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.     

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...     

Structure‐Dependent Photoinduced Electron Transfer in Fullerodendrimers with Light‐Harvesting Oligophenylenevinylene Terminals

Oligophenylenevinylene (OPV)‐terminated phenylenevinylene dendrons G1 – G4 with one, two, four, and eight “side‐arms”, respectively, were prepared and attached to C₆₀ by a 1,3‐dipolar cycloaddition of azomethine ylides generated in situ from dendritic aldehydes and N‐methylglycine. The relative electronic absorption of the OPV moiety increases progressively along the fullerodendrimer family C₆₀G1 – C₆₀G4 , reaching a 99:1 ratio for C₆₀G4 (antenna effect). UV/Vis and near‐IR luminescence and transient absorption spectroscopy was used to elucidate photoinduced energy and electron transfer in C₆₀G1 – C₆₀G4 as a function of OPV moiety size and solvent polarity (toluene, dichloromethane, benzonitrile), taking into account the fact that the free‐energy change for electron transfer is the same along the series owing to the invariability of the donor–acceptor couple. Regardless of solvent, all the fullerodendrimers exhibit ultrafast OPV→C₆₀ singlet energy transfer. In CH₂Cl₂, the OPV→C₆₀ electron transfer from the lowest fullerene singlet level (¹C₆₀*) is slightly exergonic (ΔG_CS≈0.07 eV), but is observed, to an increasing extent, only in the largest systems C₆₀G2 – C₆₀G4 with lower activation barriers for electron transfer. This effect has been related to a decrease of the reorganization energy upon enlargement of the molecular architecture. Structural factors are also at the origin of an unprecedented OPV→C₆₀ electron transfer observed for C₆₀G3 and C₆₀G4 in apolar toluene, whereas in benzonitrile, electron transfer occurs in all cases. Monitoring of the lowest fullerene triplet state by sensitized singlet oxygen luminescence and transient absorption spectroscopy shows that this level is populated through intersystem crossing and is not involved in photoinduced electron transfer.     

Diels‐alder reactions of 2‐(2‐nitroethenyl)‐1H‐pyrroles and their oxygen and sulfur analogs with quinones

Diels‐Alder reaction of 2‐(E‐2‐nitroethenyl)‐1H‐pyrrole ( 2a ) with 1,4‐benzoquinone gave the desired benzo[e]indole‐6, 9(3H)‐dione ( 4a ) in 10% yield versus a 26% yield (lit. 86% [5]) of the known N‐methyl compound ( 4b ) from the N‐(or 1)‐methyl compound ( 2b ). Protection of the nitrogen of 2a with a phenylsul‐fonyl group ( 2c ) gave a 9% yield of the corresponding N‐(or 3)‐phenylsulfonyl compound ( 4c ). The reaction of 2b with 1,4‐naphthoquinone gave in 6% yield (lit. 64% [5]) the known 3‐methylnaphtho[2,3‐e]‐indole‐6, 9(3H)‐dione ( 6 ). The reaction of 2‐(E‐2‐nitroethenyl)furan ( 8a ) gave a small yield of the desired naphtho[2,1‐b]furan‐6, 9‐dione ( 9a ), recognized by comparing its NMR spectrum with that of 4b. The corresponding reaction of 2‐(E‐2‐nitroethenyl)thiophene ( 8b ) gave a 4% yield of naphtho[2,1‐ b ]thiophene‐6,9‐dione ( 9b ), previously prepared in 24% yield [12] in a three‐step procedure involving 2‐ethenylthiophene. Introducing an electron‐releasing 2‐methyl substituent into 8a and 8b gave 12a and 12b , which, upon reaction with 1,4‐benzoquinone, gave 2‐methylnaphtho[2,1‐b]furan‐6, 9‐dione ( 13a ) and its sulfur analog ( 13b ) in yields of 4 and 8%, respectively.     

Sensitivity improvement in 19F NMR-based screening experiments: theoretical considerations and experimental applications

NMR-based binding and functional screening performed with FAXS (fluorine chemical shift anisotropy and exchange for screening) and 3-FABS (three fluorine atoms for biochemical screening) represents a potential alternative approach to high-throughput screening for the identification of novel potential drug candidates. The major limitation of this method in its current status is its intrinsic low sensitivity that limits the number of tested compounds. One approach for overcoming this problem is the use of a cryogenically cooled (19)F probe that reduces the thermal noise in the receiver circuitry. Sensitivity improvement in the two screening techniques achieved with the novel cryogenic (19)F probe technology permits an increased throughput, detection of weaker binders and inhibitors (relevant in a fragment-based lead discovery program), detection of slow binders, and reduction in protein and substrate consumption. These aspects are analyzed with theoretical simulations and experimental quantitative performance evaluation. Application of 3-FABS combined with the cryogenic (19)F probe technology to rapid screening at very low enzyme concentrations and the current detection limits reached with this approach are also presented.