On the numerical solution of ill‐conditioned linear systems by regularization and iteration

We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.     

In Vivo Biological Behavior of Polymer Scaffolds of Natural Origin in the Bone Repair Process

Autologous bone grafts, used mainly in extensive bone loss, are considered the gold standard treatment in regenerative medicine, but still have limitations mainly in relation to the amount of bone available, donor area, morbidity and creation of additional surgical area. This fact encourages tissue engineering in relation to the need to develop new biomaterials, from sources other than the individual himself. Therefore, the present study aimed to investigate the effects of an elastin and collagen matrix on the bone repair process in critical size defects in rat calvaria. The animals (Wistar rats, n = 30) were submitted to a surgical procedure to create the bone defect and were divided into three groups: Control Group (CG, n = 10), defects filled with blood clot; E24/37 Group (E24/37, n = 10), defects filled with bovine elastin matrix hydrolyzed for 24 h at 37 °C and C24/25 Group (C24/25, n = 10), defects filled with porcine collagen matrix hydrolyzed for 24 h at 25 °C. Macroscopic and radiographic analyses demonstrated the absence of inflammatory signs and infection. Microtomographical 2D and 3D images showed centripetal bone growth and restricted margins of the bone defect. Histologically, the images confirmed the pattern of bone deposition at the margins of the remaining bone and without complete closure by bone tissue. In the morphometric analysis, the groups E24/37 and C24/25 (13.68 ± 1.44; 53.20 ± 4.47, respectively) showed statistically significant differences in relation to the CG (5.86 ± 2.87). It was concluded that the matrices used as scaffolds are biocompatible and increase the formation of new bone in a critical size defect, with greater formation in the polymer derived from the intestinal serous layer of porcine origin (C24/25).     

Development of paper devices with conductive inks for sulfanilamide electrochemical determination in milk,synthetic urine,and environmental and pharmaceutical samples

Journal of Solid State Electrochemistry - This work describes a simple, rapid, and cost-effective method for fabrication of paper-based carbon electrode (US$ <0.01) using conductive ink...     

Parallel mean curvature surfaces in symmetric spaces

We present a reduction-of-codimension theorem for surfaces with parallel mean curvature in symmetric spaces.     

Gutmann's Donor Numbers Correctly Assess the Effect of the Solvent on the Kinetics of SNAr Reactions in Ionic Liquids

We report an experimental study on the effect of solvents on the model S_NAr reaction between 1‐chloro‐2,4‐dinitrobenzene and morpholine in a series of pure ionic liquids (IL). A significant catalytic effect is observed with reference to the same reaction run in water, acetonitrile, and other conventional solvents. The series of IL considered include the anions, NTf₂^?, DCN^?, SCN^?, CF₃SO₃^?, PF₆^?, and FAP^? with the series of cations 1‐butyl‐3‐methyl‐imidazolium ([BMIM]⁺), 1‐ethyl‐3‐methyl‐imidazolium ([EMIM]⁺), 1‐butyl‐2,3‐dimethyl‐imidazolium ([BM₂IM]⁺), and 1‐butyl‐1‐methyl‐pyrrolidinium ([BMPyr]⁺). The observed solvent effects can be attributed to an “anion effect”. The anion effect appears related to the anion size (polarizability) and their hydrogen‐bonding (HB) abilities to the substrate. These results have been confirmed by performing a comparison of the rate constants with Gutmann's donicity numbers (DNs). The good correlation between rate constants and DN emphasizes the major role of charge transfer from the anion to the substrate.     

Multivariate nonlinear least squares: robustness and efficiency of standard versus Beauchamp and Cornell methodologies

Simultaneous estimation in nonlinear multivariate regression contexts is a complex problem in inference. In this paper, we compare the methodology suggested in the literature for an unknown covariance matrix among response components, the methodology by Beauchamp and Cornell (B&C), with the standard nonlinear least squares approach (NLS). In the first part of the paper, we contrast B&C and the standard NLS, pointing out, from the theoretical point of view, how a model specification error could affect the estimation. A comprehensive simulation study is also performed to evaluate the effectiveness of B&C versus standard NLS under both correct and misspecified models. Several alternative models are considered to highlight the consequences of different types of specification error. An application to a real dataset within the context of quantitative marketing is presented.