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.

Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized λ-Shapley index

Abstract: In this paper, two new aggregation operators called the arithmetical interval-valued intuitionistic fuzzy generalized @l-Shapley Choquet (AIVIFGSC"g"@l) operator and the geometric interval-valued intuitionistic fuzzy generalized @l-Shapley Choquet (GIVIFGSC"g"@l) operator are proposed. These operators not only globally consider the importance of combinations or their ordered positions, but also overall reflect the correlations among combinations or their ordered positions. Based on the operational laws on interval-valued intuitionistic fuzzy values, the specific expressions of the AIVIFGSC"g"@l and GIVIFGSC"g"@l operators are given, which are also interval-valued intuitionistic fuzzy values. Meantime, some desirable properties are studied. Furthermore, two new approaches to multi-criteria group decision making under interval-valued intuitionistic fuzzy environment are proposed. Finally, a numerical example is provided to illustrate the developed procedures.

Convergence of Iterative Split-Operator Approaches for Approximating Nonlinear Reactive Transport Problems

Abstract: Numerical solutions to nonlinear reactive solute transport problems are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the iterative split-operator approach for solving nonlinear reactive transport problems.

A Tensor Framework for Multidimensional Signal Processing

Abstract: This thesis deals with ltering of multidimensional signals. A large part of the thesis is devoted to a novel filtering method termed "Normalized convolution". The method performs local expansion of a signal in a chosen lter basis which not necessarily has to be orthonormal. A key feature of the method is that it can deal with uncertain data when additional certainty statements are available for the data and/or the lters. It is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated using this technique. Perhaps the most well-known of such eects are the various 'edge effects' which invariably occur at the edges of the input data set. The method is an example of the signal/certainty - philosophy, i.e. the separation of both data and operator into a signal part and a certainty part. An estimate of the certainty must accompany the data. Missing data are simply handled by setting the certainty to zero. Localization or windowing of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coefficients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window. The use of tensors in estimation of local structure and orientation using spatiotemporal quadrature filters is reviewed and related to dual tensor bases. The tensor representation conveys the degree and type of local anisotropy. For image sequences, the shape of the tensors describe the local structure of the spatiotemporal neighbourhood and provides information about local velocity. The tensor representation also conveys information for deciding if true flow or only normal flow is present. It is shown how normal flow estimates can be combined into a true flow using averaging of this tensor eld description. Important aspects of representation and techniques for grouping local orientation estimates into global line information are discussed. The uniformity of some standard parameter spaces for line segmentation is investigated. The analysis shows that, to avoid discontinuities, great care should be taken when choosing the parameter space for a particular problem. A new parameter mapping well suited for line extraction, the Mobius strip parameterization, is de ned. The method has similarities to the Hough Transform. Estimation of local frequency and bandwidth is also discussed. Local frequency is an important concept which provides an indication of the appropriate range of scales for subsequent analysis. One-dimensional and two-dimensional examples of local frequency estimation are given. The local bandwidth estimate is used for dening a certainty measure. The certainty measure enables the use of a normalized averaging process increasing robustness and accuracy of the frequency statements.

The t expansion: A nonperturbative analytic tool for Hamiltonian systems

Abstract: A systematic nonperturbative scheme is developed to calculate the ground-state expectation values of arbitrary operators for any Hamiltonian system. Quantities computed in this way converge rapidly to their true expectation values. The method is based upon the use of the operator e/sup -t/H to contract any trial state onto the true ground state of the Hamiltonian H. We express all expectation values in the contracted state as a power series in t, and reconstruct t..-->..infinity behavior by means of Pade approximants. The problem associated with factors of spatial volume is taken care of by developing a connected graph expansion for matrix elements of arbitrary operators taken between arbitrary states. We investigate Pade methods for the t series and discuss the merits of various procedures. As examples of the power of this technique we present results obtained for the Heisenberg and Ising models in 1+1 dimensions starting from simple mean-field wave functions. The improvement upon mean-field results is remarkable for the amount of effort required. The connection between our method and conventional perturbation theory is established, and a generalization of the technique which allows us to exploit off-diagonal matrix elements is introduced. The bistate procedure is used to develop a tmore » expansion for the ground-state energy of the Ising model which is, term by term, self-dual.« less

Discrete space theory of radiative transfer I. Fundamentals

Abstract: This paper sets out a formal theory of radiative transfer in one-dimensional scattering media of arbitrary physical constitution. The theory is based on an extension of the treatment of Redheffer, in which the response of a layer of arbitrary thickness to fluxes incident on its boundaries is described by a certain linear operator. Juxtaposition of two such layers gives a third layer, whose operator can be related to those of its constituents by an operation designated as the star product. It is shown that this set of operators constitutes a semigroup under the star product, and that the infinitesimal generators of the semigroup can be computed in term s of the physical properties of the medium , point by point. This makes it possible to write equivalent discrete and differential equations from both of which transmission and reflexion operators, the emission due to internal sources, and the internal fluxes at prescribed levels in the medium can be obtained.