Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p≥3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete.     

Automatic stopped-flow determination of l-cysteine

An automatic stopped-flow method is proposed for the routine determination of microgram amounts of l-cysteine, based on its oxidation by 2,6-dichlorophenolindophenol (DPIP) in a weakly basic medium. The oxidation reaction is monitored by measuring the rate of the absorbance decrease at 615 nm, the wavelength of the maximum absorption for DPIP. Under optimal conditions, the calibration graph is linear over the range 2-32 mug/ml and the detection limit is 300 ng/ml. Most of the amino-acids tested have no effect on the rate of the oxidation reaction and are tolerated at high concentration levels. The sample throughput achieved, 80 samples per hr, allows the proposed method to be used for the routine determination of l-cysteine.     

Black hole particle emission in higher-dimensional spacetimes

In models with extra dimensions, a black hole evaporates both in the bulk and on the visible brane, where standard model fields live. The exact emissivities of each particle species are needed to determine how the black hole decay proceeds. We compute and discuss the absorption cross sections, the relative emissivities, and the total power output of all known fields in the evaporation phase. Graviton emissivity is highly enhanced as the spacetime dimensionality increases. Therefore, a black hole loses a significant fraction of its mass in the bulk. This result has important consequences for the phenomenology of black holes in models with extra dimensions and black hole detection in particle colliders.     

Studies in sigmatropic rearrangements of N-prenylindole derivatives--a formal enantiomerically pure synthesis of tryprostatin B

Rearrangement of N(a)-prenyl-N(b)-acetyltryptamine, induced by BF3.Et2O at low temperature, leads to a 2-prenyl derivative, and thence to the tricyclic tryptamine 7 and the indoline 8. Similarly, N(a)-prenyl-N(b)-phthaloyl-l-tryptophan methyl ester furnished the corresponding 2-prenyl derivative 16, a known advanced precursor of tryprostatin B. Density functional (B3LYP) calculations for the putative rearrangement transition state for N-prenylskatole show that prior coordination of BF3 to the indolic nitrogen changes the character of the subsequent sigmatropic pericyclic shifts from being entirely covalent to acquiring a significant degree of ionic character. The shifting prenyl group favours the endo over the exo mode of the transition state by 4.1 kcal mol(-1).     

Methyl 3-methyl-2H-azirine-2-carboxylate photochemistry studied by matrix-isolation FTIR and DFT calculations

The aliphatic 2H-azirine, methyl 3-methyl-2H-azirine-2-carboxylate (MMAC), has been synthesized and its monomeric form investigated by IR spectroscopy in an argon matrix, at 10 K, as well as theoretically (DFT/B3LYP/6-311++G(d,p)). Two low-energy conformers of MMAC (Ct and Cc) were found in the matrix, both exhibiting the cis conformation around the C-O bond but differing in the arrangement around the C-C(alpha) bond. The two conformers were photoreactive upon in situ broadband UV excitation (lambda > 235 nm), yielding nitrile ylide (P1) and ketene imine (P2) type products, which resulted from cleavage of the C-C or C-N bond, respectively. The kinetics of the reactions leading to the formation of P1 and P2 are of first order, with the processes being favored when the reactant is in the Cc conformation. Very interestingly, the C-N bond photocleavage, which is unusual for aliphatic 2H-azirines, was found to be preferred over the generally favored in 2H-azirines C-C bond breakage. This behavior is attributed to the presence in the molecule of the electron-withdrawing methoxycarbonyl substituent, which accelerates the intersystem crossing toward the T(1) triplet state and, in this way, favors the C-N bond cleavage. In addition to the primary photoprocesses leading to formation of P1 and P2, secondary photoprocesses leading to the decarboxylation and decarbonylation of P2 have been also observed.     

Unusual photochemical C-N bond cleavage in the novel methyl 2-chloro-3-methyl-2H-azirine-2-carboxylate

The structure, preferred conformers, vibrational spectrum, and photochemical behavior of the novel azirine, methyl 2-chloro-3-methyl-2H-azirine-2-carboxylate (MCMAC) were investigated in low-temperature matrixes and in the neat solid amorphous state by infrared spectroscopy and quantum-chemical calculations. Two conformers of the compound were observed in argon, krypton, and xenon matrixes, in agreement with the DFT(B3LYP)/6-311++G(d,p) and MP2/6-311++G(d,p) theoretical calculations. Both conformers were found to exhibit the carboxylic ester group in the cis conformation, differing in the arrangement defined by the O=C-C-Cl dihedral angle (cis and trans, for Ct and Cc forms, respectively). The Ct conformer was found to be the most stable conformer in the gaseous phase as well as in both argon and krypton matrixes, whereas the more polar Cc conformer became the most stable form in the xenon matrix and in the neat solid amorphous phase. In situ broadband UV (lambda > 235 nm) excitation of matrix-isolated MCMAC led to azirine ring C-C and C-N bond cleavages, the latter process corresponding to the most efficient reaction channel. The photochemical cleavage of the C-N bond had never been previously observed in the case of aliphatic 2H-azirines. Two electron withdrawing substituents (methoxycarbonyl group and chlorine atom) are connected to the azirine ring in the novel MCMAC azirine. The simultaneous presence of these two groups accelerates intersystem crossing toward the triplet state where cleavage of the C-N bond takes place. The primary photoproducts resulting from the C-N and C-C ring-opening reactions were also found to undergo further photochemical decarbonylation or decarboxylation reactions.     

Biopolymer Synthesized by Strains of Xanthomonas sp Isolate from Brazil Using Biodiesel-Waste

The future supplies and usage of glycerol are expected to increase as biodiesel plants increase production, and the output will greatly outpace demand. Biodiesel production has already had a significant impact on the price of refined glycerol. A major concern of glycerol producers is the reduced price of glycerol resulting from the increased production of biodiesel. Some alternative uses for this glycerol that have been investigated are substrates for fermentation process or the production of biosurfactants, fatty acids, biopolymers, and others products. This work had as objective to evaluate two strains of Xanthomonas sp isolate from Brazil for xanthan gum in orbital agitator, analizing the apparent viscosity of aqueous solutions and selecting viscosity. The experiments of xanthan gum production were realized in orbital agitator with 120 rpm agitation, for cells production, and 180rpm, for biopolymer production, under a 28 °C temperature. The rheology of the fermentation broth was analyzed by apparent viscosity and the polymer was recovered with ethanol (1:3, v/v). After its recovery, the productivity evaluation was performed. The productivity were 0.157 and 0.363 gL⁻¹ for C1 and 0.186 and 0.363 gL⁻¹ for C9 to media glycerol or glycerol and sucrose, respectively. The viscosity analysis was performed for aqueous solutions 3%, at 25 °C, the best apparent viscosity was obtained using gum synthesized with glycerol and sucrose (50:50) at 25 °C, 143 mPa.s⁻¹ from Xanthomonas sp C1.     

Black hole bombs and explosions: from astrophysics to particle physics

Black holes are the elementary particles of gravity, the final state of sufficiently massive stars and of energetic collisions. With a 40-year long history, black hole physics is a fully-blossomed field which promises to embrace several branches of theoretical physics. Here I review the main developments in highly dynamical black holes with an emphasis on high energy black hole collisions and probes of particle physics via superradiance. This write-up, rather than being a collection of well known results, is intended to highlight open issues and the most intriguing results.