Synthesis and X-ray structure of neutral Pd(IV) hydride complexes supported by β-ketoimine ligands

A series of neutral palladium(IV) hydride complexes supported by β-ketoimine ligands was synthesized. Reaction of dichlorobis(acetonitrile)palladium(II) with β-ketoamines (1–4) in dichloromethane at room temperature generated dark red solids of [PdCl₂(β-ketoimine)(H)] (6–9) in which the central carbon of the ketoimine ligand is σ-bound to the palladium. All the new complexes have been characterized by NMR and IR spectroscopy. The structure of complex(9) has been solved by X-ray crystallography.     

Holonomy Groups Coming from F-Theory Compactification

We study holonomy groups coming from F-theory compactifications. We focus mainly on SO(8) as 12−4=8 and subgroups SU(4), Spin(7), G ₂ and SU(3) suitable for descent from F-theory, M-theory and Superstring theories. We consider the relation of these groups with the octonions, which is striking and reinforces their role in higher dimensions and dualities. These holonomy groups are related in various mathematical forms, which we exhibit.     

A Kato class for the Khon Laplacian

Positivity - In this paper we establish an upper estimate and a 3G-theorem for the Green function of the Khon Laplacian $$\Delta _{{\mathbb {H}}}$$ on a domain D of the Heisenberg group $${{\mathbb...     

Multi-Material Inkjet Printing of Self-Assembling and Reacting Coatings

Inkjet printing was used to deposit alternating 100 nm layers of anionic and cationic polymers in order to form self-assembled ionic complexes on flat and fabric substrates. The layers formed are characterized by elemental analysis, microscopy and solubility. As initially deposited, layers are soluble but form insoluble complexes when they are heated and annealed. This approach has been applied to polypeptides, polymer dyes, polymers with nanoparticulate pigments and also to epoxy adhesives.     

Hardy’s Inequality for the n-Dimensional Hankel Transform

Analysis Mathematica - The purpose of this paper is to prove a Hardy type inequality associated with the n-dimensional Hankel transform (n ≥ 1) for the exponent σ0 = n(2 ? p) +...     

Exotic Hadrons and Underlying Z2,3 Symmetries

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z₂ and Z₃ symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of  _n affine Lie algebras. It has been shown that Z_2,3 invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.     

Doubling bialgebras of rooted trees

The vector space spanned by rooted forests admits two graded bialgebra structures. The first is defined by Connes and Kreimer using admissible cuts, and the second is defined by Calaque, Ebrahimi-Fard and the second author using contraction of trees. In this article, we define the doubling of these two spaces. We construct two bialgebra structures on these spaces which are in interaction, as well as two related associative products obtained by dualization. We also show that these two bialgebras verify a commutative diagram similar to the diagram verified Calaque, Ebrahimi-Fard and the second author in the case of rooted trees Hopf algebra, and by the second author in the case of cycle-free oriented graphs.     

D-brane SM-like and scalar dark matter in type IIA superstring theory

In light of the present LHC Run II at √s = 13 TeV, a SM-like string model is studied. Specifically, a singlet S scalar-extended SM given in terms of four stacks of intersecting D6-branes in a type IIA superstring compactification producing a large gauge symmetry is examined. The scales involved are dealt with. According to the dark matter relic density, the mass of the scalar dark matter beyond the SM m _S ? 10³ GeV and the corresponding Higgs portal couplings λ _SH ? 10^–8 have been obtained.