Normalization procedure for relaxation studies in NMR quantum information processing

NMR quantum information processing studies rely on the reconstruction of the density matrix representing the so-called pseudo-pure states (PPS). An initially pure part of a PPS state undergoes unitary and non-unitary (relaxation) transformations during a computation process, causing a ""loss of purity"" until the equilibrium is reached. Besides, upon relaxation, the nuclear polarization varies in time, a fact which must be taken into account when comparing density matrices at different instants. Attempting to use time-fixed normalization procedures when relaxation is present, leads to various anomalies on matrices populations. On this paper we propose a method which takes into account the time-dependence of the normalization factor. From a generic form for the deviation density matrix an expression for the relaxing initial pure state is deduced. The method is exemplified with an experiment of relaxation of the concurrence of a pseudo-entangled state, which exhibits the phenomenon of sudden death, and the relaxation of the Wigner function of a pseudo-cat state.

Effect of light-curing units on push-out fiber post bond strength in root canal dentin

The purpose of this study was to evaluate the effectiveness of different light-curing units on the bond strength (push-out) of glass fiber posts in the different thirds of the root (cervical, middle and apical) with different adhesive luting resin systems (dual-cure total-etch; dual-cured and self-etch bonding system; and dual-cure self-adhesive cements), Disks of the samples (n = 144) were used, with approximately 1 mm of thickness of 48 bovine roots restored with glass fiber posts, that were luted with resin cements photo-activated by halogen LCU (QTH, Optilux 501) and blue LED (Ultraled), with power densities of 600 and 550 mW/cm(2), respectively. A universal testing machine (MTS 810 Material Test System) was used with a 1 mm diameter steel rod at cross-head speed of 0.5 mm/min until post extrusion, with load cell of 50 kg, for evaluation of the push-out strength in the different thirds of each sample. The push-out strength values in kgf were converted to MPa and analyzed through Analysis of Variance and Tukey`s test, at significance level of 5%. The results showed that there were no statistical differences between the QTH and LED LCUs. The self-adhesive resin cement had lower values of retention. The total-etch and self-adhesive system resin cements seem to be a possible alternative for glass fiber posts cementation into the radicular canal and the LED LCU can be applied as an alternative to halogen light on photo-activation of dual-cured resin cements.

Paleomagnetic data and K-Ar ages from Mesozoic units of the Santa Marta massif: A preliminary interpretation for block rotation and translations

We report 6 K-Ar ages and paleomagnetic data from 28 sites collected in Jurassic, Lower Cretaceous and Paleocene rocks of the Santa Marta massif, to test previous hypothesis of rotations and translations of this massif, whose rock assemblage differs from other basement-cored ranges adjacent to the Guyana margin. Three magnetic components were identified in this study. A first component has a direction parallel to the present magnetic field and was uncovered in all units (D 352, I = 25.6, k = 57.35, a95 = 5.3, N = 12). A second component was isolated in Cretaceous limestone and Jurassic volcaniclastic rocks (D = 8.8, I = 8.3, k = 24.71, a95 = 13.7, N = 6), and it was interpreted as of Early Cretaceous age. In Jurassic sites with this component, Early Cretaceous K-Ar ages obtained from this and previous studies are interpreted as reset ages. The third component was uncovered in eight sites of Jurassic volcaniclastic rocks, and its direction indicates negative shallow to moderate inclinations and northeastward declinations. K-Ar ages in these sites are of Early (196.5 +/- 4.9 Ma) to early Late Jurassic age (156.6 +/- 8.9 Ma). Due to local structural complexity and too few Cretaceous outcrops to perform a reliable unconformity test, we only used two sites with (1) K-Ar ages, (2) less structural complexity, and (3) reliable structural data for Jurassic and Cretaceous rocks. The mean direction of the Jurassic component is (D = 20.4, I = -18.2, k = 46.9, a95 = 5.1, n = 18 specimens from two sites). These paleomagnetic data support previous models of northward along-margin translations of Grenvillian-cored massifs. Additionally, clockwise vertical-axis rotation of this massif, with respect to the stable craton, is also documented; the sense of rotation is similar to that proposed for the Perija Range and other ranges of the southern Caribbean margin. More data is needed to confirm the magnitudes of rotations and translations. (C) 2009 Elsevier Ltd. All rights reserved.

Precambrian geotectonic units of the Rio de La Plata craton

The main Precambrian tectonic units of Uruguay include the Piedra Alta tectonostratigraphic terrane (PATT) and Nico Perez tectonostratigraphic terrane (NPTT), separated by the Sarandi del Yi high-strain zone. Both terranes are well exposed in the Rio de La Plata craton (RPC). Although these tectonic units are geographically small, they record a wide span of geologic time. Therefore improved geological knowledge of this area provides a fuller understanding of the evolution of the core of South America. The PATT is constituted by low-to medium-grade metamorphic belts (ca. 2.1 Ga); its petrotectonic associations such as metavolcanic units, conglomerates, banded iron formations, and turbiditic deposits suggest a back-arc or a trench-basin setting. Also in the PATT, a late to post-orogenic, arc-related layered mafic complex (2.3-1.9 Ga), followed by A-type granites (2.08 Ga), and finally a taphrogenic mafic dike swarm (1.78 Ga) occur. The less thoroughly studied NPTT consists of Palaeoproterozoic high-grade metamorphic sequences (ca. 2.2 Ga), mylonites and postorogenic and rapakivi granites (1.75 Ga). The Brasiliano-Pan African orogeny affected this terrane. Neoproterozoic cover occurs in both tectonostratigraphic terranes, but is more developed in the NPTT. Over the past 15 years, new isotopic studies have improved our recognition of different tectonic events and associated processes, such as reactivation of shear zones and fluids circulation. Transamazonian and Statherian tectonic events were recognized in the RPC. Based on magmatism, deformation, basin development and metamorphism, we propose a scheme for the Precambrian tectonic evolution of Uruguay, which is summarized in the first Palaeoproterozoic tectonic map of the Rio de La Plata craton.

Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

Simultaneous determination of chromium and manganese in alumina by slurry sampling graphite furnace atomic absorption spectrometry using NbC and NaF as modifiers

This paper reports a method for the direct and simultaneous determination of Cr and Mn in alumina by slurry sampling graphite furnace atomic absorption spectrometry (SiS-SIMAAS) using niobium carbide (NbC) as a graphite platform modifier and sodium fluoride (NaF) as a matrix modifier. 350 mu g of Nb were thermally deposited on the platform surface allowing the formation of NbC (mp 3500 degrees C) to minimize the reaction between aluminium and carbon of the pyrolytic platform, improving the graphite tube lifetime up to 150 heating cycles. A solution of 0.2 mol L(-1) NaF was used as matrix modifier for alumina dissolution as cryolite-based melt, allowing volatilization during pyrolysis step. Masses (c.a. 50 mg) of sample were suspended in 30 ml of 2.0% (v/v) of HNO(3). Slurry was manually homogenized before sampling. Aliquots of 20 mu l of analytical solutions and slurry samples were co-injected into the graphite tube with 20 mu l of the matrix modifier. In the best conditions of the heating program, pyrolysis and atomization temperatures were 1300 degrees C and 2400 degrees C, respectively. A step of 1000 degrees C was optimized allowing the alumina dissolution to form cryolite. The accuracy of the proposed method has been evaluated by the analysis of standard reference materials. The found concentrations presented no statistical differences compared to the certified values at 95% of the confidence level. Limits of detection were 66 ng g(-1) for Cr and 102 ng g(-1) for Mn and the characteristic masses were 10 and 13 pg for Cr and Mn, respectively.

The Development of Dalton`s Atomic Theory as a Case Study in the History of Science: Reflections for Educators in Chemistry

The inclusion of the history of science in science curricula-and specially, in the curricula of science teachers-is a trend that has been followed in several countries. The reasons advanced for the study of the history of science are manifold. This paper presents a case study in the history of chemistry, on the early developments of John Dalton`s atomic theory. Based on the case study, several questions that are worth discussing in educational contexts are pointed out. It is argued that the kind of history of science that was made in the first decades of the twentieth century (encyclopaedic, continuist, essentially anachronistic) is not appropriate for the development of the competences that are expected from the students of sciences in the present. Science teaching for current days will benefit from the approach that may be termed the ""new historiography of science"".