Schwarz methods for inequalities with contraction operators

We prove the convergence of some multiplicative and additive Schwarz methods for inequalities which contain contraction operators. The problem is stated in a reflexive Banach space and it generalizes the well-known fixed-point problem in the Hilbert spaces. Error estimation theorems are given for three multiplicative algorithms and two additive algorithms. We show that these algorithms are in fact Schwarz methods if the subspaces are associated with a decomposition of the domain. Also, for the one- and two-level methods in the finite element spaces, we write the convergence rates as functions of the overlapping and mesh parameters. They are similar with the convergence rates of these methods for linear problems. Besides the direct use of the five algorithms for the inequalities with contraction operators, we can use the above results to obtain the convergence rate of the Schwarz method for other types of inequalities or nonlinear equations. In this way, we prove the convergence and estimate the error of the one- and two-level Schwarz methods for some inequalities in Hilbert spaces which are not of the variational type, and also, for the Navier–Stokes problem. Finally, we give conditions of existence and uniqueness of the solution for all problems we consider. We point out that these conditions and the convergence conditions of the proposed algorithms are of the same type.     

Experimental measurements of short-lived fission products from uranium,neptunium, plutonium and americium

Fission yields are especially well characterized for long-lived fission products. Modeling techniques incorporate numerous assumptions and can be used to deduce information about the distribution of short-lived fission products. This work is an attempt to gather experimental (model-independent) data on short-lived fission products. Fissile isotopes of uranium, neptunium, plutonium and americium were irradiated under pulse conditions at the Washington State University 1 MW TRIGA reactor to achieve ~10⁸ fissions. The samples were placed on an HPGe (high purity germanium) detector to initiate counting in less than 3 min post irradiation. The data was analyzed to determine which radionuclides could be quantified and compared to the published fission yield data.     

Biased Expansions of Biased Graphs and Their Chromatic Polynomials

A biased graph is a graph with a distinguished set of circles, such that if two circles in the set are contained in a theta graph, then so is the third circle of the theta graph. We introduce a new biased graph, a biased expansion of a biased graph, that satisfies certain lifting and projection properties with the original biased graph. We relate the chromatic polynomials of a biased graph and its biased expansions, thus generalizing a biased-graph result of Zaslavsky [7] and a hyperplane result of Ehrenborg and Readdy [1]. We also determine which biased expansions have supersolvable bias matroids.     

2-Hydroxymethylboronate as a reagent to detect carbohydrates: application to the analysis of the formose reaction

2-Hydroxymethylphenylboronate is described as a reagent that converts neutral 1,2-diols, as found in simple carbohydrates, into 1:1 anionic complexes that are easily detected by Fourier transform ion cyclotron resonance mass spectrometry. The value of this reagent was demonstrated through its application to analyze complex mixtures of carbohydrates formed in the formose process, often cited as a way that biologically significant carbohydrates might have been generated from formaldehyde under prebiotic conditions. Coupled with isotope studies, the reagent shows that the simplest autocatalytic cycle for the consumption of formaldehyde in this process cannot account for the bulk consumption of formaldehyde.     

Neuronal store-operated calcium entry pathway as a novel therapeutic target for Huntington's disease treatment

Huntington's disease (HD) is a neurodegenerative disorder caused by a polyglutamine expansion within Huntingtin (Htt) protein. In the phenotypic screen we identified a class of quinazoline-derived compounds that delayed a progression of a motor phenotype in transgenic Drosophila HD flies. We found that the store-operated calcium (Ca(2+)) entry (SOC) pathway activity is enhanced in neuronal cells expressing mutant Htt and that the identified compounds inhibit SOC pathway in HD neurons. The same compounds exerted neuroprotective effects in glutamate-toxicity assays with YAC128 medium spiny neurons primary cultures. We demonstrated a key role of TRPC1 channels in supporting SOC pathway in HD neurons. We concluded that the TRPC1-mediated neuronal SOC pathway constitutes a novel target for HD treatment and that the identified compounds represent a novel class of therapeutic agents for treatment of HD and possibly other neurodegenerative disorders.     

Synthesis of carbohydrates in mineral-guided prebiotic cycles

One present obstacle to the "RNA-first" model for the origin of life is an inability to generate reasonable "hands off" scenarios for the formation of carbohydrates under conditions where they might have survived for reasonable times once formed. Such scenarios would be especially compelling if they deliver pent(ul)oses, five-carbon sugars found in terran genetics, and exclude other carbohydrates (e.g., aldotetroses) that may also be able to function in genetic systems. Here, we provide detailed chemical analyses of carbohydrate premetabolism, showing how borate, molybdate, and calcium minerals guide the formation of tetroses (C(4)H(8)O(4)), heptoses (C(7)H(14)O(7)), and pentoses (C(5)H(10)O(5)), including the ribose found in RNA, in "hands off" experiments, starting with formaldehyde and glycolaldehyde. These results show that pent(ul)oses would almost certainly have formed as stable borate complexes on the surface of an early Earth beneath a humid CO(2) atmosphere suffering electrical discharge. While aldotetroses form extremely stable complexes with borate, they are not accessible by pathways plausible under the most likely early Earth scenarios. The stabilization by borate is not, however, absolute. Over longer times, material is expected to have passed from borate-bound pent(ul)oses to a branched heptulose, which is susceptible to Cannizzaro reduction to give dead end products. We show how this fate might be avoided using molybdate-catalyzed rearrangement of a branched pentose that is central to borate-moderated cycles that fix carbon from formaldehyde. Our emerging understanding of the nature of the early Earth, including the presence of hydrated rocks undergoing subduction to form felsic magmas in the early Hadean eon, may have made borate and molydate species available to prebiotic chemistry, despite the overall "reduced" state of the planet.