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.     

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.     

Synthesis, Electrochemistry and Crystal Structure of the [Ni36Pt4(CO)45]6− and [Ni37Pt4(CO)46]6− Hexaanions

The [Ni₃₆Pt₄(CO)₄₅]^6- and [Ni₃₇Pt₄(CO)₄₆]^6- clusters have been obtained in mixture upon reaction in acetonitrile of [Ni₆(CO)₁₂]^2- salts with K₂PtCl₄ in a 2.5:1 molar ratio. The two hexaanions were indistinguishable by spectroscopic techniques. Crystallization of their trimethylbenzylammonium salts led to crystals of composition 0.5[NMe₃CH₂Ph]₆[Ni₃₆Pt₄(CO)₄₅]-0.5[NMe₃CH₂Ph]₆[Ni₃₇Pt₄(CO)₄₆]·C₃H₈O, hexagonal,space group P6₃ (No. 173), a=17.853(9), c=27.127(13) Å, Z=2; final R=0.057. The metal core of the [Ni₃₆Pt₄(CO)₄₅]^6- anion consists of a Pt₄ tetrahedron fully encapsulated in a shell of 36 Ni atoms belonging to a very distorted and incomplete ₅ tetrahedron. The [Ni₃₇Pt₄(CO)₄₆]^6- hexaanion derives from the former by capping the unique triangular face of the metal polyhedron with an additional Ni(CO) fragment. The [Ni₃₆Pt₄(CO)₄₅]^6--[Ni₃₇Pt₄(CO)₄₆]^6- mixture is rapidly degraded to the known [Ni₉Pt₃(CO)₂₁]^4- cluster by exposure to carbon monoxide. Its reaction with protic acids initially affords the corresponding [H_6-nNi₃₆Pt₄(CO)₄₅]^n--[H_6-nNi₃₇Pt₄(CO)₄₆]^n- (n=5, 4) derivatives, and eventually leads to rearrangement to the known [H_6-n Ni₃₈Pt₆(CO)₄₈]^n- species. Both [Ni₃₆Pt₄(CO)₄₅]^6--[Ni₃₇Pt₄(CO)₄₆]^6- and [HNi₃₆Pt₄(CO)₄₅]^5--[HNi₃₇Pt₄(CO)₄₆]^5- mixtures have been chemically and electrochemically reduced to their corresponding [Ni₃₆Pt₄(CO)₄₅]^n--[Ni₃₇Pt₄(CO)₄₆]^n- (n=7–9) and [HNi₃₆Pt₄(CO)₄₅]^n--[HNi₃₇Pt₄(CO)₄₆]^n- (n=6–8) mixtures.     

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.     

Interaction of Naproxen with Crystalline and Amorphous Methylated β-Cyclodextrin in the Liquid and Solid State

Abstract

Interactions of naproxen (NAP) with amorphous, randomly methylated β-cyclodextrin at a degree of substitution per anhydroglucose unit of 1.8 (RAMEB) and with crystalline heptakis-(2,6-di-O-methyl)-β-cyclodextrin (DIMEB) were studied in aqueous solution and in the solid state using, respectively, phase-solubility analysis (at 25 °C, 37 °C and 47 °C) and differential scanning calorimetry (DSC) supported by X-ray powder diffractometry. RAMEB and DIMEB displayed similar solubilizing and complexing abilities towards NAP, suggesting analogous inclusion modes of the drug in the host cavity in aqueous solution. Differences were instead observed in interactions in the solid state, where the amorphizing capacity of RAMEB toward NAP (evaluated by DSC) was about twice that of DIMEB at each drug-to-carrier ratio. Assuming that inclusion complexation is also involved in solid-state interactions, molecular modelling accounted for the experimental results in terms of structural features of DIMEB, i.e. the particular inwards orientation of O-6-C-8 groups of three alternate glucoses on the primary hydroxyl side which hampers a deep penetration of NAP in the DIMEB cavity in the solid state. On the contrary, no obstruction of the cavity apparently occurs with RAMEB due its noncrystalline state. The aqueous dissolution rate of NAP from NAP-RAMEB and NAP-DIMEB blends containing 0.59, 0.73, 0.85, and 0.92 mass fraction of carrier linearly increased at decreasing drug-to-carrier ratios. The improvement was 5 to 20 times (from powders) and 50 to 200 times (from discs) the dissolution rate of NAP alone for both carrier. Therefore the choice of the amorphous RAMEB in pharmaceutical formulations can be recommended mainly for economic reasons, though the anhydrous and non-hygroscopic nature of crystalline DIMEB might be of particular advantage in case of moisture sensitive formulations.     

One-pot synthesis of stable NIR tetracene diimides via double cross-coupling

Tetracene tetracarboxylic diimides have been synthesized based on direct double ring extension of electron-deficient naphthalene diimides involving metallacyclopentadienes. Atomic structure and electronic transitions responsible for their NIR absorption spectra are investigated with quantum-chemical calculations. In light of their unique structure and admirable photophysical and electronic properties, this new molecular skeleton is promising candidate for n-type semiconductors.     

Site selectivity in the reactions of the hexanuclear platinum cluster [Pt6(mu-PtBu2)4(CO)6][CF3SO3]2

The previously reported hexanuclear cluster [Pt(6)(mu-PtBu(2))(4)(CO)(6)](2+)[Y](2) (1-Y(2): Y=CF(3)SO(3) (-)) contains a central Pt(4) tetrahedron bridged at each of the opposite edges by another platinum atom; in turn, four phosphido ligands bridge the four Pt-Pt bonds not involved in the tetrahedron, and, finally, one carbonyl ligand is terminally bonded to each metal centre. Interestingly, the two outer carbonyls are more easily substituted or attacked by nucleophiles than the inner four, which are bonded to the tetrahedron vertices. In fact, the reaction of 1-Y(2) with 1 equiv of [nBu(4)N]Cl or with an excess of halide salts gives the monochloride [Pt(6)(mu-PtBu(2))(4)(CO)(5)Cl](+)[Y], 2-Y, or the neutral dihalide derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)X(2)] (3: X=Cl; 4: X=Br; 5: X=I). Moreover, the useful unsymmetrically substituted [Pt(6)(mu-PtBu(2))(4)(CO)(4)ICl] (6) was obtained by reacting equimolar amounts of 2 and [nBu(4)N]I, and the dicationic derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)L(2)](2+)[Y](2) (7-Y(2): L=(13)CO; 8-Y(2): L=CNtBu; 9-Y(2): L=PMe(3)) were obtained by reaction of an excess of the ligand L with 1-Y(2). Weaker nitrogen ligands were introduced by dissolving the dichloride 3 in acetonitrile or pyridyne in the presence of TlPF(6) to afford [Pt(6)(mu-PtBu(2))(4) (CO)(4)L(2)](2+)[Z](2) (Z=PF(6) (-), 10-Z(2): L=MeCN; 11-Z(2): L=Py). The "apical" carbonyls in 1-Y(2) are also prone to nucleophilic addition (Nu(-): H(-), MeO(-)) affording the acyl derivatives [Pt(6)(mu-PtBu(2))(4)(CO)(4)(CONu)(2)] (12: Nu=H; 13: Nu=OMe). Complex 12 is slowly converted into the dihydride [Pt(6)(mu-PtBu(2))(4)(CO)(4)H(2)] (14), which was more cleanly prepared by reacting 3 with NaBH(4). In a unique case we observed a reaction involving also the inner carbonyls of complex 1, that is, in the reaction with a large excess of the isocyanides R-NC, which form the corresponding persubstituted derivatives [Pt(6)(mu-tPBu(2))(4)(CN-R)(6)](2+)[Y](2), (15-Y(2): R=tBu; 16-Y(2) (2-): R=-C(6)H(4)-4-C triple bond CH). All complexes were characterized by microanalysis, IR and multinuclear NMR spectroscopy. The crystal and molecular structures of complexes 3, 5, 6 and 9-Y(2) are also reported. From the redox viewpoint, all complexes display two reversible one-electron reduction steps, the location of which depends both upon the electronic effects of the substituents, and the overall charge of the original complex.