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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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Journal ArticleDOI
TL;DR: A general bifurcation theorem for potential operators is proved in this article, which describes the possible behavior of the set of solutions of an operator equation as a function of the eigenvalue parameter in a neighborhood of the bifurlcation point.

116 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the region of complete localization in a class of random operators which includes random Schrodinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight binding model.
Abstract: We study the region of complete localization in a class of random operators which includes random Schrodinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of eigenfunction correlations or by the decay of Fermi projections. (These are necessary and sufficient conditions for the random operator to exhibit complete localization in this energy region.) Using the first type of characterization we prove that in the region of complete localization the random operator has eigenvalues with finite multiplicity.

116 citations

Journal ArticleDOI
TL;DR: The Maclaurin symmetric mean operator is investigated and an approach to multiple attribute decision making (MADM) problems with intuitionistic fuzzy information is developed.
Abstract: The Maclaurin symmetric mean (MSM) was originally introduced by Maclaurin and then generalized by Detemple and Robertson. The prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments. However, the researches on MSM are very rare, especially in fuzzy decision making. In this paper, we investigate the MSM operator and extend the MSM operator to intuitionistic fuzzy environment. Some new aggregation operators based on MSM for dealing with intuitionistic fuzzy information are developed, such as the intuitionistic fuzzy Maclaurin symmetric mean (IFMSM) and the weighted intuitionistic fuzzy Maclaurin symmetric mean (WIFMSM). Some desirable properties and special cases of these operators are discussed in detail. Based on WIFMSM operator, an approach to multiple attribute decision making (MADM) problems with intuitionistic fuzzy information is developed. Finally, a practical example is provided to illustrate the practicality and effectiveness of the proposed method.

116 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries in both 1+1D and higher dimensions, and argue that the coarsegrained pictures carry over to operator spreading in generic many-body systems.
Abstract: Random quantum circuits yield minimally structured models for chaotic quantum dynamics, able to capture for example universal properties of entanglement growth We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries We study both 1+1D and higher dimensions, and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC, and the butterfly speed $v_{B}$ We find that in 1+1D the `front' of the OTOC broadens diffusively, with a width scaling in time as $t^{1/2}$ We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front Turning to higher D, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a classical droplet growth problem This implies that the width of the front of the averaged OTOC scales as $t^{1/3}$ in 2+1D and $t^{024}$ in 3+1D (KPZ exponents) We support our analytic argument with simulations in 2+1D We point out that, in a lattice model, the late time shape of the spreading operator is in general not spherical However when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC in terms of the Tracy-Widom distribution For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like model As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly We also use this mapping to give exact results for entanglement growth in 1+1D circuits

116 citations

Journal ArticleDOI
TL;DR: Instantaneous signal operators /spl Upsi//sub k/(x)=x/spl dot/x/Sup (k-1)/-xx/sup (k)/ of integer orders k are proposed to measure the cross energy between a signal x and its derivatives.
Abstract: Instantaneous signal operators /spl Upsi//sub k/(x)=x/spl dot/x/sup (k-1)/-xx/sup (k)/ of integer orders k are proposed to measure the cross energy between a signal x and its derivatives. These higher order differential energy operators contain as a special case, for k=2, the Teager-Kaiser (1990) operator. When applied to (possibly modulated) sinusoids, they yield several new energy measurements useful for parameter estimation or AM-FM demodulation. Applying them to sampled signals involves replacing derivatives with differences that lead to several useful discrete energy operators defined on an extremely short window of samples. >

116 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202236
20212,210
20202,380
20192,310
20182,164
20171,834