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.     

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 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.     

Applications of Approximation Theory to thermographic images in earthquake engineering

In this paper we show some new applications of the approximation theory, by means of the multivariate sampling Kantorovich operators, to thermographic images in seismic engineering. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A unifying approach for the study of linear sampling type operators in function spaces

Sampling series play a crucial role in Signal and Image Processing. In this note, we illustrate a general method to construct Sampling series and to determine their convergence in Orlicz spaces. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Healthy Properties of a New Formulation of Pomegranate-Peel Extract in Mice Suffering from Experimental Autoimmune Encephalomyelitis

A new formulation of a pomegranate-peel extract (PEm) obtained by PUAE (Pulsed Ultrasound-Assisted Extraction) and titrated in both ellagic acid (EA) and punicalagin is proposed, characterized and then analyzed for potential health properties in mice suffering from the experimental autoimmune encephalomyelitis (EAE). PEm effects were compared to those elicited by a formulation containing EA (EAm). Control and EAE mice were chronically administered EAm and Pem dissolved in the drinking water, starting from the day 10 post-immunization (d.p.i.), with a “therapeutic” protocol to deliver daily 50 mg/kg of EA. Treated EAE mice did not limit their daily access to the beverage, nor did they show changes in body weight, but they displayed a significant amelioration of “in vivo” clinical symptoms. “Ex vivo” histochemical analysis showed that spinal-cord demyelination and inflammation in PEm and EAm-treated EAE mice at 23 ± 1 d.p.i. were comparable to those in the untreated EAE animals, while microglia activation (measured as Ionized Calcium Binding Adaptor 1, Iba1 staining) and astrocytosis (quantified as glial fibrillar acid protein, GFAP immunopositivity) significantly recovered, particularly in the gray matter. EAm and PEm displayed comparable efficiencies in controlling the spinal pathological cellular hallmarks in EAE mice, and this would support their delivery as dietary supplementation in patients suffering from multiple sclerosis (MS).     

NMR Characterization of Lignans

Lignans are particularly interesting secondary metabolites belonging to the phenyl-propanoid biosynthetic pathway. From the structural point of view, these molecules could belong to the aryltetralin, arylnaphtalene, or dibenzylbutyrolactone molecular skeleton. Lignans are present in different tissues of plants but are mainly accumulated in seeds. Extracts from plant tissues could be characterized by using the NMR-based approach, which provides a profile of aromatic molecules and detailed structural information for their elucidation. In order to improve the production of these secondary metabolites, elicitors could effectively stimulate lignan production. Several plant species are considered in this review with a particular focus on Linum species, well recognized as the main producer of lignans.