Makespan minimization in machine dominated flowshop

In a flowshop scheduling problem, a set of jobs is processed by a set of machines. The jobs follow the same sequence in all machines. We study the flowshop scheduling problem under a new case of machine dominance that is often found in the manufacturing of computers and electronic devices. We provide a formula for makespan value for a given sequence, show that the makespan value depends only on certain jobs in the sequence, and present an algorithm that finds a sequence with minimum makespan. Numerical examples of the solution approaches are provided.     

Sub-optical resolution of single spins using magnetic resonance imaging at room temperature in diamond

There has been much recent interest in extending the technique of magnetic resonance imaging (MRI) down to the level of single spins with sub-optical wavelength resolution. However, the signal to noise ratio for images of individual spins is usually low and this necessitates long acquisition times and low temperatures to achieve high resolution. An exception to this is the nitrogen-vacancy (NV) color center in diamond whose spin state can be detected optically at room temperature. Here we apply MRI to magnetically equivalent NV spins and demonstrate fully resolved spectra with resolution well below the optical wavelength of the readout light. In addition, using a microwave version of MRI we achieved a resolution that is 1/270 in size of the coplanar striplines, which define the effective wavelength of the microwaves that were used to excite the transition. This technique can eventually be extended to imaging of large numbers of NVs in a confocal spot and possibly to image nearby dark spins via their mutual magnetic interaction with the NV spin.     

Spectrophotometric studies on oxidation of some primary alcohols by 2,2′-bipyridinium chromate. A kinetic study

Some primary alcohols were oxidized by 2,2-bipyridinium chromate (BPC) in the presence of oxalic acid and TsOH giving aldehyde as major product. The reactions were carried out in 80% MeCN-DMF (v/v) medium under varied experimental conditions. The rate depends on the first power of the concentration of BPC and fractional power on the concentrations of alcohol, oxalic acid and TsOH.     

A class of discontinuous Petrov–Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm. In this paper, we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm. This is answered in the specific case of the Helmholtz equation with L²-norm as the energy norm. We obtain uniform stability with respect to the wave number. We illustrate the method with a number of 1D numerical experiments, using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally. A 1D theoretical stability analysis is also developed.     

An efficient and solvent-free one-pot synthesis of 1,4-dihydropyridines under microwave irradiation

An efficient synthesis of 1,4-dihydropyridines using lanthanum oxide as a catalyst from aldehydes,β-ketoester and ammonium acetate without solvent under the irradiation of microwave is described.Compared with the classical Hantzsch reaction,this new method has the advantage of good yield(90-98%) and short reaction time(40-80 s).     

Three‐dimensional sloshing: A consistent finite element approach

This paper presents a new computational methodology based on Legendre's polynomials to predict the slosh and acoustic motion in nearly incompressible fluids in both rigid and flexible structures with free surface. Here, we have used a finite element formulation based on Lagrangian frame of reference to model the fluid motion derived using Hamiltonian equation of the fluid system. We formulated three hexahedral finite elements based on strain fields expressed in terms of extended Legendre's polynomials. Sloshing and acoustic motion of liquid is investigated using these newly formulated elements and inf–sup test is performed on these new elements to check the performance of these elements in modeling sloshing under two severe constraints, namely incompressibility and irrotationality. Comparisons of slosh and acoustic frequencies, and mode shapes with exact solutions are given. Dynamic analysis with earthquake and harmonic kind of forcing function is carried out to validate the formulated hexahedral elements to analyze the sloshing response. Numerical results obtained with these new finite elements, and with the present finite element formulation of the mathematical model agree well with the exact solution and as well as with published experimental literature. Copyright © 2010 John Wiley & Sons, Ltd.     

A Facile Microwave‐Assisted “One‐Pot” Synthesis of Piperazino Pyrimidinyl Acetamides,a Class of Hybrid Bis Heterocycles and Their Structural Elucidation Using NMR Spectral Techniques

An array of novel piperazino pyrimidinyl acetamides, a class of hybrid bis heterocycles are synthesized in “one‐pot” by microwave irradiation method catalyzed by heterogeneous NaHSO₄.SiO₂ catalyst in dry media and are characterized by melting point, elemental analysis, MS, FT‐IR, one‐dimensional NMR (¹H and ¹³C) and two‐dimensional ¹H‐¹H COSY and ¹H‐¹³C HSQC spectral data.