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.     

Molecular and crystal structures of ruthenium and osmium arene clusters

The molecular and crystal structures of a number of ruthenium and osmium clusters of nuclearity between three and six containing arene fragments such as C₆H₆, C₆H₃Me₃, C₆H₄Me₂ and C₆H₅Me have been investigated. Attention has been focused on the relationship between the terminal ( ⁶-coordination) and face-capping ( ₃: ²: ²: ²-coordination) bonding modes. Empirical packing potential energy calculations have been employed to investigate the intermolecular organization in the crystal. It has been shown that the arene fragments in mono-arene clusters form ribbons, while in bis-arene clusters graphitic-like interactions throughout the crystal are established. The factors controlling the ease of arene reorientational motion in the solid state has also been investigated in relation to the shape, size and geometry of the molecules and of their interlocking modes.     

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.     

Carbon-carbon coupling on tetrahedral iridium clusters: X-ray molecular structures and multinuclear NMR studies of the two isomeric forms of [Ir4(CO)6(μ3-η-HCCPh)(μ2-η-C4H2Ph2)(μ-PPh2)2]

The reactions of [HIr₄(CO)₉(Ph₂PCCPh)(μ-PPh₂)] (1) or [Ir₄(CO)₈(μ₃-η²-HCCPh)(μ-PPh₂)₂] (2) with HCCPh gave two isomeric forms of [Ir₄(CO)₆(μ₃-η²-HCCPh)(μ₂-η⁴-C₄H₂Ph₂)(μ-PPh₂)₂] (3 and 4) in good yields as the only products. These compounds were characterized with analytical and spectroscopic data including ¹H, ¹³C and ³¹P NMR (1 and 2D) spectroscopy and their molecular structures were established by X-ray diffraction studies. Compounds 3 and 4 exhibit the same distorted butterfly metal polyhedral arrangement of metal atoms with two μ-PPh₂ that occupy different positions in the structures of the two isomers. Both molecules contain a HCCPh ligand bonded in a μ₃-η²-// mode to one of the wings of the butterfly and a metallacyclic ring, which resulted from head-to-tail coupling, in the case of [Ir₄(CO)₆(μ₃-η²-HCCPh){μ₂-η⁴-(H)CC(Ph)C(H)C(Ph)}(μ-PPh₂)₂] (3) and tail-to-tail coupling, in that of [Ir₄(CO)₆(μ₃-η²-HCCPh){μ₂-η⁴-(H)CC(Ph)C(Ph)C(H)}(μ-PPh₂)₂] (4), and which is linked to two metal atoms of the second wing of the butterfly.     

Mechanochemical assembly of hydrogen bonded organic-organometallic solid compounds

Solvent-free reactions with molecular systems have been exploited to prepare hybrid organic-organometallic solids: grinding of the complex [Fe(eta 5-C5H4COOH)2] with solid bases B generates quantitatively the corresponding hydrogen bonded salts [Fe(eta 5-C5H4COOH)(eta 5-C5H4COO)][HB] (B = 1,4-diazabicyclo[2.2.2]octane, 1,4-phenylenediamine); gas-solid reactions are also possible with volatile bases.     

Formation and characterization of the hexanuclear platinum cluster [Pt6(mu-PBu(t)2)4(CO)6](CF3SO3)2 through structural, electrochemical, and computational analyses

The reaction between equimolar amounts of Pt(3)(mu-PBu(t)()(2))(3)(H)(CO)(2), Pt(3)()H, and CF(3)SO(3)H under CO atmosphere affords the triangular species [Pt(3)(mu-PBu(t)()(2))(3)(CO)(3)]X, [Pt(3)()(CO)(3)()(+)()]X (X = CF(3)SO(3)(-)), characterized by X-ray crystallography, or in an excess of acid, [Pt(6)(mu-PBu(t)()(2))(4)(CO)(6)]X(2), [Pt(6)()(2+)()]X(2)(). Structural determination shows the latter to be a rare hexanuclear cluster with a Pt(4) tetrahedral core formed by joining the unbridged sides of two orthogonal Pt(3) triangles. The dication Pt(6)()(2+)() features also extensive redox properties as it undergoes two reversible one-electron reductions to the congeners [Pt(6)(mu-PBu(t)()(2))(4)(CO)(6)](+) (Pt(6)()(+)(), E(1/2) = -0.27 V) and Pt(6)(mu-PBu(t)()(2))(4)(CO)(6) (Pt(6)(), E(1/2) = -0.54 V) and a further quasi-reversible two-electron reduction to the unstable dianion Pt(6)()(2)()(-)() (E(1/2) = -1.72 V). The stable radical (Pt(6)()(+)()) and diamagnetic (Pt(6)()) species are also formed via chemical methods by using 1 or 2 equiv of Cp(2)Co, respectively; further reduction of Pt(6)()(2+)() causes fast decomposition. The chloride derivatives [Pt(6)(mu-PBu(t)()(2))(4)(CO)(5)Cl]X, (Pt(6)()Cl(+)())X, and Pt(6)(mu-PBu(t)()(2))(4)(CO)(4)Cl(2), Pt(6)()Cl(2)(), observed as side-products in some electrochemical experiments, were prepared independently. The reaction leading to Pt(3)()(CO)(3)()(+)() has been analyzed with DFT methods, and identification of key intermediates allows outlining the reaction mechanism. Moreover, calculations for the whole series Pt(6)()(2+)() --> Pt(6)()(2)()(-)()( )()afford the otherwise unknown structures of the reduced derivatives. While the primary geometry is maintained by increasing electron population, the system undergoes progressive and concerted out-of-plane rotation of the four phosphido bridges (from D(2)(d)() to D(2) symmetry). The bonding at the central Pt(4) tetrahedron of the hexanuclear clusters (an example of 4c-2e(-) inorganic tetrahedral aromaticity in Pt(6)()(2+)()) is explained in simple MO terms.