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 article, a nonlocal operator method is proposed which is generally applicable for solving partial differential equations (PDEs) of mechanical problems, which can be regarded as the integral form "equivalent" to the differential form in the sense of nonlocal interaction model for solving the unknown field.
130 citations
TL;DR: In this paper, the authors define a hierarchy of clusters in Z2-Hilbert spaces and define a set of clusters associated with the Cartesian and tensor products associated with a cluster.
Abstract: 0. Introduction 192 1. General Definitions 195 1.1. Hilbert spaces 195 1.2. Homomorphisms of commutative C∗and W ∗-algebras 196 1.3. Permutations 197 1.4. Clusters 197 1.5. Cartesian and tensor products associated with a cluster 198 1.6. Clusterings 198 1.7. Cartesian and tensor products associated with a clustering 199 2. Distinguishable Particles 199 2.1. Elementary particles 199 2.2. Clusters of elementary particles 199 2.3. Asymptotic particles 201 2.4. Clusters of asymptotic particles 201 2.5. Identification operator 202 2.6. Existence of the asymptotic velocity 202 2.7. Short-range case 202 2.8. Long-range case – free region 203 2.9. Long-range case – asymptotic interacting Hamiltonian 204 2.10. Long-range case – modified wave operators 205 3. Second Quantization in the Category of Sets 206 3.1. Second quantization of a set 206 3.2. “Third quantization” of a set 207 3.3. Permutations that preserve species 207 3.4. Clusters with composition n ∈ Γ(E) 208 3.5. Permutations that preserve species and a clustering 208 3.6. Clusterings associated with k ∈ Γ(E) 210 3.7. Identification operators 210 4. Second Quantization in the Category of Z2-Hilbert Spaces 211 4.1. Fock spaces 211
129 citations
TL;DR: In this article, stable approximation schemes for the one-dimensional linear Schrodinger equation set in an unbounded domain were developed for the initial boundary value problem in a bounded domain with a transparent boundary condition.
129 citations
TL;DR: In this article, the problem of estimating the electric potential distribution in proximity of the heart from potential data given on the body is reformulated as a control problem in terms of a transfer operator and stabilized by means of a suitable regularization operator.
Abstract: This paper investigates the problem of estimating the electric potential distribution in proximity of the heart from potential data given on the body and is here reformulated as a control problem in terms of a «transfer» operator and stabilized by means of a suitable regularization operator. The numerical approximation by means of the finite element method of the regularized problem is investigated; convergence results and error estimates are established.
129 citations
12 Oct 2010
TL;DR: This paper presents an extensive catalog of coupled operators that is based both on a literature survey as well as real-life case studies and is organized according to a number of criteria to ease assessing the impact on models aswell as selecting the right operator for a metamodel change at hand.
Abstract: Modeling languages and thus their metamodels are subject to change. When a metamodel is evolved, existing models may no longer conform to it. Manual migration of these models in response to meta-model evolution is tedious and error-prone. To significantly automate model migration, operator-based approaches provide reusable coupled operators that encapsulate both metamodel evolution and model migration. The success of an operator-based approach highly depends on the library of reusable coupled operators it provides. In this paper, we thus present an extensive catalog of coupled operators that is based both on a literature survey as well as real-life case studies. The catalog is organized according to a number of criteria to ease assessing the impact on models as well as selecting the right operator for a metamodel change at hand.
129 citations