The remainder in Weyl's law for random two-dimensional

We prove that the average order of the remainder in counting the number of points of a random lattice inside a disc of radius . Our proof is spectral in nature. Submitted: July 2001, Revised: August 2001, Revised: March 2002.     

Intrazeolite photooxygenation of chiral alkenes. Control of facial selectivity by confinement and cation-π interactions

Depending on the nature of the substituents on the stereogenic carbon atom, the ene reaction of singlet oxygen with several chiral alkenes by confinement within thionin-supported zeolite NaY, may exhibit significant changes on facial selectivity by comparison to their photooxygenation reaction in solution. It is proposed that, apart from the conformational consequences as a result of the alkene confinement within the zeolite cavities, a synergism between Na⁺-π interactions and singlet oxygen-Na⁺ interactions plays a significant role in the transition states of ene hydroperoxidation. Within NaY, the diastereoselectivity may significantly depend on the site selectivity, as probed through specific deuterium labelling of trisubstituted alkenes bearing a gem-dimethyl group. In certain cases, a remote stereogenic centre relative to the reacting double bond may induce enhanced diastereoselection and regioselectivity.     

Remarkable change of the diastereoselection in the dye-sensitized ene hydroperoxidation of chiral alkenes by zeolite confinement

[reaction: see text] The ene reaction of singlet oxygen with chiral trisubstituted alkenes bearing an alkyl and a phenyl group at the stereogenic center is erythro diastereoselective in solution and threo diastereoselective if carried out within zeolite Na-Y. The change of the diastereoselection trend by zeolite confinement is attributed to a synergism of steric effects and cation-pi interactions.     

Computational studies on the thermal decomposition and isomerization of CHBr2O radical

The unimolecular decomposition study of dibromomethoxy radical, CHBr₂O, and its isomeric hydroxy dibromomethyl radical, CBr₂OH, is carried out using ab initio electronic molecular structure methods. Three kinds of reaction pathways are examined, C–H and C–Br bond scissions, intramolecular three-center HBr elimination and isomerization. Based on the ab initio results, energy-specific rate coefficients k(E) and thermal rate constants k(T,P) are evaluated using RRKM theory and master equation numerical analysis. Relevance to existing experimental evidence is discussed.     

Shape fabrication of millimeter-sized metal-containing carboxymethyl cellulose hollow capsules

Dropwise addition of an aqueous carboxymethyl cellulose solution to a solution of a copper or iron salt in n-butanol, leads to self-assembled, permeable millimeter sized metal-ion derivatized carboxymethyl cellulose hollow capsules of uniform dimensions and different morphologies.     

Magnetic structure of the europium fulleride ferromagnet Eu(6)C(60)

The powder neutron diffraction technique has been used for the direct observation of magnetic scattering below a Curie temperature of approximately 14 K in the fullerene-based molecular ferromagnet Eu6C60. Europium is in the divalent state with a magnetic moment of 7.1(3) muB per atom, and the configurational symmetry of the magnetic structure is body-centered cubic. Close contacts between Eu2+ and neighboring C60 units provide the signature of orbital hybridization, which can evidently account for the conducting and magnetic properties of the material.     

Ab initio molecular orbital and RRKM calculations of the thermal decomposition of CH2BrO radical

A theoretical study of the thermal decomposition and isomerization channels of bromomethoxy radical is carried out using ab initio molecular orbital methods and RRKM theory. Three kinds of reaction pathways are examined, bond scission, intramolecular three-center HBr elimination and isomerization. Energy-specific rate coefficients k(E) and thermal rate constants k(T,P) are evaluated using the ab initio data and RRKM theory. Relevance to existing experimental evidence is discussed.     

Morphological changes in the cellulose and lignin components of biomass occur at different stages during steam pretreatment

Morphological changes to the different components of lignocellulosic biomass were observed as they occurred during steam pretreatment by placing a pressure reaction cell in a neutron beam and collecting time-resolved neutron scattering data. Changes to cellulose morphology occurred mainly in the heating phase, whereas changes in lignin morphology occurred mainly in the holding and cooling phases. During the heating stage, water is irreversibly expelled from cellulose microfibrils as the elementary fibrils coalesce. During the holding phase lignin aggregates begin to appear and they increase in size most noticeably during the cooling phase. This experiment demonstrates the unique information that in situ small angle neutron scattering studies of pretreatment can provide. This approach could be useful in optimizing the heating, holding and cooling stages of pretreatments to allow the exact size and nature of lignin aggregates to be controlled in order to enhance enzyme accessibility to cellulose and therefore the efficiency of biomass conversion.     

Zero thermal expansion in a Prussian Blue analogue

Isotropic nearly zero thermal expansion (i.e., negligible volume change) is reported in a large temperature range for Fe[Co(CN)6], a member of the Prussian blue family with electronically active metal sublattices and a cubic framework structure built by a cyanide-bridged network of octahedral units. Suitable selection of metal ions and interstitial units could allow such anomalous thermal behavior to be combined with the variety of unusual electronic, optical, and magnetic properties exhibited by Prussian blue analogues.