Wiener–Tauberian type theorems for radial sections of homogenous vector bundles on certain rank one Riemannian symmetric spaces of noncompact type

We will show that an uniform treatment yields Wiener–Tauberian type results for various Banach algebras and modules consisting of radial sections of some homogenous vector bundles on rank one Riemannian symmetric spaces G/K of noncompact type. One example of such a vector bundle is the spinor bundle. The algebras and modules we consider are natural generalizations of the commutative Banach algebra of integrable radial functions on G/K. The first set of them are Beurling algebras with analytic weights, while the second set arises due to Kunze–Stein phenomenon for noncompact semisimple Lie groups.     

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.     

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.     

On the Picard bundle

Fix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g?2, and also fix an integer r such that degree(ξ)>r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles over X of rank r and determinant ξ. The Fourier-Mukai transform, with respect to a Poincaré line bundle on X×J(X), of any F∈Mξ(r) is a stable vector bundle on J(X). This gives an injective map of Mξ(r) in a moduli space associated to J(X). If g=2, then Mξ(r) becomes a Lagrangian subscheme.     

Bandwidth packing with priority classes

The bandwidth packing problem is defined as the selection and routing of messages from a given list of messages with prespecified requirements on demand for bandwidth. The messages have to be routed over a network with given topology so that the generated revenue is maximized. Messages to be routed are classified into two priority classes. An integer programming based formulation of this problem is proposed and a Lagrangean relaxation based methodology is described for solving this problem. A general purpose heuristic is then developed for generating feasible solutions of good quality. Several numerical experiments are conducted using a number of problem parameters such as number of messages, ratio of messages for lower and higher priority classes, capacity of links, and demand distribution of messages belonging to different classes and high quality solutions to the priority bandwidth packing problem are generated under the different situations.     

Synthesis,crystal structure,and magnetic properties of an alkoxo-hydroxo-bridged octanuclear copper(II) complex showing chemically significant hydrogen-bonding interactions involving a metallamacrocyclic core

A novel 16-member metallamacrocyclic octanuclear copper(II) complex of formulation [Cu8L4(OH)4] (1) has been prepared from a reaction of [Cu2L(O2CMe)] and NaOH in methanol, where L is a pentadentate trianionic Schiff base ligand N,N'-(2-hydroxypropane-1,3-diyl)bis(salicylaldimine). The complex has been characterized by analytical, structural, and spectral methods. It crystallizes in the monoclinic space group C2/c with the following unit cell dimensions: a = 30.365(3) A; b = 14.320(2) A; c = 19.019(2) A; beta = 125.33(2) degrees; V = 6746.7(13) A3; Z = 4. A total of 4589 unique data with l > 2 sigma (l) were used to refine the structure to R1(F0) = 0.0525 and wR2 = 0.1156. The structure consists of four binuclear [Cu2L]+ units linked covalently by four hydroxide ligands to form an octanuclear core which is stabilized by strong hydrogen-bonding interactions involving the hydroxide ligands. Each binuclear unit has a pentadentate ligand L showing N2O3 coordination with an endogenous alkoxide bridging atom. The magnetic susceptibility data of 1, obtained in the temperature range 14-306 K, show the presence of antiferromagnetic exchange interactions between adjacent spin-1/2 Cu(II) ions. The mu eff values are 1.54 and 0.26 microB (per copper) at 295 and 15 K, respectively. The magnetic data have been theoretically fitted using a Heisenberg spin-1/2 Hamiltonian with nearest-neighbor antiferromagnetic interactions. The spin coupling in the metallamacrocyclic ring has been modeled using four different coupling constants (J) on the basis of the structural parameters of the octanuclear core. The coupling constants obtained are J1 = -318.8, J2 = -293.3, J3 = -111.6, and J4 = -63.8 cm-1. The theoretical modeling of the susceptibility data gives a higher magnitude of the antiferromagnetic interaction within the binuclear [Cu2L]+ unit compared to those involving adjacent dimeric units.     

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.     

JR 400–NaAOT interaction: a detailed thermodynamic study of polymer–surfactant interaction bearing opposite charges

The present study entails interaction between the cationic polymer N,N-dimethylhydroxyethyl cellulose (JR 400) and the double-tailed anionic surfactant Na-bis-2-ethyhexylsulphosuccinate (NaAOT). This oppositely charged polymer and surfactant are expected to cause coacervation and precipitation; hence, we have observed formation of thick solution similar to diluted gel at [JR 400]?~?0.01 and 0.10 %?w/v in aqueous solution. Viscometry, conductometry, tensiometry, and microcalorimetry techniques are used to monitor the interaction process. The results are explained in the light of both intrachain and interchain linking by way of NaAOT reverse micelle formation. Adsorption of NaAOT monomers onto the charged side chains of the polymer shields interchain electrostatic repulsion, leading to the formation of hydrophobic microdomains and microscopic heterogeneity in the solution. The morphologies of the domains depend on the level of addition of NaAOT in the system. The different stages of physiochemical changes that arise in solution have been identified by the use of different techniques, and correlations of the results have been attempted in terms of pragmatic models.     

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.