Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

Synthesis,properties, and crystal structure of a novel 3-hydroxy-(4<Emphasis Type="Italic">H</Emphasis>)-benzopyran-4-one containing copper(II) complex,and its oxygenation and relevance to quercetinase

The preparation, spectroscopic properties, and crystal structure of [Cu(ind)(mco)] [ind is the anion of 1,3-bis(2-pyridylimino)isoindoline and mco is the anion of 3-hydroxy-(4H)-benzopyran-4-one] are reported. The complex exhibits a distorted square pyramidal geometry. The oxygenation of the title compound results in oxidative cleavage of the heterocyclic ring to give the (acetylsalicylato)copper(II) complex [Cu(asp)(ind)] (asp is the anion of acetylsalicylic acid) and CO as primary products, which reaction resembles the enzymatic reaction of quercetinase.     

Superenergy of Gravitational Waves in the Exact Theory

Gravitational waves and radiation in the exact theory are studied in a unique framework. The observer's point of view is introduced. Some results by Lichnerowicz are generalized and interpreted in terms of reference frames. This allows us to recognize the role played by the gravitational force field in the exact generalization of Bel's superenergy flux theorem. It is also possible to recover the usual concept of wave as energy transmission, by means of a suitable superenergy scalar.     

On a path-independent integral approach to fast tearing of elastomers

Summary The feasibility of a path-independent integral approach to fracture mechanics of elastomers and the objectivity of the pertinent crack stability criterion are discussed with reference to tearing with negligible mechanical dissipations.

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Sommario In questo articolo si discutono le possibilità offerte dall'impiego dell'integrale J e del relativo criterio di stabilità della cricca nello studio della frattura veloce di materiali elastomerici.

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List of symbols and abbreviations F Deformation gradient. - Feled Finite Element for Large Elastic Deformations. - T Strain energy release per unit crack growth (termedG in fracture mechanics of metals). - T _l First Piola-Kirchhoff stress tensor. - u Displacement vector. - W Stored energy function per unit of volume in the undeformed configuration. - x Spatial co-ordinates. - X Material co-ordinates.     

Synthesis and catalytic activity of a fluorous-tagged TEMPO radical

A fluorous-tagged TEMPO radical has been prepared and its catalytic activity in the chemoselective oxidation of alcohols to carbonyl compounds has been investigated. The new fluorous radical proved to be an efficient, selective and easily recoverable catalyst, which can be conveniently used in standard organic solvents and then isolated and recycled by fluorous liquid-liquid extraction.     

Total synthesis of (±)-cyclooroidin

The first total synthesis of (±)-cyclooroidin, a member of the pyrrole-imidazole alkaloid family recently isolated from the sponge Agelas oroides in optically pure form, is described. The synthesis was achieved in nine linear steps, with an overall yield of 10%. Key step was a Wolff bromoketone synthesis performed on the intermediate longamide B.     

A highly stable short alpha-helix constrained by a main-chain hydrogen-bond surrogate

Herein we describe a strategy for the preparation of artificial alpha-helices involving replacement of one of the main-chain hydrogen bonds with a covalent linkage. To mimic the C=O...H-N hydrogen bond as closely as possible, we envisioned a covalent bond of the type C=X-Y-N, where X and Y are two carbon atoms connected through an olefin metathesis reaction. Our results demonstrate that the replacement of a hydrogen bond between the i and i + 4 residues at the N-terminus of a short peptide with a carbon-carbon bond results in a highly stable constrained alpha-helix at physiological conditions as indicated by CD and NMR spectroscopies. The advantage of this strategy is that it allows access to short alpha-helices with strict preservation of molecular recognition surfaces required for biomolecular interactions.     

Biomimetic zinc funnel complexes based on calix[6]N3ArO ligands: an acid-base switch for guest binding

The coordination chemistry of Zn in an N(3)ArOH environment has been explored. The ligands are based on calix[6]arenes that present two imidazole arms and an amino phenol moiety at the narrow rim. Three different types of complexes have been characterized. One is dicationic with Zn(2+) coordinated to the three nitrogen atoms and to the oxygen of the phenol group of the calix[6]ligand. This complex is very sensitive to exogenous coordinating molecules and exists as a 5-coordinate species due to the endo-complexation of a guest. The second species is a monocationic complex for which the phenol group has been deprotonated. The resulting N(3)ArOZn complex can also bind a guest ligand albeit with a lower affinity than the dicationic complex. The third species is neutral. It can be obtained upon reaction with a base to yield a hydroxo complex or with an anion such as a chloride that coordinates the metal center from the outside of the calixarene cavity. The simultaneous binding of two anionic donors decreases the Zn Lewis acidity, allowing an impressive conformational reorganization of the system. One imidazole arm is released by the metal center. The other one undergoes self-inclusion into the pi-basic calixarene cavity because the low affinity of the metal center for neutral ligand does not allow the endo-coordination of an exogenous guest. Hence, the calix[6]N(3)ArOH-based Zn complexes act as an acid-base switch for guest binding. Several aspects of this system appear reminiscent of Zn-peptidases of the astacin and serralisin families.