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.     

On the sigma-model of deformed special geometry

We discuss the deformed sigma-model that arises when considering four-dimensional N=2$N=2$ abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry by non-holomorphic terms. We analyze the geometry of the sigma-model in terms of intrinsic torsion classes. We show that, generically, the deformed geometry is non-Kähler. We illustrate our findings with an example. We also express the deformed sigma-model in terms of the Hesse potential that underlies the real formulation of special geometry.     

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.     

Matchings in graphs of odd regularity and girth

We establish lower bounds on the matching number of graphs of given odd regularity d$d$ and odd girth g$g$, which are sharp for many values of d$d$ and g$g$. For d=g=5$d=g=5$, we characterize all extremal graphs.     

Computing the noncentral gamma distribution, its inverse and the noncentrality parameter

The noncentral gamma distribution can be viewed as a generalization of the noncentral chi-squared distribution and it can be expressed as a mixture of a Poisson density function with a incomplete gamma function. The noncentral gamma distribution is not available in free conventional statistical programs. This paper aimed to propose an algorithm for the noncentral gamma by combining the method originally proposed by Benton and Krishnamoorthy (Comput Stat Data Anal 43(2):249–267, 2003) for the noncentral distributions with the method of inversion of the distribution function with respect to the noncentrality parameter using Newton–Raphson. The algorithms are available in pseudocode and implemented as R functions. To evaluate the accuracy and speed of computation of the algorithms implemented in R, results of the distribution function, density function, quantiles and noncentrality parameter of the noncentral incomplete gamma and its particular case, the noncentral chi-squared, were obtained for the arguments settings used by Benton and Krishnamoorthy (Comput Stat Data Anal 43(2):249–267, 2003) and Chen (J Stat Comput Simul 75(10):813–829, 2005). The implemented routines performed well and, in general, were as accurate than other approximations. The R package denoted ncg is available to download on the CRAN-R package repository http://cran.r-project.org/.