Spectral dynamics of modulation instability described using Akhmediev breather theory

The Akhmediev breather formalism of modulation instability is extended to describe the spectral dynamics of induced multiple sideband generation from a modulated continuous wave field. Exact theoretical results describing the frequency domain evolution are compared with experiments performed using single mode fiber around 1550 nm. The spectral theory is shown to reproduce the depletion dynamics of an injected modulated continuous wave pump and to describe the Fermi-Pasta-Ulam recurrence and recovery towards the initial state. Realistic simulations including higher-order dispersion, loss, and Raman scattering are used to identify that the primary physical factors that preclude perfect recurrence are related to imperfect initial conditions.     

Akhmediev breather evolution in optical fiber for realistic initial conditions

We study numerically Akhmediev breather dynamics in optical fibers under initial conditions that do not correspond to an ideal infinitesimal modulation on a plane wave. We examine two modifications that are commonly encountered in realistic experiments: (i) a finite-amplitude (not necessarily weak) initial modulation; (ii) the use of pulsed excitation. In the first case, we derive an expression for the propagation distance required to generate a train of compressed breather pulses. In the second case, we show that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope.     

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

Isolation and characterisation of products from the reactions between [Co2(nta)2(μ-OH)2]2− and different ligands. The crystal structure of [Co(nta)(N,N-Et2en)]

The crystal structure of [Co(nta)(N,N-Et₂en)] (nta = nitrilotriacetate and N,N-Et₂en = N,N-diethylethylenediamine) was determined from three-dimensional X-ray diffraction data. The substituted nitrogen of N,N-diethylethylenediamine is bonded trans to the nta nitrogen with the Co—N_{(N,N Et2en)}= 2.011(5) and Co—N_(nta) = 1.950(4) Å while the cis Co—N bond is 1.953(4) Å. The Co—O bond lengths are 1.905(2) and 1.884(4) Å respectively.     

Synthesis of tetrahydroisoquinoline (TIQ)–oxazoline ligands and their application in enantioselective Henry reactions

A novel family of eleven new tetrahydroisoquinoline (TIQ)–oxazoline intermediates and five corresponding copper(II) catalysts has been developed and applied to the catalytic asymmetric Henry reaction of various aldehydes with nitromethane to provide β-hydroxy nitroalkanes in high conversion (>99%). This paper describes the synthesis of the TIQ compounds from l-dihydroxyphenylalanine (l-DOPA) as the starting material. The chiral ligands were complexed in situ with various transition metals such as Cu, Sc, Co, Zn, Ni and Mn and tested as a chiral catalyst for the Henry reaction. The reaction was optimized in terms of the metal, counter ion, solvent, temperature and over a range of substrates. The corresponding catalyst with copper(II) acetate and 2-propanol as the solvent provides the best enantioselectivities (up to 77% ee) of the corresponding nitroalcohol for 4-chlorobenzaldehyde.     

Synthesis of tetrahydroisoquinoline-diamine ligands and their application in asymmetric transfer hydrogenation

The use of the tetrahydroisoquinoline scaffold is well documented in biologically active compounds. However, reports of the utilisation of tetrahydroisoquinoline compounds in asymmetric catalysis are limited. The synthesis of novel diamine ligands possessing the tetrahydroisoquinoline (tetrahydroisoquinoline) backbone and evaluation of their activity in the asymmetric transfer hydrogenation of acetophenone are presented. The diamine ligands in conjunction with i-PrOH as the hydrogen source and [RhCl₂(Cp1)]₂ as the metal precursor proved to be the most effective of the tetrahydroisoquinoline derivatives for this catalytic system. Water was found to have a profound influence on the enantioselectivity of the reaction. Optimisation of the amount water, i-PrOH and catalytic loading content rendered the best result of 70% enantioselectivity for the (S)-1-phenylethanol isomer product.     

Maximal pivots on graphs with an application to gene assembly

We consider principal pivot transform (pivot) on graphs. We define a natural variant of this operation, called dual pivot, and show that both the kernel and the set of maximally applicable pivots of a graph are invariant under this operation. The result is motivated by and applicable to the theory of gene assembly in ciliates.