Group 6 heteroatom- and non-heteroatom-stabilized carbene complexes. beta,beta'- and alpha,beta,beta'-annulation reactions of cyclic enamines

Cyclization reactions of group 6 Fischer carbene complexes with cyclopentanone and cyclohexanone enamines are described. Enamine 3a undergoes thermal alpha,beta,beta'-annulation with alkenylcarbene complexes 1 and 2 (THF, 60 degrees C), affording semibullvalenes 5. The metalate intermediates 6, resulting from beta,beta'-annulation of the enamines 3a and 4a, were quantitatively formed by running the reaction in hexane at room temperature. Acid-promoted demetalation of 6 afforded endo-2-bicyclo[3.2.1]octen-8-ones 7 and endo/exo-2-bicyclo[3.3.1]nonen-9-ones 8 (endo/exo = 5:1). Using (S)-methoxymethylpyrrolidine-derived enamines 3b and 4b,c allowed highly enantioenriched cycloadducts endo-(+)-7 as well as endo-(-)-8 and exo-(-)-8 to be accessed. The non-heteroatom-stabilized carbene complex 10 was formed from complex 6 by Me(3)SiOTf-promoted elimination of the methoxy group, characterized by (13)C NMR, and transformed into the organic compounds 7, 7-d, and 11 as well as into bicyclo[3.2.1]octan-2,8-diones 14 and cycloheptanones 15. On the basis of this sequence, enantioenriched cycloheptanones (+)-15 were efficiently prepared in one pot from carbene complexes 2 and enamine 3b (51-55% yield, 91-96% ee). Extension of this work to simple Fischer carbene complexes 16 allowed an appropriate way to generate the nonstabilized pentacarbonyl[(phenyl(alkyl)carbene]tungsten complex 17 to be designed, for which the thermal and chemical behavior leading to compounds 18-21 is described.     

Composition of the black crusts from the Saint Denis Basilica, France, as revealed by gas chromatography-mass spectrometry

The organic fraction of black crusts from Saint Denis Basilica, France, is composed of a complex mixture of aliphatic and aromatic compounds. These compounds were studied by two different analytical approaches: tetramethyl ammonium hydroxide (TMAH) thermochemolysis in combination with gas chromatography-mass spectrometry (GC-MS), and solvent extraction, fractionation by silica column, and identification of the fraction components by GC-MS. The first approach, feasible at the microscale level, is able to supply fairly general information on a wide range of compounds. Using the second approach, we were able to separate the complex mixture of compounds into four fractions, enabling a better identification of the extractable compounds. These compounds belong to different classes: aliphatic hydrocarbons (nalkanes, n-alkenes), aliphatic and aromatic carboxylic acids (n-fatty acids, alpha,omega-dicarboxylic acids, and benzenecarboxylic acids), polycyclic aromatic hydrocarbons (PAH), and molecular biomarkers (isoprenoid hydrocarbons, diterpenoids, and triterpenoids). With each approach, similar classes of compounds were identified, although TMAH thermochemolysis failed to identify compounds present at low concentrations in black crusts. The two proposed methodological approaches are complementary, particularly in the study of polar fractions.     

Design, synthesis, and evaluation of a mechanism-based inhibitor for gelatinase A

[structure: see text] Matrix metalloproteinases (MMPs), of which 26 are known, have been implicated in a number of pathological conditions, including tumor metastasis. We have previously described the first mechanism-based inhibitor for MMPs (J. Am. Chem. Soc. 2000, 122, 6799-6800), which in chemistry mediated by the active site zinc ion selectively and covalently inhibits MMP-2, -3, and -9. Computational analyses indicated that this selectivity in inhibition of MMPs could be improved by design of new variants of the inhibitor class. We report herein the syntheses of methyl 2-(4-{4-[(2-thiiranylpropyl)sulfonyl]phenoxy}phenyl)acetate (3) and 2-(4-{4-[(2-thiiranylpropyl)sulfonyl]phenoxy}phenyl)acetic acid (4), and show that compound 3 serves as a mechanism-based inhibitor exclusively for MMP-2. This molecule should prove useful in delineating the functions of MMP-2 in biological systems.     

On the index of elliptic partial differential operators inR n

Summary Let A= be an elliptic differential operator inR _u, If, for |α|=l, the coefficients a_α are ? nearly constant ? and, for |α|<l, they tend to zero at infinity with a certain swiftness, it is proved that A is a Fredholm operator with index_x(A)=0 between a suitable weighted Sobolev space M contained in W^l,p (R n) and L^p(R ⁿ, (1+|x|)^lp)== . It is shown, by counterexamples, that the above result, holds only if n>l, p>n/(n−l) and that isomorphism results can be obtained, in general only if the coefficients a_α(|α|<l) are assumed to be ? sufficiently small ? also on compact sets. Then a Sturm-Liouville type problem is studied and a class of negative and falling off at infinity potentials V(x) is constructed in such a way that the Schr?dinger operator H=−Δ+V(x), in L²(R ⁿ), has a zero eigenvalue.

---

Sunto Sia un operatore differenziale ellittico inR ⁿ. Se, per |α|=l, i coefficienti a_α sono ? quasi costanti ? e, per |α|<l, tendono a zero all'infinito con una certa rapidità, si dimostra che A è un operatore di Fredholm con indice_X(A)=0 tra un opportuno spazio di Sobolev con peso M contenuto in W^l,p(R ⁿ) ed L^p(R ⁿ, (1+|x|)^lp)== . Si prova, mediante controesempi, che tale risultato è valido solo se n>l, p>n/(n−l) e che teoremi di isomorfismo si possono ottenere, in generale, solo se si assume che i coefficienti a_α (|α|<l) sono ? sufficientemente piccoli ? anche su insiemi compatti. Si studia quindi un problema del tipo Sturm-Liouville e si costruisce una classe di potenziali V(x) negativi e convergenti a zero all'infinito, tali che l'operatore di Schr?dinger H=−δ+V(x) in L²(R ⁿ) abbia un autovalore nullo.

---

---

Entrata in Redazione il 10 agosto 1977.

---

Work supported by C.N.R. (G.N.A.F.A.).     

Recent advances in electrochemical water technologies for the treatment of antibiotics: A short review

This short review presents a critical overview of the most recent works published in the literature related to the use of electrochemical advanced oxidation processes (EAOPs) for the treatment of antibiotics present in synthetic and real wastewaters. The first section focuses on novelties within the traditional EAOPs, including electrochemical oxidation and electrochemical Fenton-based processes. The second section is devoted to new electrochemical technologies, including heterogeneous electro-Fenton, electrochemically activated persulfate processes, and combined processes. Future perspectives about these processes are also presented to aid the continuous evolution of research in the area.     

How a single photon can mediate entanglement between two others

We describe a novel quantum information protocol, which probabilistically entangles two distant photons that have never interacted. Different from the entanglement swapping protocol, which requires two pairs of maximally entangled photons as the input states, as well as a Bell-state measurement (BSM), the present scheme only requires three photons: two to be entangled and another to mediate the correlation, and no BSM, in a process that we call “entanglement mediation”. Furthermore, in analyzing the paths of the photons in our arrangement, we conclude that one of them, the mediator, exchanges information with the two others simultaneously, which seems to be a new quantum-mechanical feature.     

John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.     

A space–time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains

We present the first space–time hybridizable discontinuous Galerkin (HDG) finite element method for the incompressible Navier–Stokes and Oseen equations. Major advantages of a space–time formulation are its excellent capabilities of dealing with moving and deforming domains and grids and its ability to achieve higher-order accurate approximations in both time and space by simply increasing the order of polynomial approximation in the space–time elements. Our formulation is related to the HDG formulation for incompressible flows introduced recently in, e.g., [N.C. Nguyen, J. Peraire, B. Cockburn, A hybridizable discontinuous Galerkin method for Stokes flow, Comput. Methods Appl. Mech. Eng. 199 (2010) 582–597]. However, ours is inspired in typical DG formulations for compressible flows which allow for a more straightforward implementation. Another difference is the use of polynomials of fixed total degree with space–time hexahedral and quadrilateral elements, instead of simplicial elements. We present numerical experiments in order to assess the quality of the performance of the methods on deforming domains and to experimentally investigate the behavior of the convergence rates of each component of the solution with respect to the polynomial degree of the approximations in both space and time.