Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Microwave-accelerated Dimroth rearrangement for the synthesis of 4-anilino-6-nitroquinazolines. Application to an efficient synthesis of a microtubule destabilizing agent

A useful and rapid access to 4-anilino-6-nitroquinazolines was investigated in a multi-gram scale via microwave-accelerated condensation and Dimroth rearrangement of the starting anilines with imines obtained by reaction of anthranilonitriles with formamide dimethylacetal. A novel short and efficient route to Azixa™ (EPi28495, MPC-6827), a microtubule destabilizing agent and apoptosis inducer, was performed with success demonstrating that well controlled parameters offer comfortable using of microwave technology with safe and environmental benefits.     

Differential non-destructive image current detection in a fourier transform quadrupole ion trap

Dual-detector differential non-destructive Fourier transform detection in a quadrupole ion trap is shown to improve signal intensity and reduce noise compared with spectra recorded using a single detector. A larger area detector in each end-cap electrode is machined to fit its hyperbolic shape and so minimize field imperfections on the z-axis. Argon, acetophenone and bromobenzene spectra were recorded to allow a comparison between single- and dual-detector (differential) modes of detection and to demonstrate the improvement achieved with differential detection. Copyright 1999 John Wiley & Sons, Ltd.     

Few-cycle solitons in supercontinuum generation dynamics

We review several propagation models that do not rely on the slowly-varying-envelope approximation (SVEA), and can thus be considered as fundamental models addressing the formation and propagation of few-cycle pulsed field structures and solitary waves arising in the course of intense ultrashort optical pulse evolution in nonlinear media and beyond octave-bandwidth optical spectrum broadening. These generic models are: the modified-Korteweg-de Vries (mKdV), the sine-Gordon (sG), and the mixed mKdV-sG equations. To include wave polarization dynamics, the vector extensions of both mKdV and sG equations are introduced. Multi-octave-spanning supercontinuum generation and few-cycle soliton structures are highlighted from numerical simulations.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

A Pulsed Field Gradient NMR Technique for the Determination of the Structure of Suspensions of Non-Brownian Particles with Application to Packings of Spheres

The internal structure of systems of particles in a liquid is studied with a novel NMR technique based on the measurement of the squared modulus of the magnetization in presence of a pulsed field gradient. The formalism is analogous to the one used in classical scattering techniques (light, X-rays, neutrons); it allows similar information to be obtained about the structure (in particular, the structure factorS(q)). The main improvement is that the range of particles sizes is 10 μm to 1 mm, as compared with the range of the scattering techniques (<5 μm). The NMR technique was validated by studying packings of spherical particles of mean diameter 240 μm created by sedimentation. The profile of the experimental squared modulus of the magnetization versus the wave vector provides results for the mean size of particles and the compacity. The main feature is that it depends on the pair distribution function, and the present results are in good agreement with a model based on the Percus–Yevick approximation. This technique is then particularly adapted to systems such as non-Brownian suspensions, fluidized beds, porous media, and sediments.