Problemas de bifurcação de corank2 com dois parâmetros e a formulação por caminhos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

XPES studies of oxides of second- and third-row transition metals including rare earths

X-ray photoelectron spectroscopy has been employed to investigate oxides of second- and third-row transition metals, including those of rare earths. Systematics in the spin—orbit splittings and binding energies of core levels of the metals are described. In most of the cases studied, the dependence of the spin—orbit splittings on the atomic number Z is given by the relation ΔE = a(Z - Z0)4, where a is the quantum defect parameter and Z0 is the effective screening. Core-level binding energies are found to increase with the oxidation state of the metal. Most of the core-level binding energies are related to the atomic number Z by the expression E = x(Z - Z0)2, giving rise to linear plots of ln E versus ln Z. Specific features of individual oxides, with respect to satellites, multiplet structure, configuration mixing, and other properties are also discussed. The spectra of PrO2, Pr6O11, TbO2 and Tb4O7 are reported for the first time.

Discovery of three polymorphs of 7-fluoroisatin reveals challenges in using computational crystal structure prediction as a complement to experimental screening

A combined computational and experimental polymorph search was undertaken to establish the crystal forms of 7-fluoroisatin, a simple molecule with no reported crystal structures, to evaluate the value of crystal structure prediction studies as an aid to solid form discovery. Three polymorphs were found in a manual crystallisation screen, as well as two solvates. Form I ( P2(1)/c, Z0 1), found from the majority of solvent evaporation experiments, corresponded to the most stable form in the computational search of Z0 1 structures. Form III ( P21/ a, Z0 2) is probably a metastable form, which was only found concomitantly with form I, and has the same dimeric R2 2( 8) hydrogen bonding motif as form I and the majority of the computed low energy structures. However, the most thermodynamically stable polymorph, form II ( P1 , Z0 2), has an expanded four molecule R 4 4( 18) hydrogen bonding motif, which could not have been found within the routine computational study. The computed relative energies of the three forms are not in accord with experimental results. Thus, the experimental finding of three crystalline polymorphs of 7- fluoroisatin illustrates the many challenges for computational screening to be a tool for the experimental crystal engineer, in contrast to the results for an analogous investigation of 5- fluoroisatin.

Development of a monoclonal antibody binding okadaic acid and dinophysistoxins-1, -2 in proportion to their toxicity equivalence factors

Okadaic acid (OA) and structurally related toxins dinophysistoxin-1 (DTX-1), and DTX-2, are lipophilic marine biotoxins. The current reference method for the analysis of these toxins is the mouse bioassay (MBA). This method is under increasing criticism both from an ethical point of view and because of its limited sensitivity and specificity. Alternative replacement methods must be rapid, robust, cost effective, specific and sensitive. Although published immuno-based detection techniques have good sensitivities, they are restricted in their use because of their inability to: (i) detect all of the OA toxins that contribute to contamination; and (ii) factor in the relative toxicities of each contaminant. Monoclonal antibodies (MAbs) were produced to OA and an automated biosensor screening assay developed and compared with ELISA techniques. The screening assay was designed to increase the probability of identifying a MAb capable of detecting all OA toxins. The result was the generation of a unique MAb which not only cross-reacted with both DTX-1 and DTX-2 but had a cross-reactivity profile in buffer that reflected exactly the intrinsic toxic potency of the OA group of toxins. Preliminary matrix studies reflected these results. This antibody is an excellent candidate for the development of a range of functional immunochemical-based detection assays for this group of toxins.

Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

CLASSICAL EQUIVALENCE OF LAMBDA-R-PHI-2 THEORIES

It is shown that the action functional S[g, phi] = integral d4 x square-root -g[R/k(1 + klambdaphi2) + partial derivative(mu)phi partial derivative(mu)phi] describes, in general, one and the same classical theory whatever may be the value of the coupling constant lambda.

Constraints on spin-3/2 and excited spin-1/2 fermions coming from the leptonic Z0-partial width

We consider effective interactions among excited spin-1/2 and spin-3/2 leptons with the usual ones. Assuming that these new leptons are lighter than the Z0, we study the constraints on their masses and compositeness scale coming from the leptonic Z0 partial width.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Raman spectroscopic study of the antimonate mineral bahianite Al5Sb35+O14(OH)2

Raman spectroscopy has been used to characterise the antimonate mineral bahianite Al5Sb35+O14(OH)2 , a semi-precious gem stone. The mineral is characterised by an intense Raman band at 818 cm-1 assigned to Sb3O1413- stretching vibrations. Other lower intensity bands at 843 and 856 cm-1 are also assigned to this vibration and this concept suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 669 and 682 cm-1 are probably assignable to the OSbO antisymmetric stretching vibrations. Raman bands at 1756, 1808 and 1929 cm-1 may be assigned to δ SbOH deformation modes, whilst Raman bands at 3462 and 3495 cm-1 are assigned to AlOH stretching vibrations. Complexity in the low wave number region is attributed to the composition of the mineral.

A Raman spectroscopic study of the antimonite mineral peretaite Ca(SbO)4(OH)2(SO4)2•2H2O

Raman spectra of mineral peretaite Ca(SbO)4(OH)2(SO4)2•2H2O were studied, and related to the structure of the mineral. Raman bands observed at 978 and 980 cm-1 and a series of overlapping bands observed at 1060, 1092, 1115, 1142 and 1152 cm-1 are assigned to the SO42- ν1 symmetric and ν3 antisymmetric stretching modes. Raman bands at 589 and 595 cm-1 are attributed to the SbO symmetric stretching vibrations. The low intensity Raman bands at 650 and 710 cm-1 may be attributed to SbO antisymmetric stretching modes. Raman bands at 610 cm-1 and at 417, 434 and 482 cm-1 are assigned to the SO42- 4 and 2 bending modes, respectively. Raman bands at 337 and 373 cm-1 are assigned to O-Sb-O bending modes. Multiple Raman bands for both SO42- and SbO stretching vibrations support the concept of the non-equivalence of these units in the coquandite structure.

A comparative study of the effect of calibration conditions on the water equivalence of a range of gel dosimeters

Gel dosimeters are of increasing interest in the field of radiation oncology as the only truly three-dimensional integrating radiation dosimeter. There are a range of ferrous-sulphate and polymer gel dosimeters. To be of use, they must be water-equivalent. On their own, this relates to their radiological properties as determined by their composition. In the context of calibration of gel dosimeters, there is the added complexity of the calibration geometry; the presence of containment vessels may influence the dose absorbed. Five such methods of calibration are modelled here using the Monte Carlo method. It is found that the Fricke gel best matches water for most of the calibration methods, and that the best calibration method involves the use of a large tub into which multiple fields of different dose are directed. The least accurate calibration method involves the use of a long test tube along which a depth dose curve yields multiple calibration points.

Years 2 to 6 students' ability to generalise : models, representations and theory for teaching and learning

Over the last three years, in our Early Algebra Thinking Project, we have been studying Years 3 to 5 students’ ability to generalise in a variety of situations, namely, compensation principles in computation, the balance principle in equivalence and equations, change and inverse change rules with function machines, and pattern rules with growing patterns. In these studies, we have attempted to involve a variety of models and representations and to build students’ abilities to switch between them (in line with the theories of Dreyfus, 1991, and Duval, 1999). The results have shown the negative effect of closure on generalisation in symbolic representations, the predominance of single variance generalisation over covariant generalisation in tabular representations, and the reduced ability to readily identify commonalities and relationships in enactive and iconic representations. This chapter uses the results to explore the interrelation between generalisation and verbal and visual comprehension of context. The studies evidence the importance of understanding and communicating aspects of representational forms which allowed commonalities to be seen across or between representations. Finally the chapter explores the implications of the studies for a theory that describes a growth in integration of models and representations that leads to generalisation.

A Raman spectroscopic study of the antimony mineral klebelsbergite Sb4O4(OH)2(SO4)

Many minerals based upon antimonite and antimonate anions remain to be studied. Most of the bands occur in the low wavenumber region, making infrared spectroscopy difficult to use. This problem can be overcome by using Raman spectroscopy. Raman spectra of the mineral klebelsbergite Sb4O4(OH)2(SO4) were studied, and related to the structure of the mineral. Raman bands observed at 971 cm-1 and a series of overlapping bands are observed at 1029, 1074, 1089, 1139 and 1142 cm-1 are assigned to the SO42- ν1 symmetric and ν3 antisymmetric stretching modes. Two Raman bands are observed at 662 and 723 cm-1 and assigned to the SbO ν3 antisymmetric and ν1 symmetric stretching modes. The intense Raman bands at 581, 604 and 611 cm-1 are assigned to the ν4 SO42- bending modes. Two overlapping bands at 481 and 489 cm-1 are assigned to the ν2 SO42- bending mode. Low intensity bands at 410, 435 and 446 cm-1 may be attributed to OSbO bending modes. The Raman band at 3435 cm-1 is attributed to the OH stretching vibration of the OH units. Multiple Raman bands for both SO42- and SbO stretching vibrations support the concept of the non-equivalence of these units in the klebelsbergite structure. It is proposed that two sulphate anions are distorted to different extents in the klebelsbergite structure.

The phosphate mineral sigloite Fe3+Al2(PO4)2(OH)3·7(H2O), an exception to the paragenesis rule – a vibrational spectroscopic study

The secondary phosphate mineral sigloite Fe3+Al2(PO4)2(OH)3·7H2O is the exception to the rule that phosphate mineral paragenesis is related to the final phase of hydrothermal mineralization at low temperatures. Sigloite was formed as an oxidation pseudomorph after paravauxite, during the last supergene paragenetic stage. We have studied the secondary phosphate mineral sigloite Fe3+Al2(PO4)2(OH)3·7H2O using vibrational spectroscopic techniques. Because the mineral is a phosphate mineral, it is readily studied by spectroscopic techniques as the phosphate and hydrogen phosphate units are readily measured. Indeed, sigloite shows the presence of both phosphate and hydrogen phosphate units in its structure. Raman bands at 1009 cm−1 with shoulders at 993 and 1039 cm−1 are assigned to stretching vibrations of and units. The Raman band at 993 cm−1 is assigned to the ν1 symmetric stretching mode of the POH units, whereas the Raman band at 1009 cm−1 is assigned to the ν1 symmetric stretching mode. Raman bands observed at 506, 528, 571, 596, 619 and 659 cm−1 are attributed to the ν4 out of plane bending modes of the PO4 and H2PO4 units. The Raman bands at 2988, 3118 and 3357 cm−1 are assigned to water stretching vibration. The series of bands at 3422, 3449, 3493, 3552 and 3615 cm−1 are assigned to the OH stretching vibrations of the hydroxyl units. The observation of multiple bands gives credence to the non-equivalence of the OH units in the sigloite structure.