Weighted Inequalities for Multilinear Potential Operators and their Commutators

We prove weighted strong inequalities for the multilinear potential operator T_f{cal T}_{phi} and its commutator, where the kernel ϕ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator M_j,L^Bmathcal{M}_{varphi,L^{B}} associated to an essentially nondecreasing function φ and to the Orlicz space L ^B for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator T_f{cal T}_{phi}.     

Embedding a Planar Hypercoordinate Carbon Atom into a [4n+2] π-System

Through delicate tuning of the electronic structure, we report herein a rational design of seventeen new putative global minimum energy structures containing a planar tetra- or pentacoordinate carbon atom embedded in an aromatic hydrocarbon. These structures are the result of replacing three consecutive hydrogen atoms of an aromatic hydrocarbon by less electronegative groups, forming a multicenter σ-bond with the planar hypercoordinate carbon atom and participating in the π-electron delocalization. This strategy that maximizes both mechanical and electronic effects through aromatic architectures can be extended to several molecular combinations to achieve new and diverse compounds containing planar hypercoordinate carbon centers.     

Tripolyphosphate as Precursor for REPO4:Eu3+ (RE = Y, La, Gd) by a Polymeric Method

A modification of the Pechini method was applied to obtain luminescent rare earth orthophosphates. The developed synthetic route is based on the ability of the tripolyphosphate anion () to act both as a complexing agent and as an orthophosphate precursor. Heating of aqueous solutions containing RE³⁺, Eu³⁺, , citric acid, and ethylene glycol led to polymeric resins. The ignition of these resins at different temperatures yielded luminescent orthophosphates. The produced nanosized phosphors (YPO₄:Eu³⁺, (Y,Gd)PO₄:Eu³⁺, and LaPO₄:Eu³⁺) were analyzed by infrared and luminescence spectroscopies, X-ray diffractometry, and scanning electron microscopy.     

Foot and mouth disease virus concentration and purification by affinity chromatography

Foot and mouth disease virus, (FMDV) from a crude cell lysate was purified in a single step by affinity chromatography with heparin as a ligand. The virus eluted from an Heparin-Ultrogel A₄R column at 1M sodium chloride in 10 mM sodium phosphate buffer, pH 7.0, while most cell protein and albumin did so at lower concentrations of sodium chloride in the same buffer. Purity of the eluted fraction containing the virus was assessed by SDS-PAGE, HPLC, ultracentrifugation, and UV absorption spectrum. With this method, intact viral particles are recovered in high yield (over 90%) and specific virus purity increases nearly 1000-fold. The capacity of the Chromatographic matrix for the virus was found to be 1.1 mg viral mass per mL of hydrated gel.     

Electron-transfer mechanism in the N-demethylation of N,N-dimethylanilines by the phthalimide-N-oxyl radical

The reactivity of the phthalimide N-oxyl radical (PINO) toward the N-methyl C-H bond of a number of 4-X-substituted N,N-dimethylanilines (X = OMe, OPh, CF(3), CO(2)Et, CN) has been investigated by product and kinetic analysis. PINO was generated in CH(3)CN by reaction of N-hydroxyphthalimide (NHPI) with Pb(OAc)(4) or, for the kinetic study of the most reactive substrates (X = OMe, OPh), with tert-butoxyl radical produced by 266 nm laser flash photolysis of di-tert-butyl peroxide. The reaction was found to lead to the N-demethylation of the N,N-dimethylaniline with a rate very sensitive to the electron donating power of the substituent (rho(+) = -2.5) as well as to the oxidation potential of the substrates. With appropriately deuterated N,N-dimethylanilines the intermolecular and intramolecular deuterium kinetic isotope effects (DKIEs) were measured for some substrates (X = OMe, CO(2)Et, CN) with the following results. First, intramolecular DKIE [(k(H)/k(D))(intra)] was found to be always different and higher than intermolecular DKIE [(k(H)/k(D))(inter)]; second, no intermolecular DKIE [(k(H)/k(D))(inter) = 1] was observed for X = OMe, whereas substantial values of (k(H)/k(D))(inter) were exhibited by X = CO(2)Et (4.8) and X = CN (5.8). These results, while are incompatible with a single step hydrogen atom transfer from the N-C-H bond to the N-oxyl radical, as proposed for the reaction of PINO with benzylic C-H bonds, can be nicely interpreted on the basis of a two-step mechanism involving a reversible electron transfer from the aniline to PINO leading to an anilinium radical cation, followed by a proton-transfer step that produces an alpha-amino carbon radical. In line with this conclusion the reactivity data exhibited a good fit with the Marcus equation and a lambda value of 37.6 kcal mol(-1) was calculated for the reorganization energy required in this electron-transfer process. From this value, a quite high reorganization energy (>60 kcal mol(-1)) is estimated for the PINO/NHPI(-H)(-) self-exchange reaction. It is suggested that the N-demethylated product derives from the reaction of the alpha-amino carbon radical with PINO to form either a cross-coupling product or an alpha-amino carbocation. Both species may react with the small amounts of H(2)O present in the medium to form a carbinolamine that, again by hydrolysis, can be eventually converted into the N-demethylated product.     

The Aubry set for periodic Lagrangians on the circle

For periodic convex Lagrangians on \(\mathbb{S}^1\), we show that, generically, in the sense of Mañé, there exists a dense open set of cohomology classes such that the Aubry set of these Lagrangians is a hyperbolic periodic orbit. This allows us to prove Mañé’s conjecture on \(\mathbb{S}^1\).     

Polynomial-time algorithms for regular set-covering and threshold synthesis

A set-covering problem is called regular if a cover always remains a cover when any column in it is replaced by an earlier column. From the input of the problem - the coefficient matrix of the set-covering inequalities - it is possible to check in polynomial time whether the problem is regular or can be made regular by permuting the columns. If it is, then all the minimal covers are generated in polynomial time, and one of them is an optimal solution. The algorithm also yields an explicit bound for the number of minimal covers. These results can be used to check in polynomial time whether a given set-covering problem is equivalent to some knapsack problem without additional variables, or equivalently to recognize positive threshold functions in polynomial time. However, the problem of recognizing when an arbitrary Boolean function is threshold is NP-complete. It is also shown that the list of maximal non-covers is essentially the most compact input possible, even if it is known in advance that the problem is regular.     

Surface-enhanced raman scattering on dendrimer/metallic nanoparticle layer-by-layer film substrates

In this paper, the fabrication, characterization, and application of unique layer-by-layer (LBL) films of dendrimers and metallic nanoparticles is reported. Silver nanoparticles (d = approximately 20 nm) are produced in solution by sodium citrate reduction and incorporated into thin films with generation 1 and 5 DAB-Am dendrimers (polypropylenimine dendrimers with amino surface groups) by the LBL technique. The resulting nanocomposite films are characterized by UV-visible surface plasmon absorption and atomic force microscopy (AFM) measurements, and employed as substrates for surface-enhanced Raman scattering (SERS) of 2-naphthalenethiol. Through variation of the molecular size (dendrimer generation) and concentration of the cross-linker used, as well as the number of layers produced, the optical properties of several different possible architectures are studied. In the films, Ag nanoparticles are shown to be effectively immobilized and stabilized with increased control over their spacing and aggregation. Moreover, the films are shown to be excellent substrates for SERS measurements, demonstrating significant enhancement capability. As expected, large electromagnetic enhancement of Raman scattering signals is found to be strongly dependent on interparticle coupling between neighboring metallic nanoparticles. Finally, the possibility of detecting SERS signals from architectures with intervening layers between the metal nanoparticles and analyte molecules is explored. It is shown that although there are decreases in intensity with increasing number of intervening layers (as is expected from the distance dependence of SERS), electromagnetic enhancement is still able to function at these distances, thus offering the possibility of developing sensors with external layers that are chemically selective for specific analytes.     

Some properties of reduced density matrices,correlated and uncorrelated,for pure and mixed states

Some results pertaining to the form of Γ⁽¹⁾ usually assumed in density functional theory, the properties of natural states of mixed states, their variational characterization, and a representation of pure states through reproducing kernels are given.