Антиклассическое приближение в задаче об отражении электромагнитной волны от неоднородной среды

Expressions are derived for the reflection coefficients of electromagnetic waves with "p" and "s" type polarizations from a semi-infinite dielectric medium having an inhomogeneous layer. The influence of the layer was taken into account by the method of perturbation theory in a quadratic approximation of the layer thickness. A method is proposed for converting expressions derived using perturbation theory into other expressions that give more accurate values of the reflection coefficient. The angular dependences of the reflection coefficient obtained by the developed method are compared with those obtained by the numerical solution of electrodynamic equations. Requirements for the layer characteristics are formulated to minimize the error of the analytical solution.

Per-Pixel Extrusion Mapping with Correct Silhouette

Per-pixel extrusion mapping consists of creating a virtual geometry stored in a texture over a polygon model without increasing its density. There are four types of extrusion mapping, namely, basic extrusion, outward extrusion, beveled extrusion, and chamfered extrusion. These different techniques produce satisfactory results in the case of plane surfaces, but when it is about the curved surfaces, the silhouette is not visible at the edges of the extruded forms on the 3D surface geometry because they not take into account the curvature of the 3D meshes. In this paper, we presented an improvement that consists of using a curved ray-tracing to correct the silhouette problem by combining the per-pixel extrusion mapping techniques and the quadratic approximation computed at each vertex of the 3D mesh.

Enhanced quadratic approximation integrated with butterfly optimization: a new search algorithm tested on structural and mathematical problems

The Butterfly Optimization Algorithm (BOA) is a swarm based technique, inspired from mating and food searching process of butterflies, developed in last year. Experiments indicate that BOA provides substantial exploration capability on conventional non-constrained benchmark problems, however for the cases with more complex and noisy domains the algorithm can easily be trapped into local minima due to its restricted exploitation behavior. To tackle this issue, current study deals with introducing an alternative search strategy to explore the region of the search domain with high certainty. Such that, firstly a weighted agent is defined and then a quadratic search is performed in the vicinity of this pre-defined agent. This alternative search strategy is named as Enhanced Quadratic Approximation (EQA) and it is combined with BOA method to improve its exploitation behavior and provide an efficient search algorithm. Thus, obtained new method is named as Enhanced Quadratic Approximation Integrated with Butterfly Optimization (EQB) algorithm. Different properties of proposed EQB are tested on mathematical and structural benchmark problems. Acquired results show that the introduced algorithm, in comparison with its parent method and some other well-stablished reported algorithms in the literature, provides a competitive performance in terms of stability, accuracy and convergence rate.

Extension of Dasgupta’s Technique for Higher Degree Approximation

In the present paper, rational wedge functions for degree two approximation have been computed over a pentagonal discretization of the domain, by using an analytic approach which is an extension of Dasgupta’s approach for linear approximation. This technique allows to avoid the computation of the exterior intersection points of the elements, which was a key component of the technique initiated by Wachspress. The necessary condition for the existence of the denominator function was established by Wachspress whereas our assertion, induced by the technique of Dasgupta, assures the sufficiency of the existence. Considering the adjoint (denominator) functions for linear approximation obtained by Dasgupta, invariance of the adjoint for degree two approximation is established. In other words, the method proposed by Dasgupta for the construction ofWachspress coordinates for linear approximation is extended to obtain the coordinates for quadratic approximation. The assertions have been supported by considering some illustrative examples.

Exact and inexact decompositions of trade price indices

A reasonable concept for the true trade price index in situations where low-price countries capture market shares from high-price countries is the average price paid by importers for the same quality of good or service from all exporting countries. However, decompositions of trade price indices are usually inexact in the sense that the average price used as the underlying aggregator formula is not exactly reproduced. In this paper, we compare analytically exact and inexact decompositions of trade price indices, paying particular attention to the bias in aggregate inflation occurring from applying the first-order Taylor series approximation and not the quadratic approximation lemma to a geometric average price. Our calculations, using the Norwegian clothing industry as an illustration, reveal that the bias in aggregate inflation over the sample period of 1997–2016 is quite substantial and as much as 0.6 percentage point in some years. We therefore conclude that the quadratic approximation lemma should be used in practice to exactly reproduce the underlying aggregator formula.