Hybrid subconvexity bounds for $$L(1/2,\hbox {sym}^{2} f \otimes \chi )$$ L ( 1 / 2 , sym 2 f ⊗ χ )

The Ramanujan Journal - Let $$k\ge 2$$ be an even integer, and let M be a positive integer. We prove a hybrid subconvexity bound for $$L(1/2,\text {sym}^2 f\otimes \chi )$$ with the associated...     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Does core size matter in the kinetics of ligand exchanges of monolayer-protected Au clusters?

This paper compares the kinetics of exchanges of phenylethanethiolate ligands (PhC2S-) of the monolayer-protected clusters (MPCs) Au(38)(SC2Ph)(24) and Au(140)(SC2Ph)(53) with p-substituted arylthiols (p-X-PhSH), where X = NO(2), Br, CH(3), OCH(3), and OH. First-order rate constants at 293 K for exchange of the first ca. 25% of the ligands on the molecule-like Au(38)(SC2Ph)(24) MPC, measured using (1)H NMR, vary linearly with the in-coming arythiol concentration; ligand exchange is an overall second-order reaction. Remarkably, the second-order rate constants for ligand exchange on Au(38)(SC2Ph)(24) are very close to those of corresponding exchange reactions on the larger nanoparticle Au(140)(SC2Ph)(53) MPCs. These are the first results that quantitatively show that the chemical reactivity of different sized nanocrystals is almost independent of size; presumably, this is because the locus of the initial ligand exchanges is a common kind of site, thought to be the nanocrystal vertexes. The rates of later stages of exchange (beyond ca. 25%) differ for Au(38) and Au(140) cores, the latter being much slower presumably due to its larger terrace-like surface atom content. The reverse exchange reaction was studied for Au(38)(p-X-arylthiolate)(24) MPCs (X = NO(2), Br, and CH(3)), where the in-coming ligand is now phenylethanethiol. Remarkably, the rate constants of both forward and reverse exchanges display identical substituent effects, which implies a concurrent bonding of both in-coming and leaving ligands to the Au core in the rate-determining step, as in an associative mechanism. X = NO(2) gives the fastest rates, and the ratio of forward and reverse rate constants gives an equilibrium constant of K(EQ,PE) = 4.0 that is independent of X.     

Effect of Co-solvent on the Palladium Catalyzed Alkoxycarbonylation of Allyl Bromide in Supercritical CO_2

We have studied the palladium-catalyzed alkoxycarbonylation of allyl bromide in supercritical (sc) CO2 and found the reaction rate in sc CO2 was lower than those in some organic solvents1. The possible reason was the lower solubility of sc CO2 for the palladium catalyst. As an effective approach to improve the solubility of varieties of solutes, cosolvent such as ethanol has been widely used in the sc CO2 extraction2,3. Based on the above consideration, we chose several organic reagents…     

DETECTION OF T_g BY MODULATED DIFFERENTIAL SCANNING CALORIMETRY

The glassy transition of the polyethylene terephthalate (PET) sampleswhich have been subjected to solvent induced crystallization (SINC) was investigated bymodulated differential scanning calorimetry (MDSC) and density measurement. The dif-ferential of heat capacity signal, d C_p/dT from MDSC, was used to monitor the SINCprocess. It reveals that the T_g temperature shifts to higher value with the advancement ofSINC. When the toluene-immersing time was longer (168h), the detection of T_g becomemore difficult, because some smaller peaks emerged at the lower temperatures and theseare explained as the movement of small segments in the amorphous region. These observedresults are due to the morphology and structure introduced by the SINC process.     

Mitochondria-targeted ratiometric fluorescent probes for micropolarity and microviscosity and their applications

Two fluorescent "off-on" probes YYH1 and YYH2 were used for bioimaging mitochondrial polarity and viscosity.     

Matrix-isolation FT-IR spectra and theoretical study of dimethyl sulfate

The preferred conformations of dimethyl sulfate and their vibrational spectra were studied by matrix-isolation FT-IR spectroscopy and theoretical methods (DFT and MP2, with basis sets of different sizes, including the quadruple-zeta, aug-cc-pVQZ basis). Conformer GG (of C2 symmetry and exhibiting OSOC dihedral angles of 74.3 degrees ) was found to be the most stable conformer in both the gaseous phase and isolated in argon. Upon annealing of the matrix, the less stable observed conformer (GT; with C1 symmetry) quickly converts to the GG conformer, with the resulting species being embedded in a matrix-cage which corresponds to the most stable matrix-site for GG form. The highest energy TT conformer, which was assumed to be the most stable conformer in previous studies, is predicted by the calculations to have a relative energy of ca. 10 kJ mol-1 and was not observed in the spectra of the matrix-isolated compound.     

Complete pi-facial diastereoselectivity in Diels-Alder reactions of dissymmetric 2,4-cyclohexadienones

[reaction: see text] The studies in the Diels-Alder reactions of 5-methoxy-masked o-benzoquinone (1a, R = OMe) and simple dissymmetric 2,4-cyclohexadienones 1b-e with methyl vinyl ketone, styrene, and benzyl vinyl ether are described. The dienones 1b-e reacted with dienophiles to form syn adducts (dienophile approach is syn to allylic methoxy group) exclusively.