The non-abelian tensor square of residually finite groups

Let m, n be positive integers and p a prime. We denote by \(\nu (G)\) an extension of the non-abelian tensor square \(G \otimes G\) by \(G \times G\). We prove that if G is a residually finite group satisfying some non-trivial identity \(f \equiv ~1\) and for every \(x,y \in G\) there exists a p-power \(q=q(x,y)\) such that \([x,y^{\varphi }]^q = 1\), then the derived subgroup \(\nu (G)'\) is locally finite (Theorem A). Moreover, we show that if G is a residually finite group in which for every \(x,y \in G\) there exists a p-power \(q=q(x,y)\) dividing \(p^m\) such that \([x,y^{\varphi }]^q\) is left n-Engel, then the non-abelian tensor square \(G \otimes G\) is locally virtually nilpotent (Theorem B).     

Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

In this paper, we present a novel approach to quantify regular or chaotic dynamics of either smooth or non-smooth dynamical systems. The introduced method is applied to trace regular and chaotic stick–slip and slip–slip dynamics. Stick–slip and slip–slip periodic and chaotic trajectories are analyzed (for the investigated parameters, a stick–slip dynamics dominates). Advantages of the proposed numerical technique are given.     

Metal-sensitive and thermostable trypsin from the crevalle jack (<Emphasis Type="Italic">Caranx hippos</Emphasis>) pyloric caeca: purification and characterization

Background

Over the past decades, the economic development and world population growth has led to increased for food demand. Increasing the fish production is considered one of the alternatives to meet the increased food demand, but the processing of fish leads to by-products such as skin, bones and viscera, a source of environmental contamination. Fish viscera have been reported as an important source of digestive proteases with interesting characteristics for biotechnological processes. Thus, the aim of this study was to purify and to characterize a trypsin from the processing by-products of crevalle jack (Caranx hippos) fish.

Results

A 27.5 kDa trypsin with N-terminal amino acid sequence IVGGFECTPHVFAYQ was easily purified from the pyloric caeca of the crevalle jack. Its physicochemical and kinetic properties were evaluated using N-α-benzoyl-_DL-arginine-p-nitroanilide (BApNA) as substrate. In addition, the effects of various metal ions and specific protease inhibitors on trypsin activity were determined. Optimum pH and temperature were 8.0 and 50°C, respectively. After incubation at 50°C for 30 min the enzyme lost only 20% of its activity. K _m , k_cat, and k _cat /K _m values using BApNA as substrate were 0.689 mM, 6.9 s^-1, and 10 s^-1 mM^-1, respectively. High inhibition of trypsin activity was observed after incubation with Cd²⁺, Al³⁺, Zn²⁺, Cu²⁺, Pb²⁺, and Hg²⁺ at 1 mM, revealing high sensitivity of the enzyme to metal ions.

Conclusions

Extraction of a thermostable trypsin from by-products of the fishery industry confirms the potential of these materials as an alternative source of these biomolecules. Furthermore, the results suggest that this trypsin-like enzyme presents interesting biotechnological properties for industrial applications.

     

Thermal tools in the evaluation of decayed and weathered wood polymer composites prepared by in situ polymerization

This study aims to apply thermal tools in the evaluation of decayed and weathered wood polymer composites prepared by in situ polymerization with and without cross-linkers. Pinewood samples were impregnated with methyl methacrylate using glycidyl methacrylate and methacrylic acid as cross-linkers by vacuum/pressure. The polymerization was carried out in an oven at 90 °C for 10 h using benzoyl peroxide as catalyst. All samples were exposed to decay and artificial weathering tests. The characterization was performed by mass loss, color changes, optical images, wettability, thermogravimetric analysis (by means of DTG) and differential scanning calorimetry analyzes. The mass loss was higher in untreated wood in comparison with the composites, ~2.5–10 times. Cross-linked composites showed the highest resistance to fungal biodeterioration. The reduction in L*, chroma and b* confirmed loss of original yellow tones and increase in dark and dull tones of samples. The wettability was very affected by irregularities of the samples’ surface. Only DTG showed a shifting in the temperature of thermal events related to polysaccharides and lignin after exposure to decay and weathering. DTG was the best thermal technique for evaluation of decaying and weathering of wood composites.     

Transport of mass and energy of polyatomic gases in magnetic fields computed by a Monte Carlo algorithm

The transport of mass through a rectangular channel and of energy between parallel surfaces of polyatomic gases in the Knudsen regime and in the presence of external magnetic fields is calculated by means of a Monte Carlo algorithm. A four-parameter mathematical model is proposed that takes into account the dynamical aspects of molecule-surface interactions and the influence of external magnetic fields on the angular momentum of polyatomic molecules. The Monte Carlo algorithm makes use of the Latin super-cube sampling method, correlated samplings, and the concept of importance sampling. The four parameters are determined by an optimised method based on the Monte Carlo algorithm and on experimental results for the mass flux rate of the gases N₂ and CO in the presence of external magnetic fields through a rectangular channel with surfaces coated with Au. The optimised values of the parameters are used to determine the behaviour of the mass flux rate through a rectangular channel and the heat flux between two parallel plates for the gases N₂ and CO as a function of the applied magnetic field. The calculated curves fit the experimental data well.Received: 18 February 2003, Accepted: 2 September 2003, Published online: 12 December 2003PACS: 05.60.-k, 51.60. + aCorrespondence to: G.M. Kremer     

Cross-Properties Relations in 3D Percolation Networks: I. Network Characteristic Length Determination

This work developed efficient methods to determine the hydraulic characteristic length of percolation networks. The proposed methods are based on the determination of the percolation threshold using the Hoshen–Kopelman algorithm extended to 3D networks. The methods were tested with simple cubic site-bond network models with and without spatial correlations. It was shown that the proposed methods outperformed the algorithms based on the simulation of the porosimetry curve.*Author for correspondence: Fax +55-21-2562-8300; e-mail: paulo@peq.coppe.ufrj.br     

Hydrogenated BN monolayers: A first principles study

In the present contribution we apply first principles calculations to investigate the electronic structures and stability of BN hydrogenated monolayers which include a substitutional carbon atom. For comparison, additional C hydrogenated structures are considered. The obtained results demonstrate that BN chair-like monolayers are more stable than boat-like configurations. It is found that the most stable structures present bond angles quite similar to the characteristic one observed for s p ³ hybridization. Moreover, a net magnetic moment arises from the introduction of a substitutional carbon impurity. In addition, the results indicate that carbon substitutionals can induce a remarkable reduction of the work function.