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     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Decision methods for linearly ordered Heyting algebras

The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.     

Oxidation of cysteine to cysteic acid in proteins by peroxyacids, as monitored by immobilized pH gradients.

It has often been debated whether the presence of persulfate in a polyacrylamide gel could lead to the oxidation of cysteine (Cys) in proteins to cysteic acid. In fact, direct incubation of bovine serum albumin (BSA) with peroxodisulfate and periodate barely alters the isoelectric point (pI) and does not produce any cysteic acid. In contrast, caroate (peroxomonosulfate) and perphthalate strongly lower the pI of BSA. In the former case it as demonstrated that 4-Cys (of a total of 35) were converted into cysteic acid. Perphthalate was found to be, by far, the strongest oxidant: 15 (of 35) Cys residues were oxidized to cysteic acid and all methionine groups were destroyed.     

High-performance liquid chromatographic determination of D-amino acid oxidase activity.

A new procedure for the assay of D-amino acid oxidase activity has been developed. alpha-Ketoisovaleric acid, derived from D-valine, was estimated by high-performance liquid chromatography after reaction with o-phenylenediamine to give the corresponding quinoxalinol derivative. alpha-Ketovaleric acid was used as an internal standard to ensure the reproducibility of the method. As an example of application, kidney cortex homogenates were analyzed for their D-amino acid oxidase activity. The advantages of the presented procedure for the determination of the enzymatic activity in biological samples compared with previously reported procedures are discussed.     

Origin, nature, and fate of the fluorescent state of the green fluorescent protein chromophore at the CASPT2//CASSCF resolution

Ab initio CASPT2//CASSCF relaxation path computations are employed to determine the intrinsic (e.g., in vacuo) mechanism underlying the rise and decay of the luminescence of the anionic form of the green fluorescent protein (GFP) fluorophore. Production and decay of the fluorescent state occur via a two-mode reaction coordinate. Relaxation along the first (totally symmetric) mode leads to production of the fluorescent state that corresponds to a planar species. The second (out-of-plane) mode controls the fluorescent state decay and mainly corresponds to a barrierless twisting of the fluorophore phenyl moiety. While a "space-saving" hula-twist conical intersection decay channel is found to lie only 5 kcal mol(-1) above the fluorescent state, the direct involvement of a hula-twist deformation in the decay is not supported by our data. The above results indicate that the ultrafast fluorescence decay observed for the GFP chromophore in solution is likely to have an intrinsic origin. The possible effects of the GFP protein cavity on the fluorescence lifetime of the investigated chromophore model are discussed.     

The ring-opening reaction of chromenes: a photochemical mode-dependent transformation

The efficiency of the photochemical ring-opening of chromenes (or benzopyrans) depends on the vibronic transition selected by the chosen excitation wavelength. In the present work, ab initio CASPT2//CASSCF calculations are used to determine the excited-state ring-opening reaction coordinate for 2H-chromene (C) and 2,2-diethyl-2H-chromene (DEC) and provide an explanation for such an unusual mode-dependent behavior. It is shown that excited-state relaxation and decay occur via a multimodal and barrierless (or nearly barrierless) reaction coordinate. In particular, the relaxation out of the Franck-Condon involves a combination of in-plane skeletal stretching and out-of-plane modes, while the second part of the reaction coordinate is dominated exclusively by a different out-of-plane mode. Population of this last mode is shown to be preparatory with respect to both C-O bond breaking and decay via an S(1)/S(0) conical intersection. The observed mode-dependent ring-opening efficiency is explained by showing that the vibrational mode corresponding to the most efficient vibronic transition has the largest projection onto the out-of-plane mode of the reaction coordinate. To support the computationally derived mechanism, we provide experimental evidence that the photochemical ring-opening reaction of 2,2-dimethyl-7,8-benzo(2H)chromene, that similarly to DEC exhibits a mode-dependent photoreaction, has a low ( approximately 1 kcal mol(-1)) activation energy barrier.     

Molecular Size and Electronic Structure Combined Effects on the Electrogenerated Chemiluminescence of Sulfurated Pyrene‐Cored Dendrimers

The electrochemistry, photophysics, and electrochemically generated chemiluminescence (ECL) of a family of polysulfurated dendrimers with a pyrene core have been thoroughly investigated and complemented by theoretical calculations. The redox and luminescence properties of dendrimers are dependent on the generation number. From low to higher generation it is both easier to reduce and oxidize them and the emission efficiency increases along the family, with respect to the polysulfurated pyrene core. The analysis of such data evidences that the formation of the singlet excited state by cation–anion annihilation is an energy‐deficient process and, thus, the ECL has been justified through the triplet–triplet annihilation pathway. The study of the dynamics of the ECL emission was achieved both experimentally and theoretically by molecular mechanics and quantum chemical calculations. It has allowed rationalization of a possible mechanism and the experimental dependence of the transient ECL on the dendrimer generation. The theoretically calculated Marcus electron‐transfer rate constant compares very well with that obtained by the finite element simulation of the whole ECL mechanism. This highlights the role played by the thioether dendrons in modulating the redox and photophysical properties, responsible for the occurrence and dynamics of the electron transfer involved in the ECL. Thus, the combination of experimental and computational results allows understanding of the dendrimer size dependence of the ECL transient signal as a result of factors affecting the annihilation electron transfer.