Natural Density of Rectangular Unimodular Integer Matrices

In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the density of rectangular matrices with Hermite normal form [O Id]. Connections with Cesaro's Theorem on the density of coprime integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page

Kaon and Pion production in relativistic heavy-ion collisions

The BUU transport model is applied to study strangeness and pion production in nucleus-nucleus collisions. Starting from proton induced reactions, we further investigate Si+Au, Au+Au and Pb+Pb collisions in the energy range between 2 and 40 A$\cdot$GeV and compare with data and with other transport calculations. The $q \bar q$ annihilation, or resonance, channel simulated by the string model in meson-nucleon collisions at $\sqrt{s} > 2$ GeV is introduced. The importance of this channel for a good description of the proton-nucleus data on $K^+$ production is demonstrated. We, furthermore, show that the meson-meson collisions contribute significantly to the $K \bar K$ production in heavy-ion collisions above 5 A GeV and improve an agreement with data on the $K^+/\pi^+$ ratio. Finally, we study the influence of the in-medium modifications of the FRITIOF model on the pion and kaon production.Comment: 20 pages, 25 figures, added statistical errors in figure

Kaon production from 1 to 40 A GeV

Kaon production is studied within the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.Comment: 6 pages, 4 figures, Proc. of the Int. Workshop on Hot and Dense Matter in Relativistic Heavy Ion Collisions, 09-12.04.2006, Budapes

Kaon production from 1 to 40 A GeV

Kaon production is studied within the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model. Results are compared with experiment and with other models. The influence of the kaon potential on the kaon azimuthal distributions at SIS energies is considered. We also discuss the role of the many-body collisions at high-density phase of reaction.Comment: 6 pages, 4 figures, Proc. of the Int. Workshop on Hot and Dense Matter in Relativistic Heavy Ion Collisions, 09-12.04.2006, Budapes

Wing shielding of high velocity jet and shock-associated noise with cold and hot flow jets

Jet exhaust noise shielding data are presented for cold and hot flows (ambient to 1,100 K) and pressure ratios from 1.7 to 2.75. A nominal 9.5-cm diameter conical nozzle was used with simple shielding surfaces that were varied in length from 28.8 to 114.3 cm. The nozzle was located 8.8 cm above the surfaces. The acoustic data with the various sheilding lengths are compared to each other and to that for the nozzle alone. In general, short shielding surfaces that provided shielding for subsonic jets did not provide as much shielding for jets with shock noise, however, long shielding surfaces did shield shock noise effectively

Multi-loop Control Systems of Compensators for Powerful Sounding Pulses Generators

Construction principles of multi-loop control systems of compensators for powerful sounding pulses generators are presented. A method for controlling a compensating system using fuzzy logic and forecast control ideas is described. Proposed compensating system is able to solve different problems: reactive power compensation, harmonic elimination. The system is based on a combination of a thyristor compensator and an active power filter. Some practical results with Matlab-Simulink are presented to check the proposed control performance

Solutions for Liquid Nitrogen Pre-Cooling in Helium Refrigeration Cycles

Pre-cooling of helium by means of liquid nitrogen is the oldest and one of the most common process features used in helium liquefiers and refrigerators. Its two principle tasks are to allow or increase the rate of pure liquefaction, and to permit the initial cool-down of large masses to about 80 K. Several arrangements for the pre-cooling process are possible depending on the desired application. Each arrangement has its proper advantages and drawbacks. The aim of this paper is to review the possible process solutions for liquid nitrogen pre-cooling and their particularities

Phase ordering of two-dimensional symmetric binary fluids: a droplet scaling state

The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains itself, throughout the viscous hydrodynamic regime, by a `coalescence-induced coalescence' mechanism. Scaling is recovered (with length scale $l \sim t$, as in $d=3$). The crossover to the inertial hydrodynamic regime is delayed even longer than in $d=3$; on entering it, full symmetry is finally restored and we find $l\sim t^{2/3}$, regardless of the initial state.Comment: 4 pages, three figures include

Profound effect of profiling platform and normalization strategy on detection of differentially expressed microRNAs

Adequate normalization minimizes the effects of systematic technical variations and is a prerequisite for getting meaningful biological changes. However, there is inconsistency about miRNA normalization performances and recommendations. Thus, we investigated the impact of seven different normalization methods (reference gene index, global geometric mean, quantile, invariant selection, loess, loessM, and generalized procrustes analysis) on intra- and inter-platform performance of two distinct and commonly used miRNA profiling platforms. We included data from miRNA profiling analyses derived from a hybridization-based platform (Agilent Technologies) and an RT-qPCR platform (Applied Biosystems). Furthermore, we validated a subset of miRNAs by individual RT-qPCR assays. Our analyses incorporated data from the effect of differentiation and tumor necrosis factor alpha treatment on primary human skeletal muscle cells and a murine skeletal muscle cell line. Distinct normalization methods differed in their impact on (i) standard deviations, (ii) the area under the receiver operating characteristic (ROC) curve, (iii) the similarity of differential expression. Loess, loessM, and quantile analysis were most effective in minimizing standard deviations on the Agilent and TLDA platform. Moreover, loess, loessM, invariant selection and generalized procrustes analysis increased the area under the ROC curve, a measure for the statistical performance of a test. The Jaccard index revealed that inter-platform concordance of differential expression tended to be increased by loess, loessM, quantile, and GPA normalization of AGL and TLDA data as well as RGI normalization of TLDA data. We recommend the application of loess, or loessM, and GPA normalization for miRNA Agilent arrays and qPCR cards as these normalization approaches showed to (i) effectively reduce standard deviations, (ii) increase sensitivity and accuracy of differential miRNA expression detection as well as (iii) increase inter-platform concordance. Results showed the successful adoption of loessM and generalized procrustes analysis to one-color miRNA profiling experiments