Total choosability of multicircuits I

A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2‐regular graph). In this pair of papers, it is proved that every multicircuit C has total choosability (i.e., list total chromatic number) ch′′(C) equal to its ordinary total chromatic number χ′′(C). In the present paper, the kernel method is used to prove this for every multicircuit that has at least two vertices with degree less than its maximum degree Δ. The result is also proved for every multicircuit C for which χ′′(C)≥Δ+2. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 26–43, 2002     

Total choosability of multicircuits II

A multicircuit is a multigraph whose underlying simple graph is a circuit (a connected 2‐regular graph). In this paper, the method of Alon and Tarsi is used to prove that all multicircuits of even order, and some regular and near‐regular multicircuits of odd order have total choosability (i.e., list total chromatic number) equal to their ordinary total chromatic number. This completes the proof that every multicircuit has total choosability equal to its total chromatic number. In the process, the total chromatic numbers of all multicircuits are determined. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 44–67, 2002     

Double Ramification Cycles and Quantum Integrable Systems

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085–1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with the first descendant of the unit of the cohomological field theory only. We study various examples which provide, in very explicit form, new (1+1)-dimensional integrable quantum field theories whose classical limits are well-known integrable hierarchies such as KdV, Intermediate Long Wave, extended Toda, etc. Finally, we prove polynomiality in the ramification multiplicities of the integral of any tautological class over the double ramification cycle.     

The Development of the Theory of Strong Electrolyte Solutions

The expression for Gibbs energy of electrolyte solutions has been derived taking into account the contribution of interactions of the hydrated shells of ions. It is in good agreement with data for the dependence of the hydration number on concentration. The contribution of different interactions to the activity coefficient depending on concentration has been analyzed. The possibility of determining parameters which characterize the composition of hydrated shells of individual atoms from experimental data has been considered.     

Nanoaggregates of copper porphyrazine in floating layers and Langmuir-Schaefer films

Aggregation behavior of unsubstituted copper porphyrazine (CuPaz) on the water surface was studied by analysis of compression curves, Brewster angle microscopy (BAM), and optical spectroscopy. The structure and stability of the CuPaz aqua aggregates in the floating layers are determined by hydration degree that depends on initial surface concentration and surface pressure. Langmuir-Schaefer (LS) films of CuPaz were prepared by deposition of the variously structured floating layers and studied by X-ray scattering technique and optical spectroscopy. Stable and labile structures were detected and compared with the floating CuPaz aqua aggregates. Conditions of formation of the stable four-stacked nanoaggregates in LS films were determined. A model comprising both nucleation of CuPaz on the water surface and structural transformations in the solid films is proposed.     

Probing the flexibility of internal rotation in silylated phenols with the NMR scalar spin-spin coupling constants

The rotation of a trimethylsiloxy (TMSO) group in three silylated phenols (with three different ortho substituents -H, -CH3, and -C(CH3)3) was studied with the NMR (n)J(Si,C), n = 2, 3, 4, 5, scalar spin-spin coupling between the (29)Si nucleus of the TMSO group and the (13)C nuclei of the phenyl ring. The internal rotation potential calculated with the B3LYP and MP2 calculation methods including the effect of a solvent environment (gas phase, chloroform, and water) was used for the calculation of the dynamical averages of the scalar coupling constants in the framework of the rigid-bender formalism. Solvent effects, the quality of the rotational potential, and the applicability of the classical molecular dynamic to the problem is discussed. Quantum effects have a sizable impact on scalar couplings, particularly for the internal rotational states well localized within the wells of the potential surfaces for the TMSO group. The overall difference between the experimental and theoretical scalar couplings calculated for the global energy-minima structures (static model) decreases substantially for both model potentials (B3LYP, MP2) when the molecular motion of the TMSO group is taken into account. The calculated data indicate that the inclusion of molecular motion is necessary for the accurate calculation of the scalar coupling constants and their reliable structural interpretation for any system which possesses a large-amplitude motion.     

Palladium nanoparticles supported on an organic-inorganic fluorinated hybrid material. Application to microwave-based heck reaction

Phosphine-free palladium nanoparticles were embedded in a fluorous organic-inorganic hybrid material 6b prepared by the sol-gel process. The use of Pdn.6b in the Heck coupling reaction under microwave irradiation has been investigated. Recycling studies have shown that the catalyst can be readily recovered and reused several times without significant loss of activity. Reactions and recovery of the solid-supported palladium catalyst system can be carried out in the presence of air, without any particular precaution.     

Thiosugars--derivatization agents for chiral resolution of homoleucines

o-Phthaldialdehyde was used in combination with a series of six thiosugars for the pre-column chiral derivatization of selected primary amino acids. The diastereomers were resolved on a conventional reversed-phase column and with fluorescence detection. A surprisingly effective resolution of 1-isoindolyl-(1-thioglycosides) derived from 1-thio-beta-L-fucose was observed.     

Carboxylate–phenolate tautomerism in 5‐[(nitrophenyl)diazenyl]salicylate anions

Aryldiazenyl derivatives of salicylic acid and their salts are used as dyes. In these structures, the carboxylate groups are engaged in short contacts with the cations and in hydrogen bonds with water molecules, if present. If both O atoms of the carboxylate group take part in such interactions, the negative charge is delocalized over the two atoms. In the absence of hydrogen bonds and contacts with cations, the negative charge is localized on one of the O atoms. In the crystal structures of tetramethylammonium 2‐hydroxy‐5‐[(E)‐(4‐nitrophenyl)diazenyl]benzoate and tetramethylammonium 2‐hydroxy‐5‐[(E)‐(2‐nitrophenyl)diazenyl]benzoate, both C₄H₁₂N⁺·C₁₃H₈N₃O₅⁻, all the interactions between the cations and anions are weak, and their effect on the geometry of the anions is negligible. Under these conditions, the 2‐nitro‐substituted anion is an almost pure phenol–carboxylate tautomer, whereas in the 4‐nitro‐substituted anion, the phenolic H atom is shifted towards the carboxylate group, and thus the structure of this anion is intermediate between the phenol–carboxylate and phenolate–carboxylic acid tautomeric forms. The probable formation of such an intermediate form is supported by quantum chemical calculations. Being the characteristic feature of this form, a short distance between the phenolic and carboxylate O atoms is observed in the 4‐nitro‐substituted anion, as well as in the structures of some 3,5‐dinitrosalicylates reported in the literature.