Sparse approximate solutions to stochastic Galerkin equations

In this Note, we formulate a sparse Krylov-based algorithm for solving large-scale linear systems of algebraic equations arising from the discretization of randomly parametrized (or stochastic) elliptic partial differential equations (SPDEs). We analyze the proposed sparse conjugate gradient (CG) algorithm within the framework of inexact Krylov subspace methods, prove its convergence and study its abstract computational cost. Numerical studies conducted on stochastic diffusion models show that the proposed sparse CG algorithm outperforms the classical CG method when the sought solutions admit a sparse representation in a polynomial chaos basis. In such cases, the sparse CG algorithm recovers almost exactly the sparsity pattern of the exact solutions, which enables accelerated convergence. In the case when the SPDE solution does not admit a sparse representation, the convergence of the proposed algorithm is very similar to the classical CG method.     

1,3-Dipolar cycloaddition of chalcones and arylidene-1,3-dicarbonyls with diazosulfone for the regioselective synthesis of functionalized pyrazoles and pyrazolines

A convenient method for the synthesis of 3-acylpyrazoles and pyrazole-3-carboxylates using diazosulfone as a reactive 1,3-dipole and a diazomethane equivalent is reported here. Chalcones, arylidenemalonates and other arylidene-1,3-dicarbonyls performed well as the dipolarophiles in the reaction with the diazosulfone which took place under simple base mediated conditions (Cs₂CO₃ or NaOEt in EtOH). In few cases, the initial cycloadducts, the intermediate pyrazoline derivatives, could also be isolated and characterized. The pyrazoline derivatives undergo an alkoxide mediated 1,4-elimination, viz. decarboxylation-detosylation to afford the pyrazole derivatives.     

Glasner sets and polynomials in primes

A set of integers is said to be Glasner if for every infinite subset of the torus and there exists some such that the dilation intersects every integral of length in . In this paper we show that if denotes the th prime integer and is any non-constant polynomial mapping the natural numbers to themselves, then is Glasner. The theorem is proved in a quantitative form and generalizes a result of Alon and Peres (1992).

     

The dielectric constant effect upon the acid hydrolysis of ethyl acetate

The dielectric constant effect upon the rate of acid hydroly.sis of ethyl acetate is presented from the standpoint of electrostatics and the results compared to like effects upon the acid hydrolysis of methyl propionate.     

Synthesis of substituted alkoxy benzene minilibraries, for the discovery of new insect olfaction or gustation inhibitors

We describe methods for the rapid generation of minilibraries of substituted alkoxy benzenes (consisting of 4-5 compounds), for screening as insect olfaction or gustation inhibitors. Synthetic or commercially available monoalkoxy benzene compounds were mixed and reacted with various alkyl halides to afford a first set of minilibraries. A second and third set were generated from allyloxy minilibraries via the Claisen rearrangement and subsequent alkylation of the ortho-allyl phenols. We have chosen to prepare a collection of small libraries (as opposed to one large library) to test the response insects exhibit toward blends of compounds. We demonstrate how our minilibraries can be screened, both against insect antennae and against expressed pheromone-binding proteins from the gypsy moth, Lymantria dispar.     

Nitrite and Nitric Oxide Interconversion at Mononuclear Copper(II): Insight into the Role of the Red Copper Site in Denitrification

Nitrite (NO₂⁻) and nitric oxide (NO) interconversion is crucial for maintaining optimum NO flux in mammalian physiology. Herein we demonstrate that [ L ₂Cu^II(nitrite)]⁺ moieties (in 2 a and 2 b ; where, L = Me₂PzPy and Me₂PzQu ) with distorted octahedral geometry undergo facile reduction to provide tetrahedral [ L ₂Cu^I]⁺ (in 3 a and 3 b ) and NO in the presence of biologically relevant reductants, such as 4-methoxy-2,6-di-tert-butylphenol (4-MeO-2,6-DTBP, a tyrosine model) and N-benzyl-1,4-dihydronicotinamide (BNAH, a NAD(P)H model). Interestingly, the reaction of excess NO gas with [ L ₂Cu^II(MeCN)₂]²⁺ (in 1 a ) provides a putative {CuNO}¹⁰ species, which is effective in mediating the nitrosation of various nucleophiles, such as thiol and amine. Generation of the transient {CuNO}¹⁰ species in wet acetonitrile leads to NO₂⁻ as assessed by Griess assay and ¹⁴N/¹⁵N-FTIR analyses. A detailed study reveals that the bidirectional NO_x-reactivity, namely, nitrite reductase (NIR) and NO oxidase (NOO), at a common Cu^II site, is governed by the geometric-preference-driven facile Cu^II/Cu^I redox process. Of broader interest, this study not only highlights potential strategies for the design of copper-based catalysts for nitrite reduction, but also strengthens the previous postulates regarding the involvement of red copper proteins in denitrification.     

Interaction between excitons determines the non-linear response of nanocrystals

The non-linear response of semiconductor quantum dots is investigated using three-pulse photon echo peak shift (3PEPS) experiments and simulations. The third-order non-linear response is modeled by a three-level system, utilizing Brownian oscillators to model the line-broadening functions. Our results show that biexciton formation and exciton–exciton scattering significantly influence the non-linear response of quantum dots. The exciton to biexciton excited state absorption pathways are also investigated for quantum dots with different crystal structures. Our calculations suggest that the probability of excited state absorption to the biexcitonic state is higher for zinc-blende structured nanocrystals.