Geometry and Classificatin of Solutions of the Classical Dynamical Yang–Baxter Equation

The classical Yang–Baxter equation(CYBE) is an algebraic equation central in the theory of integrable systems. Its nondegenerate solutions were classified by Belavin and Drinfeld. Quantization of CYBE led to the theory of quantum groups. A geometric interpretation of CYBE was given by Drinfeld and gave rise to the theory of Poisson–Lie groups. The classical dynamical Yang–Baxter equation (CDYBE) is an important differential equation analogous to CYBE and introduced by Felder as the consistency condition for the differential Knizhnik–Zamolodchikov–Bernard equations for correlation functions in conformal field theory on tori. Quantization of CDYBE allowed Felder to introduce an interesting elliptic analog of quantum groups. It becomes clear that numerous important notions and results connected with CYBE have dynamical analogs. In this paper we classify solutions to CDYBE and give geometric interpretation to CDYBE. The classification and interpretation are remarkably analogous to the Belavin–Drinfeld picture. Received: 24 March 1997 / Accepted: 20 June 1997     

Using the coordinates of the mass centers of atomic groups in analyzing vibrations of large molecules

We show that in describing the vibrations of molecules it is worthwhile to use coordinates that include the mass centers of atomic groups. We note special features of the program implementation of the approach in application to the earlier devised set of “Spectrum-structure” and LEV programs. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 42–47, January–February, 2000.     

Infrared spectra of brassinolide and castasterone steroid phytohormones and their 24-epi derivatives

Absorption bands in IR spectra of brassinolide, castasterone, and their 24-epi derivatives in the frequency range 3800–1000 cm^–1 have been interpreted. A number of spectral features distinguishing brassinolide from castasterone have been found. The conducted analysis shows that the structural differences manifest themselves in IR spectra of the investigated brassinosteroids in the region of stretching vibrations of CO–H, C=O, C–OH, C–O–C, CH₃, CH₂, and CH groups. The main distinctions in IR spectra of brassinolides and castasterones are due to the B ring structure.     

Luminescence studies of porphyrin exchange in pregnant females

Results of investigations of the level of proto- and coporphyrins in erythrocytes and excretion of coproto- and uroporphyrins from the organism for two control groups are presented. The first group consisted of healthy males and females 20–33 years of age; the second group was consisted of females with nonpathological pregnancy. Levels of proto- and coporphyrins in erythrocytes and copro- and uroporphyrins in urine are investigated. A reliable (P<0.03) increase in the protoporphyrin concentration in erythrocytes of pregnant females compared to the first control group is found. The average protoporphyrin levels in the first and second groups are 344±18 and 488±20 μg/liter, respectively. Coporphyrin levels in these groups differ insignificantly. Coporphyrin excretion from the organism of pregnant females has shown a tendency to increase for pregnancy terms of up to eight weeks and decrease for long terms (more than 32 weeks). Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 5, pp. 633–636, September–October, 1997.     

New insights into nanocomposite adsorbents for water treatment: A case study of polystyrene-supported zirconium phosphate nanoparticles for lead removal

By encapsulating zirconium phosphate (ZrP) nanoparticles into three macroporous polystyrene resins with various surface groups, i.e., −CH₂Cl, −SO₃ ⁻, and −CH₂N⁺(CH₃)₃ three nanocomposite adsorbents (denoted as ZrP–Cl, ZrP–S, and ZrP–N) were fabricated, respectively for lead removal from water. Effect of the functional groups on nano-ZrP dispersion and effect of ZrP immobilization on the mechanical strength of the resulting nanocomposites were investigated. The presence of the charged functional groups (−SO₃ ⁻ and −CH₂N⁺(CH₃)₃) are more favorable than the neutral −CH₂Cl group to improve nano-ZrP dispersion (i.e., to achieve smaller ZrP nanoparticles). ZrP–N and ZrP–S had higher capacity than ZrP–Cl for lead removal. As compared to ZrP–N, ZrP–S exhibits higher preference toward lead ion at high calcium levels as a result of the potential Donnan membrane effect. On the other hand, nano-ZrP immobilization would simultaneously reinforce both the compressive strength and the wear performance of the resulting nanocomposites with the ZrP loadings up to 5 wt%. The results reported herein would shed some light on the generation of environmental nanocomposites with high capacity and excellent mechanical strength.     

Twisted Traces of Quantum Intertwiners¶and Quantum Dynamical R-Matrices¶Corresponding to Generalized Belavin–Drinfeld Triples

We consider weighted traces of products of intertwining operators for quantum groups U _q (?), suitably twisted by a “generalized Belavin–Drinfeld triple”. We derive two commuting sets of difference equations – the (twisted) Macdonald–Ruijsenaars system and the (twisted) quantum Knizhnik–Zamolodchikov–Bernard (qKZB) system. These systems involve the nonstandard quantum R-matrices defined in a previous joint work with T. Schedler ([ESS]). When the generalized Belavin–Drinfeld triple comes from an automorphism of the Lie algebra ?, we also derive two additional sets of difference equations, the dual Macdonald–Ruijsenaars system and the \textit{dual} qKZB equations. Received: 20 March 2000 / Accepted: 11 December 2000     

Absorption spectra of benzene-isooctane mixtures in the wavelength range 1620–1820 nm

Experimental absorption spectra of benzene, isooctane, and their mixtures are obtained in the wavelength range λ = 1620–1820 nm in which the first overtones of vibrational frequencies of CH, CH₂, and CH₃ hydrocarbon groups are located. Positions of fundamental absorption bands of benzene are refined. Absorption spectra of benzene-isooctane mixtures are shown to intersect in a narrow area near λ ≈ 1695 nm. The main maximum of benzene absorption at λ = 1671.5 ± 0.5 nm, where the influence of isooctane absorption is practically absent, is proposed for determining the content of benzene in benzene-isooctane mixtures. A linear calibration curve for λ = 1671.5 nm that encompasses the full range of benzene concentrations (0–100%) is presented. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 631–634, September–October, 2008.     

Hydroquinone–Benzonitrile System: Intramolecular Charge-Transfer and Computational Studies

A novel intramolecular donor–acceptor system of hydroquinone–benzonitrile was synthesized. Its photo-induced intramolecular charge-transfer (ICT) transition was confirmed by (1) shift of its emission maximum with increasing solvent polarity, (2) high dipole moment for the ICT excited state calculated from the Lippert equation, and (3) its HOMO and LUMO. According to the extent of separation between HOMO and LUMO, it is suggested that substituent position (ortho, meta, or para) in the donor–acceptor biphenyls is not a key point for the photo-induced intramolecular charge transfer and the donor with two alkoxy or hydroxy groups has more photo-induced charge transfer transitions than the one with one alkoxy or hydroxy group. In other words, the hydroquinone–benzonitrile system displays more photo-induced charge transfer transitions than 4COB (4-cyano-4′-butyloxybiphenyl).     

Electro- and Magneto-Optical Properties of Films of Polycomplexes of 4-Methacryloyloxy-(4′-Carboxy-3′-Oxy)Azobenzene with Metals

The electrical conductivity, photoconductivity, and electrical and magneto-optical properties of the films of new polycomplexes of 4-methacryloyloxy-(4′-carboxy-3′-oxy)-azobenzene with nickel and cobalt have been investigated. The electrical conductivity and photoconductivity in the visible region of light are determined by the orientation effects of azobenzene groups as well as by generation and transfer of charge carriers between them. A change in the spatial orientation of photoinduced dipole moments of azobenzene groups in an external electric or magnetic field is attributed to the appearance of forces acting on electrically charged magnetic ions of a metal and that are rigidly connected with these groups. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 4, pp 499–503, July–August, 2005.     

Is the hydration number of a non-electrolyte additive with length and constituents of the solute molecule?

Sound velocity and density were measured at 298.15 K in a number of very diluted aqueous solutions of simple non-electrolytes: alcohols, amines and acids. From these data the adiabatic compressibilities were calculated, and further the hydration numbers of solutes using the Passynski formula. It was found that all the homologous series under investigation exhibit linear concentration dependence of compressibility – and, consequently, that of the hydration numbers – up to concentrations of ca. 0.01 mole fraction or more. The slopes of these dependences are decreasing and n_h's are increasing with the molecular mass of the solute. This observation suggests that hydration numbers n_h are additive with the constituents of the molecule. Moreover, it would also imply the conclusion that local loss in compressibility of water solvent caused by hydration is very short in distance. To test the above assumption the hydration numbers were calculated using partial hydration numbers (i.e. those assigned to specific functional groups of the solute molecules), the latter are fitted parameters. The obtained values of partial n_h's are ca. 0.5 for –OH group, ca. 1.15 for –COOH and –NH₂ and from 0.5 to ca. 1.3 for hydrocarbon elements of the hydrophobic chain (–CH₂– and –CH₃ groups). The obtained total n_h's are surprisingly close to the experimentally obtained hydration numbers. There are, however, systems where differences between calculated and experimental n_h's are exceeding the experimental uncertainty; they are amino acids and diols, particularly α, ω-diols. The reasons are, most possibly, interaction of the hydration shells of the hydroxyl groups in the latter case and formation of two charged sites in the zwitterionic form of the former ones.     

Infrared spectra of S-and R-isomers of biologically active brassinosteroids

Comparative analysis of IR spectra of S-and R-isomers differing in the configuration of OH groups in the side chain of biologically active 24-epi-and 28-homocastasterones and 24-epi-and 28-homobrassinolides is carried out. Stretching vibration frequencies of H-bonded OH groups of isomers of corresponding brassinosteroids practically coincide. The optical density in maxima of these bands is higher in spectra of the R-isomers. Alteration in the configuration of the OH groups weakly influences also the band intensities of CH3, CH₂, and CH groups. Band intensities of stretching vibrations of associated C=O groups of S-and R-isomers also neglibibly differ from each other. Their frequency characteristics do not experience substantial changes. These features differ considerably in IR spectra of castasterones and brassinolides. For castasterones, the difference in frequencies of band maxima of free and bound C=O groups amounts to ∼15 cm⁻¹; for brassinolides, 23 cm⁻¹. Intensities of both bands are approximately equal in spectra of castasterones. The band intensity of free C=O groups of brassinolides is considerably lower than that of H-bonded ones. The above spectral differences can be used to identify these brassinosteroids. Frequencies of both symmetric and antisymmetric deformation vibrations of CH₃ and CH₂ groups are close in spectra of all brassinosteroids studied. The frequency of CH₂ in a CH₂-OC group belongs only to brassinolides; of deformation vibrations of CH in a CH-C=O group, to castasterones. The frequency of stretching vibrations of C-O-C and C-O groups is observed only in spectra of brassinolides. In the region 1130–900 cm⁻¹ of IR spectra of brassinosteroids, stretching vibrations of CC, CCH, and C-OH groups are predominantly observed. In the frequency range 1130–995 cm⁻¹, the optical density of band maxima of S-isomers is higher than that of R-isomers, which can be used to identify isomers. At the same time frequencies of corresponding bands of isomers practically coincide. Differences in the structure of the side chain of brassinosteroids do not influence essentially the frequency characteristics of the IR spectra. The exception is the band related to stretching vibrations ν(C23-OH) of the side chain which features a considerable frequency ν_max ≈ 983 cm⁻¹ only in spectra of R-isomers of homocastasterone and brassinolide. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 623–630, September–October, 2008.     

Deformation Quantization and the Baum–Connes Conjecture

 Alternative titles of this paper would have been ``Index theory without index' or ``The Baum–Connes conjecture without Baum.' In 1989, Rieffel introduced an analytic version of deformation quantization based on the use of continuous fields of C ^* -algebras. We review how a wide variety of examples of such quantizations can be understood on the basis of a single lemma involving amenable groupoids. These include Weyl–Moyal quantization on manifolds, C ^* -algebras of Lie groups and Lie groupoids, and the E-theoretic version of the Baum–Connes conjecture for smooth groupoids as described by Connes in his book Noncommutative Geometry. Concerning the latter, we use a different semidirect product construction from Connes. This enables one to formulate the Baum–Connes conjecture in terms of twisted Weyl–Moyal quantization. The underlying mechanical system is a noncommutative desingularization of a stratified Poisson space, and the Baum–Connes Conjecture actually suggests a strategy for quantizing such singular spaces. Received: 30 April 2002 / Accepted: 2 October 2002 Published online: 17 April 2003 RID="⋆" ID="⋆" Supported by a Fellowship from the Royal Netherlands Academy of Arts and Sciences (KNAW). Communicated by H. Araki, D. Buchholz and K. Fredenhagen     

Controlled surface functionalization of silica-coated magnetic nanoparticles with terminal amino and carboxyl groups

General and versatile methods for the functionalization of superparamagnetic, silica-coated, maghemite nanoparticles by surface amino and/or carboxyl groups have been established. The nanoparticles were synthesized using co-precipitation from aqueous solutions and coated with a thin layer of silica using the hydrolysis and condensation of tetraethoxysilane (TEOS). For the amino functionalization, 3-(2-aminoethylamino)propylmethyldimethoxysilane (APMS) was grafted onto the nanoparticle surfaces in their aqueous suspensions. The grafting process was followed by measurements of the ζ-potential and a determination of the concentration of the surface amino groups with conductometric titrations. The surface concentration of the amino groups could be varied by increasing the amount of APMS in the grafting process up to approximately 2.3 –NH₂ groups per nm². The carboxyl functionalization was obtained in two ways: (i) by a ring-opening linker elongation reaction of the surface amines at the functionalized nanoparticles with succinic anhydride (SA) in non-aqueous medium, and (ii) by reacting the APMS and SA first, followed by grafting of the carboxyl-terminated reagent onto the nanoparticle surfaces. Using the first method, the SA only reacted with the terminal primary amino groups (–NH₂) of the surface-grafted APMS molecules. Infra-red spectroscopy (ATR FTIR) and mass spectrometry (HRMS) showed that the second method enables the bonding of up to two SA molecules per one APMS molecule, since the SA reacted with both the primary (–NH₂) and secondary amino (–NH–) groups of the APMS molecule. When using both methods, the ratio between the surface amino and carboxyl groups can be controlled.     

Lie algebras of nonstandard relativity groups

It is shown that representations of Lie algebras of the possible nonstandard spacetime symmetry groups may be derived from the representations of the Poincaré group. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

IR spectra of stigmastane series brassinosteroids differing in configuration and number of diol groups

IR spectra of steroid phytohormones of the stigmastane series (22R, 23R)-28-homocastasterone and (22R,23R)-28-homosecasterol and their isomers (22S,23S)-28-homocastasterone and (22S,23S)-28-homosecasterol have been analyzed. The 28-homocastasterone molecule contains diol groups in ring A and in the side chain whereas that of 28-homosecasterol has one diol group in the side chain. The lack of two OH groups in ring A of homosecasterol compared to homocastasterone results in the appearance of stretching vibrational bands of H–C= (ν_max = 3025 cm^–1) and –C=C (ν_max = 1656 cm^–1) groups of ring A. Substantial changes are observed in the area of OH stretching vibrations. Homocastasterones pressed in KBr possess twice as many OH groups as homosecasterols such that absorption band total intensities in IR spectra of both isomers caused by H-bonds of the diol groups in the side chain amount to 65% whereas the share of the 2α,3α group is only 35% of the total intensity. Hence the contribution from the side-chain OH groups of the studied brassinosteroids to the integral optical density of the bands exceeds that from the ring-A OH groups. In dilute CHCl3 solutions of the brassinosteroids, the conformations of the brassinosteroid side chains are not the same. As a result, intramolecular H-bonds of different energy are created. The optical density D_max in band maxima of free OH groups for homocastasterones is three times higher than that for the corresponding band maxima of homosecasterol. This implies that D_max for bands of free OH groups of the homocastasterone ring-A diol group is greater, in contrast with the relatively greater D_max for bands of homosecasterol side-chain OH groups bound by an intermolecular H-bond. The homocastasterone diol groups also form intramolecular Hbonds more actively. The lack of the diol group in ring A of the homosecasterols does not affect the frequencies of the C=O stretching vibrations. This leads to the conclusion that the C=O group forms intermolecular H-bonds only with the side-chain OH groups of brassinosteroids pressed in KBr.     

Vibrational spectra of the products of interaction of enzymes with a monocarboxylcellulose matrix

By the method of IR spectroscopy it is established that the process of sorption of celiase, trypsin, chymotrypsin, streptase, plasminogen, and plasmin by monocarboxylcellulose (the content of COOH groups is 15 wt.%) is mainly identical. The determining role in the mechanism of binding of monocarboxylcellulose with the considered medicinal enzymes belongs to electrostatic interactions with the formation of ionic bonds between the COO⁻ groups of the matrix and charged amine groups of protein molecules. It is established that the process of interaction of plasmin with oxidized cellulose takes a more active course than with other investigated enzymes. It is shown that the activity of interaction of the enzymes with monocarboxylcellulose can be evaluated by a change in the relative intensity of the band of stretching vibrations of C=O groups. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 6, pp. 771–774, November–December, 1999.     

Non-Douglas–Kazakov phase transition of two-dimensional generalized Yang–Mills theories

In two-dimensional Yang–Mills and generalized Yang–Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density, the value of which should everywhere be between zero and one. This density itself is determined by means of a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas–Kazakov phase transition. In generalized Yang–Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas–Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with the order of the phase transition not equal to three. A class of these non-typical models is also studied.     

Intramolecular and intermolecular hydrogen bonds in aminophenols

IR-Fourier spectroscopy methods are adopted to study intramolecular and intermolecular hydrogen bonds that form in CCl₄ solutions of aminophenol derivatives and in a solid phase of these compounds pressed in KBr. If a hydroxyl group is present in the molecule in the ortho-position to an amino group, then intramolecular interactions between OH and NH groups will take place in aminophenol solutions. Intramolecular O–H⋅⋅⋅O=S=O and N–H⋅⋅⋅O=S=O hydrogen bonds are found in solutions of compounds containing a sulfonamide fragment. Additional acylation of the amino group causes an intramolecular O–H⋅⋅⋅O=C hydrogen bond to form in solutions. Functional groups OH, NH, SO₂, and C=O interact with one another in various ways in the solid phase to form intermolecular hydrogen bonds in aminophenols.     

Calculation and interpretation of the ir spectra of a number of N-acetylpyridinium salts

Based on calculation of frequencies and modes of normal vibrations of salts of N-acyl-4-dimethylaminopyridinium with N-acyl groups of different structures (acetyl, methoxycarbonyl, dimethylcarbamoyl), an interpretation is given of the IR spectra of the corresponding N-acyloinic cations. It is shown that the differences recorded in the experimental spectra of the salts are due to interaction between skeletal deformational vibrations of the aromatic ring and the deformational vibrations of acyl groups and to the manifestation of the characteristic vibrations of proper acyl groups. The stretching and deformational vibrations of the 4-dimethylamino group are insensitive to the nature of the acyl fragment. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 1, pp. 26–28, January–February, 2000.     

Random Unitary Matrices, Permutations and Painlevé

This paper is concerned with certain connections between the ensemble of n×n unitary matrices – specifically the characteristic function of the random variable tr(U) – and combinatorics – specifically Ulam's problem concerning the distribution of the length of the longest increasing subsequence in permutation groups – and the appearance of Painlevé functions in the answers to apparently unrelated questions. Among the results is a representation in terms of a Painlevé V function for the characteristic function of tr(U) and (using recent results of Baik, Deift and Johansson) an expression in terms of a Painlevé II function for the limiting distribution of the length of the longest increasing subsequence in the hyperoctahedral groups. Received: 2 December 1998 / Accepted: 12 May 1999