Bisymplectic Grassmannians of planes

The bisymplectic Grassmannian \({{\,\mathrm{I_2Gr}\,}}(k,V)\) parametrizes k-dimensional subspaces of a vector space V which are isotropic with respect to two general skew-symmetric forms; it is a Fano projective variety which admits an action of a torus with a finite number of fixed points. In this work, we study its equivariant cohomology with complex coefficients when \(k=2\); the central result of the paper is an equivariant Chevalley formula for the multiplication of the hyperplane class by any Schubert class. Moreover, we study in detail the case of \({{\,\mathrm{I_2Gr}\,}}(2, {\mathbb {C}}^6)\), which is a quasi-homogeneous variety, we analyse its deformations, and we give a presentation of its cohomology.

     

Valorization of Okara by Enzymatic Production of Anti-Fungal Compounds for Plant Protection

Okara is a soybean transformation agri-food by-product, the massive production of which currently poses severe disposal issues. However, its composition is rich in seed storage proteins, which, once extracted, can represent an interesting source of bioactive peptides. Antimicrobial and antifungal proteins and peptides have been described in plant seeds; thus, okara is a valuable source of compounds, exploitable for integrated pest management. The aim of this work is to describe a rapid and economic procedure to isolate proteins from okara, and to produce an enzymatic proteolyzed product, active against fungal plant pathogens. The procedure allowed the isolation and recovery of about 30% of okara total proteins. Several proteolytic enzymes were screened to identify the proper procedure to produce antifungal compounds. Antifungal activity of the protein digested for 24 h with pancreatin against Fusarium and R. solani mycelial growth and Pseudomonas spp was assessed. A dose-response inhibitory activity was established against fungi belonging to the Fusarium genus. The exploitation of okara to produce antifungal bioactive peptides has the potential to turn this by-product into a paradigmatic example of circular economy, since a field-derived food waste is transformed into a source of valuable compounds to be used in field crops protection.     

Phase transition in dually weighted colored tensor models

Tensor models are a generalization of matrix models (their graphs being dual to higher-dimensional triangulations) and, in their colored version, admit a 1/N expansion and a continuum limit. We introduce a new class of colored tensor models with a modified propagator which allows us to associate weight factors to the faces of the graphs, i.e. to the bones (or hinges) of the triangulation, where curvature is concentrated. They correspond to dynamical triangulations in three and higher dimensions with generalized amplitudes. We solve analytically the leading order in 1/N of the most general model in arbitrary dimensions. We then show that a particular model, corresponding to dynamical triangulations with a non-trivial measure factor, undergoes a third-order phase transition in the continuum characterized by a jump in the susceptibility exponent.     

Erratum and addendum to “Two-point b.v.p. for multivalued equations with weakly regular r.h.s.”

In this paper, we define a topological index for compact multivalued maps in convex metrizable subsets of a locally convex topological vector space in order to correct the proofs of Theorems 4.1 and 4.2 in Benedetti et al. (2011) [1].     

Matroid Polytopes and their Volumes

We express the matroid polytope P _M of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of P _M . This gives a combinatorial expression for the degree of an arbitrary torus orbit closure in the Grassmannian Gr _k,n . We then derive analogous results for the independent set polytope and the underlying flag matroid polytope of M. Our proofs are based on a natural extension of Postnikov’s theory of generalized permutohedra.     

1-Substituted morpholino ethenes—III: Carbocyclic and aliphatic heterocyclic compounds from 5-membered ring derivatives

[4+2] Cycloaddition reaction of 1-(cyclopenten-1-y1)-1-morpholino ethene with β-nitrostyrene leads to tetrahydroindan and tetrahydroindanone derivatives. A [4+2] adduct of interest is also obtained in the reaction of the same substrate with mesyl chloride. Reactivity of the same electrophiles with the morpholino enamine of cyclopentyl-methyl ketone is also examined. Some stereochemical aspects of the above mentioned reactions are discussed.     

Nonlinear pulse propagation and phase velocity of laser-driven plasma waves

Laser evolution and plasma wave excitation by a relativistically intense short-pulse laser in underdense plasma are investigated in the broad pulse limit, including the effects of pulse steepening, frequency redshifting, and energy depletion. The nonlinear plasma wave phase velocity is shown to be significantly lower than the laser group velocity and further decreases as the pulse propagates owing to laser evolution. This lowers the thresholds for trapping and wave breaking and reduces the energy gain and efficiency of laser-plasma accelerators that use a uniform plasma profile.