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.     

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.     

Template evaporation method for controlling anatase nanocrystal size in ordered macroporous TiO2

The importance of pure-phase titanium oxide materials as catalysts, sensors, and photonic band-gap materials has been growing steadily. Recently, more attention has been focused on nanostructured titanium oxide showing controlled and periodic porosity on a nanometric scale. The nanocrystal size control of porous nanostructured titanium oxide in an anatase form is a crucial step for the organic template method. Simple template removal by evaporation in an inert atmosphere is reported in this article and compared with the calcination technique usually reported in the literature. The proposed method allows the formation of a double-porous (macro and meso) anatase phase. We demonstrate that it highly preserves the macropore order into a titanium oxide material and induces narrowly dispersed mesopores by controlling the nano-crystal size that is kept around 6 nm. For the proposed method, polystyrene beads are particularly suitable as templates, being evaporated in the temperature range of anatase existence. The final high surface area makes the materials appealing for applications as photocatalysts or sensors.     

A New Technique for Preserving Conservation Laws

Foundations of Computational Mathematics - This paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We...     

Synthesis and structural characterization of isomeric coumarino‐1,2‐oxaphosphole derivatives

The coumarino‐[3,4‐c]‐3H‐10‐methyl‐2‐oxo‐2‐phenyl‐1,2‐oxaphosphole was prepared by the addition of PhPCl₂ to 3‐acetylcoumarin in the presence of acetic anhydride. Its conversion to the isomeric coumarino‐[3,4‐c]‐9H‐9‐methyl‐2‐oxo‐2‐phenyl‐1,2‐oxaphosphole was studied in different reaction conditions. The structures of the two isomers were determined by X‐ray crystallography and by ab initio molecular orbital calculations.