A normalizing system of natural deduction for intuitionistic linear logic

 The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination. Received: 10 October 2000 / Revised version: 26 July 2001 / Published online: 2 September 2002 Mathematics Subject Classification (2000): 03F52, 03F05 Keywords or phrases: Linear logic – Natural deduction – General elimination rules     

Novel dinitroxide mediating agent for stable free‐radical polymerization

A novel dinitroxide mediating agent that was suitable for stable free‐radical polymerization was synthesized and used in the block copolymerization of styrene and t‐butyl styrene. Quantitative yields of a novel dinitroxide based on 1,6‐hexamethylene diisocyanate and 4‐hydroxy‐2,2,6,6‐tetramethyl‐1‐piperidinyloxy were obtained. Various experimental parameters, including the nitroxide‐to‐initiator molar ratio, were examined, and it was determined that the polymerization was most controlled under conditions similar to those of conventional 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated stable free‐radical polymerization. Moreover, the dinitroxide mediator proved to be a viable route for the facile two‐step synthesis of triblock copolymers of styrene and t‐butyl styrene. However, the dinitroxide mediation process resulted in a higher than expected level of nitroxide decomposition, which resulted in polymers possessing a terminal alkoxyamine and an adjacent hydroxylamine rather than a preferred internal bisalkoxyamine. This decomposition resulted in the formation of diblock copolymer species during the triblock copolymer synthesis. Gel permeation chromatography was used to monitor the chain‐end decomposition kinetics, and the determined observed rate constant (5.89 × 10^?5 s^?1) for decomposition agreed well with previous studies for other dinitroxide mediating agents. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1547–1556, 2004     

Simplicial trees are sequentially Cohen–Macaulay

This paper uses dualities between facet ideal theory and Stanley–Reisner theory to show that the facet ideal of a simplicial tree is sequentially Cohen–Macaulay. The proof involves showing that the Alexander dual (or the cover dual, as we call it here) of a simplicial tree is a componentwise linear ideal. We conclude with additional combinatorial properties of simplicial trees.     

Determination of anions in rainwater by capillary electrophoresis with conductivity detection

A routine method for the determination of chloride, nitrate and sulfate anions in rainwater by capillary electrophoresis was developed. The system uses an end-column non-suppressed conductivity detector. Linear calibration plots were generated from 0.050 to 20 mg/l, which is the range generally found in wet depositions. Accuracy and precision were evaluated by analyzing certified standards of simulated rainwater and environmental samples, or by comparing CE results with those obtained by IC, the reference technique for anion analysis in wet deposition. The reproducibility of the method was satisfactory except at the lower and upper limits of the analytical range. Sensitivity lay in the range of few μg/l.     

The rate of homolysis of adducts of peroxynitrite to the C=O double bond.

Nucleophilic addition of the peroxynitrite anion, ONOO(-), to the two prototypical carbonyl compounds, acetaldehyde and acetone, was investigated in the pH interval 7.4-14. The process is initiated by fast equilibration between the reactants and the corresponding tetrahedral adduct anion, the equilibrium being strongly shifted to the reactant side. The adduct anion also undergoes fast protonation by water and added buffers. Consequently, the rate of the bimolecular reaction between ONOO(-) and the carbonyl is strongly dependent on the pH and on the concentration of the buffer. The pK(a) of the carbonyl-ONOO adduct was estimated to be approximately 11.8 and approximately 12.3 for acetone and acetaldehyde, respectively. It is shown that both the anionic and the neutral adducts suffer fast homolysis along the weak O-O bond to yield free alkoxyl and nitrogen dioxide radicals. The yield of free radicals was determined to be about 15% with both carbonyl compounds at low and high pH, while the remainder collapses to molecular products in the solvent cage. The rate constants for the homolysis of the adducts vary from ca. 3 x 10(5) to ca. 5 x 10(6) s(-1), suggesting that they cannot act as oxidants in biological systems. This small variation around a mean value of about 10(6) s(-1) suggests that the O-O bond in the adduct is rather insensitive to its protonation state and to the nature of its carbonyl precursor. An overall reaction scheme was proposed, and all the corresponding rate constants were evaluated. Finally, thermokinetic considerations were employed to argue that the formation of dioxirane as an intermediate in the reaction of ONOO(-) with acetone is an unlikely process.     

Sensing the physicochemical nature of he and ne in micropores by adsorption measurements

He and Ne in contact with molecular sieves in the form of crystalline A zeolites and amorphous carbon molecular sieves fibers (CMSF) were studied by adsorption measurements. Classification of the effective enclosure of zeolitic apertures and of graphitic constrictions, as determined by recent temperature-programmed desorption mass spectrometry (TPD-MS) studies of adsorption of He and Ne onto these materials, was utilized in making a prudent choice of samples and experimental conditions. In view of the former TPD information, the behaviors of adsorption and volumetric measurements reported herein are straightforwardly interpreted. The combined TPD, adsorption isotherms, and dead volume data deepen the understanding of the physicochemical nature of adsorbed gas, where gas adsorption in the vicinity of pore constrictions and/or apertures as well as on the inner surface areas of pores and/or cages could be resolved. Previous conclusions that the huge activation energies measured for Ne/CMSF at high temperatures are unlikely to characterize chemical desorption but reflect those required for overcoming the barrier of effectively constricted apertures were confirmed by the volumetric data presented here. At 77 K, considerable He adsorption was observed in the porous solids and found to be responsible for abnormal deduced values of dead volumes. The occurrence of significant adsorption of He onto A zeolites and CMSF at 77 K warrants the realization that in cases concerning porous materials, volumetrically deduced quantities should not be taken for granted, but should be carefully considered and uniquely interpreted in relation to the specific experimental conditions under which they are taken.     

(CuBr)3P4Se4: A Low Symmetric Variant of the (CuI)3P4Se4 Structure Type

Bright orange (CuBr)₃P₄Se₄ is obtained from the reaction of CuBr, P, and Se in stoichiometric amounts (CuBr : P : Se = 3 : 4 : 4). The composition and the crystal structure of the compound were determined from single crystal X‐ray diffraction data. Lattice constants are a = 33.627(2) Å, b = 6.402(1) Å, c = 19.059(1) Å, β = 90.19(3) °, V = 4103.2(3) ų, and Z = 12. The compound crystallizes in a structure that is related to (CuI)₃P₄Se₄. Cages of β‐P₄Se₄ are stacked along the b‐axis and are separated by columns of copper(I) bromide. However, the coordination of the β‐P₄Se₄ cage molecules to the copper atoms in the CuBr columns in (CuBr)₃P₄Se₄ is quite different from (CuI)₃P₄Se₄. The monoclinic compound (space group: P2₁, no. 4) has an almost orthorhombic metric in combination with a threefold superstructure in [100]. Structural aspects of (CuBr)₃P₄Se₄ are discussed with respect to the heavier homologue (CuI)₃P₄Se₄.     

Porous MoS2 synthesized by ultrasonic spray pyrolysis

The hydrodesulfurization (HDS) activity of molybdenum sulfide-based catalysts is localized to the edges of this layered solid and is, therefore, highly dependent on the technique used to prepare the material. Here, ultrasonic spray pyrolysis (USP) was used to synthesize porous, nanostructured MoS2. Low surface area powders, not useful for catalysis, are generally produced by USP. This work shows that when combined with a dissolvable template, USP is capable of producing high surface area materials. An aqueous solution of ammonium tetrathiomolybdate and colloidal silica was nebulized and pyrolyzed to give a MoS2/SiO2 composite material. Leaching with HF removed the sacrificial SiO2, resulting in a highly porous MoS2 network with surface areas as high as 250 m2/g. Cobalt-promoted MoS2 networks were also synthesized. The thiophene HDS activities of these materials were substantially higher than those of unsupported MoS2 and RuS2 standards, illustrating the enhanced dispersion of the HDS active phase achieved by this synthetic technique.     

Vilsmeier formylation of 5,10,15-triphenylcorrole: expected and unusual products

5,10,15-Triphenylcorrole (1) reacts with the Vilsmeier reagent (POCl(3)/DMF) to give the corresponding 3-formyl derivative 3 as the major product. The regioselectivity of the reaction was proven by X-ray crystallography and only traces of the 2-formyl isomer were observed. A more polar product is also observed and this compound becomes the major product when an excess of DMF is used for the preparation of the Vilsmeier reagent, while the formation of the 3-formyl isomer is almost completely suppressed. X-ray crystallography allowed us to identify this compound as the fully substituted N-ethane bridged derivative 4, formed from the attack of the Vilsmeier reagent at the inner core of the macrocycle. This compound is unique among porphyrinoid macrocycles, and further confirms the peculiarity of corrole chemistry.