An Index for 4 Dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on S ³ × time. Our index receives contributions from states invariant under at least one supercharge and captures all information – that may be obtained purely from group theory – about protected short representations in 4 dimensional superconformal field theories. In the case of the theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in AdS ₅ × S ⁵ and find perfect agreement at large N and small charges. Our index does not reproduce the entropy of supersymmetric black holes in AdS ₅, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the theory. We note that entropy for some small supersymmetric AdS ₅ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the Yang Mills theory.     

Coupling Adsorption-Photocatalytic Degradation of Methylene Blue and Maxilon Red

Journal of Fluorescence - The MB and MR removal process by two mechanisms of adsorption using rice straw (absence of UV light) and photodegradation on TiO2 surfaces was investigated. MB and MR...     

Optimized Degradation of Eosin Dye Through UV-ZnO NPs Catalyzed Reaction

Journal of Fluorescence - The present study is set out to determine the photocatalytic degradation potential of ZnO nanoparticles for effective degradation of Eosin dye. The heterogeneous...     

Progressive Regularization of Variational Inequalities and Decomposition Algorithms

For nonsymmetric operators involved in variational inequalities, the strong monotonicity of their possibly multivalued inverse operators (referred to as the Dunn property) appears to be the weakest requirement to ensure convergence of most iterative algorithms of resolution proposed in the literature. This implies the Lipschitz property, and both properties are equivalent for symmetric operators. For Lipschitz operators, the Dunn property is weaker than strong monotonicity, but is stronger than simple monotonicity. Moreover, it is always enforced by the Moreau–Yosida regularization and it is satisfied by the resolvents of monotone operators. Therefore, algorithms should always be applied to this regularized version or they should use resolvents: in a sense, this is what is achieved in proximal and splitting methods among others. However, the operation of regularization itself or the computation of resolvents may be as complex as solving the original variational inequality. In this paper, the concept of progressive regularization is introduced and a convergent algorithm is proposed for solving variational inequalities involving nonsymmetric monotone operators. Essentially, the idea is to use the auxiliary problem principle to perform the regularization operation and, at the same time, to solve the variational inequality in its approximately regularized version; thus, two iteration processes are performed simultaneously, instead of being nested in each other, yielding a global explicit iterative scheme. Parallel and sequential versions of the algorithm are presented. A simple numerical example demonstrates the behavior of these two versions for the case where previously proposed algorithms fail to converge unless regularization or computation of a resolvent is performed at each iteration. Since the auxiliary problem principle is a general framework to obtain decomposition methods, the results presented here extend the class of problems for which decomposition methods can be used.     

Errata Corrige: Pseudomonotone Variational Inequalities: Convergence of the Auxiliary Problem Method

Journal of Optimization Theory and Applications -     

Synthesis of novel phthalazine derivatives as pharmacological activities

Phthalazine derivatives attached to amino acid derivatives were synthesized with high yields. The reaction of phthalazine derivatives with different phthalyl and tosylamino acids such as glycine, alanine, phenylalanine, valine, serine, and threonine in the presence of N,N-dicyclo hexylcarbodiimide (DCC) as a dehydrating agent reagent yielded high yields of the afforded compounds. Phthalylamino acids derivatives were obtained by deprotection of phthalazine derivatives, with the latter heating with hydrazine hydrate. The chemical structures of all phthalazine derivatives were affirmed by elemental analysis and spectral data (IR, MS, ¹HNMR, and ¹³C NMR). Screening out and estimation of the synthesized derivatives for their cytotoxic and antioxidant activity were done, and most of them showed powerful activity in comparison with standard drugs.     

An Improved Method for the Efficient Conversion of Unstaurated Alcohols,Ethers and Esters to Their Corresponding Aldehydes,Ketones, Enol Ethers and Enol Esters

Catalytic conversion of unsaturated alcohols to their corresponding aldehydes and ketones with nonacarbonyl diiron in benzene at 40–50 C are performed efficiently in high yields. The efficient preparation of some enol ethers and also preperation of a few esters from their corresponding unsaturated ethers and esters are also performed by this method.