One-step recursive method for solving systems of differential equations

In this work an iteration one-step method to integrate systems of nonlinear ordinary differential equations with initial values is presented     

Fluorescent boron Schiff bases dyes for staining silk fibroin: Green synthesis,structural characterization,DFT, and photophysical properties

Five novel organoboron complexes were synthesized in just 15 min via microware irradiation, by one pot multicomponent reactions between diverse aryl aldehydes with benzoylhydrazide, or 4‐nitrobenzoylhidrazine and diphenyl boronic acid, in a 1:1:1 ratio in benzene. The products were characterized by ¹H, ¹³C, ¹¹B NMR, UV, IR, spectroscopy and high‐resolution mass spectrometry (HRMS). The molecular structure was also determined by single‐crystal X‐ray diffraction for two complexes, which showed the tetra‐coordination of the boron atoms giving rise to distorted tetrahedral molecular geometry with a strong intermolecular C‐H···π interactions. In spite of the low quantum yields exhibited by the series in solution, some complexes stained uniformly the silk fibroins emitting enough fluorescence to allow its characterization by confocal microscopy. Boron as chelate center of the five complexes resulted not to be toxic for B16F10 cells, these compounds are appropriate for their used in medical applications.     

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.     

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.