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: A quasi-Newton algorithm for solving fluid-structure interaction problems to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect.
Abstract: We propose a quasi-Newton algorithm for solving fluid-structure interaction problems. The basic idea of the method is to build an approximate tangent operator which is cost effective and which takes into account the so-called added mass effect. Various test cases show that the method allows a significant reduction of the computational effort compared to relaxed fixed point algorithms. We present 2D and 3D fluid-structure simulations performed either with a simple 1D structure model or with shells in large displacements.
284 citations
Book•
23 Aug 2016
TL;DR: Ergodic Theory: Topological Dynamical Systems, Minimality and Recurrence, Measure-Preserving Systems, Recurrence and Ergodicity, Mean Ergodic Theorem, Mixing Dynamical System, Markov Operators on C*-algebra C(K) and the Koopman Operator.
Abstract: What is Ergodic Theory?.- Topological Dynamical Systems.- Minimality and Recurrence.- The C*-algebra C(K) and the Koopman Operator.- Measure-Preserving Systems.- Recurrence and Ergodicity.- The Banach Lattice Lp and the Koopman Operator.- The Mean Ergodic Theorem.- Mixing Dynamical Systems.- Mean Ergodic Operators on C(K).- The Pointwise Ergodic Theorem.- Isomorphisms and Topological Models.- Markov Operators.- Compact Semigroups and Groups.- Topological Dynamics Revisited.- The Jacobs-de Leeuw-Glicksberg Decomposition.- Dynamical Systems with Discrete Spectrum.- A Glimpse at Arithmetic Progressions.- Joinings.- The Host-Kra-Tao Theorem.- More Ergodic Theorems.- Appendix A: Topology.- Appendix B: Measure and Integration Theory.- Appendix C: Functional Analysis.- Appendix D: The Riesz Representation Theorem.- Appendix E: Theorems of Eberlein, Grothendieck, and Ellis.
283 citations
TL;DR: In this paper, it was shown that this trivial reparameterization invariance has non-trivial consequences: it relates coefficients of terms of different orders in the 1 m expansion and requires linear combinations of these operators to be multiplicatively renormalised.
283 citations
TL;DR: The proposed methods based on q‐ ROFWBM and q‐ROFWGBM operators are very useful to deal with MAGDM problems and are developed based on these operators.
Abstract: In the real multi-attribute group decision making (MAGDM), there will be a mutual relationship between different attributes. As we all know, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between parameters. In addition, in describing uncertain information, the eminent characteristic of q-rung orthopair fuzzy sets (q-ROFs) is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. In this paper, we combine the BM operator with q-rung orthopair fuzzy numbers (q-ROFNs) to propose the q-rung orthopair fuzzy BM (q-ROFBM) operator, the q-rung orthopair fuzzy weighted BM (q-ROFWBM) operator, the q-rung orthopair fuzzy geometric BM (q-ROFGBM) operator, and the q-rung orthopair fuzzy weighted geometric BM (q-ROFWGBM) operator, then the MAGDM methods are developed based on these operators. Finally, we use an example to illustrate the MAGDM process of the proposed methods. The proposed methods based on q-ROFWBM and q-ROFWGBM operators are very useful to deal with MAGDM problems.
280 citations
TL;DR: In this article, the spectral weights used for the unfolding of two-component spinor eigenstates are decomposed as the sum of the spectral values of the corresponding spinor states.
Abstract: We show that the spectral weights W mK (k ) used for the unfolding of two-component spinor eigenstates ∣ ∣ ψ SC mK ⟩=|α⟩|ψ SC mK ,α⟩+|β⟩|ψ SC mK ,β⟩ can be decomposed as the sum of the pa ...
280 citations