The Hopf Property for Subgroups of Hyperbolic Groups

A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology 35 (2) 1999, 301–321).     

Painlevé analysis,conservation laws,and symmetry of perturbed nonlinear equations

We consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generator. When the perturbed KdV equation is subjected to Painlevé analysisa la Weiss, it is found that the resonance position changes compared to the unperturbed one. We prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter to be small. We determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation we determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painlevé analysis does not produce a positive answer for the perturbed NLS equation. So here we have two contrasting examples of perturbed nonlinear equations: one passes the Painlevé test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painlevé test, though its Lax pair is found in another way.     

Enantioselective, chirally templated sol-gel thin films

Enantioselective surfactant-templated thin films were fabricated through the sol-gel (SG) process. The enantioselectivity is general in the sense that it discriminates between pairs of enantiomers not used for the imprinting process. The chiral cationic surfactant (-)-N-dodecyl-N-methylephedrinium bromide (1) was used as the surfactant template, and after its extraction chiral domains were created. The chiral discriminative feature of these films was examined by challenging with pure enantiomer solutions for rebinding. Selective adsorption was shown using (R)- and (S)-propranolol, (R)-2 and (S)-2, respectively, and (R)- and (S)-2,2,2-trifluoro-1-(9-anthryl)ethanol, (R)-3 and (S)-3, respectively, as the chiral probes. The selective adsorption was measured by fluorescence analysis, and the chiral selectivity factors were found to be 1.6 for 2 and 2.25 for 3. In both cases, (R)-enantiomer was adsorbed preferably. The resulting material was characterized by transmission electron microscopy, by diffraction, and by surface area measurements, and was found to be semicrystalline with short-range ordered domains (50 A) of hexagonal symmetry.     

First example of the C-alkylation of indoles with Baylis-Hillman acetates

Baylis-Hillman acetates undergo S_N2′ allylic substitution with indoles in the presence of 20 mol % of indium tribromide under mild conditions to afford a new class of substituted indoles in high yields with (E)-stereoselectivity. The stereochemistry of the products was assigned by various NMR experiments.     

Raman spectroscopy of tris-(hydroxymethyl)aminomethane as a model system for the studies of α-chymotrypsin activation by crown ether in organic solvents

Raman spectroscopy is employed to study tris-(hydroxymethyl)aminomethane and its complexes with 18-crown-6. The results obtained are used to interpret the known effect of α-chymotrypsin activation by crown ether in organic solvents. Raman spectra of the samples lyophilized from aqueous solutions at various pH values are measured in solid state, acetonitrile and cyclohexane.     

Spray reagents for the detection of amino-acids on thin-layer plates

Three spray reagents for the detection of amino-acids on silica-gel thin-layer chromatography plates are reported. The reagents produce various colours, which may be used to identify some of the amino-acids directly, and assist in their detection.     

Ultrafast energy-electron transfer cascade in a multichromophoric light-harvesting molecular square

A molecular square with dimensions of about 4 nm, incorporating sixteen pyrene chromophores attached to four ditopic bay-functionalized perylene bisimide chromophores, has been synthesized by coordination to four Pt(II) phosphine corner units and fully characterized via NMR spectroscopy and ESI-FTICR mass spectrometry. Steady-state and time-resolved emission as well as femtosecond transient absorption studies reveal the presence of a highly efficient (>90%) and fast photoinduced energy transfer (k(en) approximately equal to 5.0 x 10(9) s(-1)) from the pyrene to the perylene bisimide chromophores and a very fast and efficient electron transfer (>94%, k(et) approximately equal to 5 x 10(11) up to 43 x 10(11) s(-1)). Spectrotemporal parametrization indicates upper excited-state electron-transfer processes, various energy and electron-transfer pathways, and chromophoric heterogeneity. Temperature-dependent time-resolved emission spectroscopy has shown that the acceptor emission lifetime increases with decreasing temperature from which an electron-transfer barrier is obtained. The extremely fast electron-transfer processes (substantially faster and more efficient than in the free ligand) that are normally only observed in solid materials, together with the closely packed structure of 20 chromophoric units, indicate that we can consider the molecular square as a monodisperse nanoaggregate: a molecularly defined ensemble of chromophores that partly behaves like a solid material.