Abstract:
We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

Abstract:
We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their $f$-vectors. We also use characters to give a generalization of Stanley's $(-1)$-color theorem. A $q$-analog version of this family of characters is also studied.

Abstract:
Because the electrical installations are nowadays a lot of options and variants, it is necessary to evaluate these complex installation process from several perspectives and objectively. Due to the complexity of evaluation of electrical installation is design a methodology that uses multi-criteria analysis - MCA.

Abstract:
Studienziel: Ziel dieser Studie ist es, zu kl ren, wie zuverl ssig die in der Literatur angegebenen klassischen Dermatommodelle (Darstellung der Schmerzausstrahlung bei L sion einzelner Nervenwurzeln) den entsprechenden Segmenten der Lendenwirbels ule zugeordnet werden k nnen. Methode: Es werden eigene Ergebnisse und externe Studien, die sich mit bandscheibenbedingten Schmerzprojektionen besch ftigen, verglichen. Die Literatursuche erfolgt EDV-unterstützt. Ergebnisse: Bezüglich der Dermatomverl ufe im Bereich der unteren LWS gibt es keine eindeutigen übereinstimmungen. Es besteht ein Widerspruch zwischen der am h ufigsten auftretenden Schmerzprojektion (S1) und dem am h ufigsten operierten Segment (L4/L5). Schlu folgerung: Trotz wissenschaftlich fundierter Modelle ist die Schmerzausstrahlung gegenüber den klassischen Dermatommodellen ein nur bedingt geeigneter Parameter zur Segmentdefinition.

Abstract:
We investigate a method to determine the temperature-density relation of the intergalactic medium (IGM) at z~2-4 using quasar absorption line systems. Using a simple model combined with numerical simulations we show that there is a lower cutoff in the distribution of column density (NHI) and line width (b parameter). The location of this cutoff can be used to determine the temperature-density relation (under certain conditions). We describe and test an algorithm to do this. The method works as long as the amplitude of fluctuations on these scales (~100 kpc) is sufficiently large. Models with less power can mimic higher temperatures. A preliminary application is made to data from two quasar lines-of-sight, and we determine an upper limit to the temperature of the IGM. Finally, we examine the full distribution of b-parameters and show that this is completely specified by just two parameters: the temperature of the gas and the amplitude of the power spectrum. Using the temperature upper limit measured with the NHI-b cutoff method, we derive an upper limit to the amplitude of the power spectrum.

Abstract:
Numerical hydrodynamical simulations are used to predict the expected absorption properties of the Lyman-Alpha forest for a variety of Cold Dark Matter dominated cosmological scenarios: CHDM, OCDM, LCDM, SCDM, and tCDM. Synthetic spectra are constructed duplicating the resolution, signal-to-noise ratio, and wavelength coverage of several published high resolution spectra, and their statistical properties compared on the basis of the flux distribution of the spectra, the distribution of coefficients in a wavelet decomposition of the spectra, and the distributions of absorption line profile parameters. Agreement between the measured and predicted cumulative distributions is found at the few to several percent level. The best-fitting models to the flux distribution correspond to normalizations on the scale of the cosmological Jeans length of 1.3 < sigma_J < 1.7 at z=3. No single model provides an acceptable match to all the distributions. Larger median Doppler parameters are found in the measured spectra than predicted by all but the lowest normalization models (CHDM and tCDM), which provide poor fits to the flux distributions. The discrepancy in Doppler parameters is particularly large for absorption systems optically thin at the Lyman-Alpha line-centre. This may indicate the need to introduce additional energy injection throughout the IGM, as may be provided by late HeII reionization (z_HeII~3.5) or supernovae-driven winds from young galaxies. The models require a hydrogen ionization rate at redshifts 1.73.5 than predicted from current QSO counts.

Abstract:
The nucleophilic substitution of substituted o-nitrochlorobenzenes with substituted methanethiolates, catalysed with triethylamine or pyridine, has been used to prepare a series of appropriately substituted methyl-o-nitrophenylsulfides. The prepared compounds were identified by their 1H- and 13C-NMR spectra. The base catalysed ring closure of methyl 2-(methoxycarbonylmethylsulfanyl)-3,5-dinitrobenzenecarboxylate only results in an attack of carbanion on the ester group, not on a nitro group as with the other compounds prepared. The cyclisation product is methyl 3-hydroxy-5,7-dinitrobenzo[b]thiophene-2-carboxylate (11).

Abstract:
We use three dimensional hydrodynamic simulations to investigate the effects of a soft X-ray background, that could have been produced by an early generation of mini-quasars, on the subsequent cooling and collapse of high redshift pregalactic clouds. The simulations use an Eulerian adaptive mesh refinement technique with initial conditions drawn from a flat Lambda-dominated cold dark matter model cosmology to follow the nonequilibrium chemistry of nine chemical species in the presence of both a soft ultraviolet Lyman-Werner H_2 photodissociating flux and a soft X-ray background extending to 7.2 keV. Although we vary the normalization of the X-ray background by two orders of magnitude, the positive feedback effect of the X-rays on cooling and collapse of the pregalactic cloud expected due to the increased electron fraction is quite mild, only weakly affecting the mass threshold for collapse and the fraction of gas within the cloud that is able to cool. Inside most of the cloud we find that H_2 is in photodissociation equilibrium with the soft UV flux. The net buildup of the electron density needed to enhance H_2 formation occurs too slowly compared to the H_2 photodissociation and dynamical timescales within the cloud to overcome the negative impact of the soft UV photodissociating flux on cloud collapse. However, we find that even in the most extreme cases the first objects to form do rely on molecular hydrogen as coolant and stress that our results do not justify the neglect of these objects in models of galaxy formation.

Abstract:
We present results from three-dimensional hydrodynamic simulations of the high redshift collapse of pregalactic clouds including feedback effects from a soft H2 photodissociating UV radiation field. The simulations use an Eulerian adaptive mesh refinement technique to follow the nonequilibrium chemistry of nine chemical species with cosmological initial conditions drawn from a popular Lambda-dominated cold dark matter model. The results confirm that the soft UV background can delay the cooling and collapse of small halos (~10^6 Msun). For reasonable values of the photo-dissociating flux, the H2 fraction is in equilibrium throughout most of the objects we simulate. We determine the mass threshold for collapse for a range of soft-UV fluxes and also derive a simple analytic expression. Continuing the simulations beyond the point of initial collapse demonstrates that the fraction of gas which can cool depends mostly on the virial mass of the halo and the amount of soft-UV flux, with remarkably little scatter. We parameterize this relation, for use in semi-analytic models.