SINGULARITY THEORY AND FORCED SYMMETRY BREAKING IN EQUATIONS

A theory of bifurcation equivalence for forced symmetry breaking bifurcation problems is developed. We classify (O(2), 1) problems of corank 2 of low codimension and discuss examples of bifurcation problems leading to such symmetry breaking.

EPR, FT-IR and XRD investigation of soils from Parana, Brazil

Samples of Araucaria area soil from Parana state, Brazil, were separated by particle size fractionation and investigated by electron paramagnetic resonance (EPR) in X-Band of 9.5 GHz at room temperature and 77K, infra-red spectroscopy and X-ray diffractometry. The paramagnetic species in the soil samples were identified by comparison with EPR spectra of some minerals studied recently by our group, several soil types and/or soil components investigated in the literature. The value of g = 2.1 (Delta H = 85 mT) indicated the presence of ferrihydrite. Hematite was identified by g = 2.1 (Delta H = 100 mT) and g = 4.3 for Fe(3+) lines of the concentrated dominium and diluted dominium. Kaolinite was identified by IR and EPR with the resonance at g = 4.3 attributed to Fe(3+) ions in isolated sites of tetrahedral and octahedral symmetry with rhombic distortion. The resonances at g = 3.7 and g = 4.9 were attributed to Fe(3+) in more highly symmetrical environment than rhombic symmetry, but not in axial symmetry. Three signals around g = 2 were attributed to radiation defects, plus additional resonances at g = 2.8 and 9.0. Signals less intense than those at g = 2.1, 3.7, and 6.5, observed for clear grains of soil, were attributed to presence of Fe(3+) in quartz which was identified by IR and XDR. (C) 2011 Elsevier B.V. All rights reserved.

Scrutinizing the ZW(+)W(-) vertex at the Large Hadron Collider at 7 TeV

We analyze the potential of the CERN Large Hadron Collider running at 7 TeV to search for deviations from the Standard Model predictions for the triple gauge boson coupling ZW(+)W(-) assuming an integrated luminosity of 1 fb(-1). We show that the study of W(+)W(-) and W(+/-)Z productions, followed by the leptonic decay of the weak gauge bosons can improve the present sensitivity on the anomalous couplings Delta g(1)(Z), Delta kappa(Z), lambda(Z), g(4)(Z), and (lambda) over bar (Z) at the 2 sigma level. (C) 2010 Elsevier B.V. All rights reserved.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Conversion coefficients from air kerma to personal dose equivalent in mammography

In this work, the scattered X-ray beams produced by a mammography unit with a Mo/Mo, Mo/Rh and W/Rh anode/filter combinations were applied in the evaluation of the Hp(10, 0) and mean conversion coefficients from air kerma to the personal dose equivalent ((C) over barH(p(10,0 degrees))). The higher values of H(p)(10,0 degrees) are related to the Mo/Rh combination whereas the lower ones are for the W/Rh target/filter. (C) over barH(p(10,0 degrees)) values are in the range 0.19-0.54 Sv/Gy, where the higher values comprise the W/Rh combination. (C) 2009 Elsevier Ltd. All rights reserved.

Weak antilocalization in HgTe quantum wells near a topological transition

The anomalous alternating magnetoresistivity in HgTe quantum wells with thicknesses of 5.8 and 8.3 nm, i.e., near the transition from the direct band spectrum to an inverted spectrum, has been revealed and analyzed. It has been shown that the revealed anomalous alternating magnetoresistivity in wells with an inverted spectrum is well described by the theory developed by S.V. Iordanskii et al. [JETP Lett. 60, 206 (1994)] and W. Knap et al. [Phys. Rev. B 53, 3912 (1996)]. A detailed comparison of the experimental data with the theory indicates the presence of only the cubic term in the spin splitting of the electronic spectrum. The applicability conditions of the mentioned theory are not satisfied in a well with a direct gap and, for this reason, such a certain conclusion is impossible. The results indicate the existence of a strong spin-orbit interaction in symmetric HgTe quantum wells near the topological transition.

Classification of quantum relativistic orientable objects

Extending our previous work `Fields on the Poincare group and quantum description of orientable objects` (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3 + 1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

X-ray spectroscopy applied to radiation shielding calculation in mammography

The protective shielding design of a mammography facility requires the knowledge of the scattered radiation by the patient and image receptor components. The shape and intensity of secondary x-ray beams depend on the kVp applied to the x-ray tube, target/filter combination, primary x-ray field size, and scattering angle. Currently, shielding calculations for mammography facilities are performed based on scatter fraction data for Mo/Mo target/filter, even though modern mammography equipment is designed with different anode/filter combinations. In this work we present scatter fraction data evaluated based on the x-ray spectra produced by a Mo/Mo, Mo/Rh and W/Rh target/filter, for 25, 30 and 35 kV tube voltages and scattering angles between 30 and 165 degrees. Three mammography phantoms were irradiated and the scattered radiation was measured with a CdZnTe detector. The primary x-ray spectra were computed with a semiempirical model based on the air kerma and HVL measured with an ionization chamber. The results point out that the scatter fraction values are higher for W/Rh than for Mo/Mo and Mo/Rh, although the primary and scattered air kerma are lower for W/Rh than for Mo/Mo and Mo/Rh target/filter combinations. The scatter fractions computed in this work were applied in a shielding design calculation in order to evaluate shielding requirements for each of these target/filter combinations. Besides, shielding requirements have been evaluated converting the scattered air kerma from mGy/week to mSv/week adopting initially a conversion coefficient from air kerma to effective dose as 1 Sv/Gy and then a mean conversion coefficient specific for the x-ray beam considered. Results show that the thickest barrier should be provided for Mo/Mo target/filter combination. They also point out that the use of the conversion coefficient from air kerma to effective dose as 1 Sv/Gy is conservatively high in the mammography energy range and overestimate the barrier thickness. (c) 2008 American Association of Physicists in Medicine.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

THE PYROCHLORE SUPERGROUP OF MINERALS: NOMENCLATURE

A new scheme of nomenclature for the pyrochlore supergroup, approved by the CNMNC-IMA, is based on the ions at the A, B and Y sites. What has been referred to until now as the pyrochlore group should be referred to as the pyrochlore supergroup, and the subgroups should be changed to groups. Five groups are recommended, based on the atomic proportions of the B atoms Nb, Ta, Sb, Ti, and W. The recommended groups are pyrochlore, microlite, romite, betafite, and elsmoreite, respectively. The new names are composed of two prefixes and one root name (identical to the name of the group). The first prefix refers to the dominant anion (or cation) of the dominant valence [or H(2)O or rectangle] at the Y site. The second prefix refers to the dominant cation of the dominant valence [or H(2)O or rectangle] at the A site. The prefix "" keno-"" represents "" vacancy"". Where the first and second prefixes are equal, then only one prefix is applied. Complete descriptions are missing for the majority of the pyrochlore-supergroup species. Only seven names refer to valid species on the grounds of their complete descriptions: oxycalciopyrochlore, hydropyrochlore, hydroxykenomicrolite, oxystannomicrolite, oxystibiomicrolite, hydroxycalcioromite, and hydrokenoelsmoreite. Fluornatromicrolite is an IMA-approved mineral, but the complete description has not yet been published. The following 20 names refer to minerals that need to be completely described in order to be approved as valid species: hydroxycalciopyrochlore, fluornatropyrochlore, fluorcalciopyrochlore, fluorstrontiopyrochlore, fluorkenopyrochlore, oxynatropyrochlore, oxyplumbopyrochlore, oxyyttropyrochlore-(Y), kenoplumbopyrochlore, fluorcalciomicrolite, oxycalciomicrolite, kenoplumbomicrolite, hydromicrolite, hydrokenomicrolite, oxycalciobetafite, oxyuranobetafite, fluornatroromite, fluorcalcioromte, oxycalcioromite, and oxyplumboromite. For these, there are only chemical or crystalstructure data. Type specimens need to be defined. Potential candidates for several other species exist, but are not sufficiently well characterized to grant them any official status. Ancient chemical data refer to wet-chemical analyses and commonly represent a mixture of minerals. These data were not used here. All data used represent results of electron-microprobe analyses or were obtained by crystal-structure refinement. We also verified the scarcity of crystal-chemical data in the literature. There are crystalstructure determinations published for only nine pyrochlore-supergroup minerals: hydropyrochlore, hydroxykenomicrolite, hydroxycalcioromite, hydrokenoelsmoreite, hydroxycalciopyrochlore, fluorcalciopyrochlore, kenoplumbomicrolite, oxycalciobetafite, and fluornatroromite. The following mineral names are now discarded: alumotungstite, bariomicrolite, bariopyrochlore, bindheimite, bismutomicrolite, bismutopyrochlore, bismutostibiconite, calciobetafite, ceriopyrochlore-(Ce), cesstibtantite, ferritungstite, jixianite, kalipyrochlore, monimolite, natrobistantite, partzite, plumbobetafite, plumbomicrolite, plumbopyrochlore, stannomicrolite, stetefeldtite, stibiconite, stibiobetafite, stibiomicrolite, strontiopyrochlore, uranmicrolite, uranpyrochlore, yttrobetafite-(Y), and yttropyrochlore-(Y).