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.

Interpolation and multiple attenuation with migration operators

Abstract: A hyperbolic Radon transform (RT) can be applied with success to attenuate or interpolate hyperbolic events in seismic data. However, this method fails when the hyperbolic events have apexes located at nonzero offset positions. A different RT operator is required for these cases, an operator that scans for hyperbolas with apexes centered at any offset. This procedure defines an extension of the standard hyperbolic RT with hyperbolic basis functions located at every point of the data gather. The mathematical description of such an operator is basically similar to a kinematic poststack time-migration equation, with the horizontal coordinate being not midpoint but offset. In this paper, this transformation is implemented by using a least-squares conjugate gradient algorithm with a sparseness constraint. Two different operators are considered, one in the time domain and the other in the frequency-wavenumber domain (Stolt operator). The sparseness constraint in the time-offset domain is essential for resampling and for interpolation. The frequency-wavenumber domain operator is very efficient, not much more expensive in computation time than a sparse parabolic RT, and much faster than a standard hyperbolic RT. Examples of resampling, interpolation, and coherent noise attenuation using the frequency-wavenumber domain operator are presented. Near and far offset gaps are interpolated in synthetic and real shot gathers, with simultaneous resampling beyond aliasing. Waveforms are well preserved in general except when there is little coherence in the data outside the gaps or events with very different velocities are located at the same time. Multiples of diffractions are predicted and attenuated by subtraction from the data.

A Borg-Levinson theorem for trees

Abstract: We prove that the Dirichelet-to-Neumann map for a Schrodinger operator on a finite simply connected tree determines uniquely the potential on that tree.

Oscillation and variation for singular integrals in higher dimensions

Abstract: In this paper we continue our investigations of square function inequalities in harmonic analysis. Here we investigate oscillation and variation inequalities for singular integral operators in dimensions d > 1. Our estimates give quantitative information on the speed of convergence of truncations of a singular integral operator, including upcrossing and A jump inequalities.

On vector variational inequalities

Abstract: In this paper, we study vector variational inequalities. The concept of weaklyC-pseudomonotone operator is introduced. By employing the Fan lemma, we establish several existence results. The new results extend and unify existence results of vector variational inequalities for monotone operators under a Banach space setting. In particular, existence results for the generalized vector complementarity problem with weaklyC-pseudomonotone operators in Banach space are obtained.

FR-operator approach to the H/sub 2/ analysis and synthesis of sampled-data systems

Abstract: Recently, a frequency-domain operator called frequency response (FR) operator was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid FR-operator, we define an H/sub 2/-norm for sampled-data systems in this paper. Then, sampled-data H/sub 2/ control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems. For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H/sub 2/-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified. >