QUASI-TOPOLOGICAL QUANTUM FIELD THEORIES AND Z(2) LATTICE GAUGE THEORIES

We consider a two-parameter family of Z(2) gauge theories on a lattice discretization T(M) of a three-manifold M and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Gamma. We show that there is a region Gamma(0) subset of Gamma where the partition function and the expectation value h < W-R(gamma)> i of the Wilson loop can be exactly computed. Depending on the point of Gamma(0), the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of M. The Wilson loop on the other hand, does not depend on the topology of gamma. However, for a subset of Gamma(0), < W-R(gamma)> depends on the size of gamma and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

Influence of the magnetization damping on dynamic hysteresis loops in single domain particles

This article reports on the influence of the magnetization damping on dynamic hysteresis loops in single-domain particles with uniaxial anisotropy. The approach is based on the Neel-Brown theory and the hierarchy of differential recurrence relations, which follow from averaging over the realizations of the stochastic Landau-Lifshitz equation. A new method of solution is proposed, where the resulting system of differential equations is solved directly using optimized algorithms to explore its sparsity. All parameters involved in uniaxial systems are treated in detail, with particular attention given to the frequency dependence. It is shown that in the ferromagnetic resonance region, novel phenomena are observed for even moderately low values of the damping. The hysteresis loops assume remarkably unusual shapes, which are also followed by a pronounced reduction of their heights. Also demonstrated is that these features remain for randomly oriented ensembles and, moreover, are approximately independent of temperature and particle size. (C) 2012 American Institute of Physics. [doi:10.1063/1.3684629]

THE STRUCTURE OF FREE AUTOMORPHIC MOUFANG LOOPS

We describe the structure of a free loop of rank n in the variety of automorphic Moufang loops as a subdirect product of a free group and a free commutative Moufang loop, both of rank n. In particular, the variety of automorphic Moufang loops is the join of the variety of groups and the variety of commutative Moufang loops.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Wilson's disease: an analysis of 28 Brazilian children

OBJECTIVES: Clinical-laboratory and evolutionary analysis of twenty-eight patients with Wilson's disease. METHODS: Twenty-eight children (twelve females and sixteen males) with Wilson's disease were evaluated retrospectively between 1987 and 2009, with a follow-up of 72 months (1 -240 months). The clinical, laboratory, and histologic features at diagnosis were recorded at the end of the study. RESULTS: The median age at diagnosis was 11 years (2 -18 years). Twelve patients were asymptomatic, seven had hepatitis symptoms, five had raised aminotransferase levels, three had hepatomegaly associated with neurological disorders, one had fulminant hepatitis with hemolytic anemia, and six patients presented with a Kayser-Fleischer ring. A histological analysis revealed that six children had chronic hepatitis, seven had cirrhosis, two had steatosis, one had portal fibrosis, and one had massive necrosis. The treatment consisted of D-penicillamine associated with pyridoxine for 26 patients. Adverse effects were observed in the other two patients: one presented with uncontrollable vomiting and the other demonstrated elastosis perforans serpiginosa. At the end of the study, all 26 treated patients were asymptomatic. Twenty-four of the patients were treated with D-penicillamine and pyridoxine, and two were treated with trientine and zinc sulfate. A liver transplant was performed in one patient with fulminant hepatitis, but the final patient died 48 hours after admission to the intensive care unit. CONCLUSIONS: Family screenings associated with early treatment are important in preventing Wilson's disease symptoms and potentially fatal disease progression. The study suggests that Wilson's disease must be ruled out in children older than two years presenting with abnormal levels of hepatic enzymes because of the heterogeneity of symptoms and the encouraging treatment results obtained so far.

Urinary copper excretion before and after oral intake of D-penicillamine in parents of patients with Wilson's disease

Background: Urinary copper excretion higher than 100 mu g/24 h is useful for diagnosing Wilson's disease. D-Penicillamine challenge test may produce higher levels than 1400 mu g/24 h, allowing for better diagnostic accuracy. This study investigated whether heterozygotes reach this value and compared copper serum levels, ceruloplasmin, and urinary copper excretion before and after administering D-penicillamine to the parents of Wilson's disease patients. Methods: Fifty parents of adult patients were enrolled to obtain copper serum levels and ceruloplasmin along with 24-h urinary copper excretion before and after administering 1 g D-penicillamine. Results: Serum ceruloplasmin and copper levels were significantly lower in fathers than in mothers (mean 21.8 x 27.8 mg%; 71.4 x 88.0 mu g%; p <= 0.001). The mean of basal 24-h urinary copper excretion was higher in fathers (26.2 x 18.7 mu g/24 h, p = 0.01), but did not differ between the genders after D-penicillamine (521.7 x 525.3, range 31.6-1085.1 mu g/24 h, p = 0.8). Conclusions: The mean values of serum copper, ceruloplasmin, and basal urinary copper excretion were different between males and females. The current diagnostic threshold of 24-h urinary copper excretion after D-penicillamine was not reached by heterozygotes. The increased urinary copper excretion after D-penicillamine challenge was much higher than fivefold the upper limit of normal urinary copper excretion in the majority of heterozygotes and should not be taken into account when diagnosing Wilson's disease. (C) 2011 Editrice Gastroenterologica Italiana S.r.l. Published by Elsevier Ltd. All rights reserved.

Dynamic symmetry loss of high-frequency hysteresis loops in single-domain particles with uniaxial anisotropy

Understanding how magnetic materials respond to rapidly varying magnetic fields, as in dynamic hysteresis loops, constitutes a complex and physically interesting problem. But in order to accomplish a thorough investigation, one must necessarily consider the effects of thermal fluctuations. Albeit being present in all real systems, these are seldom included in numerical studies. The notable exceptions are the Ising systems, which have been extensively studied in the past, but describe only one of the many mechanisms of magnetization reversal known to occur. In this paper we employ the Stochastic Landau-Lifshitz formalism to study high-frequency hysteresis loops of single-domain particles with uniaxial anisotropy at an arbitrary temperature. We show that in certain conditions the magnetic response may become predominantly out-of-phase and the loops may undergo a dynamic symmetry loss. This is found to be a direct consequence of the competing responses due to the thermal fluctuations and the gyroscopic motion of the magnetization. We have also found the magnetic behavior to be exceedingly sensitive to temperature variations, not only within the superparamagnetic-ferromagnetic transition range usually considered, but specially at even lower temperatures, where the bulk of interesting phenomena is seen to take place. (C) 2011 Elsevier B.V. All rights reserved.

Hard Thermal Loops in the n-Dimensional phi(3) Theory

We derive a closed-form result for the leading thermal contributions which appear in the n-dimensional I center dot (3) theory at high temperature. These contributions become local only in the long wavelength and in the static limits, being given by different expressions in these two limits.