Approximate Solutions and Error Bounds for Solving Matrix Differential Equations Without Increasing the Dimension of the Problem

In this paper we present a method for solving initial value problems related to second order matrix differential equations. This method is based on the existence of a solution of a certain algebraic matrix equation related to the problem, and it avoids the increase of the dimension of the problem for its resolution. Approximate solutions, and their error bounds in terms of error bounds for the approximate solutions of the algebraic problem, are given.     

Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrixRiccati equation with analytic coefficients is approximatedby a rational matrix function with a prefixed accuracy. Thisrational matrix function is locally defined as the exact solutionof a Riccati problem with matrix polynomial coefficients obtainedby truncation of the Taylor expansions of the matrix coefficientsof the original problem.     

Electrochemical Sensor Based on Casein and Carbon Black for Bisphenol A Detection

Bisphenol A (BPA) is an environmental endocrine disrupting chemical, which can lead to various adverse health effects. Aiming to develop effective tools for the detection of BPA, this work reports a low cost and stable film based on casein (CAS) and Carbon Black (CB). The proposed material (CAS‐CB) showed structures of CAS surrounded by CB agglomerates observed by Scanning Electron Microscopy while Fourier Transform Infrared Spectroscopy analysis illustrated characteristic bands of casein. Cyclic Voltammetry (CV) and linear sweep voltammetry (LSV) were used to investigate the electrochemical behavior of BPA using the CAS‐CB. Under optimal conditions, LSV detection presented a limit of detection of 0.25 μmol L^?1 in a linear range from 0.49 to 24 μmol L^?1. Additionally, the working electrode (GC) modified by the proposed film (CAS‐CB) was applied for BPA sensing in environmental and milk samples. The results showed recoveries between 95.4 to 114 % attesting the efficiency of this new material, which has simplicity in the preparation, high conductivity, and adsorption capability.     

Polyethyleneimine‐Coated Gold Nanoparticles: Straightforward Preparation of Efficient DNA Delivery Nanocarriers

A novel one‐pot method for the synthesis of polyethyleneimine (PEI)‐coated gold nanoparticles (AuPEI‐NPs) that combines the reductant–stabilizer properties of PEI with microwave irradiation starting from hydrogen tetrachloroaurate acid (HAuCl₄) and branched PEI 25 kDa (b25kPEI) was explored. The method was straightforward, green, and low costing, for which the Au/PEI ratio (1:1 to 1:128 w/w) was a key parameter to modulate their capabilities as DNA delivery nanocarriers. Transfection assays in CHO‐k1 cells demonstrated that AuPEI‐NPs with 1:16 and 1:32 w/w ratios behaved as effective DNA gene vectors with improved transfection efficiencies (twofold) and significantly lower toxicity than unmodified b25kPEI and Lipofectamine 2000. The transfection mediated by these AuPEI‐NP–DNA polyplexes preferentially used the caveolae‐mediated route for intracellular internalization, as shown by studies performed by using specific internalization inhibitors as well as colocalization with markers of clathrin‐ and caveolae‐dependent pathways. The AuPEI‐NP polyplexes preferentially used the more efficient caveolae internalization pathway to promote transfection, a fact that supports their higher transfection efficiency relative to that of Lipofectamine 2000. In addition, intracellular trafficking of the AuPEI‐NPs was studied by transmission electron microscopy.     

Electrochemical sensor for estriol hormone detection in biological and environmental samples

A stable conducting film for sensing using reduced graphene oxide (RGO), gold nanoparticles (GNPs), and potato starch (PS) is proposed. The characterization of the nanomaterials was obtained by ultraviolet and visible spectroscopy, dynamic light scattering, zeta potential, Fourier transform infrared spectroscopy, atomic force microscopy, and cyclic voltammetry. The voltammetric behavior of the RGO-GNPs-PS/GCE electrodes was studied in the presence of estriol and the results showed a high anodic peak current at 0.64 V. Under optimal conditions, an analytical curve was obtained, in which the anodic peak estriol was linear in the range from 1.5 to 22 μmol L^?1, with a detection limit of 0.48 μmol L^?1. The modified electrodes were applied for determination of estriol in environmental and biological samples. The proposed electrode was used for estriol determination in water and urine samples, which presented a recovery range from 92.1 to 106%, showing that RGO-GNPs-PS/GCE is a viable alternative for the detection of estriol and can be attractive for several electrochemical applications.