Does the Big Rip survive quantization?

It is known that certain quantum cosmological models present quantum behavior for large scale factors. Since quantization can suppress past singularities, it is natural to inquire whether quantum effects can prevent future singularities. To this end, a Friedmann–Robertson–Walker quantum cosmological model dominated by a phantom energy fluid is investigated. The classical model displays accelerated expansion ending in a Big Rip. The quantization is performed in three different ways, which turn out to lead to the same result, namely there is a possibility that quantum gravitational effects could not remove the Big Rip.     

Die Kenntnisse von den ?therischen Oelen

Ohne Zusammenfassung     

On weighted heights of random trees

Consider the family treeT of a branching process starting from a single progenitor and conditioned to havev=v(T) edges (total progeny). To each edge <e> we associate a weightW(e). The weights are i.i.d. random variables and independent ofT. The weighted height of a self-avoiding path inT starting at the root is the sum of the weights associated with the path. We are interested in the asymptotic distribution of the maximum weighted path height in the limit asv=n. Depending on the tail of the weight distribution, we obtain the limit in three cases. In particular ify ² P(W(e)> y)0, then the limit distribution depends strongly on the tree and, in fact, is the distribution of the maximum of a Brownian excursion. If the tail of the weight distribution is regularly varying with exponent 0<2, then the weight swamps the tree and the answer is the asymptotic distribution of the maximum edge weight in the tree. There is a borderline case, namely,P(W(e)> y)cy ^–2 asy, in which the limit distribution exists but involves both the tree and the weights in a more complicated way.     

On the equivalence of renormalizations in standard and dimensional regularizations of 2D four-fermion interactions

We discuss the problem of equivalence between the standard (integer-dimensional d=2) and the d=2+ dimensional renormalization schemes for the complete U_N-symmetrical four-fermion interaction model. To ensure the multiplicative renormalizability of the theory, we need three charges in the first case; in the second, we need an infinite series of independent charges g {g_n, n=0, 1, ...}. After the usual MS-renormalization. there exists a UV-finite renormalization of fields. Charges gg'(g) exist such that the renormalized Green's functions in the limit 0 depend only on the three lower charges g'_n(g) with n=0, 1, 2. rather than on the whole set. This ensures the possibility of establishing the equivalence of the two renormalization schemes. The results of calculations in the MS scheme up to two loops for the -functions, and up to three loops for the anomalous field dimension are presented. These are presented together with the derivation of the projection technique relations, which allows one to express the higher renormalized composite operators of the 4F-interaction via the lower ones in the limit 0.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 1, pp. 27–46, April, 1996.Translated by L. O. Chekhov.     

Bis(ligand) Rhenium(V) and Technetium(V) Complexes of Two Naturally Occurring Binding Moieties (Oxazoline and Thiazoline)

Attempts to prepare tris(ligand) metal complexes of technetium in intermediate oxidation states with potentially bidentate oxazoline- and thiazoline-containing ligands were unsuccessful; when pertechnetate was reduced in the presence of excess ligand, TcO(2).xH(2)O was produced. Instead, by reaction with preformed M.O cores, a series of oxotechnetium(V) and oxorhenium(V) complexes of the formula MOXL(2) (M = Re, X = Br; M = Tc, X = Cl) and HL = 2-(2'-hydroxyphenyl)-2-oxazoline (Hoz), 2-(2'-hydroxy-3'-methylphenyl)-2-oxazoline (Hmoz), 2-(2'-hydroxyphenyl)-2-thiazoline (Hthoz), and 2-(2'-hydroxyphenyl)-2-benzoxazoline (Hhbo) have been prepared. These compounds have been characterized by a variety of techniques including single-crystal X-ray diffraction. Crystals of Hthoz (C(9)H(9)NOS) are monoclinic, with space group P2(1)/n, a = 7.5342(6) ?, b = 12.2187(6) ?, c = 9.3942(8) ?, beta = 94.233(7) degrees, and Z = 4; those of TcOCl(thoz)(2) (C(18)H(16)ClN(2)O(3)S(2)Tc) are monoclinic, with space group P2(1)/n, a = 16.506(1) ?, b = 7.664(1) ?, c = 16.3216(6) ?, beta = 111.154(4) degrees, and Z = 4; those of ReOBr(oz)(2) (C(18)H(16)BrN(2)O(5)Re) are orthorhombic, with space group Pbca, a = 12.864(2) ?, b = 25.369(2) ?, c = 11.025(2) ?, and Z = 8. The structures were solved by direct (Hthoz) or Patterson (metal complexes) methods and were refined by full-matrix least-squares procedures to R = 0.033, 0.032, and 0.028 for 1600, 3152, and 2651 reflections with I >/= 3sigma(I), respectively. In the two complexes, the geometry around the metals is distorted octahedral with the halide ligands in each bound cis, and one phenolate oxygen from one ligand in each bound trans to the metal-oxo linkage. In ReOBr(oz)(2), the two oxazoline nitrogens are coordinated trans to one another; in TcOCl(thoz)(2), the two thiazoline nitrogens are found cis to one another.     

Counting the number of solutions in combustion and reactive flow problems

Summary Computational methods and comparison theory enable, when combined, an enhanced capability for counting the number of solutions in combustion equations. Very good lower bounds for the last turning point reveal a stable high temperature explosion branch for very small positive exothermicity.     

Copper-Silica Sol-Gel Catalysts: Structural Changes of Cu Species upon Thermal Treatment

In this work the encapsulation of copper species in sol-gel silica catalysts thermally treated up to 1100°C was studied. XRD, TPR, BET data showed the occurrence of a vitrification/densification process upon treatment at temperatures higher than 900°C leading to the partial or complete encapsulation of the copper species by the silica matrix. As result of this process the copper catalyst particles become unavailable for the reaction with gas phase molecules and are not active for reactions such as carbon monoxide oxidation.     

Synthesis and antimicrobial testing of 2-amino-6-hydroxymethyl-4-(3H)pyrido[3,2-d]pyrimidinone

Synthesis of 2-amino-6-hydroxymethyl-4-(3H)pyrido[3,2-d]pyrimidinone ( 5 ) from 2-amino-6-methyl-4-(3H)-pyrido[3,2-d]pyrimidinone ( 2 ) was accomplished by selenium dioxide oxidation of 2 to the aldehyde 4 followed by sodium borohydride reduction. Compound 2 was available in four steps from 5-aminouracil or in two steps from 5-nitroisocytosine ( 3a ). Catalytic reduction of 4 or 5 gave a mixture of 2-amino-6-methyl-5,6,7,8-tetrahydro-4-(3H)pyrido[3,2-d]pyrimidinone ( 6a ) and the 6-hydroxymethyl compound 6b . These compounds showed only weak inhibitory activity in the coupled reactions catalyzed by 7,8-dihydro-6-hydroxymethylpterin pyrophosphokinase and 7,8-dihydropteroate synthetase from E. Coli. No significant antibacterial activity was observed.