On minimum power connectivity problems

Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as well as inapproximability results, for some classic network design problems under the power minimization criteria. Our main result is for the problem of finding a min-power subgraph that contains k internally-disjoint vs-paths from every node v to a given node s: we give a polynomial algorithm for directed graphs and a logarithmic approximation algorithm for undirected graphs. In contrast, we will show that the corresponding edge-connectivity problems are unlikely to admit even a polylogarithmic approximation.     

A hybrid asymptotic solution for the scattering by a pair ofparallel perfectly conducting wedges

The overlapping transition regions of the double diffraction by a pair of parallel wedge edges are considered for the hybrid case where the gap between the edges is small compared to the distances from the source and the observation point (plane-wave-far-field limit) and the scatterer as a whole is large (or infinite). A closed-form asymptotic solution for the scattered field continuous at all angles of incidence and scattering is constructed for this case. The peculiar feature of this solution is a hybrid representation of the field singly diffracted by the first wedge: a part of it is described by a nonuniform, geometrical theory of diffraction (GTD) expression, while the other part is described in terms of the uniform theory of diffraction (UTD). The rest of the diffracted ray fields are described by nonuniform expressions, with singularities mutually canceling on summation. This solution is applied to the scattering by a perfectly conducting rectangular cylinder with appropriate geometrical parameters, and agreement with moment method calculation is demonstrated     

Elimination of infinities in equivalent edge currents, Part II: Physical optics components

A solution finite for all directions of illumination and observation is derived for the physical optics (PO) components of equivalent edge currents. The solution is based on the uniform asymptotic theory of endpoint evaluation of integrals. An extension taking into account the variation of the surface metric with the distance from the edge is presented, and a similar extension for including slope diffraction is indicated. The expressions derived complement the results of our previous work on elimination of infinities from the fringe components of equivalent currents.     

A uniform GTD solution for the far-field scattering by polygonal cylinders and strips

The results of our recent asymptotic treatment of the double diffraction by a pair of parallel perfectly conducting wedges are applied to polygonal cylinders and strips. The combination of the appropriate nonuniform expression for the doubly diffracted ray field with the nonuniform geometrical theory of diffraction (GTD) expressions for the singly diffracted fields yields a uniform, closed-form solution for the far scattered field valid throughout the overlapping transition regions. The advantage over the existing uniform GTD solution for a polygonal cylinder consists in the extension from strictly grazing to nearly grazing incidence. For a strip, the present solution improves upon the accuracy of the previous uniform high-frequency solutions.     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.     

Microspheres of Mixed Proteins

This paper describes the synthesis of mixed proteinaceous microspheres (MPMs) by the sonochemical method. The current fundamental research follows the research of Suslick and co‐workers who have developed a method by which high‐intensity ultrasound is used to make aqueous suspensions of proteinaceous microcapsules filled with water‐insoluble liquids. 1 By using high‐intensity ultrasound, we have synthesized microspheres made of a few different proteins. The three proteins used in the current experiments are bovine serum albumin (BSA), green fluorescent protein (GFP), and cyan fluorescent protein–glucose binding protein–yellow fluorescent fused protein (CFP‐GBP‐YFP). The two synthesized microspheres made of mixed proteins are BSA‐GFP and BSA‐(CFP‐GBP‐YFP). This paper presents the characterization of the sonochemically produced microspheres of mixed proteins. It also provides an estimate of the efficiency of the sonochemical process in converting the native proteins to microspheres.     

Practical anodes for Li-ion batteries comprising metallurgical silicon particles and multiwall carbon nanotubes

Journal of Solid State Electrochemistry - Silicon is considered to be a very attractive anode material for next-generation lithium-ion batteries due to its high theoretical capacity...     

Alternating subgroups of Coxeter groups

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.