Fractional monodromy: parallel transport of homology cycles

A 2n-dimensional completely integrable system gives rise to a singular fibration whose generic fiber is the n-torus Tⁿ. In the classical setting, it is possible to define a parallel transport of elements of the fundamental group of a fiber along a path, when the path describes a loop around a singular fiber, it defines an automorphism of π₁(Tⁿ) called monodromy transformation [J.J. Duistermaat, On global action-angle coordinates, Communications on Pure and Applied Mathematics 33 (6) (1980) 687–706]. Some systems give rise to a non-classical setting, in which the path can wind around a singular fiber only by crossing a codimension 1 submanifold of special singular fibers (a wall), in this case a non-classical parallel transport can be defined on a subgroup of the fundamental group. This gives rise to what is known as monodromy with fractional coefficients [N. Nekhoroshev, D. Sadovskiì, B. Zhilinskiì, Fractional monodromy of resonant classical and quantum oscillators, Comptes Rendus Mathematique 335 (11) (2002) 985–988]. In this article, we give a precise meaning to the non-classical parallel transport. In particular we show that it is a homologic process and not a homotopic one. We justify this statement by describing the type of singular fibers that generate a wall that can be crossed, by describing the parallel transport in a semi-local neighbourhood of the wall of singularities, and by producing a family of 4-dimensional examples.     

Infinitesimally stable and unstable singularities of 2-degrees of freedom completely integrable systems

In this article we give a list of 10 rank zero and 6 rank one singularities of 2-degrees of freedom completely integrable systems. Among such singularities, 14 are the singularities that satisfy a non-vanishing condition on the quadratic part, the remaining 2 are rank 1 singularities that play a role in the geometry of completely integrable systems with fractional monodromy. We describe which of them are stable and which are unstable under infinitesimal completely integrable deformations of the system.      

Ultrafast intersystem crossing and spin dynamics of zinc meso-tetraphenylporphyrin covalently bound to stable radicals

tert-Butylphenylnitroxide (BPNO(?)) and α,γ-bisdiphenylene-β-phenylallyl (BDPA(?)) stable radicals are each attached to zinc meso-tetraphenylporphyrin (ZnTPP) at a fixed distance using one of the ZnTPP phenyl groups. BPNO(?) and BDPA(?) are oriented para (1 and 3, respectively) or meta (2 and 4, respectively) relative to the porphyrin macrocycle. Following photoexcitation of 1-4, transient optical absorption spectroscopy is used to observe excited state quenching of (1)*ZnTPP by the radicals and time-resolved electron paramagnetic resonance (TREPR) spectroscopy is used to monitor the spin dynamics of the paramagnetic product states. The presence of BPNO(?) or BDPA(?) accelerates the intersystem crossing rate of (1)*ZnTPP about 10- to 500-fold in 1-4 depending on the structure compared to that of (1)*ZnTPP itself. In addition, the lifetime of (3)*ZnTPP in 1 is shorter than that of (3)*ZnTPP itself as a result of enhanced intersystem crossing (EISC) from (3)*ZnTPP to the ground state. The TREPR spectra of the three unpaired spins produced within 1 and 2 show spin-polarized excited doublet (D(1)) and quartet (Q) states and subsequent formation of a spin-polarized ground state radical (D(0)). All three signals are absorptive for 1 and emissive for 2. Polarization inversion of the Q state is observed on a tens of nanoseconds time scale in 2, while no polarization inversion is observed for 1. The lack of polarization inversion in 1 is attributed to the short lifetime of the doublet-quartet manifold as a result of the very large exchange interaction. The TREPR spectra of 3 and 4 show ground state radical polarization at X-band (9.5 GHz) at room temperature, but not at 85 K, and similarly no polarization is observed at W-band (94 GHz). No evidence of excited doublet or quartet states is observed, indicating that the exchange interaction is both weak and temperature dependent. These results show that although ultrafast EISC produces (3)*ZnTPP within 1-4, the magnitude of the exchange interactions between the three relevant spins in the resulting (3)*ZnTPP-BPNO(?) and (3)*ZnTPP-BDPA(?) systems dramatically alters their spin dynamics.     

Dimethyl ether as circular hydrogen carrier: Catalytic aspects of hydrogenation/dehydrogenation steps

The intermittent nature of renewable resources requires for most applications the development of efficient and cost-effective technologies for steady supply of ...     

Comparison of two different isolation methods of benzimidazoles and their metabolites in the bovine liver by solid-phase extraction and liquid chromatography–diode array detection

A new analytical method that uses high performance liquid chromatography–diode array detector (HPLC–DAD) was developed for the analysis of 14 benzimidazoles residues, including metabolites, in bovine liver. Samples were extracted using two different extraction procedures: with phosphate buffer after enzymatic hydrolysis (method A) or using organic solvent, i.e. acetonitrile (method B). Then, samples were purified on a strong cation exchange (SCX) cartridge and analyzed in HPLC/DAD. The recovery percentages, obtained spiking the matrix (liver) at concentrations of 500 and 100 μg kg^?1 with a standard mixture of benzimidazoles, were in the range 6–101% and 80–102% for methods A and B, respectively. The repeatability of the methods was assessed in all cases by the % of correlation value (CV) that was lower than 19%. The limits of quantification (LOQs) in the matrix for methods A and B were in the range 40–60 and 20–50 μg kg^?1, respectively. The best of the two methods, method B, was used for the analysis of 10 bovine liver samples.     

Synthesis of 3(2- and 4-Pyridinyl)-1,3,4-oxadiazol-2(3H)ones

The synthetic objective of preparing halo- and halo- plus alkoxy-substituted pyridyloxadiazolones was achieved by allowing an alkali metal salt of an oxadiazolone to displace a leaving group on a halo- or halo- plus alkoxy-substituted pyridine, respectively. Other routes failed to give the desired compounds, and they are briefly discussed.     

Stability of hydromagnetic laminar flows in an inclined heated layer

Laminar flows of conducting fluids with an imposed magnetic field play an important role in many applications, for instance in geophysics, astrophysics, e.g. when dealing with solar winds, industry, biology, in metallurgy, in biofilms, etc. Also many engineering applications require heating at the boundaries. The inclination has been examined by some authors mainly in theoretical applications, geophysical studies, and materials processing. In Falsaperla et al. (Laminar hydromagnetic flows in an inclined heated layer, 2016) we have investigated analytical solutions of stationary laminar flows of an inclined layer filled with a hydromagnetic fluid heated from below and subject to the gravity field. In this article we study linear instability and nonlinear stability of some of the above solutions and investigate the critical stability/instability thresholds.     

Convexity of Multi-valued Momentum Maps

A famous theorem of Atiyah, Guillemin and Sternberg states that, given a Hamiltonian torus action, the image of the momentum map is a convex polytope. We prove that this result can be extended to the case in which the action is non-Hamiltonian. Our generalization of the theorem states that, given a symplectic torus action, the momentum map can be defined on an appropriate covering of the manifold and its image is the product of a convex polytope along a rational subspace times the orthogonal vector space. We also prove that this decomposition in direct product is stable under small equivariant perturbations of the symplectic structure; this, in particular, means that the property of being Hamiltonian is locally stable. The technique developed allows us to extend the result to any compact group action and also to deduce that any symplectic n-torus action, with fixed points, on a compact 2n-dimensional manifold, is Hamiltonian.