Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.     

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).     

Synthesis of lupeol derivatives and their antileishmanial and antitrypanosomal activities

The natural product lupeol 1 was isolated from aerial parts of Vernonia scorpioides with satisfactory yield, which made it viable to be used as starting material in semisynthetic approach. Ten lupeol derivatives 2–11 were prepared by classical procedures. Including, five new esters derivatives 7–11, which were obtained by structural modifications in the isopropylidene fragment. All semisynthetic compounds and lupeol 1–11 were confirmed by ¹H NMR, ¹³C NMR and HRMS. Their antiprotozoal activity was evaluated in vitro against L. amazonensis and T. cruzi. Derivative 6 showed the best antitrypanosomal activity (IC₅₀ = 12.48 μg/mL) and the lowest cytotoxic derivative (CC₅₀ = 161.50 μg/mL). The mechanism of action of the most active derivatives (4, 6 and 11) is not dependent from the enzyme trypanothione reductase.     

Patterns—a fundamental idea of mathematical thinking and learning

Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics.     

Modules of piecewise polynomials and their freeness

Partially supported by NSF Grant DMS-9004123 and ARO through MSI Cornell (DAAG 29-85-C-0018)     

The coexistence of γ(γ′) and θ alumina observed by STM and LEED on top of oxide layer grown on CoAl(1 0 0)

We report the coexistence of γ(γ′) and θ alumina grown on the CoAl(1 0 0) surface. Both phases were observed after annealing of alumina at 1150 K by means of scanning tunnelling microscopy (STM). The crystal structures of γ(γ′) and θ alumina were indexed based on low energy electron diffraction (LEED) and STM experimental data.     

Electrochemical impedance spectroscopy and linear polarization applied to evaluation of porosity of phosphate conversion coatings on electrogalvanized steels

In this work, electrochemical impedance spectroscopy and linear polarization are used in determining porosity of zinc phosphates, and of nickel and manganese modified zinc phosphates on electrogalvanized steel. The porosity of the phosphate layers ranges from 0.1% for the manganese-modified hopeite to 8% for hopeite, using the linear polarization and the electrochemical impedance spectroscopy techniques. The porosity values measured using the two techniques were in agreement. All impedance spectra of coated samples showed two steps, with two capacitive arcs and an inductive looping.