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.     

A BEM for transient thermoelastic analysis of a functionally graded layer on a homogeneous substrate under thermal shock

Transient thermoelastic analysis of isotropic and linear thermoelastic bimaterials, which are constituted by a functionally graded (FG) layer attached to a homogeneous substrate, subjected to thermal shock is presented in this paper. For this purpose, a boundary element method for transient linear coupled thermoelasticity is developed. The material properties of the FG layer are assumed to be continuous functions of the spatial coordinates. The boundary-domain integral equations are derived by using the fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear thermoelastic solids in the Laplace-transformed domain. For the numerical solution, a collocation method with piecewise quadratic approximation is implemented. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gastroprotective Effects of Polyphenols against Various Gastro-Intestinal Disorders: A Mini-Review with Special Focus on Clinical Evidence

Polyphenols are classified as an organic chemical with phenolic units that display an array of biological functions. However, polyphenols have very low bioavailability and stability, which make polyphenols a less bioactive compound. Many researchers have indicated that several factors might affect the efficiency and the metabolism (biotransformation) of various polyphenols, which include the gut microbiota, structure, and physical properties as well as its interactions with other dietary nutrients (macromolecules). Hence, this mini-review covers the two-way interaction between polyphenols and gut microbiota (interplay) and how polyphenols are metabolized (biotransformation) to produce various polyphenolic metabolites. Moreover, the protective effects of numerous polyphenols and their metabolites against various gastrointestinal disorders/diseases including gastritis, gastric cancer, colorectal cancer, inflammatory bowel disease (IBD) like ulcerative colitis (UC), Crohn’s disease (CD), and irritable bowel syndrome (IBS) like celiac disease (CED) are discussed. For this review, the authors chose only a few popular polyphenols (green tea polyphenol, curcumin, resveratrol, quercetin), and a discussion of their proposed mechanism underpinning the gastroprotection was elaborated with a special focus on clinical evidence. Overall, this contribution would help the general population and science community to identify a potent polyphenol with strong antioxidant, anti-inflammatory, anti-cancer, prebiotic, and immunomodulatory properties to combat various gut-related diseases or disorders (complementary therapy) along with modified lifestyle pattern and standard gastroprotective drugs. However, the data from clinical trials are much limited and hence many large-scale clinical trials should be performed (with different form/metabolites and dose) to confirm the gastroprotective activity of the above-mentioned polyphenols and their metabolites before recommendation.     

Misfit-Dislocation Induced Surface Morphology of InGaAs/GaAs Heterostructures

The correlation between the surface cross-hatched morphology and the interfacial misfit dislocations in partially relaxed InGaAs/GaAs heterostructures was studied by means of atomic force microscopy and electron-beam induced current mode in a scanning electron microscope. A close correspondence between the misfit-dislocation network at the interface and the surface morphology shows that the cross-hatch development results primarily from the misfit-dislocation generation. Statistical analysis of the surface roughness reveals an anisotropy in strain relaxation of the epitaxial layers, which results from an asymmetry in the misfit-dislocation formation.     

Structure and physical properties of rare-earth zinc antimonides REZn1-xSb2 (RE=La, Ce, Pr, Nd, Sm, Gd, Tb)

The ternary rare-earth zinc antimonides REZn_1-xSb₂ (RE=La, Ce, Pr, Nd, Sm, Gd, Tb) were prepared by heating at 1050 °C followed by annealing at 600 °C. For all members, single-crystal X-ray diffraction studies indicated that the Zn deficiency is essentially fixed, corresponding to the formula REZn_0.6Sb₂, with no appreciable homogeneity range. These compounds adopt the HfCuSi₂-type structure (Pearson symbol tP8, space group P4/nmm, Z=2). Single-crystal electrical resistivity measurements confirmed the occurrence of an abrupt resistivity decrease near 4 K for RE=Ce, and a less pronounced one for RE=La, Pr, and Gd. Except for the ferromagnetic Ce (T_c=2.5 K) and antiferromagnetic Tb (T_N=10 K) members, all remaining compounds exhibit no long-range magnetic ordering down to 2 K, instead showing temperature-independent (RE=La), van Vleck (RE=Sm), or Curie-Weiss paramagnetism (RE=Pr, Nd, Gd).