Conservation of Resonant Periodic Solutions for the One-Dimensional Nonlinear Schrödinger Equation

We consider the one-dimensional nonlinear Schrödinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the mass term). We investigate conservation of small amplitude periodic solutions for a large measure set of frequencies. In particular we show that there are infinitely many periodic solutions which continue the linear ones involving an arbitrary number of resonant modes, provided the corresponding frequencies are large enough, say greater than a certain threshold value depending on the number of resonant modes. If the frequencies of the latter are close enough to such a threshold, then they can not be too distant from each other. Hence we can interpret such solutions as perturbations of wave packets with large wave number.     

A class of 3-dimensional manifolds with bounded first eigenvalue on 1-forms

Let be the framebundle over an oriented, Riemannian surface . Denote by the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree 1. We prove that for all with canonical metrics of volume 1.

     

A Novel L-Shaped Fluorescent Probe for AIE Sensing of Zinc (II) Ion by a DR/NIR Response

In the field of optical sensors, small molecules responsive to metal cations are of current interest. Probes displaying aggregation-induced emission (AIE) can solve the problems due to the aggregation-caused quenching (ACQ) molecules, scarcely emissive as aggregates in aqueous media and in tissues. The addition of a metal cation to an AIE ligand dissolved in solution can cause a “turn-on” of the fluorescence emission. Half-cruciform-shaped molecules can be a winning strategy to build specific AIE probes. Herein, we report the synthesis and characterization of a novel L-shaped fluorophore containing a benzofuran core condensed with 3-hydroxy-2-naphthaldehyde crossed with a nitrobenzene moiety. The novel AIE probe produces a fast colorimetric and fluorescence response toward zinc (II) in both in neutral and basic conditions. Acting as a tridentate ligand, it produces a complex with enhanced and red-shifted emission in the DR/NIR spectral range. The AIE nature of both compounds was examined on the basis of X-ray crystallography and DFT analysis.     

Physical and Chemical Characterization of Cellulose Based Textiles Modified by Periodate Oxidation

Conversion of dihydroxyl groups to dialdehyde by periodate oxidation is a useful method widely used in derivatization of cellulose to activate the polymer to further reactions as grafting polymerization. To investigate the cellulose behavior at different level of oxidation and to better understand the influence of the crystallinity on the effects induced by oxidative reactions on different cellulose materials, linen and cotton textiles have been oxidized with periodate solutions in different conditions. Oxidized cellulose samples have been characterized by several techniques: solid-state ¹³C NMR, Wide Angle X-Ray diffraction, and SEM. Moreover the mechanical properties of the untreated and oxidized yarns have been evaluated by means of tensile tests, the oxidation degree has been measured by means of the hydroxylamine hydrochloride method.     

Resummation of Perturbation Series and Reducibility for Bryuno Skew-Product Flows

We consider skew-product systems on 핥^d ×l SL(2,ℝ) for Bryuno base flows close to constant coefficients, depending on a parameter, in any dimension d, and we prove reducibility for a large measure set of values of the parameter. The proof is based on a resummation procedure of the formal power series for the conjugation, and uses techniques of renormalisation group in quantum field theory.     

Stability for Quasi-Periodically Perturbed Hill's Equations

We consider a perturbed Hill's equation of the form +(p₀(t)+ɛp₁(t))ϕ=0, where p₀ is real analytic and periodic, p₁ is real analytic and quasi-periodic and ɛ ∈ℝ is ``small'. Assuming Diophantine conditions on the frequencies of the decoupled system, i.e. the frequencies of the external potentials p₀ and p₁ and the proper frequency of the unperturbed (ɛ=0) Hill's equation, but without making any assumptions on the perturbing potential p₁ other than analyticity, we prove that quasi-periodic solutions of the unperturbed equation can be continued into quasi-periodic solutions if ɛ lies in a Cantor set of relatively large measure in where ɛ₀ is small enough. Our method is based on a resummation procedure of a formal Lindstedt series obtained as a solution of a generalized Riccati equation associated to Hill's problem.     

Polar effects in free-radical reactions. A new type of homolytic aromatic alkylation by silver catalyzed oxidation of acetone by peroxydisulphate in the presence of olefins.

Silver catalyzed peroxydisulphate oxidation of acetone in the presence of olefins and protonated heteroaromatic bases leads to compound I via addition of acetonyl radical to the olefin and scavenging of the resulting radical adduct by the aromatic base.     

Reactivity of the A-CH=N-NR-CX-B system. 4-R-5-hydroxy-5-phenyl-2,3,4,5-letrahydro-1,2,4-triazine-3-thiones

The behaviour of phenylglyoxal thiosemicarbazones towards aqueous sodium hydroxide have been studied. Examples of addition compounds, 5-hydroxy-5-phenyl-2,3,4,5-tetrahydro-1,2,4-triazine-3-thiones, are reported.     

Solid-state study of hydrazonium tartrate and deuterated hydrazonium tartrate enantiomers

A study of the crystallographic, optical, and thermochemical properties of hydrazonium tartrate and deuterated hydrazonium tartrate enantiomers is described. Crystals of the enantiomers are orthorhombic with a tetramolecular cell. The space group is P2₁2₁2₁ with the lattice parameters a₀ = 7.640 ± 0.002 Å, b₀ = 13.441 ± 0.003 Å, and c₀ = 7.029 ± 0.002 Å. No change in lattice parameters is observed on deuteration. Optical second harmonic powder analysis shows the crystals to be phase matchable at 1.06 μm with d^2ω = 11 d^2ωα-SiO₂. The optical nonlinearity being unaffected by deuterium substitution is attributed to the nonlinear electronic polarizability of the hydrogen bonds. Crystals are transparent from 239 nm to 1.61 μm. Deuteration shifts the long wavelength cutoff to 2.07 μm, without affecting the band edge.