Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Characteristics investigation on heat transfer growth of sonochemically synthesized ZnO-DW based nanofluids inside square heat exchanger

Journal of Thermal Analysis and Calorimetry - In recent decades, the growth of heat transfer using nanomaterials in the conventional base fluid has caught the attention of researchers...     

The square lattice shuffle

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Sodium trichloro­methane­sulfonate monohydrate

Sodium trichloro­methane­sulfonate monohydrate, Na⁺·CCl₃SO₃⁻·H₂O, crystallizes in P2₁/a with all the atoms located in general positions. The trichloro­methane­sulfonate (trichlate) anion consists of pyramidal SO₃ and CCl₃ groups connected via an S—C bond in a staggered conformation with approximate C_3v symmetry. The water mol­ecule is hydrogen bonded to the sulfonate O atoms, with one water H atom forming weak bifurcated O—H⋯O hydrogen bonds to two different trichlate ions. Two water O atoms and three O atoms from different SO₃ groups form a square‐pyramidal arrangement around the sodium ion.     

A virtual boundary method with improved computational efficiency using a multi‐grid method

The flow around spherical, solid objects is considered. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by extrapolation from the flow field. The source terms are determined iteratively, as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. A multi‐grid scheme has been used to enhance the computational efficiency of the solution of the force equations. The method has been evaluated for flow around both moving and stationary spherical objects at very low and intermediate Reynolds numbers. The results shows a second order accuracy of the method both at creeping flow and at Re=100. The multi‐grid scheme is shown to enhance the convergence rate up to a factor 10 as compared to single grid approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Nanostructured Ion-Selective MCM-48 Membranes

Templated MCM-48 silica was prepared using CTAB as surfactant. The MCM-48 powders and thin films were characterized by different techniques. MCM-48 layers were deposited on macroporous α-alumina supports and silicon nitride microsieves. The water permeability of MCM-48 was compared with the permeability of conventional mesoporous γ-alumina membranes. The applicability of MCM-48 as ion-selective electric field-driven switchable interconnect for microfluidic devices was demonstrated.     

On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max‐Lin‐2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max‐k‐Lin‐2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Solutions of the WDVV Equations and Integrable Hierarchies of KP Type

We show that reductions of KP hierarchies related to the loop algebra of SL_n with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten– Dijkgraaf–E. Verlinde–H. Verlinde equations.     

Spectral Analysis of the Differential Operator in Wavelet Bases

We analyze the spectral properties of the differential operator in wavelet bases. The problem is studied on a periodic domain, with periodized wavelets. An algorithm for finding the eigenvalue function of the differential operator is presented, and general conditions that ensure a "nicely behaving" eigenvalue function are derived.