A modified Lyapunov method and its applications to ODE

Here, we propose a method to obtain local analytic approximate solutions of ordinary differential equations with variable coefficients, or even some nonlinear equations, inspired in the Lyapunov method, where instead of polynomial approximations, we use truncated Fourier series with variable coefficients as approximate solutions. In the case of equations admitting periodic solutions, an averaging over the coefficients gives global solutions. We show that, under some restrictive condition, the method is equivalent to the Picard-Lindelöf method. After some numerical experiments showing the efficiency of the method, we apply it to equations of interest in physics, in which we show that our method possesses an excellent precision even with low iterations.     

A stainless steel multi‐well plate (SS‐MWP) for high‐throughput Raman analysis of dilute solutions

The use of Raman spectroscopy for the qualitative and quantitative analysis of dilute aqueous solutions is of interest to the biopharmaceutical manufacturing sector. However, the inherent weakness of the Raman effect, coupled with spectral variability due to spurious signals from sample holders, can produce significant problems for chemometric‐based high‐throughput assays. Therefore, there is a need for a multi‐well sample holder that ensures robust and repeatable measurements, in particular from dilute aqueous solutions such as cell culture media. Here we demonstrate the efficacy of a novel, electropolished, stainless steel multi‐well plate (SS‐MWP) sample holder with 96 wells for dilute aqueous solution analysis. A comprehensive study of the spectroscopic behaviour was carried out and comparisons made with multi‐well plates fabricated from polystyrene, polypropylene, and aluminium. A key factor in the validation studies is the use of intrinsically weak Raman scattering systems, e.g. water and dilute glucose solutions. The data collected show that the SS‐MWPs are much superior in terms of robustness, resistance to chemical attack, and measurement reproducibility and as such are the ideal sample holders for Raman analysis of dilute solutions. Copyright © 2010 John Wiley & Sons, Ltd.     

Incommensurate modulated structure of the ferromagnetic shape-memory Ni2MnGa martensite

The ferromagnetic shape memory (MSM) alloy Ni₂MnGa undergoes a martensitic transformation (MT) at T=220 K on cooling. The structure of this phase is studied by powder X-ray diffraction experiment. The analysis of the experimental data combined with the huge information reported in literature allowed to conclude that the Ni₂MnGa martensite shows an incommensurate modulated structure closely related to a five-fold layered superstructure. The symmetry of the basic structure is found to be orthorhombic. The structure is refined by Rietveld method with superspace group Immm(00γ)s00 having a=4.2187(1) Å, b=5.5534(1) Å and c=4.1899(1) Å and modulation vector q=0.4248(3)c*. The results show that the modulation is mainly related to the periodic shuffling of the atomic layers perpendicular to the c-axis of the orthorhombic basic structure.     

A cellular FRET-based sensor for beta-O-GlcNAc, a dynamic carbohydrate modification involved in signaling

beta-O-N-Acetyl-d-glucosamine (O-GlcNAc) is a dynamic carbohydrate modification that is involved in cell signaling and has been implicated in a variety of disease states, including Alzheimer's and type-II diabetes. Despite the importance of this modification, little is known about the spatial and temporal localization of O-GlcNAc during signaling. This is due to the lack of methods for the study of O-GlcNAc in living cell systems. Herein we report the first genetically encoded FRET-based sensor for the detection of O-GlcNAc dynamics in live mammalian cells.     

Ultracold Rb-OH collisions and prospects for sympathetic cooling

We compute ab initio cross sections for cold collisions of Rb atoms with OH radicals. We predict collision rate constants of order 10(-11) cm3/s at temperatures in the range 10-100 mK at which molecules have already been produced. However, we also find that in these collisions the molecules have a strong propensity for changing their internal state, which could make sympathetic cooling of OH in a Rb buffer gas problematic in magnetostatic or electrostatic traps.     

Pseudokobusine

The title compound, hetisan-6,11β,15β-triol, C₂₀H₂₇NO₃, is a hetisane-type diterpenoid alkaloid. It consists of six six-membered rings and two five-membered rings. The fused-ring system contains three chair, two boat, one distorted boat and two envelope conformations. Intramolecular and intermolecular hydrogen bonds are present between the O atoms, with O⃛O separations of 3.006 (3) and 2.743 (3) Å, as well as an O⃛N intermolecular interaction of 2.887 (3) Å.     

Nitrenium ions. Reactions of N,N-dimethyl-p-benzoyloxyanilineiminium chloride with indoles and indolizines. X-ray structure of unexpected [2-chloro-4-(4-dimethylaminophenyl-ONN-azoxy)phenylldimethylamine (azoxy derivative)

N,N-Dimethyl-p-nitrosoaniline reacts with benzoyl chloride affording a complex salt containing a cation, a hybrid between a nitrenium ion and an iminium ion. The salt reacts with nucleophiles (indoles, indolizines) yielding compounds characterized by a new carbon-nitrogen bond, derived from the nitrenium ion form. According to the type of nucleophile, the reaction, to differing extents, is in competition with an electron transfer process which leads to the formation of the dimer of the nucleophile and of the azoxy corresponding to the N,N-dimethyl-p-nitrosoaniline. In one of the reactions studied, a chlorinated azoxy derivative was also isolated, and its structure was elucidated by X-ray analysis.     

Fiber formation in water by a mono-urea dicarboxylic acid

Fibers formed by a mono-urea dicarboxylic acid derivative in water were analyzed by SEM, IR and XRD. The resulting data were used to develop a model of the molecular aggregation leading to fiber formation.