A non-diagonal singularity-free model in torsion gravity

In the context of torsion (teleparallel) gravity, we focus on discussing the spin effects of Dirac particles associated with the non-diagonal singularity-free model (Mars space-time). We see that the vector part depends on the radial r and z directions and the axial-vector will be along the radial direction, that is, it will be symmetric about radial direction. Furthermore, the t = 0 case of the Mars metric is considered, thence it is seen that the axial-vector vanishes.     

(6′RS,8′RS,2E)- und (6′RS,8′SR,2E)-3-Methyl-3-(2y,2′,6′-trimethyl-7′-oxabicyclo[4.3.0]non-9′-en-8′-yl)-2-propenal ([(5RS,8RS)- und (5RS,8SR)-5,8-Epoxy-5,8-dihydro-ionyloinden]acetaldehyd): Synthese und Röntgenstrukturanalyse

Synthesis and X-Ray Structure of (6′RS,8′RS,2E)- and (6′RS,8′SR,2E)-3-Methyl-3-(2′,2′,6′-trimethyl-7′-oxabicyclo[4.3.0]non-9′-en-8′-yl)-2-propenal ([(5RS,8RS)- and (5RS,8SR)-5,8-Epoxy-5,8-dihydro-ionylidene]acetaldehyde) To check our previous spectroscopic assignments of the structures of trans- and cis-substituted furanoid end groups of carotenoid-5,8-epoxides, we now have synthesized the title compounds. An X-ray structure determination of a single crystal of the trans-isomer (±)- -10A is in agreement with the ¹ H-NMR spectroscopic arguments: isomers with Δδ (H? C(7), H? C(8)) = 0.15–0.22 ppm and J > 1.4 for H? C(7) belong to the cis-series; Δδ in trans-compounds is < 0.07 ppm, and H? C(7) appears as a broad singulett.     

Luteochrome; spektroskopische,chiroptische und chromatographische Eigenschaften

Two Optically Active Luteochromes: Preparation, Spectra and Chiroptical and Chromatographic Properties Selective rearrangement of (5R,6S,5′ R,6′S)-5,6:5′, 6′ -diepoxy-5,6,5′, 6′ -tetrahydro- β,β -carotene with the aid ofan ethereal solution of malonic acid leads to the mixture of the C(8′)-epimeric luteochromes. HPLC separation gave the pure isomers. This is the first report on th preparation of optically active luteochromes.     

Spinor Frenet Equations in Three Dimensional Lie Groups

In this paper, we study spinor Frenet equations in three dimensional Lie groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for some special cases of three dimensional Lie groups.     

A flexible approach to ranking with an application to MBA Programs

We develop a model for flexibly ranking multi-dimensional alternatives/units into preference classes via Mixed Integer Programming. We consider a linear aggregation model, but allow the criterion weights to vary within pre-specified ranges. This allows the individual alternatives/units to play to their strengths. We illustrate the use of the model by considering the Financial Times Global MBA Program rankings and discuss the implications. We argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking, providing an argument for sorting or what we call flexible ranking.     

A variational method of optimal control problems for nonlinear Schrödinger equations

Calculating the control function that is in the coefficients of the nonlinear Schrodinger equation and minimizes the objective functional consisting of two integrals is main aim of this article. After proving the existence and uniqueness of the solution, we have constituted an algorithm using the method of gradient of projection. Results are tested on a quantum‐mechanical problem. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 82–89, 2004.     

Expression of stress proteins in cultured human cells as a sensitive indicator of metal toxicity

Human cell lines cultured under standardized conditions are found to react after a wide variety of aggressive but sub-lethal treatments by expressing stress proteins, mainly of the HSP68, HSP70 and HSP90 families. The stress reaction is a repair mechanism which rapidly takes place after minute damages caused to cell structures. It was therefore proposed to develop a sensitive biomarker to monitor environmental pollution, especially related to metals, based on the evaluation of stress protein production. This was achieved by computer-assisted densitometric analysis of autoradiographies of electrophoretically separated (35)S-labelled proteins. The results indicate that our biological models consisting in HT29 and HepG2 cell-lines react to low concentrations of cadmium or nickel by a clear-cut increase of stress proteins expression. In most cases, this effect is much more significant and much more rapid to observe than changes in growth curves. It may constitute a reliable index of cell susceptibility to environmental aggressions.     

Catalytic wet air oxidation of 2-nitrotoluidine and 2,4-dinitrotoluene

The rates of wet air oxidation of 2-nitrotoluidine and 2,4-dinitrotoluene in the presence of excess oxygen and at different temperatures and oxygen pressures was investigated. Oxidation experiments were carried out at temperatures between 180 and 225^oC and oxygen partial pressures of 1,0-3,0 MPa, in a 280 mL glass vessel-inserted stainless steel reactor. Copper sulfate (CuSO₄ .5H₂O) was used as a catalyst, and the effect of catalyst loading was studied by varying the concentration: 0.75, 2.5 and 25 mg/L as Cu²⁺. Addition of Cu²⁺ ions in the reaction media accelerated 2-nitrotoluidine oxidation nearly ten times even if it exists in trace amount in the reaction medium (0.75 ppm Cu²⁺). Unfortunately copper did not show catalytic effect for the oxidation of 2,4-dinitrotoluene. This revised version was published online in August 2006 with corrections to the Cover Date.     

A semilinear elliptic equation with a mild singularity at u = 0: Existence and homogenization

In this paper we consider singular semilinear elliptic equations whose prototype is the following

$\{\begin{array}{cc}?divA(x)Du=f(x)g(u)+l(x)\hfill & \text{in}\mathrm{\Omega },\hfill \\ u=0\hfill & \text{on}?\mathrm{\Omega },\hfill \end{array}$

where Ω is an open bounded set of ${\mathbb{R}}^N,N\ge 1$, $A\in L^{\infty }{(\mathrm{\Omega })}^{N\times N}$ is a coercive matrix, $g:[0,+\infty [\to [0,+\infty ]$ is continuous, and $0\le g(s)\le \frac{1}{s^{\gamma }}+1$ for every $s>0$, with $0<\gamma \le 1$ and $f,l\in L^r(\mathrm{\Omega })$, $r=\frac{2N}{N+2}$ if $N\ge 3$, $r>1$ if $N=2$, $r=1$ if $N=1$, $f(x),l(x)\ge 0$ a.e. $x\in \mathrm{\Omega }$.We prove the existence of at least one nonnegative solution as well as a stability result; we also prove uniqueness if $g(s)$ is nonincreasing or “almost nonincreasing”.Finally, we study the homogenization of these equations posed in a sequence of domains ${\mathrm{\Omega }}^{\epsilon }$ obtained by removing many small holes from a fixed domain Ω.