Пучки Гельмгольца--Гаусса с квадратичной радиальной зависимостью

A new class of localized solutions of paraxial parabolic equation is introduced. Each solution is a product of some Gaussian-type localized axisymmetric function (different from the fundamental mode) and an amplitude factor. The latter can be expressed via an arbitrary solution of the Helmholtz equation on an auxiliary two-sheet complex surface. The class under consideration contains well known and novel solutions, including those describing optical vortices of various orders.

How Much Would You Pay to Change a Game before Playing It?

Envelope theorems provide a differential framework for determining how much a rational decision maker (DM) is willing to pay to alter the parameters of a strategic scenario. We generalize this framework to the case of a boundedly rational DM and arbitrary solution concepts. We focus on comparing and contrasting the case where DM’s decision to pay to change the parameters is observed by all other players against the case where DM’s decision is private information. We decompose DM’s willingness to pay a given amount into a sum of three factors: (1) the direct effect a parameter change would have on DM’s payoffs in the future strategic scenario, holding strategies of all players constant; (2) the effect due to DM changing its strategy as they react to a change in the game parameters, with the strategies of the other players in that scenario held constant; and (3) the effect there would be due to other players reacting to a the change in the game parameters (could they observe them), with the strategy of DM held constant. We illustrate these results with the quantal response equilibrium and the matching pennies game and discuss how the willingness to pay captures DM’s anticipation of their future irrationality.

Operations scheduling in building tunnels of mining projects

This article proposes a heuristic algorithm to solve a problem of sequencing jobs in the mining tunnel construction, from input data, such as: the number of machines, the number of jobs, the number of stages and the time preparation and operation of the works in each of the stages, with the objective of minimizing the total occupation time processing all stages, resulting in increased operational efficiency of this type of project. The results obtained using the algorithm developed have a total time of occupancy to three jobs with three stages of 39 units of time compare to 59 units of time by an arbitrary solution, thus confirming that it is significant in implementing the algorithm to a problem that exhibits these characteristics.

Amartya Sen. The Idea of Justice. London: Penguin Books Ltd. 2009. 468 pages. Hardback. £ 25.00.

Justice is comparative in nature and may have plural impartial dimensions. Provision of justice, in an ‘ideal sense’, is non-pragmatic and is therefore impossible to deliver, argues the Nobel Laureate, Amartya Sen. He divides the existing theories of justice into two categories: the transcendental institutionalism and the Comparative School. The transcendental institutionalism, led by eminent enlightenment philosophers like Locke, Hobbes, Rousseau and Kant holds that a just society can be maintained by ensuring justice in the ‘ideal sense’. The provision of ‘ideal justice’ is based on the notion of either right or wrong. To provide justice in the ‘ideal sense’ the society must enjoy access to ‘just institutions’. John Rawl, the more recent contributor to transcendental tradition, came up with his theory of ‘justice as fairness’ in the mid twentieth century. The comparative school of justice propagated by Adam Smith, Marquis de Condorcet, Carl Marx and Stuart Mill lays emphasis upon looking at ‘justice’ in a comparative sense and on the basis of what the society is actually able to realise.Sen, disagreeing with both the schools of thought, however, is seen leaning towards the comparative school. The author gives the example of three children and a single flute to demonstrate how the ‘ideal justice’ and the ‘comparative’ school fail to hold water in certain situations. Three children—Carla, Anne and Bob, claim their right to a specific flute on different but competing principles. Carla manufactured the flute, Anne is the only one among the three who can play the flute, while Bob is the poorest of the three and does not have any toy to play with. Sen questions how ‘ideal justice’ may be provided with the transcendental approach, or how the ‘comparative assessment’ would lead to an impartial and non-arbitrary solution, in the case of the ‘three children and a flute’. Despite his disagreement with both the schools of thought, Sen aligns himself with the comparative school. However he believes that for provision of ‘impartial justice’ competing principles need not essentially be unique; these could be plural as well. The plurality of competing principles is the essence of Sen’s ‘idea of Justice’.

An Energy Analysis of Amplitude Death of a Pair of Oscillators With Delayed Coupling

This paper presents an energy analysis of the amplitude death, a phenomenon that the individual oscillators cease to oscillate when coupled and go to an equilibrium motion instead, of a pair of coupled oscillators with time delay that are slightly perturbed from two undamped oscillators and with delayed coupling. The energy analysis reveals that amplitude death, as well as the stability of the phase-locked periodic solutions, can be justified by the sign of the averaged total powers along a special function with harmonic entries, rather than along arbitrary solution of the coupled oscillators as in the application of the method of Lyapunov’s function for stability analysis. An illustrative example is given to show the effectiveness of the present method.

The Spectral Line-Based Weighted-Sum-of-Gray-Gases Model in Nonisothermal Nonhomogeneous Media

An approach is developed to extend the previously developed spectral-line weighted-sum-of-gray-gases (SLW) model to nonisothermal, nonhomogeneous media. The distinguishing feature of the SLW gas property model is that it has been developed for use in arbitrary solution methods of the radiative transfer equation (RTE). A spatial dependence of the gray gas absorption cross sections on local temperature, pressure, and mole fraction is introduced through the absorption-line blackbody distribution function. Incorporating this spatial dependence results in significant improvement over the use of spatially uniform gray gas absorption cross sections in comparisons with line-byline benchmarks.

A Spectral Line-Based Weighted-Sum-of-Gray-Gases Model for Arbitrary RTE Solvers

This paper presents an approach for generating weighted-sum-of-gray gases (WSGG) models directly from the line-by-line spectra of H2O. Emphasis is placed on obtaining detailed spectral division among the gray gases. Thus, for a given model spectrum, the gray gas weights are determined as blackbody fractional functions for specific subline spectral regions at all temperatures. The model allows the absorption coefficient to be the basic radiative property rather than a transmissivity or band absorptance, etc., and can be used with any arbitrary solution method for the Radiative Transfer Equation (RTE). A single absorption cross section spectrum is assumed over the entire spatial domain in order to fix the subline spectral regions associated with a single spectral calculation. The error associated with this assumption is evaluated by comparison with line-by-line benchmarks for problems of nonisothermal and nonhomogeneous media.

The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer

The weighted-sum-of-gray-gases approach for radiative transfer in nongray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (nonscattering media within a black-walled enclosure), any nongray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-I approximation for the equivalent gray media solutions. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95 percent) that are achieved.