Completeness for flat modal fixpoint logics

This paper exhibits a general and uniform method to prove axiomatic completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ(x,p₁,…,p_n), where x occurs only positively in γ, we obtain the flat modal fixpoint language L_?(Γ) by adding to the language of polymodal logic a connective ?_γ for each γ∈Γ. The term ?_γ(φ₁,…,φ_n) is meant to be interpreted as the least fixed point of the functional interpretation of the term γ(x,φ₁,…,φ_n). We consider the following problem: given Γ, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language L_?(Γ) on Kripke structures. We prove two results that solve this problem.First, let be the logic obtained from the basic polymodal by adding a Kozen-Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective ?_γ. Provided that each indexing formula γ satisfies a certain syntactic criterion, we prove this axiom system to be complete.Second, addressing the general case, we prove the soundness and completeness of an extension of . This extension is obtained via an effective procedure that, given an indexing formula γ as input, returns a finite set of axioms and derivation rules for ?_γ, of size bounded by the length of γ. Thus the axiom system is finite whenever Γ is finite.     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

A Mechanistically and Operationally Simple Route to Metal–N-Heterocyclic Carbene (NHC) Complexes

We have been puzzled by the involvement of weak organic and inorganic bases in the synthesis of metal–N-heterocyclic carbene (NHC) complexes. Such bases are insufficiently strong to permit the presumed required deprotonation of the azolium salt (the carbene precursor) prior to metal binding. Experimental and computational studies provide support for a base-assisted concerted process that does not require free NHC formation. The synthetic protocol was found applicable to a number of transition-metal- and main-group-centered NHC compounds and could become the synthetic route of choice to form M–NHC bonds.     

Semilinear elliptic equations and systems with diffuse measures

We study the equation −, where g(·, s) is finite outside sets of zero H ¹-capacity, , and μ is a diffuse measure. As an application, we provide a positive answer to a question of Lucio Boccardo concerning existence of solutions of an elliptic system with absorption.

A Lucio “Tu se’ lo mio maestro e ’l mio autore” (Dante, Inferno, I, 85)

     

Magnesium‐Catalyzed Hydroboration of Terminal and Internal Alkynes

A magnesium‐catalyzed hydroboration of alkynes providing good yields and selectivities for a wide range of terminal and symmetrical and unsymmetrical internal alkynes has been developed. The compatibility with many functional groups makes this magnesium catalyzed procedure attractive for late stage functionalization. Experimental mechanistic investigations and DFT calculations reveal insights into the reaction mechanism of the magnesium catalyzed protocol.     

Thorough evaluation of the validity of conventional enantio-gas chromatography in the analysis of volatile chiral compounds in mandarin essential oil: A comparative investigation with multidimensional gas chromatography

The present research is focused on the determination of the enantiomeric distribution of chiral compounds, contained in mandarin essential oils, by means of conventional chiral gas chromatography with flame ionization detection (enantio-GC-FID); the results attained were compared with those derived from heart-cutting multidimensional GC-mass spectrometry (MDGC/MS), to evaluate the reliability of the monodimensional technique as a tool for quality control. The Deans-switch MDGC system was equipped with two GC ovens, which were connected via a heated transfer line, a flame ionization detector (FID1) in the first dimension and a quadrupole MS as second-dimension detector. The a priori knowledge of potential co-elutions concerning target compounds (an enantiomer and an interfering compound), when using enantio-GC-FID, could enable the use of corrected enantiomer excess values. Correction factors could be calculated through a preliminary GC-FID analysis (using an apolar column), considering the peak areas of the known interferences. The method used for the calculation of a so-called “coelution correction factor” is described, along with some examples.     

Synthesis and Ruthenium-Catalyzed Enantioselective Hydrogenation of 3-O-Substituted 1,3-Dihydroxypropan-2-ones. Part 2

A number of 3-O-substituted 1,3-dihydroxypropan-2-ones have been synthesized in view of their potential use as prochiral precursors of optically active glycerols. Indeed, the oxo-ethers have been reduced to the corresponding 3-O-substituted glycerols via chiral Ru complexes derived from (S)-binap, ( =(?)-(S)-2,2′-bis(diphenylphosphino)-1,1′-binaphthalene) with enantiomeric excesses up to 93%. The steric course of the catalytic reduction appears to be essentially dependent on the steric encumbrance of the substituents; indeed, a dramatic increase of the enantiomeric excess is observed when the bulky trityl group is substituted by the less encumbering benzyl or octadecyl groups.     

Synthesis of 4,5-dihydro-2,4-benzoxazepin-3( 1H)ones and 1,3,4,5-tetrahydro-2,4-benzoxazepines

o- Aminomethylbeiizyl alcohols (X) easily cyclize with phosgene in an aqueous alkaline medium to form 4,5-dihydro-2,4-benzoxazepin-3(1H)ones (IV) and with aldehydes in acidic conditions to yield 1,3,4,5-tetrahydro-2,4-benzoxazepines (V). The characteristics and chemical behaviour of these new heterocyclic ring systems are reported.