Topic
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.
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TL;DR: In this paper, the Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian.
Abstract: The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
489 citations
01 May 2001
TL;DR: In this article, the authors enlarge the operator-based methodology of hysteresis operators by elements that allow the description of systems with hysteretic and creep effects, and use this concept for real-time inverse feedforward controller for piezo-electric actuators.
Abstract: Since the beginning of the 1990s, hysteresis operators have been employed on a larger scale for the linearisation of hysteretic transducers. One reason for this is the increasing number of mechatronic applications that use solid-state actuators based on magnetostrictive or piezo-electric material or shape memory alloys. All of these actuator types show strong hysteretic effects. In addition to hysteresis, piezo-electric actuators show strong creep effects. Thus, the objective of the paper is to enlarge the operator-based methodology of hysteresis operators by elements that allow the description of systems with hysteresis and creep. To reach this objective, following the procedure used for hysteretic systems, creep operators are introduced to form, together with the hysteresis operators, a system operator for the simultaneous consideration of both phenomena. With regard to applications in control and measurement technology, the existence, uniqueness, Lipschitz continuity and thus input-output stability of its inverse operator are theoretically supported by functional analytical methods. Subsequently, the efficiency of this new concept is demonstrated, in practice, by a real-time inverse feedforward controller for piezo-electric actuators. Using this control concept, the tracking errors caused by hysteretic and creep effects are reduced by approximately one order of magnitude.
483 citations
TL;DR: It is shown, that with the help of all those f(x), which are necessary when constructing a k(x,y), an F(x) can be constructed which has the properties of the measures of fuzziness introduced by A. De Luca and S. Termini.
474 citations
TL;DR: In this paper, the authors derive and discuss a formula, due to Magnus, for the exponential representation of the operator solution to Schrodinger's equation when the Hamiltonian is time dependent.
Abstract: We derive and discuss a formula, due to Magnus, for the exponential representation of the operator solution to Schrodinger's equation when the Hamiltonian is time dependent. The formula gives a unitary time‐displacement operator in every order of approximation. We study the usefulness of the first‐ and second‐order approximations for the kind of problem posed by the semiclassical theory of inelastic collisions, basing our discussion on two exactly soluble two‐state problems. The algebraic structure of the Magnus formula is in itself useful; to illustrate this, we solve exactly the problems of the linearly forced harmonic oscillator and the harmonic oscillator with time‐dependent force constant.
469 citations
TL;DR: It is shown that the methods previously used to obtain asymptotic spreading results and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving operator can be extended to a recursions with a periodic order preservingoperator.
Abstract: It is shown that the methods previously used by the author [Wei82] and by R. Lui [Lui89] to obtain asymptotic spreading results and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving operator can be extended to a recursion with a periodic order preserving operator. The operator can be taken to be the time-one map of a continuous time reaction-diffusion model, or it can be a more general model of time evolution in population genetics or population ecology in a periodic habitat. Methods of estimating the speeds of spreading in various directions will also be presented.
467 citations