On nonlinear gauge theories

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk–Mr?un and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.     

Hartogs Phenomena and Antisyzygies for Systems of Differential Equations

We introduce the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility conditions. The system obtained possesses the property of removability of compact singularities. We write explicit computations in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclude with a study of systems of non-maximal rank.      

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place in atomic systems like Bose-Einstein condensates in alkali gases with two-body and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in the absence of any quantum effect and can be formulated in the framework of a mean field theory, in terms of the minimization of a thermodynamic potential. We study from a thermodynamic point of view all the stationary solutions of the cubic-quintic nonlinear Schrödinger equation which describes our system. We show that solitonic localized solutions connect the gaseous and liquid phases. Furthermore, we also perform a numerical simulation in the presence of linear gain and three-body recombination where a rich dynamics, including the emergence of self-organization behavior, is found.     

A novel hydroxy functionalized polyester obtained by ring opening copolymerization of L‐lactide with a pyrolysis product of cellulose

A hydroxylactone ((1R,5S)‐1‐hydroxy‐3,6‐dioxabicyclo [3.2.1] octan‐2‐one, abbreviated as LAC) obtained from catalytic pyrolysis of cellulose was investigated as a monomer in the synthesis of polyesters by ring‐opening polymerization (ROP) with L ‐lactide. Although stannous octoate resulted inactive, ROP initiated by zirconium (IV) acetylacetonate afforded novel copolyesters from LAC and lactide mixtures in the bulk at 110 °C. Copolymers were obtained with different LAC content (from 19 to 45%) with a random microstructure as established by detailed NMR analysis. FTIR spectrometry confirmed the presence in the polymer chain of the OH groups originally present in LAC, which do not react during polymerization due to steric hindrance and inter/intramolecular hydrogen bonding. Reaction with trichloroacetylisocyanide proved that OH groups of the polyesters can be readily derivatized. The application of LAC as a comonomer enables the insertion of the alcohol functionality in polylactide avoiding protection/deprotection steps and potentially expanding the realm of biomaterials affordable from carbohydrate feedstock. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 247–257, 2009     

Enantiopure N-Boc piperidine-2-ethanol for the synthesis of (+)- and (−)-dumetorine,and (+)- and (−)-epidihydropinidine

The convenient synthesis of both enantiomers of the piperidine alkaloids such as dumetorine and epidihydropinidine is described. Pure enantiomers of 2-(2-hydroxy-ethyl)-piperidine-1-carboxylic acid tert-butyl ester are used as a common starting material. The syntheses are based on a RCM reaction and on methylation of the piperidine ring according to Beak–Lee methodology, respectively.     

A highly efficient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-DMT]

A new, practical and very convenient stereocontrolled synthesis of (S)-2′,6′-dimethyltyrosine [(S)-Dmt] 4 was accomplished in a good yield, starting from the chiral synthon 1,4-N,N-[(S)-phenylethyl]-piperazine-2,5-dione 1. The procedure, which is an extension of our original strategy and occurs with a high level of stereoselectivity (>98%), is simple and inexpensive allowing us to prepare the unnatural α-aminoacid (S)-Dmt also on a multi-gram scale.     

Alkylation of nucleic acids by the antitumor agent COMC

[reaction: see text]. Mass spectral data are presented indicating that the antitumor agent 2-crotonyloxymethyl-2-cyclohexenone (COMC) is capable of alkylating oligonucleotides via a mechanism involving an electrophilic exocyclic enone intermediate. Under physiological conditions, the exocyclic enone is likely the glutathionylated 2-exomethylenecyclohexenone. This supports a recent hypothesis that the antitumor activity of COMC arises from alkylation of nucleic acids and/or proteins critical to cell function and not from competitive inhibition of glyoxalase I by an adduct of COMC and glutathione.     

Nucleophilic addition of the thiocyanate ion to ferrocenyl-stabilised carbocations

The reaction of ferrocenylmethylcarbocations with the ambident thiocyanate ion produces only the isothiocyanate isomer.     

Probing fragment complementation by rigid-body docking: in silico reconstitution of calbindin D9k

Fragment complementation is gaining an increasing impact as a nonperturbing method to probe noncovalent interactions within protein supersecondary structures. In this study, the fast Fourier transform rigid-body docking algorithm ZDOCK has been employed for in silico reconstitution of the calcium binding protein calbindin D9k, from its two EF-hands subdomains, namely, EF1 (residues 1-43) and EF2 (residues 44-75). The EF1 fragment has been used both in its wild type and in nine mutant forms, in line with in vitro experiments. Consistent with in vitro data, ZDOCK reconstituted the proper fold of wild-type and mutated calbindin, locating the nativelike structures (i.e., holding a root-mean-square deviation < 1 A with respect to the X-ray structure) among the first 10 top-scored solutions out of 4000. Moreover, the three independent in silico reconstitutions of wild-type calbindin ranked a nativelike structure at the top of the output list, that is, the best scored one. The algorithm has been also successfully challenged in reconstituting the EF2 homodimer from two identical copies of the monomer. Furthermore, quantitative models consisting of linear correlations between thermodynamic data and ZDOCK scores were built, providing a tested tool for very fast in silico predictions of the free energy of association of protein-protein complexes solved at the atomic level and known to not undergo significant conformational changes upon binding.