Monodromy for principal bundles

Given a strongly semistable principal bundle E_G over a curve, in Biswas et al. (2006) [4], a group-scheme for it was constructed, which was named as the monodromy group-scheme. Here we extend the construction of the monodromy group-scheme to principal bundles over higher dimensional varieties.     

Mechanisms of TiO2 nanoparticle transport in porous media: role of solution chemistry, nanoparticle concentration, and flowrate

The controlled self-assembly of multi-components in one system represents the capability integrating intermolecular interactions and functions of components and is believed the key procedure leading to multifunctional materials finally. In pursuing this goal, we used a double-chain cationic surfactant with a benzoic acid group at the end of one tail to encapsulate Keggin-type polyanion clusters via electrostatic interaction, obtaining uniform supramolecular hybrid reverse micelles, which served as hydrogen-bonding donors. Five pyridine derivatives containing conjugated and non-conjugated groups were chosen as hydrogen-bonding acceptors to bind with reverse micelles. Through mixing with these components according to chemical stoichiometry, the hybrid reverse micelle changed to a new self-assembly precursor through intermolecular hydrogen bonding. The as-prepared reverse micelles bearing conjugated pyridine groups exhibit supramolecular liquid crystal properties, which were characterized by differential scanning calorimetry, polarizing optical microscopy, and X-ray diffraction. The length and number of the alky chain in the pyridine derivatives, as well as the charges of polyoxometalates were also studied with regard to the liquid crystal structure. The synergistic effect of among three components was analyzed, and the liquid crystal properties could be conveniently adjusted through the modification of the hydrogen-bonding acceptor components.     

Pulsed field gradient NMR study of phenol binding and exchange in dispersions of hollow polyelectrolyte capsules

The distribution and exchange dynamics of phenol molecules in colloidal dispersions of submicron hollow polymeric capsules is investigated by pulsed field gradient NMR (PFG-NMR). The capsules are prepared by layer-by-layer assembly of polyelectrolyte multilayers on silica particles, followed by dissolution of the silica core. In capsule dispersion, (1)H PFG echo decays of phenol are single exponentials, implying fast exchange of phenol between a free site and a capsule-bound site. However, apparent diffusion coefficients extracted from the echo decays depend on the diffusion time, which is typically not the case for the fast exchange limit. We attribute this to a particular regime, where apparent diffusion coefficients are observed, which arise from the signal of free phenol only but are influenced by exchange with molecules bound to the capsule, which exhibit a very fast spin relaxation. Indeed, relaxation rates of phenol are strongly enhanced in the presence of capsules, indicating binding to the capsule wall rather than encapsulation in the interior. We present a quantitative analysis in terms of a combined diffusion-relaxation model, where exchange times can be determined from diffusion and spin relaxation experiments even in this particular regime, where the bound site acts as a relaxation sink. The result of the analysis yields exchange times between free phenol and phenol bound to the capsule wall, which are on the order of 30 ms and thus slower than the diffusion controlled limit. From bound and free fractions an adsorption isotherm of phenol to the capsule wall is extracted. The binding mechanism and the exchange mechanism are discussed. The introduction of the global analysis of diffusion as well as relaxation echo decays presented here is of large relevance for adsorption dynamics in colloidal systems or other systems, where the standard diffusion echo decay analysis is complicated by rapidly relaxing boundary conditions.     

Influence of the chelate ligand structure on the amide methanolysis reactivity of mononuclear zinc complexes

Zinc complexes of three new amide-appended ligands have been prepared and isolated. These complexes, [(dpppa)Zn](ClO4)2 (4(ClO4)2; dpppa = N-((N,N-diethylamino)ethyl)-N-((6-pivaloylamido-2-pyridyl)methyl)-N-((2-pyridyl)methyl)amine), [(bdppa)Zn](ClO4)2 (6(ClO4)2; bdppa = N,N-bis((N,N-diethylamino)ethyl)-N-((6-pivaloylamido-2-pyridyl)methyl)amine), and [(epppa)Zn](ClO4)2 (8(ClO4)2; epppa = N-((2-ethylthio)ethyl)-N-((6-pivaloylamido-2-pyridyl)methyl)-N-((2-pyridyl)methyl)amine), have been characterized by X-ray crystallography (4(ClO4)2 and 8(ClO4)2), 1H and 13C NMR, IR, and elemental analysis. Treatment of 4(ClO4)2 or 8(ClO4)2 with 1 equiv of Me4NOH.5H2O in methanol-acetonitrile (5:3) results in amide methanolysis, as determined by the recovery of primary amine-appended forms of the chelate ligand following removal of the zinc ion. These reactions proceed via the initial formation of a deprotonated amide intermediate ([(dpppa-)Zn]ClO4 (5) and [(epppa-)Zn]ClO4 (9)) which in each case has been isolated and characterized (1H and 13C NMR, IR, elemental analysis). Treatment of 6(ClO4)2 with Me4NOH.5H2O in methanol-acetonitrile results in the formation of a deprotonated amide complex, [(bdppa-)Zn]ClO4 (7), which was isolated and characterized. This complex does not undergo amide methanolysis after prolonged heating in a methanol-acetonitrile mixture. Kinetic studies and construction of Eyring plots for the amide methanolysis reactions of 4(ClO4)2 and 8(ClO4)2 yielded thermodynamic parameters that provide a rationale for the relative rates of the amide methanolysis reactions. Overall, we propose that the mechanistic pathway for these amide methanolysis reactions involves reaction of the deprotonated amide complex with methanol to produce a zinc methoxide species, the reactivity of which depends, at least in part, on the steric hindrance imparted by the supporting chelate ligand. Amide methanolysis involving a zinc complex supported by a N2S2 donor chelate ligand (3(ClO4)2) is more complicated, as in addition to the formation of a deprotonated amide intermediate free chelate ligand is present in the reaction mixture.     

Chaotic dynamics of the heat semigroup on Riemannian symmetric spaces

We show that the heat semigroup generated by certain perturbations of the Laplace–Beltrami operator on the Riemannian symmetric spaces of noncompact type is chaotic   on their L^p$L^p$-spaces when 2<p<∞$2<p<\infty$. Both the range of p and the range of chaos-inducing perturbation are sharp. This extends a result of Ji and Weber [17] where it was shown that under identical conditions the heat operator is subspace-chaotic on these spaces.     

On the F-fundamental group scheme

Let X be a smooth projective variety defined over a perfect field k of positive characteristic, and let FX be the absolute Frobenius morphism of X. For any vector bundle E→X, and any polynomial g with non-negative integer coefficients, define the vector bundle using the powers of FX and the direct sum operation. We construct a neutral Tannakian category using the vector bundles with the property that there are two distinct polynomials f and g with non-negative integer coefficients such that . We also investigate the group scheme defined by this neutral Tannakian category.     

Torelli Theorem for the Deligne–Hitchin Moduli Space

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X.     

Flat Partial Connections on a Three Manifold Equipped with a Codimension One Foliation

Given a compact connected oriented three manifold, equipped with a codimension one foliation, such that the Bott connection on the normal bundle is flat, a 2-form on the space parametrizing flat partial connections on it has been constructed. This form is closed. In the special case where the foliated three manifold is a surface bundle over the circle, this 2-form is identified with a certain 2-form on the parameter space for a class of paths in the representation space for the surface group. The 2-form, in question, on the parameter space for paths is constructed from the natural symplectic form on the representation space for a surface group.