Quotient graphs for power graphs

In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of its quotient graphs. We apply here that procedure to the proper power graph $\mathcal{P}_0(G)$ of a finite group $G$, finding a formula for the number $c(\mathcal{P}_0(G))$ of its components which is particularly illuminative when $G\leq S_n$ is a fusion controlled permutation group. We make use of the proper quotient power graph $\widetilde{\mathcal{P}}_0(G)$, the proper order graph $\mathcal{O}_0(G)$ and the proper type graph $\mathcal{T}_0(G)$. We show that all those graphs are quotient of $\mathcal{P}_0(G)$ and demonstrate a strong link between them dealing with $G=S_n$. We find simultaneously $c(\mathcal{P}_0(S_n))$ as well as the number of components of $\widetilde{\mathcal{P}}_0(S_n)$, $\mathcal{O}_0(S_n)$ and $\mathcal{T}_0(S_n)$

Optimal boundary control of a viscous Cahn-Hilliard system with dynamic boundary condition and double obstacle potentials

In this paper, we investigate optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see the preprint arXiv:1308.5617) to the (simpler) Allen-Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.Comment: Key words: optimal control; parabolic obstacle problems; MPECs; dynamic boundary conditions; optimality conditions. arXiv admin note: substantial text overlap with arXiv:1308.561

Algebraic computing in general relativity and supergravity : space-time embeddings and higher dimensional theories

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Purification and Characterization of Invertase from Aspergillus terreus

Invertase was produced from Aspergillus terreus under optimized culture conditions at six days of incubation with pH 7.0 and 25°C, in Czapek Dox media by solid state fermentation (SSF). The enzyme was partially purified by dialysis followed by DEAE-column chromatography. Purification fold and enzyme yield, while stabled at 20-40°C with pH 3.0-5.0. The activation energy for substrate conversion was 1.87Kcal/mol. Thin layer chromatography (TLC) shown that glucose and fructose were the products of sucrose hydrolysis. The partial purified enzyme was immobilized with different metals, while Fe+3 gave highest activity with residual activity 76.52%. Storage activity for immobilized enzyme at 4°C after 2 and 4 weeks were 70.94 % and 58.42% respectively. Key words: Invertase, Purification, Immobilizatio

Relating phase field and sharp interface approaches to structural topology optimization

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement