Novel solvable many-body problems

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type (“acceleration equals forces”) which determine the motion of points in the complex plane. These models are solvable, namely their con?guration at any time can be obtained from the initial data by algebraic operations, amounting to the determination of the zeros of a known time-dependent polynomial in the independent variable z. Some of these models are multiply periodic, isochronous or asymptotically isochronous; others display scattering phenomena.     

Mechanistic studies of UV assisted [4 + 2] cycloadditions in synthetic efforts toward vibsanin E

Quantum chemical DFT calculations at the B3LYP/6-31G(d) level have been used to study the stereochemical course of the photochemical cycloaddition of enone 9 with dienes. The observed products of this photochemically induced cycloaddition showed a stereoselectivity, which is opposite to what would be expected by FMO considerations. The quantum chemical calculations revealed that the unusual stereoselectivity of the reaction can be rationalized by assuming a stereospecific photochemical cis-trans isomerization of enone 9 to trans isomer 9a followed by a thermal Diels-Alder reaction of the diene onto the highly reactive trans enone. The photochemical reaction step involves the selective formation of a twisted triplet intermediate, which accounts for the selectivity of the reaction.     

N,N-Dimethylethylenediamine in direct and direct template syntheses of Cu(II)/Cr(III) complexes

Four new heterometallic Cu(II)/Cr(III) complexes with N,N-dimethylethylenediamine (dmen) and its novel Schiff-base derivatives, N′-[(1Z)-3-amino-1,3-dimethylbutylidene]-N,N-dimethylethane-1,2-diamine (dmenac) and N′-((1Z)-3-{[2-(dimethylamino)ethyl]amino}-1,3-dimethylbutylidene)-N,N-dimethylethane-1,2-diamine (dmen₂ac), have been easily prepared by self-assembly and characterized by spectroscopic methods and single crystal X-ray analysis. The structures of all the complexes are assisted by numerous hydrogen bonds that provide a web of interactions and mould the supramolecular architectures of the compounds. Variable-temperature (1.8–300 K) magnetic susceptibility measurements reveal Curie-Weiss paramagnetic behavior of all the compounds, supported by EPR studies.     

The study of cyclooctene oxidation with molecular oxygen catalyzed by VSi2

The catalytic effect of VSi₂ on initial stages of the liquid-phase oxidation of cyclooctene by molecular oxygen was studied. The vanadium disilicide influences on the oxidation process in the presence of hydroperoxide. VSi₂ takes part in a radical formation stage by catalysis of hydroperoxide decomposition reaction. The catalyst was investigated before and after reaction using FTIR spectroscopy. From the data obtained, the kinetic model of the catalytic oxidation process was proposed and the equation for the reaction rate was derived. The equation has described all observed dependences of reaction rate on the concentration of reactants and content of catalyst.      

Determination of 1-hydroxypyrene in human urine by HPLC with electrochemical detection at a boron-doped diamond film electrode

A high-performance liquid chromatographic method with electrochemical detection (HPLC-ED) at a boron-doped diamond film electrode with preliminary separation and preconcentration by solid-phase extraction (SPE) has been developed for the determination of 1-hydroxypyrene (1-HP) in human urine. 1-HP is among the most widely used biomarkers of exposure to polycyclic aromatic hydrocarbons. Optimal HPLC-ED conditions have been found: mobile phase methanol-0.05 mol L(-1) phosphate buffer pH 5.0 (80:20, v/v), detection potential +1,000 mV versus Ag/AgCl (3 mol L(-1) KCl), and flow rate 0.8 mL min(-1). For SPE, LiChrolut(?) RP-18 E cartridges were used. The extraction yield was (87.0 ± 5.8)% (n = 5). The concentration dependence of 1-HP was measured in the concentration range from 0.01 to 10 μmol L(-1) (2.18-2,180 μg L(-1)) using methanolic solutions resulting from the SPE pretreatment of spiked human urine samples. The limit of detection (signal-to-noise ratio 3) and the limit of quantification (signal-to-noise ratio 10) of the biomarker were 0.013 μmol L(-1) (2.84 μg L(-1)) and 0.043 μmol L(-1) (9.39 μg L(-1)), respectively, which is sufficient for its determination in the urine of persons exposed to polycyclic aromatic hydrocarbons.     

Nilpotent Gelfand pairs and spherical transforms of Schwartz functions I: rank-one actions on the centre

The spectrum of a Gelfand pair of the form ${(K\ltimes N,K)}$ , where N is a nilpotent group, can be embedded in a Euclidean space ${{\mathbb R}^d}$ . The identification of the spherical transforms of K-invariant Schwartz functions on N with the restrictions to the spectrum of Schwartz functions on ${{\mathbb R}^d}$ has been proved already when N is a Heisenberg group and in the case where N?=?N _3,2 is the free two-step nilpotent Lie group with three generators, with K?=?SO₃ (Astengo et?al. in J Funct Anal 251:772–791, 2007; Astengo et?al. in J Funct Anal 256:1565–1587, 2009; Fischer and Ricci in Ann Inst Fourier Gren 59:2143–2168, 2009). We prove that the same identification holds for all pairs in which the K-orbits in the centre of N are spheres. In the appendix, we produce bases of K-invariant polynomials on the Lie algebra ${{\mathfrak n}}$ of N for all Gelfand pairs ${(K\ltimes N,K)}$ in Vinberg’s list (Vinberg in Trans Moscow Math Soc 64:47–80, 2003; Yakimova in Transform Groups 11:305–335, 2006).     

Monolayers of an amphiphilic para-carboxy-calix[4]arene act as templates for the crystallization of acetaminophen

The title compound, 5,11,17,23-tetra-carboxy-25,26,27,28-tetradodecyloxy-calix[4]arene, 1, has been studied at the air–water interface, self-assembled as Langmuir monolayers, for its ability to interact with an active pharmaceutical ingredient (API), acetaminophen (APAP), and to initiate its crystallization. The Π/A isotherm study shows that there is a clear interaction between 1 and APAP causing an expansion of the monolayer. In addition to the known phase transition occurring at a surface tension of 38 mN m^?1, an additional kink is observed in the compression isotherm for concentrations of APAP above 40 mM suggesting that this API is causing an additional phase transition of the monolayer. Interface-initiated crystallization studies show that the presence of a monolayer spread on a supersaturated solution of APAP (26 g L^?1) triggers this API crystal growth from the interface. The transfer of 1-based monolayers on glass surfaces has been carried out using the Langmuir–Blodgett technique. The so-produced monolayers have been shown to template the crystallization of APAP. LB films of 1 have characterized using imaging and spectroscopic ellipsometry. The results suggest that each monolayer has an average thickness of 18 Å, which is consistent with the molecular structure of 1 self-organized parallel to the interface with the alkyl chains pointing out parallel to the axis of the macrocycle and without interdigitation of the alkyl chains. The presence of APAP in the subphase during the LB transfer causes a limited but relevant increase in the layer thickness. The study of the capabilities of the LB films to initiate crystallization of APAP is also demonstrated showing the influence of the monolayer packing on the quantity of formed crystals.     

Photoelectron spectra and structures of three cyclic dipeptides: PhePhe, TyrPro, and HisGly

We have investigated the electronic structure of three cyclic dipeptides: cyclo(Histidyl-Glycyl) (cHisGly), cyclo(Tyrosyl-Prolyl) (cTyrPro), and cyclo(Phenylalanyl-Phenylalanyl) (cPhePhe) in the vapor phase, by means of photoemission spectroscopy and theoretical modeling. The last compound was evaporated from the solid linear dipeptide, but cyclised, losing water to form cPhePhe in the gas phase. The results are compared with our previous studies of three other cyclopeptides. Experimental valence and core level spectra have been interpreted in the light of calculations to identify the basic chemical properties associated with the central diketopiperazine ring, and with the additional functional groups. The valence spectra are generally characterized by a restricted set of outer valence orbitals separated by a gap from most other valence orbitals. The theoretically simulated core and valence spectra of all three cyclic dipeptides agree reasonably well with the experimental spectra. The central ring and the side chains act as independent chromophores whose spectra do not influence one another, except for prolyl dipeptides, where the pyrrole ring is fused with the central ring. In this case, significant changes in the valence and core level spectra were observed, and explained by stronger hybridization of the valence orbitals.     

Catalytic enantioselective synthesis of azacycloalkenes via intermolecular rhodium carbenoid C–H insertion/ring-closing metathesis sequence

Enantiomerically enriched cyclopropanes and products of C–H insertion reactions were obtained in excellent combined yields and enantioselectivities as a consequence of rhodium-catalyzed decomposition of vinyl diazoacetate in the presence of tert-butoxycarbonyl-(Boc)-protected amines as trapping agents. A series of enantiomerically enriched six- to eight-membered nitrogen-containing heterocycles were subsequently prepared via ring-closing metathesis of the dienes catalyzed by ruthenium benzylidene complex.     

Photoelectron spectra of some antibiotic building blocks: 2-azetidinone and thiazolidine-carboxylic Acid

X-ray photoelectron spectra of the core and valence levels of the fundamental building blocks of β-lactam antibiotics have been investigated and compared with theoretical calculations. The spectra of the compounds 2-azetidinone and the 2- and 4-isomers of thiazolidine-carboxylic acid are interpreted in the light of theoretical calculations. The spectra of the two isomers of thiazolidine-carboxylic acid are rather similar, as expected, but show clear effects due to isomerization. Both isomers are analogues of proline, which is well-known to populate several low energy conformers in the gas phase. We have investigated the low energy conformers of thiazolidine-4-carboxylic acid theoretically in more detail and find some spectroscopic evidence that multiple conformers may be present. The measured valence levels are assigned for all three compounds, and the character of the frontier orbitals is identified and analyzed.