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, the superhorizon conservation of the curvature perturbation ζ in single-field inflation was shown to hold as an operator statement and all ζ-correlators are time independent at all orders in the loop expansion.
Abstract: In this paper, we prove that the superhorizon conservation of the curvature perturbation ζ in single-field inflation holds as an operator statement. This implies that all ζ-correlators are time independent at all orders in the loop expansion. Our result follows directly from locality and diffeomorphism invariance of the underlying theory. We also explore the relationship between the conservation of ζ, the single-field consistency relation and the renormalization of composite operators.
125 citations
TL;DR: The variational case when one is interested in the solving of a primal-dual pair of convex optimization problems with complexly structured objectives is presented, which is illustrated by numerical experiments in image processing.
Abstract: We introduce and investigate the convergence properties of an inertial forward-backward-forward splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitzian operator. By making use of the product space approach, we expand it to the solving of inclusion problems involving mixtures of linearly composed and parallel-sum type monotone operators. We obtain in this way an inertial forward-backward-forward primal-dual splitting algorithm having as main characteristic the fact that in the iterative scheme all operators are accessed separately either via forward or via backward evaluations. We present also the variational case when one is interested in the solving of a primal-dual pair of convex optimization problems with complexly structured objectives, which we also illustrate by numerical experiments in image processing.
124 citations
TL;DR: In this paper, a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator, was established and applied to suitably chosen differential operators.
Abstract: We establish a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator. By applying the theorem to suitably chosen differential operators A, we obtain a simple proof of Alberti’s rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiability of Lipschitz functions can hold only for absolutely continuous measures and that every top-dimensional Ambrosio–Kirchheim metric current in Rd is a Federer–Fleming flat chain.
124 citations
Book•
16 Aug 2009
TL;DR: In this paper, the Paneitz operator and paneitz curvature are used to represent the Laplacian and Q-curvature, respectively, in the context of Conformally Covariant Families.
Abstract: Spaces, Actions, Representations and Curvature.- Conformally Covariant Powers of the Laplacian, Q-curvature and Scattering Theory.- Paneitz Operator and Paneitz Curvature.- Intertwining Families.- Conformally Covariant Families.
124 citations
TL;DR: In this article, a decision-making method based on weighted geometric aggregation operators was proposed to solve the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN).
124 citations