Fermionic solution of the Andrews-Baxter-Forrester model. II. Proof of Melzer's polynomial identities

We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn.     

Structures of boron chelates of mono- and diacylketene aminals

The molecular and crystal structures of diphenylboron chelates of acetylketeneN-benzoylaminal and 2-(N-benzoyl)diaminomethylene-4-dimethylaminomethylenecyclohexane-1,3-dione and the structure of the difluoroboron complex of diacetylketeneN-benzoylaminal were established. It was found that the aminovinylcarbonyl fragment of the ligand is involved in the formation of a boron-containing ring. A delocalized -electron system over the NCCCO fragment of the chelate ring is characteristic of the molecules studied both in crystals and solutions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2541–2546, October, 1996.     

Structure–retardation factor relationship of natural amino acids in two different mobile phases of RP-TLC

Abstract

Separation of amino acids (AAs) and their simple and inexpensive determination/identification is an interesting topic in biological and protein science, different food industries, and drug factories. Also, the presentation of the chromatographic behavior of compounds in a predictive model can be effective to estimate the structural/chemical properties of analyte and mobile phases. In this work for the first time, retardation factor (R_F) of 42 AAs in reversed-phase thin layer chromatography (RP-TLC) was modeled. Acetonitrile-sodium azide solution and 1,2 dioxane-sodium azide solution were two mobile phases which have been studied in this work. Results showed that the values of R_F are correlated with the structural properties of AAs and these properties had some similarities and differences in two noted mobile phases. For the TLC data in two mobile phases, five parametric linear models were suggested (R²_train = 0.93 and 0.97; R²_test = 0.93 and 0.99). The models were also evaluated with different statistical approaches. It was shown that increasing the sum of geometrical distances between N and O in AAs causes decreasing their R_F in RP-TLC using both mobile phases. Other structural effects of AAs on their separation in the desired RP-TLC system were also discussed.     

Conductance of potassium halides near the temperature of maximum density of water

The conductances of dilute aqueous solutions of KCl, KBr, and KI have been measured over the temperature range 2 to 8°C and have been analyzed by the Fuoss-Hsia equation. The ionic Walden products at infinite dilution have been discussed in terms of local viscosity. The temperature dependence of these products suggest that near the temperature of maximum density of water, the structure-breaking ability of these ions changes in a regular way.     

4-Hydroxy-2-quinolones 113. Synthesis and antitubercular activity of N-R-amides of 4-hydroxy-6-methyl-2-oxo-1-propyl-1,2,5,6,7,8-hexahydroquinoline-3-carboxylic acid

A preparative method has been developed and the synthesis has been effected of anilides and heterylamides of 4-hydroxy-6-methyl-2-oxo-1-propyl-1,2,5,6,7,8-hexahydroquinoline-3-carboxylic acid. A comparative analysis has been carried out of the structure and antitubercular properties of the synthesized compounds and their analogs unsubstituted in the quinoline nucleus. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 405–414, March, 2007.     

Cyclocondensation of 2-Aminobenzimidazole with Dimedone and Its Arylidene Derivatives

The reactions of 2-aminobenzimidazole with substituted benzaldehydes and dimedone, 2-arylidene derivatives of dimedone, 9-arylhexahydro-1H-xanthene-1,8(2H)-diones and also with dimedone and DMF have been studied. The direction of formation of the pyrimidine ring has been established and discussed. An X-ray structural investigation of 2,2-dimethyl-2,3-dihydrobenzimidazo[1,2-a]quinazolin-4(1H)-one has been carried out.     

Relationship between the molecular structure of amino acids and dipeptides and thermal sublimation effects

This paper reports on our mass spectrometric study of sublimation of glycine and DL-alanyl-glycine (Ala-gly). The sublimation enthalpy of Ala-gly has been determined by generalization of the data obtained and the results of AM1 quantum-chemical calculations. A relationship has been found between the sublimation enthalpy (ΔH _subl), heat capacity (C _P), and the sum of bond lengths (Σn _i l _i ) in 17 α-amino acid and 9 dipeptide molecules. Correlations are suggested for evaluating ΔH _subl of amino acids and peptides.     

Transition metal 1,2-bidentate thiolates as building blocks and their construction into cluster complexes

Simple fragments of transition metal 1,2-bidentate thiolates, the so-called building blocks of the general compositions ML₃, ML₂, ML, M(O)L₂, ML₂L, MLL, etc. have been proposed to constitute the di-, tri- and tetranuclear complexes concerned in this review. Structureal regularities and characteristics have been discussed and summarized according to the thiolato ligands edt and pdt, bdt and tdt, mp, and mpo, and mpp, respectively.Abbreviations H₂mpo o-mercaptophenol - Hmpo 2-mercaptopyridine-N-oxide - R₂dtc N,N-dialkyldithiocarbamate - Haet 2-aminoethanethiol - H₂bdt o-benzenedithiol - H₂pdt 1,2-propanedithiol - H₂tdt toluene-3,4-dithiol - Hmpp-mppH bis-(3-hydroxy-2-pyridyl)disulfide - Hmp-mpH bis-(2-oxyphenyl)disulfide - H₂edt 1,2-ethanedithiol - dppe 1,2-bis(diphenylphosphino)ethane - H₂tedt 3,4,5,6-tetrachlorobenzene-1,2-dithiol - H₂tpdt 3-thiapentane-1,5-dithiol - H₂mnt maleonitriledithiol - Him imidazole - Bz benzyl - py pyridine     

4-Hydroxy-2-quinolones 131. Bromination of 3-allyl-4-hydroxy-2-oxo-1,2-dihydroquinoline

The bromination of 3-allyl-4-hydroxy-2-oxo-1,2-dihydroquinoline by molecular bromine is accompanied by the closure of a five membered furan ring and gives the corresponding 2-bromomethyl-3,9-dihydro-2H-furo[2,3-b]quinolin-4-one. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1677–1686, November, 2007.