators. We conclude with a counterexample to a relation between hyponormal and subnormal operators. The reader is advised that additional facts about hyponormal operators may be found in [l1]. We shall denote the spectrum and the resolvent set of an operator by o(T) and p(T), respectively. The spectral radius R,,(T) sup {j z : z E a(T)}. The numerical range = closure {z: z Tx.x) 11 x = 1} is designated by W(T). Throughout the paper the underlyingvector space is always a separable Hilbert space H.