Equisingular Deformations of Sandwiched Singularities

We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.     

Crystal structures of 4,7-phenanthrolino-5,6:5′,6′-pyrazine tetrahydrate and 1,4,5,8,9,12-hexaazatriphenylene dihydrate

The crystal structures of 4,7-phenanthrolino-5,6:5,6-pyrazine tetrahydrate (I) and 1,4,5,8,9,12-hexaazatriphenylene dihydrate (II) have been determined from low temperature (173 K) x-ray single crystal diffraction data. I crystallizes in the triclinic system, space group P with a = 11.2687(6), b = 12.4766(6), c = 12.7068(7) Å, = 113.4740(10), = 91.605(2), = 114.587(2)°, V = 1449.33(13) ų, and Z = 4. II crystallizes in the orthorhombic system, space group Pca2₁ with a = 18.187(2), b = 9.2576(11), c = 6.9672(8) Å, V = 1173.0(2) ų, and Z = 4. In both structures the planar heterocyclic molecules stack with interplanar distances down to 3.3 Å, which is consistent with self--complexation. The crystal water molecules provide links between the columns of stacked molecules through hydrogen bonds. In each compound the N-C bond lengths fall into two distinct groups (mean values 1.330(3) vs 1.361(1) Å in I and 1.320(3) vs 1.357(5) Å in II), as do the C-C bonds of the central phenyl rings (1.411(4) vs 1.467(1) Å in I and 1.405(5) vs 1.458(4) Å in II).     

Experimental study of the shock response of an HMX-based explosive

Experiments have been fired in which the HMX-based explosive EDC37 was subjected to one-dimensional shocks generated by plate impact. The response of the explosive to sustained shocks, double shocks and a short-pulse shock was monitored using embedded particle velocity gauges and shock tracker gauges. The final stages of the growth to detonation process were similar for all of the different input profiles. A strong reactive wave grows and accelerates to overtake and dominate the initial shock. It is shown that the curves showing the growth of the shock and the reactive wave in the sustained shock experiments can be normalised to give universal curves. These curves provides a reference against which to compare the explosive's response, not only to single sustained shocks, but also to double shock and short-pulse inputs. The treatment provides an empirical route for predicting the effects of sustained and more complex shocks on EDC37. PACS 47.40.-x; 82.33.Vx     

Studies on pectin coating of liposomes for drug delivery

The present study investigated the surface coating of charged liposomes by three different types of pectin (LM, HM and amidated pectin) by particle size determinations and zeta potential measurements. The pectins and the pectin coated liposomes were visualized by atomic force microscopy. The adsorption of pectin onto positive liposomes yielded a reproducible increase in particle size and a shift of the zeta potential from positive to negative side for all three pectin types, whereas the adsorption of pectin onto negative liposomes did not render any significant changes probably due to electrostatic repulsion. The positive liposomes coated with HM-pectin gave the largest pectin coated particles with the least negative zeta potential, while the opposite was observed for the LM-pectin coated positive liposomes. Furthermore, results from dynamic light scattering revealed narrow size distributions, indicating that the degree of aggregation was low for the pectin coated liposomes. As liposomes are able to encapsulate drugs and pectin has been found to be mucoadhesive, these pectin coated liposomes may be potential drug delivery systems.     

On the cotangent cohomology of rational surface singularities with almost reduced fundamental cycle

We prove dimension formulas for the cotangent spaces T ¹ and T ² for a class of rational surface singularities by calculating a correction term in the general dimension formulas. We get that it is zero if the dual graph of the rational surface singularity X does not contain a particular type of configurations, and this generalizes a result of Theo de Jong stating that the correction term c (X ) is zero for rational determinantal surface singularities. In particular our result implies that c (X ) is zero for Riemenschneiders quasi‐determinantal rational surface singularities, and this also generalizes results for quotient singularities. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mono-, di- and trinuclear 2,3,5,6-tetrakis(2-pyridyl)pyrazine (tppz)-containing copper(II) complexes: syntheses, crystal structures and magnetic properties

Three new copper(ii) complexes of formula [Cu(tppz)(NCO)(2)].0.4H(2)O (1), [Cu(2)(tppz)Br(4)](2) and [Cu(3)(tppz)(C(5)O(5))(3)(H(2)O)(3)].7H(2)O (3)[tppz = 2,3,5,6-tetrakis(2-pyridyl)pyrazine; C(5)O(5)(2-) = croconate, dianion of 4,5-dihydroxycyclopent-4-ene-1,2,3-trione] have been synthesised and structurally characterized by X-ray diffraction methods. The structure of complex is made up of neutral [Cu(tppz)(NCO)(2)] mononuclear units and uncoordinated water molecules. The mononuclear units are grouped by pairs to give a rather short copper-copper distance of 3.9244(4) angstroms. The structure of complex 1 consists of neutral tppz-bridged [Cu(2)(tppz)Br(4)] dinuclear units, the copper-copper separation across tppz being 6.6198(1) angstroms. The dinuclear units are further connected through weak, double out-of-plane Cu-Br...Cu bridges [Br(1)...Cu(1a) 4.0028(17) angstroms] creating tetranuclear entities, the copper-copper separation through this interaction being 4.3299(21) angstroms. The structure of complex 3 is built of neutral [Cu(3)(tppz)(C(5)O(5))(3)(H(2)O)(3)] trinuclear units and uncoordinated water molecules. Tppz and one of the croconate groups act as bridging ligands, the former exhibiting the bis-terdentate coordination mode and the latter adopting an unusual asymmetrical bis-bidentate bridging mode through three adjacent oxygen atoms. The other two croconate groups exhibit the bidentate coordination mode. The intramolecular copper-copper separations are 6.5417(9)(across tppz) and 4.3234(9) angstroms (through bis-bidentate croconato). The magnetic properties of 2 and 3 have been investigated in the temperature range 1.9-300 K. The magnetic behaviour of complex 2 is that of an antiferromagnetically coupled copper(II) dimer (J = -40.9 cm(-1), the Hamiltonian being H = -JS(A).S(B)). In the case of compound , the chi(M) T vs. T plot is typical of an overall antiferromagnetic coupling with a low-lying spin doublet being fully populated at T < 10 K. The values of the intramolecular antiferromagnetic interactions in 3 are -19.9 (across tppz) and -32.9 cm(-1)(through bridging croconato). Density functional type calculations were performed on model dinuclear fragments of 3 in order to analyze the efficiency of the exchange pathways involved and also to substantiate the coupling parameters.     

Preparation and structural studies on dibutyltin(IV) complexes with pyridine mono- and dicarboxylic acids

A number of organotin(IV) complexes with pyridine mono- and dicarboxylic acids (containing ligating -COOH group(s) and aromatic {N} atoms) were prepared in the solid state. The bonding sites of the ligands were determined by means of FT-IR spectroscopic measurements. It was found that in most cases the -COO⁻ groups form bridges between two central {Sn} atoms, thereby leading to polymeric (oligomeric) complexes. On this basis, the experimental ¹¹⁹Sn Mössbauer spectroscopic data were treated with partial quadrupole splitting approximations. The calculations predicted the existence of complexes with octahedral (oh) and trigonal-bipyramidal (tbp) structures, but the formation of complexes with pentagonal-bipyramidal (pbp) structures could not be ruled out. Single-crystals of 2-picolinic and pyridine-2,6-dicarboxylic acid Bu₂Sn(IV)²⁺ complexes were obtained. The X-ray diffraction studies revealed that the central {Sn} atoms are in a pbp environment with bond distances characteristic of organotin(IV) compounds. The two butyl groups are located in axial positions. ¹¹⁹Sn NMR measurements in dmso solution and in the solid state indicated that the polymeric structures of the complexes are not retained in solution. The results of the solid-state ¹¹⁹Sn NMR measurements for compounds 1a, 2a and 6a are in agreement with the structures predicted by Mössbauer spectroscopy and revealed by X-ray diffraction.     

Reflexive modules on normal surface singularities and representations of the local fundamental group

We consider the Riemann-Hilbert correspondence on the complement of a normal surface singularity (X,x). Through a closure operation we obtain a correspondence between the category of finite dimensional representations of the local fundamental group and the category of left D_X,x-modules that are reflexive as O_X,x-modules. We show that under this correspondence profinite representations correspond to invariant modules and that these admit a canonical structure as left D_X,x-modules. We prove that the fundamental module is an invariant module if and only if (X,x) is a quotient singularity. Finally we investigate some algebraisation aspects.     

Synthesis of uvaretin,an antitumour and antimicrobial flavonoid

The flavonoid uvaretin (1-(2,4-di-hydroxy-6-methoxy-3-((2-hydroxy phenyl)-methyl)-phenyl)-3-phenyl-1-propanone), known to be active against some tumours and several bacteria, has been synthesized in six steps from 2′,4′,6′-trimethoxyacetophenone, 2-hydroxybenzaldehyde and benzaldehyde.