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.     

Reconstruction of Superoperators from Incomplete Measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[ρ_j] that originate from a set of four linearly independent “test” states ρ_j (j = 1,2,3,4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator ρ = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.We have originally dedicated this paper to Asher Peres on the occasion of his 70th birthday. Unfortunately, since the submission of the paper for publication Asher Peres passed away so we dedicate this paper to his memory.     

Phenotype MicroArray Profiling of Zymomonas mobilis ZM4

In this study, we developed a Phenotype MicroArray? (PM) protocol to profile cellular phenotypes in Zymomonas mobilis, which included a standard set of nearly 2,000 assays for carbon, nitrogen, phosphorus and sulfur source utilization, nutrient stimulation, pH and osmotic stresses, and chemical sensitivities with 240 inhibitory chemicals. We observed two positive assays for C-source utilization (fructose and glucose) using the PM screen, which uses redox chemistry and cell respiration as a universal reporter to profile growth phenotypes in a high-throughput 96-well plate-based format. For nitrogen metabolism, the bacterium showed a positive test results for ammonia, aspartate, asparagine, glutamate, glutamine, and peptides. Z. mobilis appeared to use a diverse array of P-sources with two exceptions being pyrophosphate and tripolyphosphate. The assays suggested that Z. mobilis uses both inorganic and organic compounds as S-sources. No stimulation by nutrients was detected; however, there was evidence of partial inhibition by purines and pyrimidines, NAD, and deferoxamine. Z. mobilis was relatively resistant to acid pH, tolerating a pH down to about 4.0. It also tolerated phosphate, sulfate, and nitrate, but was rather sensitive to chloride and nitrite. Z. mobilis showed resistance to a large number of diverse chemicals that inhibit most bacteria. The information from PM analysis provides an overview of Z. mobilis physiology and a foundation for future comparisons of other wild-type and mutant Z. mobilis strains.     

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.     

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.