Unitarily invariant norm inequalities for operators

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then $$|||A_{1}A_{2}^{*}+A_{2}A_{3}^{*}+...+A_{n}A_{1}^{*}|||\leq|||\sum_{i=1}^{n}A_{i}A_{i}^{*}|||,$$ for all unitarily invariant norms. We also show that if $A_{1},A_{2},A_{3},A_{4}$ are projections in ${\mathbb B}({\mathscr H})$, then &&|||(\sum_{i=1}^{4}(-1)^{i+1}A_{i})\oplus0\oplus0\oplus0|||&\leq&|||(A_{1}+|A_{3}A_{1}|)\oplus (A_{2}+|A_{4}A_{2}|)\oplus(A_{3}+|A_{1}A_{3}|)\oplus(A_{4}+|A_{2}A_{4}|)||| for any unitarily invariant norm.Comment: 10 pages, Accepted pape

Cooperative co-evolution with differential grouping for large scale optimization

Cooperative co-evolution has been introduced into evolutionary algorithms with the aim of solving increasingly complex optimization problems through a divide-and-conquer paradigm. In theory, the idea of co-adapted subcomponents is desirable for solving large-scale optimization problems. However, in practice, without prior knowledge about the problem, it is not clear how the problem should be decomposed. In this paper, we propose an automatic decomposition strategy called differential grouping that can uncover the underlying interaction structure of the decision variables and form subcomponents such that the interdependence between them is kept to a minimum. We show mathematically how such a decomposition strategy can be derived from a definition of partial separability. The empirical studies show that such near-optimal decomposition can greatly improve the solution quality on large-scale global optimization problems. Finally, we show how such an automated decomposition allows for a better approximation of the contribution of various subcomponents, leading to a more efficient assignment of the computational budget to various subcomponents

Radiance cache optimization for global illumination

Radiance caching methods have proven efficient for global illumination. Their goal is to compute precisely illumination values (incident radiance or irradiance) at a reasonable number of points lying on the scene surfaces. These points, called records, are stored in a cache used for estimating illumination of other points in the scene. Unfortunately, with records lying on glossy surfaces, the irradiance value alone is not sufficient to evaluate the reflected radiance; each record should also store the incident radiance for all incident directions. Memory storage can be reduced with projection techniques using spherical harmonics or other basis functions. These techniques provide good results with low shininess BRDFs. However, they get impractical for shininess of even moderate value since the number of projection coefficients increase drastically. In this paper, we propose a new radiance caching method, that handles highly glossy surfaces, while requiring a low memory storage. Each cache record stores a coarse representation of the incident illumination thanks to a new data structure called Equivalent Area light Sources (EAS), capable of handling fuzzy mirror surfaces. In addition, our method proposes a new simplification of the interpolation process since it avoids the need for expressing and evaluating complex gradients

Facies analysis and paleoenvironmental reconstruction of Upper Cretaceous sequences in the eastern Para-Tethys Basin, NW Iran

Upper Cretaceous mixed carbonate-siliciclastic sequences are among the most important targets for hydrocarbon exploration in the Moghan area, located in the eastern Para-Tethys Basin. Despite of their significance, little is known about their facies characteristics and depositional environments. Detailed facies analysis and paleoenvironmental reconstruction of these sequences have been carried out in eight surface sections. Accordingly, four siliciclastic facies, eight carbonate facies and one volcanic facies have been recognized. Detailed facies descriptions and interpretations, together with the results of facies frequency analysis, standard facies models and Upper Cretaceous depositional models of Para-Tethys Basin, have been integrated and a non-rimmed carbonate platform is presented. This platform was affected by siliciclastic influx, in the form of coastal fan delta and submarine fans in the shallow- to deep-marine parts, respectively. This model is interpreted to be shallower in the central and northeastern parts of the Moghan area. Toward the southeast and southwest, this shallow platform turns into deep marine settings along steep slopes without remarkable marginal barriers

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations

In-situ nanocomposite in friction stir welding of 6061-T6 aluminum alloy to AZ31 magnesium alloy

Prior to friction stir welding (FSW), silicon carbide (SiC) nanopowders were placed inside the groove on the adjacent side of magnesium sheet. In order to make a good distribution of these nanoparticles, first, friction stir processing (FSP) with a pinless tool was conducted on this side. Second, using a frustum pin tool, a combination of two travel speeds (25 and 35¿mm/min) and three rotation speeds (550, 600 and 650¿rpm) were employed to obtain the optimal conditions for FSW of AZ31 magnesium alloy to 6061 aluminum alloy. The joint fabricated at 35¿mm/min and 650¿rpm, exhibited improvement of 28% in tensile strength and enhancement about three times in elongation, compared with the joint without nanoparticles. SiC nanoparticles had an effective role on the grain refining of the stirred zone and improving the microstructural characteristics of the banded structure zone. Due to the decreased grain size and the presence of ceramic nanoparticles (SiC) with high value of hardness, the hardness level of the reinforced samples was greater than that of the non-reinforced samples. Fracture of the non-reinforced sample was completely brittle, while in the reinforced samples, fracture features changed to the ductile mode.Peer ReviewedPostprint (author's final draft

Efficient Resource Allocation in Cooperative Co-Evolution for Large-Scale Global Optimization

Cooperative co-evolution (CC) is an explicit means of problem decomposition in multipopulation evolutionary algorithms for solving large-scale optimization problems. For CC, subpopulations representing subcomponents of a large-scale optimization problem co-evolve, and are likely to have different contributions to the improvement of the best overall solution to the problem. Hence, it makes sense that more computational resources should be allocated to the subpopulations with greater contributions. In this paper, we study how to allocate computational resources in this context and subsequently propose a new CC framework named CCFR to efficiently allocate computational resources among the subpopulations according to their dynamic contributions to the improvement of the objective value of the best overall solution. Our experimental results suggest that CCFR can make efficient use of computational resources and is a highly competitive CCFR for solving large-scale optimization problems