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.

The sharp weighted bound for general Calderon-Zygmund operators

Abstract: For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of Perez-Treil-Volberg reduced the problem to a testing condition on indicator functions, which is verified in this paper. The proof consists of the following elements: (i) a variant of the Nazarov-Treil-Volberg method of random dyadic systems with just one random system and completely without bad parts; (ii) a resulting representation of a general Calderon-Zygmund operator as an average of dyadic shifts; and (iii) improvements of the Lacey-Petermichl-Reguera estimates for these dyadic shifts, which allow summing up the series in the obtained representation.

Correlation functions for M^N/S_N orbifolds

Abstract: We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold The path integral with twist operators is replaced by a path integral on a covering space with no operator insertions Thus, even though the CFT is defined on the sphere, the correlators are expressed in terms of partition functions on Riemann surfaces with a finite range of genus g For large N, this genus expansion coincides with a 1/N expansion The contribution from the covering space of genus zero is `universal' in the sense that it depends only on the central charge of the CFT For 3-point functions we give an explicit form for the contribution from the sphere, and for the 4-point function we do an example which has genus zero and genus one contributions The condition for the genus zero contribution to the 3-point functions to be non--vanishing is similar to the fusion rules for an SU(2) WZW model We observe that the 3-point coupling becomes small compared to its large N limit when the orders of the twist operators become comparable to the square root of N - this is a manifestation of the stringy exclusion principle

Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making

Abstract: The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information, and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quadratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggregation operators to NS, and proposed some new aggregation operators. Firstly, we presented some new operational laws for neutrosophic numbers (NNs) based on Hamacher operations and studied their properties. Then, we proposed the generalized neutrosophic number Hamacher weighted averaging (GNNHWA) operator, generalized neutrosophic number Hamacher ordered weighted averaging (GNNHOWA) operator, and generalized neutrosophic number Hamacher hybrid averaging (GNNHHA) operator, and explored some properties of these operators and analyzed some special cases of them. Furthermore, we gave a new method based on these operators for multiple attribute group decision making problems with neutrosophic numbers, and the operational steps were illustrated in detail. Finally, an application example is given to verify the proposed method and to demonstrate its effectiveness.

Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

Abstract: We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in nonintegrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse-grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the ``Floquet-Fredrickson-Andersen'' model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.