Angles in normed spaces

The concepts of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to the Euclidean space, and there exist also various extensions to non-Euclidean spaces of different types. In particular, it is very interesting to investigate or to combine (geometric) properties of possible concepts of angle functions and angle measures in finite-dimensional real Banach spaces (= Minkowski spaces). However, going into this direction one will observe that there is no monograph or survey reflecting the complete picture of the existing literature on such concepts in a satisfying manner. We try to close this gap. In this expository paper (containing also new results, and new proofs of known results) the reader will get a comprehensive overview of this field, including further related aspects, as well. For example, angular bisectors, their applications, and angle types which preserve certain kinds of orthogonality are discussed. The latter aspect yields, of course, an interesting link to the large variety of orthogonality types in such spaces.     

Stress relaxation after a step strain in uniaxial extension of polyisobutylene and polyethylene

The morphology of molten polymeric materials is known to be less sensitive to shear than to extensional deformations. However, it is not easy to characterise molten polymeric materials in simple extensional flows due to the large number of experimental difficulties involved. This has led to the effective absence of a structure-preserving, morphology probing technique similar to the ones commonly found in shear, i.e., the equivalent of stress relaxation and oscillatory experiments. It is the aim of the present work to demonstrate the usefulness of a recently developed experimental technique that enables stress relaxation experiments after a step strain in uniaxial extension to be performed. Results are presented for two model melts (polyisobutylene, PIB, of different molecular weights) and for a series of linear low-density polyethylenes, LLDPE, in which the molecular structure (molecular weight, MW, molecular weight distribution, MWD and degree of long chain branching, LCB) is changed systematically. It is shown that, for both types of materials, stress relaxation experiments in extension yield quantitatively correct results and that this technique is more sensitive to differences in molecular structure than oscillatory experiments in shear.     

Obtaining nanocomposites of polyamide 6 and cellulose whiskers via extrusion and injection molding

Nanocomposites of polyamides with cellulose whiskers are difficult to obtain by conventional processing of extrusion and injection molding because of the low thermal stability of the cellulosic nanostructures and the relatively high processing temperature of polyamides, which is higher than the temperature of thermal degradation of cellulose whiskers. Thus, in this study cellulose whiskers were coated with polyamide 6 (PA6) in order to increase their thermal stability and prevent the formation of agglomerates. This coating on cellulose whiskers allows their application to obtain nanocomposites with polyamides, whose processing temperatures are relatively high, around 250 °C. Cellulose whiskers (CWs) were obtained from cotton fibers by acid hydrolysis. The freeze-dried CWs were coated with PA6 by dispersing them in formic acid; PA6 was solubilized in this suspension. The cellulose-coated whiskers (CCWs) were characterized by X-ray diffraction, differential scanning calorimetry (DSC), thermogravimetry (TG), scanning electron microscopy (SEM-FEG) and infrared spectroscopy. SEM-FEG and TG results showed that the PA6 coating on CWs prevented high agglomeration of dried CWs and promoted an increase in their thermal stability from 180 to 280 °C, allowing the use of CCWs to obtain nanocomposites with PA6 using conventional processing routes, such as extrusion and injection molding, at appropriate processing temperatures. In this way, 1 wt% CCWs was used to prepare nanocomposites with PA6. The PA6 + 1CW nanocomposites were compared to neat PA6 without CWs. The samples were characterized by tensile tests and DSC, and the results showed that the PA6 coating on CWs was effective in raising the thermal stability of CWs, improving the dispersion of CWs in the matrix of PA6, resulting in a 45 % increase in the elastic modulus of the nanocomposite with only 1 wt% of coated cellulose whiskers in comparison to neat PA6.     

Radionuclide, Metal and Non-metal Levels in Percolated Water from Soils Fertilized with Phosphogypsum

Phosphogypsum (PG) is a by-product of the phosphate fertilizer industry, which is produced by precipitation during the wet process of phosphate rocks. While commercial uses, in agriculture and in manufacturing gypsum board and Portland cement, consume less than a few percent of this by-product, the vast majority is disposed of on land in gypsum. In Brazil, three main industries are responsible for the production and storage of about 5.5 × 10⁶ tons per year. PG may contain trace metals, non-metals, fluorides and natural radionuclides. Since, in Brazil, PG has been used for many years as soil amendment, it is important to know its availability, mainly in aquatic environments used for human consumption. In this case, more restrictive limits must be adopted. This work aimed to evaluate the mobility of metals in sand and clayey soils and, consequently, the contamination of drainage water through greenhouse-scale leaching and transport of toxic elements and radionuclides from soils fertilized with PG to crops. In general, it was observed that elemental concentrations were below the actual detection limit of the equipment for all conditions of interest, indicating a low mobility of the analyzed elements in the soil.     

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.

     

Unusual extensional behavior of a polystyrene/HIPS blend

The present work focuses on the study of the rheological behavior in extension of three different polystyrene melts (a general-purpose polystyrene, GPPS, a high-impact polystyrene, HIPS, and a 50/50 blend of both), in particular the behavior at failure and at rupture in extension that are (ultimately) related with the materials' ability to endure the various stages of extension-dominated processing sequences such as thermoforming. The aim is to try to explore possible synergistic effects arising in extension-dominated flows by means of physically blending the two base materials. The rheological characterization was performed in terms of both the linear and non-linear viscoelastic behavior, in shear and extensional flows. The results show that blending the two materials has important consequences on the extensional behavior, the blend showing a higher degree of extension-thickening than either GPPS or HIPS and that there is indeed a synergistic effect in what regards the rupture and failure behavior.     

Anisotropic self-organization of hybrid silica based xerogels containing bridged positively charged 1,4-diazoniabicycle[2.2.2]octane chloride group

Anisotropic self-organized hybrid silica based xerogels were obtained. The ordered structure was imposed by the double charged 1,4-diazoniabicycle[2.2.2]octane chloride group bonded in a bridged way. This was confirmed by the presence of well defined X-ray diffraction peaks corresponding to an interplanar distance with the same length estimated for the organic bridged groups. The material was characterized by elemental analysis using CHN technique and the chloride ion was analyzed by a potentiometric titration. (13)C and (29)Si CP MAS solid state NMR spectroscopy and thermogravimetric analysis were also performed. The material that can be obtained in the form of powders and transparent monoliths or films, is thermally stable up to 260 degrees C and the samples with high organic content presented birefringence properties.     

Synthesis,structures and magnetic properties of three metal-organic frameworks containing manganese(II)

Two new Mn(II) coordination polymers formed with molecular formula [Mn(H₂O)₂(HBTC)·(H₂O)] 1 and [Mn(H₂O)₂(4,4′bipy)(HBTC)₂]·(H4,4′bipy)₂ 2, where BTC = 1,2,4-benzenetricarboxylate and 4,4′bipy = 4,4′bipydine, have been synthesized via hydrothermal approach and characterized by single crystal X-ray diffraction techniques. 1 is composed of Mn–H₂O–Mn 1D chains and further the chains are linked by HBTC ligands to form a 2D network in the ab plane; 2 is constructed by Mn–4,4′bipy–Mn 1D chains along the b direction with Mn²⁺ ions coordinated to H₂BTC and water as terminal ligands to form a 2D network. We also prepared a third compound with the molecular formula of [Mn(H₂O)(HBTC)·(H₂O)] which has been recently structurally reported elsewhere. The magnetic properties of the three compounds have been studied in detail under variable temperatures.