THE WAVE EQUATION APPROACH TO THE TWO-DIMENSIONAL INVERSE PROBLEM FOR A GENERAL BOUNDED DOMAIN WITH PIECEWISE SMOOTH MIXED BOUNDARY CONDITIONS

1 IntroductionLet fl be a simply connected bounded domain in R2 with a smooth boundary 0fl. Considerthe two-dimensional Robin problemwhere k denotes differentiation aIong the inward pointing normal to 0n and 7 is a positiv('constan. Denote its eigenvalues, counted according to multiplicity, byZayed alld Hassall[15'16] l1ave discussed the probleln (1. 1)-(1.2) fOr small / large impedance7 and have determned some geometric quantities of the don1ain n, using tl1e asymptotic ex-pansion of tlie s…     

On Minimum Edge Ranking Spanning Trees

In this paper, we introduce the problem of computing a minimum edge ranking spanning tree (MERST); i.e., find a spanning tree of a given graph G whose edge ranking is minimum. Although the minimum edge ranking of a given tree can be computed in polynomial time, we show that problem MERST is NP-hard. Furthermore, we present an approximation algorithm for MERST, which realizes its worst case performance ratio where n is the number of vertices in G and Δ* is the maximum degree of a spanning tree whose maximum degree is minimum. Although the approximation algorithm is a combination of two existing algorithms for the restricted spanning tree problem and for the minimum edge ranking problem of trees, the analysis is based on novel properties of the edge ranking of trees.     

Micromechanical modeling of shock-induced chemical reactions in heterogeneous multi-material powder mixtures

Shock waves create a unique environment of high pressure, temperature, strain rate, and gradients thereof. Chemical reactions that occur in this regime can lead to the synthesis of new materials that are not possible under conventional conditions. Shock-induced chemical reactions (also known as shock synthesis) is difficult to study experimentally due to the small time and space scales over which it occurs. To aid in our understanding, numerical simulations of shock-induced chemical reactions (SICR) are performed on the mesoscopic level. The model reaction, Nb+2Si⇌NbSi₂, is chosen for this research because it has been studied extensively. Comparisons of the calculated results with the available experimental data are presented to validate the modeling process, and additional calculations are used to determine the reaction threshold.     

The muon anomalous magnetic moment from a generic charged Higgs with SUSY

We study the contribution of a generic charged Higgs (H⁺) to the muon anomalous magnetic moment a_μ with the SUSY soft breaking parameters. We find out that the deviation between the experimental data and the predicted SM value on a_μ can be explained by the two-loop charged Higgs diagrams even with m_H⁺∼400 GeV.