A non-adapted sparse approximation of PDEs with stochastic inputs

We propose a method for the approximation of solutions of PDEs with stochastic coefficients based on the direct, i.e., non-adapted, sampling of solutions. This sampling can be done by using any legacy code for the deterministic problem as a black box. The method converges in probability (with probabilistic error bounds) as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples. We show that the method is well suited for truly high-dimensional problems.     

Characterization of a peptide family from the skin secretion of the Middle East Tree Frog Hyla savignyi by composition‐based de novo sequencing

A new tryptophyllin‐like peptide family was found in the skin secretion of the tree frog Hyla savignyi. Peptides were characterized by database‐independent sequencing strategies and specific ion fragmentation features were investigated. Skin secretions from specimens of Hyla savignyi were collected by mild electrical stimulation. Peptides were separated by reversed‐phase nano‐high‐performance liquid chromatography (nanoHPLC) and mass spectra were acquired online by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (FTICR‐MS). Peptides were characterized by manual de novo sequencing and by composition‐based sequencing (CBS), appearing mostly as C‐terminal free acids and as their acid amide analogs. Amide peptides yielded lower intensities of y‐type ions after collision‐induced dissociation (CID) than their acid analogs. A mechanism of internal b‐ion formation (positive ion mode) and of CO₂ elimination (negative ion mode) is proposed. We also exemplified phenomena such as the proline effect and formation of non‐direct sequence ions after sequence rearrangements. The occurrence of rearrangement products, of internal ions and of the proline effect made the CID spectra highly complex. CBS analysis nevertheless resulted in successful and highly reliable sequence analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

An extended transportation problem: a DEA-based approach

The transportation problem is an important network structured linear programming problem that arises in several contexts and that has received a great deal of attention in the literature. The existing transportation problems are limited to consideration unit of shipping cost or profit along an arc. However, in many real applications, various attributes are usually considered in a transportation problem. The current paper, proposes an extension to this problem in the presence of multiple in-commensurate inputs and outputs for each arc. The concept of relative efficiency is defined for each possible transportation plan. Two linear programming models are proposed to determine the transportation plan with the maximum efficiency. A numerical example is used to illustrate the applicability of the approach.     

Three-Component Reaction of Triphenylphosphine,Dimethyl Acetylenedicarboxylate,and Aldehyde Benzoylhydrazones: An Efficient One-Pot Synthesis of Stable Phosphorus Ylides

Protonation of the reactive 1:1 intermediate produced in the reaction between dimethyl acetylenedicarboxylate and triphenylphosphine by benzoylhydrazones leads to vinylphosphonium salts, which undergo Michael addition with the conjugate base of the NH acid to produce highly fanctionalized, salt-free phosphorus ylides in excellent yields.     

On the deformation theory of Calabi-Yau structures in strongly pseudo-convex manifolds

We study the deformation theory of Calabi-Yau structures in strongly pseudo-convex manifolds with trivial canonical bundles. Our approach could be considered as an alternative proof for a theorem of H. Laufer on the deformation of strongly pseudo-convex surfaces.     

Transition metal ions as cores in the construction of an unprecedented large macrocycle

New macrocyclic complexes have been prepared by reacting diethylenetriamine, benzil and a metal ion [cobalt(II), nickel(II) and copper(II)] in a 2:2:1 ratio in MeOH. The complexes were characterized by elemental analysis, spectroscopic data (u.v., i.r. and e.p.r.) magnetic susceptibility and conductivity measurements and are probably covalent. The metal ions are paramagnetic in a free spin state and appear to possess a slightly distorted octahedral geometry. A cyclic voltametric study on the copper complex indicates a reversible redox couple (CuIICuI,E = –0.48 V) in DMSO, which means that the macrocycle is capable of stabilizing the CuIICuI process.     

A concise and diversity-oriented strategy for the synthesis of benzofurans and indoles via Ugi and Diels-Alder reactions

A one-pot synthesis of diverse benzofurans and indoles from readily available starting materials was achieved via the sequential Ugi four-component reaction, intramolecular Diels-Alder reaction, and oxidative aromatization.     

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.     

Fourier Algebras on Topological Foundation *-Semigroups.

We introduce the notion of the Fourier and Fourier-Stieltjes algebras of a topological *-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras.