Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

XRR and GISAXS study of silicon oxynitride films

Thin films of silicon oxynitride have largely replaced pure silicon oxide films as gate and tunnel oxide films in modern technology due to their superior properties in terms of efficiency as boron barrier, resistance to electrical stress and high dielectric strength. A single chamber system for plasma enhanced chemical vapor deposition was employed to deposit different films of SiO_xN_yH_z with 0.85 < x < 1.91. All films were previously characterized by Rutherford back-scattering and infrared spectroscopy to determine the stoichiometry and the presence of various bonding configurations of constituent atoms. We used X-ray reflectivity to determine the electron density profile across the depth, and we showed that the top layer is densified. Moreover, grazing incidence small-angle X-ray scattering was used to study inhomogeneities (clustering) in the films, and it is shown that plate-like inhomogeneities exist in the top and sphere-like particles at the bottom part of the film. Their shape and size depend on the stoichiometry of the films.     

Investigation of the lability of furan and its derivatives in nucleophilic substitution reactions by the mindo/3 method

The a complexes of furan, thiophene, pyrrole, pyridine, and benzene with the hydride ion were calculated by the MINDO/3 method. The affinities of the indicated aromatic rings and a number of substituted furans for the H^– ion were estimated. It is shown that the relative magnitude of the affinity correlates qualitatively with the experimental data on the relative rates of the reaction of the examined compounds with nucleophilic reagents. The following order of increasing reactivities of unsubstituted aromatic rings was obtained: pyrrole相似文献   

Gas-phase structure of protonated histidine and histidine methyl ester: combined experimental mass spectrometry and theoretical ab initio study

Gas-phase H/D exchange experiments with CD3OD and D2O and quantum chemical ab initio G3(MP2) calculations were carried out on protonated histidine and protonated histidine methyl ester in order to elucidate their bonding and structure. The H/D exchange experiments show that both ions have three equivalent fast hydrogens and one appreciably slower exchangeable hydrogen assigned to the protonated amino group participating in a strong intramolecular hydrogen bond (IHB) with the nearest N(sp2) nitrogen of the imidazole fragment and to the distal ring NH-group, respectively. It is taken for granted that the proton exchange in the IHB is much faster than the H/D exchange. Unlike in other protonated amino acids (glycine, proline, phenylalanine, tyrosine, and tryptophan) studied earlier, the exchange rate of the carboxyl group in protonated histidine is slower than that of the amino group. The most stable conformers and the enthalpies of neutral and protonated histidine and its methyl ester are calculated at the G3(MP2) level of theory. It is shown that strong intramolecular hydrogen bonding between the amino group and the imidazole ring nitrogen sites is responsible for the stability and specific properties of the protonated histidine. It is found that the proton fluctuates between the amino and imidazole groups in the protonated form across an almost vanishing barrier. Proton affinity (PA) of histidine calculated by the G3(MP2) method is 233.2 and 232.4 kcal mol(-1) for protonation at the imidazole ring and at the amino group nitrogens, respectively, which is about 3-5 kcal mol(-1) lower than the reported experimental value.     

1,8-bis(dimethylethyleneguanidino)naphthalene: tailoring the basicity of bisguanidine "proton sponges" by experiment and theory

1,8-bis(dimethylethyleneguanidino)naphthalene (DMEGN), the second example of a peralkyl guanidine "proton sponge" based on the 1,8-naphthalene backbone, was prepared and fully characterized. The crystal structure analysis of monoprotonated DMEGN reveals an unsymmetrical intramolecular hydrogen bridge. A decrease in the basicity with respect to the noncyclic parent 1,8-bis(tetramethylguanidino)naphthalene was found. Nevertheless, a new proton sponge provides a new crossbar in the ladder of highly basic neutral organic compounds. A detailed theoretical study of DMEGN and related cyclic guanidines explains this surprising experimental result. Homodesmotic reactions reveal that the intramolecular hydrogen bond contributes effectively 10 kcal/mol to proton affinity of DMEGN.     

Isothermal Degradation of PVC/MBS Blends

The process of thermal degradation of poly(vinyl chloride)/poly(methyl methacrylate-butadiene-styrene) (PVC/MBS) blends was investigated by means of isothermal thermogravimetry in nitrogen. The total mass loss was determined after 120 min. The kinetic parameters of the degradation process were determined by applying two kinetic models: the model which assumes autocatalytic degradation (Prout-Tompkins) and the model of two-dimensional diffusion. It was established that the thermal degradation at lower degrees of conversion (α<0.20) was well described by the former model, but the latter model was applicable at higher degrees of conversion. The thermal stability of blends at a certain temperature of isothermal degradation depends on the blend composition and the shell/core ratio in MBS, and on the adhesion in the boundary layer in PVC/MBS blends. This revised version was published online in July 2006 with corrections to the Cover Date.     

Entirely circular quartics in the pseudo-Euclidean plane

A curve in the pseudo-Euclidean plane is circular if it passes through at least one of the absolute points. If it does not share any point with the absolute line except the absolute points, it is said to be entirely circular.     

Acid-Catalyzed RNA-Oligomerization from 3’,5’-cGMP

The assembly of ancient informational polymers from nucleotide precursors is the central challenge of life's origin on our planet. Among the possible solutions, dry polymerization of 3’,5’-cyclic guanosine monophosphate (3’,5’-cGMP) has been proposed as a candidate to create oligonucleotides of 15–20 units in length. However, the reported sensitivity of the reaction to the presence of cations raised questions of whether this chemistry could be relevant in a geological context. The experiments in this study show that the presence of cations is not restrictive as long as the reaction is conducted in an acidic environment, in contrast to previous reports that suggested optimal conditions at pH 9.     

Approximation of Functions by the Szász-Mirakjan-Kantorovich Operator

We characterize the approximation of functions in the L_p-norm by the Szász-Mirakjan-Kantorovich operator. We prove a direct and a strong converse inequality of type B in terms of an appropriate K-functional.