Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Partial projective representations and partial actions II

This paper is a continuation of Dokuchaev and Novikov (2010) [8]. The interaction between partial projective representations and twisted partial actions of groups considered in Dokuchaev and Novikov (2010) [8] is treated now in a categorical language. In the case of a finite group G, a structural result on the domains of factor sets of partial projective representations of G is obtained in terms of elementary partial actions. For arbitrary G we study the component pM'(G) of totally-defined factor sets in the partial Schur multiplier pM(G) using the structure of Exel's semigroup. A complete characterization of the elements of pM'(G) is obtained for algebraically closed fields. (C) 2011 Elsevier B.V. All rights reserved.

Clinical and Microbiologic Evaluation, by Real-Time Polymerase Chain Reaction, of Non-Surgical Treatment of Aggressive Periodontitis Associated With Amoxicillin and Metronidazole

Background: The aim of the present study is to evaluate the clinical and microbiologic changes resulting from non-surgical periodontal treatment associated with amoxicillin and metronidazole in individuals with aggressive periodontitis. Methods: Fifteen individuals with aggressive periodontitis received non-surgical periodontal treatment and 45 days after completion of treatment were treated with antibiotics. Clinical data and samples of subgingival plaque were collected at baseline, 45 days after the non-surgical periodontal treatment, and 1 month after the use of antimicrobial agents. After 3 and 6 months, only clinical data were collected. The presence and quantification of Aggregatibacter actinomycetemcomitans, Porphyromonas gingivalis (Pg), Tannerella forsythia (Tf), Treponema denticola (Td), and Dialister pneumosintes were determined by real-time polymerase chain reaction. Results: All clinical parameters, with the exception of clinical attachment level (CAL), had significantly (P<0.05) improved at the end of the third month after non-surgical therapy associated with antibiotics. There was significant (P<0.05) reduction in the quantities of Td and Tf. After 1 month, there were significant (P<0.05) reductions in the frequencies of Pg and Tf. Conclusion: Non-surgical mechanical treatment associated with the use of amoxicillin and metronidazole led to an improvement in all clinical parameters studied, except for CAL, and significantly reduced the amount of subgingival Tf and Td. J Periodontal 2012;83:744-752.

Permian non-marine bivalves of the Falkland Islands and their palaeoenvironmental significance

We describe the occurrence of non-marine bivalves in exposures of the Middle Permian (Capitanian) Brenton Loch Formation on the southern shore of Choiseul Sound, East Falklands. The bivalves are associated with ichnofossils and were collected from a bed in the upper part of the formation, within a 25 cm thick interval of dark siltstones and mudstones with planar lamination, overlain by massive sandstones. The shells are articulated, with the valves either splayed open or closed. At the top of the succession, mudstone beds nearly 1.5 m above the bivalve-bearing layers yielded well-preserved Glossopteris sp. cf. G. communis leaf fossils. The closed articulated condition of some shells indicates preservation under high sedimentation rates with low residence time of bioclasts at the sediment/water interface. However, the presence of specimens with splayed shells is usually correlated to the slow decay of the shell ligament in oxygen-deficient bottom waters. The presence of complete carbonized leaves of Glossopteris associated with the bivalve-bearing levels also suggests a possibly dysoxic-anoxic bottom environment. Overall, our data suggest that the bivalves were preserved by abrupt burial, possibly by distal sediment flows into a Brenton Loch lake, and may represent autochthonous to parautochthonous fossil accumulations. The shells resemble those of anthracosiids and are herein assigned to Palaeanodonta sp. aff. P. dubia, a species also found in the Permian succession of the Karoo Basin, South Africa. Our results confirm that (a) the true distributions in space and time of all Permian non-marine (freshwater) bivalves are not yet well known, and (b) there is no evidence for marine conditions in the upper part of the Brenton Loch Formation.

MHD numerical simulations of colliding winds in massive binary systems - I. Thermal versus non-thermal radio emission

In the past few decades detailed observations of radio and X-ray emission from massive binary systems revealed a whole new physics present in such systems. Both thermal and non-thermal components of this emission indicate that most of the radiation at these bands originates in shocks. O and B-type stars and WolfRayet (WR) stars present supersonic and massive winds that, when colliding, emit largely due to the freefree radiation. The non-thermal radio and X-ray emissions are due to synchrotron and inverse Compton processes, respectively. In this case, magnetic fields are expected to play an important role in the emission distribution. In the past few years the modelling of the freefree and synchrotron emissions from massive binary systems have been based on purely hydrodynamical simulations, and ad hoc assumptions regarding the distribution of magnetic energy and the field geometry. In this work we provide the first full magnetohydrodynamic numerical simulations of windwind collision in massive binary systems. We study the freefree emission characterizing its dependence on the stellar and orbital parameters. We also study self-consistently the evolution of the magnetic field at the shock region, obtaining also the synchrotron energy distribution integrated along different lines of sight. We show that the magnetic field in the shocks is larger than that obtained when the proportionality between B and the plasma density is assumed. Also, we show that the role of the synchrotron emission relative to the total radio emission has been underestimated.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

MAXIMAL PSEUDOCOMPACT AND MAXIMAL R-CLOSED SPACES

In this paper a space X is pseudocompact if it is Tychonoff and every real-valued continuous function on X is bounded. We obtain conditions under which a Tychonoff space is maximal pseudocompact and study conditions under which a regular space is maximal R-closed.

Residence Time Distribution Models Derived from Non-Ideal Laminar Velocity Profiles in Tubes

The theoretical E-curve for the laminar flow of non-Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks-in-series models of residence time distribution (RTD). In this work, four RTD models derived from non-ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

Optimized Duration of Clopidogrel Therapy Following Treatment with the Endeavor Zotarolimus-Eluting Stent in Real-World Clinical Practice (OPTIMIZE) Trial: Rationale and design of a large-scale, randomized, multicenter study

Background Current recommendations for antithrombotic therapy after drug-eluting stent (DES) implantation include prolonged dual antiplatelet therapy (DAPT) with aspirin and clopidogrel >= 12 months. However, the impact of such a regimen for all patients receiving any DES system remains unclear based on scientific evidence available to date. Also, several other shortcomings have been identified with prolonged DAPT, including bleeding complications, compliance, and cost. The second-generation Endeavor zotarolimus-eluting stent (E-ZES) has demonstrated efficacy and safety, despite short duration DAPT (3 months) in the majority of studies. Still, the safety and clinical impact of short-term DAPT with E-ZES in the real world is yet to be determined. Methods The OPTIMIZE trial is a large, prospective, multicenter, randomized (1: 1) non-inferiority clinical evaluation of short-term (3 months) vs long-term (12-months) DAPT in patients undergoing E-ZES implantation in daily clinical practice. Overall, 3,120 patients were enrolled at 33 clinical sites in Brazil. The primary composite endpoint is death (any cause), myocardial infarction, cerebral vascular accident, and major bleeding at 12-month clinical follow-up post-index procedure. Conclusions The OPTIMIZE clinical trial will determine the clinical implications of DAPT duration with the second generation E-ZES in real-world patients undergoing percutaneous coronary intervention. (Am Heart J 2012;164:810-816.e3.)

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

Thermal effective Lagrangian of static gravitational fields

We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in d space-time dimensions.

Field dependent transition to the non-linear regime in magnetic hyperthermia experiments: Comparison between maghemite, copper, zinc, nickel and cobalt ferrite nanoparticles of similar sizes

Further advances in magnetic hyperthermia might be limited by biological constraints, such as using sufficiently low frequencies and low field amplitudes to inhibit harmful eddy currents inside the patient's body. These incite the need to optimize the heating efficiency of the nanoparticles, referred to as the specific absorption rate (SAR). Among the several properties currently under research, one of particular importance is the transition from the linear to the non-linear regime that takes place as the field amplitude is increased, an aspect where the magnetic anisotropy is expected to play a fundamental role. In this paper we investigate the heating properties of cobalt ferrite and maghemite nanoparticles under the influence of a 500 kHz sinusoidal magnetic field with varying amplitude, up to 134 Oe. The particles were characterized by TEM, XRD, FMR and VSM, from which most relevant morphological, structural and magnetic properties were inferred. Both materials have similar size distributions and saturation magnetization, but strikingly different magnetic anisotropies. From magnetic hyperthermia experiments we found that, while at low fields maghemite is the best nanomaterial for hyperthermia applications, above a critical field, close to the transition from the linear to the non-linear regime, cobalt ferrite becomes more efficient. The results were also analyzed with respect to the energy conversion efficiency and compared with dynamic hysteresis simulations. Additional analysis with nickel, zinc and copper-ferrite nanoparticles of similar sizes confirmed the importance of the magnetic anisotropy and the damping factor. Further, the analysis of the characterization parameters suggested core-shell nanostructures, probably due to a surface passivation process during the nanoparticle synthesis. Finally, we discussed the effect of particle-particle interactions and its consequences, in particular regarding discrepancies between estimated parameters and expected theoretical predictions. Copyright 2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi. org/10.1063/1.4739533]