Expressions for the perfect matching numbers of cubicl x m x n lattices and their asymptotic values

A general expression of the perfect matching number for thel x m x n cubic lattice was conjectured and examined for infinitely large systems. The asymptotic value of the square of the perfect matching number was calculated by numerical integration. The present treatment will give a key to obtain the true analytic solution of the perfect matching numbers for the 3-dimensional lattices.     

Kinetics and mechanism of aquation of [Cr(NCS)(edtrp)]-, [Cr(NCS)(R-pdtrp)]-, [Cr(edtrp)(NCSHg)]+ and [Cr(R-pdtrp) (NCSHg)]+ complexes. Unexpected rate retardation in strongly acidic media for NCS- ligand release

Three new complex ions, [Cr(NCS)(R-pdtrp)]^-, [Cr(R-pdtrp)(NCSHg)]⁺ and [Cr(edtrp)(NCSHg)]⁺, that are derivatives of the trans-equatorial isomers of [Cr(R-pdtrp)(H₂O)]⁰ and [Cr(edtrp)(H₂O)]⁰ (edtrp= ethylenediamine-N,N,N-tripropionate, R-pdtrp= R-propane-1,2-diamine-N,N,N-tripropionate) have been obtained and characterized in solution. Rate constants and activation parameters, including, in two cases, volumes of activation, have been determined. Rate retardation for NCS^- ligand release has been observed with increasing acidity within the pH 0–2 range. The mechanism of the reactions has been discussed.     

Structural characterization of the trans-equatorial isomer of (aqua)(ethylenediamine-N,N,N′-tripropionato)chromium(III) trihydrate,[Cr(edtrp)(H2O)] · 3H2O

The structure of trans-equatorial [Cr(edtrp)(H₂O)] · 3H₂O (edtrp^3– is the anion of ethylenediamine-N,N,N-tripropionic acid) was determined by single crystal X-ray diffraction. The chromium(III) ion is surrounded octahedrally by the two nitrogen and three oxygen atoms of the quinquedentate edtrp^3–, forming a five-membered diamine ring and the three six-membered -propionato chelate rings. The remaining coordination position is occupied by the H₂O ligand. The crystal structure conformation is compared to the result of recent molecular mechanics analysis. The ring strain of R and G chelate rings was found to be in agreement with the previously proposed mechanisms for the C—N bond cleavage and recombination.     

Dissolution behavior of tetrafluoroethylene-based fluoropolymers for 157-nm resist materials

We have synthesized various main-chain fluorinated polymers and studied base-resin properties, such as transparency at 157 nm, solubility in a standard alkaline developer, and lithographic performance. Main-chain-fluorinated polymers were synthesized by copolymerization of tetrafluoroethylene (TFE) with cyclic monomers, especially newly synthesized norbornene derivatives. We studied the correlation between pK_a(OH) and the solubility of the copolymers of TFE and functional (fluoroalkyl alcohol group) norbornenes. Their solubility depends on the pK_a value of the fluoroalkyl alcohol groups.We studied the impact of the polymerization initiators on base-resin properties. High transparency was obtained by using the fluorocarbon initiator. It was also confirmed that the monocyclic component improves dry-etch resistance and that fluorination at the terminal groups improves alkaline solubility.In addition, we found that the development characteristics of TFE/norbornene copolymers were significantly improved by the stereoselective (endo versus exo) partial protection of the hydroxyl groups in the fluoroalkyl alcohol moiety attached to norbornene unit. The polymer protected only in the exo position of the norbornene unit in the copolymer had a higher R_max and a higher contrast. Positive-working resists based on these fluoropolymers were developed and 55 nm dense lines could be delineated by exposure at 157 nm wavelength with an alternating phase shift mask on a 0.9 NA 157 nm exposure tool.     

Electroreduction of nitrite on gold electrode modified with Cu-containing nitrite reductase model complex

A gold electrode modified with copper complexes containing a tridentate aromatic amine compound (bis(6-methyl-2-pyridylmethyl)amine ethyl sulfide, which is a model for the nitrite reduction centre of copper-containing nitrite reductase, catalyzed electrochemically the reduction of nitrite to nitrogen monoxide under acidic conditions.     

Application of Pesticide Quantification in Unpolished Rice by LC-Dopant-Assisted Atmospheric Pressure Photoionization-MS

We applied liquid chromatography-dopant-assisted atmospheric pressure photoionization-mass spectrometry to quantify four distinct pesticides (isoprothiolane, fenitrothion, fthalide, and ethophenprox) in unpolished rice flour. Although the effect of acetone as a dopant on enhancement of ionization differed among the pesticides, the analytical results by LC-DA-APPI-MS with a dopant flow rate of 50 μL min^?1 were not only repeatable (relative SD < 9%, n = 3) but also comparable to those by gas chromatography–mass spectrometry.     

Reaction of α,β‐unsaturated ketones with cerium(IV) salts in alcohol

Reaction of α,β‐unsaturated ketones with cerium(IV) salts or lanthanide triflates in alcohols gave good yields of the corresponding β‐alkoxy compounds. In the case of 2‐cyclopentenone and 2‐cyclohexenone, the 1,1,3‐trialkoxy acetal derivatives were obtained preferentially accompanied by β‐alkoxyketone, except 2‐cycloheptenone. However, in the reaction of 2‐cycloheptenone with alcohol using cerium(IV) sulfate (CS)‐molecular sieve, 1,1,3‐trialkoxy derivatives were obtained. Also, in the cases of 1‐penten‐3‐one, 4‐hexen‐3‐one and 3‐hepten‐2‐one, 1,1,3‐trialkoxy derivatives were obtained preferentially. Copyright © 2006 John Wiley & Sons, Ltd.     

Functionalization of a Single C−F Bond of Trifluoromethylarenes Assisted by an ortho-Silyl Group Using a Trityl-Based All-in-One Reagent with Ytterbium Triflate Catalyst

Catalytic thiolation and azidation of a single C−F bond of trifluoromethylarenes were achieved assisted by an ortho-silyl group with all-in-one reagents to generate a trityl cation and nucleophiles. The reactions catalyzed by ytterbium triflate efficiently afforded a wide variety of difluoromethylenes avoiding the further C−F bond cleavage, by virtue of the mild conditions without the generation of a Brønsted acid.     

Cationic Rh(I) catalyst in fluorinated alcohol: mild intramolecular cycloaddition reactions of ester-tethered unsaturated compounds

In fluorinated alcohols, the cationic Rh(I) species, which is derived from [Rh(COD)Cl]2 and AgSbF6, efficiently catalyzed intramolecular [4+2] cycloaddition reactions of ester-tethered 1,3-diene-8-yne derivatives. The catalytic system was also effective in intramolecular [5+2] cycloaddition reactions of ester-tethered omega-alkynyl vinylcyclopropane compounds.