On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities

An immediate generalization of the classical McKay correspondence for Gorenstein quotient spaces ? ^r /G in dimensions r ≥ 4 would primarily demand the existence of projective, crepant, full desingularizations. Since this is not always possible, it is natural to ask about special classes of such quotient spaces which would satisfy the above property. In this paper we give explicit necessary and sufficient conditions under which 2-parameter series of Gorenstein cyclic quotient singularities have torus-equivariant resolutions of this specific sort in all dimensions.     

On the global distance between two algebraic points on a curve

We prove diophantine inequalities involving various distances between two distinct algebraic points of an algebraic curve. These estimates may be viewed as extensions of classical Liouville's inequality. Our approach is based on a transcendental construction using algebraic functions. Next we apply our results to Hilbert's irreducibility Theorem and to some classes of diophantine equations in the circle of Runge's method.     

Brownian dynamics simulations of shear-thickening in dilute polymer solutions

A versatile model describing the shear thickening behaviour of dilute polymer solutions in high shear flows is presented. The polymer macromolecules are modelled as Hookean elastic dumbbells which deform affinely during flow. In addition, the dumbbells feel a retractive anisotropic hydrodynamic drag and an isotropic Brownian force. Furthermore, it is assumed that high shear rate increases the probability of molecules forming associations and this is described through expressions for the frequencies of association and dissociation, without explicitly accounting for finite extensibility, hydrodynamic interaction or excluded volume effects. Thus, a reversible kinetic process is incorporated into the model, which results in two diffusion equations for the associated and dissociated dumbbells. Numerical simulations predict shear thickening for specific range of parameters, which are physically meaningful and related to molecular characteristics of the polymer. A comparison against experimental data reported in the literature revealed very promising results, thus confirming the ability of this model to predict shear thickening under a wide range of conditions, for various polymer models.Nomenclature A A factor in the frequency of association - B Frequency of dissociation - B ₀ Reference frequency of dissociation - c Concentration of polymer solution - c _i Concentration of singlets (i = 1) and doublets (i = 2) in the solution - c ^* The overlap concentration - D _t Translation coefficient of molecule - F _i (Q) Spring force for a singlet (i = 1) and for a doublet (i = 2) - F Frequency of association - F ₀ Reference frequency of association - H _i Dumbbell spring constant for a singlet (i = 1) and for a doublet (i = 2) - k Boltzman's constant - k _H Huggins constant - MW Molecular weight - MW _c Critical molecular weight for formation of entanglements - n Number density of molecules in the polymer solution - n ₀ Number density of dumbbells at equilibrium - n _i Number density of singlets (i = 1) and doublets (i = 2) - Q Vector defining the size and orientation of a dumbbell - t Time - T Absolute temperature - x Degree of multimerization - W Interaction energy between the two components of a doublet Greek letters a Dimensionless anisotropy parameter - Shear rate - _i Friction coefficient of singlets (i = 1) and doublets (i = 2) - _i Intrinsic viscosity of singlets (i = 1) and doublets (i = 2) - _red Reduced viscosity of solution - _sp Specific viscosity - Viscosity of the polymer solution of concentration c - _s Viscosity of the solvent - (t) White noise - K ^T Velocity gradient tensor - _Hi Time constant of a singlet (i = 1) and a doublet (i = 2) - ₁ Length scale of singlets (standard deviation of singlet lengths at equilibrium) - ₂ Length scale of doublets - T _p Stress tensor - T _xy Shear Stress (xy element of T _p ) - T _pi Contributions to the stress tensor of singlets (i = 1) and doublets (i = 2) - ₀ Equilibrium configuration distribution function of Q - _i Configuration distribution function of singlets (i = 1) and doublets (i = 2)     

Development of a quasi-dynamic pharmacophore model for anti-complement peptide analogues

Three quasi-dynamic pharmacophore models have been constructed for the complement inhibitor peptide compstatin, using first principles. Uniform sampling along 5-ns molecular dynamics trajectories provided dynamic conformers that are thought to represent the entire conformational space for nine training set molecules, compstatin, four active analogues, and four inactive analogues. The pharmacophore models were built using mixed physicochemical and structural properties of residues indispensable for structural stability and activity. Owing to the size and flexibility of compstatin, one-dimensional probability distributions of intrapharmacophore point distances, angles, and dihedral angles of different analogues spread over wide and overlapping ranges. More robust two-dimensional distance-angle probability distributions for two pharmacophore models discriminated individual analogues in terms of specific distance-angle pairs, but overall failed to identify the active and the inactive analogues as two distinct groups. Two-dimensional distance-dihedral angle probability distributions in a third pharmacophore model allowed discrimination of the groups of active and inactive analogues more effectively, with the highest-activity analogue having distinct behavior. The present study indicates that more stringent structural constraints should be used for a set of structurally similar but flexible peptides, as opposed to organic molecules, to convert dynamic conformers into pharmacophore models. Flexibility is a general aspect of the structure and function of peptides and should be taken into account in ligand-based pharmacophore design. However, the discrimination of activity using multidimensional probability surfaces depends on the peptide system, the selection of the training set, the molecular dynamics protocol, and the selection of the type and number of pharmacophore points.     

Unusual collision-induced dissociation of fluorated and non-fluorated alpha-nitrotoluene analogs in a gas chromatograph triple-stage quadrupole mass spectrometer under electron-capturing negative-ion chemical ionization conditions

Unusual collision-induced dissociation (CID) of perfluorated and non-perfluorated alpha-nitrotoluene analogs in a gas chromatograph triple-stage quadrupole (TSQ) mass spectrometer (GC-QqQ-MS) under electron-capturing negative-ion chemical ionization conditions is reported. CID of [M - 1]- of alpha-nitro-2,3,4,5,6-pentafluorotoluene (C6F5CH2-NO2) and alpha-nitro-2,5-difluorotoluene (C6H3F2CH2-NO2) produced an intense ion with m/z 66. By using 15N- or 18O-labelled C6F5CH2-NO2 analogs, we found that this anion has the formula C3NO. By contrast, CID of [M - 1]- of alpha-nitrotoluene (C6H5CH2-NO2) and alpha-nitro-3,5-difluorotoluene (C6H3F2CH2-NO2) produced an anion with m/z 86 with the formula C3H4NO2. The expected CID of the C-N-bond of all alpha-nitrotoluene analogs to form the nitrite anion (NO2-, m/z 46) did not occur. We propose mechanisms for the formation of the anions C3NO and C3H4NO2 in the collision chamber of the TSQ mass spectrometer. The most likely structures for the anion C3NO are :C=C=C=N--O and N triple bond C-C triple bond C--O-. The unique CID behavior of C6F5CH2--NO2 can be utilized to unequivocally identify and accurately quantify nitrite in biological fluids by GC-tandem MS.     

Silicon Analogues of Triarylmethanol Hosts. Inclusion Properties and Host–guest Structures: A Comparative Study

The simple triarylmethanol hosts, 2 and 4, and their silicon analogues, 1 and 3, have been studied for comparison of the formation of crystalline inclusion compounds. Clathrate formation experiments showed that replacement of the carbinol C atoms in 2 and 4 by Si atoms to give 1 and 3 resulted in a distinct increase of the capability to form inclusion compounds with organic guests, in particular with alcohols. Moreover, the naphthyl derivatives are much more efficient than the phenyl species, irrespective of the carbinol and silanol features. In order to investigate and compare the guest recognition modes and packing relations of hosts 1–4 in their crystalline inclusion compounds, 11 selected co-crystals, namely 1·DMSO (2:1), 3·EtOH (1:1), 3· i-PrOH (1:1), 3·acetone (1:1), 3·DMSO (1:1), 3·THF (1:1), 3·piperidine (1:1), 4·acetone (1:1), 4·DMSO (1:1), 4·1,4-dioxane (1:1) and 4·benzene (1:1), were studied by X-ray diffraction from single crystals. The survey contains additional 11 crystal structures from the literature and provides a detailed discussion of isostructurality relationships.Supplementary Data relevant to this publication have been deposited with the Cambridge Crystallographic Data Centre as supplementary publications nos. CCDC 274780–274790.     

An improved method for Lewis acid catalyzed phosphoryl transfer with Ti(t-BuO)4

Several inorganic esters have been evaluated as phosphoryl transfer catalysts. Of these, Ti(t-BuO)(4) was found to be the most effective catalyst giving excellent yields of the desired phosphate esters. The loading of the catalyst could be reduced to a little as 5 mol % for a majority of substrates with no loss in the yield of product. This methodology is significantly more versatile than using TiCl(4) and is suitable for the phosphorylation of more complex carbohydrates and molecules of biological interest.     

Glandulaurencianols A–C,brominated diterpenes from the red alga, Laurencia glandulifera and the sea hare, Aplysia punctata

Glandulaurencianols A and B were isolated from the organic extract of the red alga, Laurencia glandulifera, collected from the island of Crete in South Greece. Investigation of the mollusk, Aplysia punctata, collected from the coast of Nea Makri, Central Greece, resulted in the isolation of glandulaurencianols A and C. The structures of the new metabolites, as well as their relative configurations, were established on the basis of thorough analyses of their spectroscopic data.