Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Approaches for multicopper oxidases in the design of electrochemical sensors for analytical applications

We report an effective approach for the construction of a biomimetic sensor of multicopper oxidases by immobilizing a cyclic-tetrameric copper(II) species, containing the ligand (4-imidazolyl)ethylene-2-amino-1-ethylpyridine (apyhist), in the Nafion (R) membrane on a vitreous carbon electrode surface. This complex provides a tetranuclear arrangement of copper ions that allows an effective reduction of oxygen to water, in a catalytic cycle involving four electrons. The electrochemical reduction of oxygen was studied at pH 9.0 buffer solution by using cyclic voltammetry, chronoamperometry, rotating disk electrode voltammetry and scanning electrochemical microscopy techniques. The mediator shows good electrocatalytic ability for the reduction of O(2) at pH 9.0, with reduction of overpotential (350 mV) and increased current response in comparison with results obtained with a bare glassy carbon electrode. The heterogeneous rate constant (k(ME)`) for the reduction of O(2) at the modified electrode was determined by using a Koutecky-Levich plot. In addition, the charge transport rate through the coating and the apparent diffusion coefficient of O(2) into the modifier film were also evaluated. The overall process was found to be governed by the charge transport through the coating, occurring at the interface or at a finite layer at the electrode/coating interface. The proposed study opens up the way for the development of bioelectronic devices based on molecular recognition and self-organization. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of the C-factor and Dentin Preparation Method in the Bond Strength of a Mild Self-etch Adhesive

This study evaluated the effect of the C-factor and dentin preparation method (DPM) in the bond strength (BS) of a mild self-etch adhesive; the study also observed the SEM superficial aspects of the corresponding smear layer. For purposes of this study, 25 molars (n=5) were used in a bond strength test. The molars were divided into two parts (buccal and lingual): one part received a Class V cavity (C-factor=3) and the other received a flat surface (C-factor=0) with the same bur type (coarse diamond or carbide bur and fine diamond or carbide bur), both within the same dentin depth. Five teeth were prepared with wet 60-grit and 600-grit SiC papers. After restoration with Clearfil SE Bond, microtensile beans (0.8 mm(2)) were prepared and tested after 24 hours in a universal testing machine (0.5 mm/minute). An additional two teeth for each DPM were prepared for SEM evaluation of the smear layer superficial aspects. The BS values were submitted to one-way ANOVA, considering only the DPM (flat surfaces) and two-way ANOVA (C-Factor x DPM, considering only burs) with p=0.05. Although the DPM in the flat surfaces was not significant, the standard deviations of carbide bur-prepared specimens were markedly lower. The BS was significantly lower in cavities. The fine carbide bur presented the most favorable smear layer aspect. It was concluded that different dentin preparation methods could not prevent the adverse effect in bond strength of a high C-factor. A coarse cut carbide bur should be avoided prior to a mild self-etch adhesive, because it adversely affected bond strength. In contrast, a fine cut carbide bur provided the best combination: high bond strength with low variability, which suggests a more reliable bond strength performance.

Self-assembling of phenothiazine compounds investigated by small-angle X-ray scattering and electron paramagnetic resonance spectroscopy

Small-angle X-ray scattering (SAXS) and electron paramagnetic resonance (EPR) have been carried out to investigate the structure of the self-aggregates of two phenothiazine drugs, chlorpromazine (CPZ) and trifluoperazine (TFP), in aqueous solution. In the SAXS studies, drug solutions of 20 and 60 mM, at pH 4.0 and 7.0, were investigated and the best data fittings were achieved assuming several different particle form factors with a homogeneous electron density distribution in respect to the water environment. Because of the limitation of scattering intensity in the q range above 0.15 angstrom(-1), precise determination of the aggregate shape was not possible and all of the tested models for ellipsoids, cylinders, or parallelepipeds fitted the experimental data equally well. The SAXS data allows inferring, however, that CPZ molecules might self-assemble in a basis set of an orthorhombic cell, remaining as nanocrystallites in solution. Such nanocrystals are composed of a small number of unit cells (up to 10, in c-direction), with CPZ aggregation numbers of 60-80. EPR spectra of 5- and 16-doxyl stearic acids bound to the aggregates were analyzed through simulation, and the dynamic and magnetic parameters were obtained. The phenothiazine concentration in EPR experiments was in the range of 5-60 mM. Critical aggregation concentration of TFP is lower than that for CPZ, consistent with a higher hydrophobicity of TFP. At acidic pH 4.0 a significant residual motion of the nitroxide relative to the aggregate is observed, and the EPR spectra and corresponding parameters are similar to those reported for aqueous surfactant micelles. However, at pH 6.5 a significant motional restriction is observed, and the nitroxide rotational correlation times correlate very well with those estimated for the whole aggregated particle from SAXS data. This implies that the aggregate is densely packed at this pH and that the nitroxide is tightly bound to it producing a strongly immobilized EPR spectrum. Besides that, at pH 6.5 the differences in motional restriction observed between 5- and 16-DSA are small, which is different from that observed for aqueous surfactant micelles.

Cytogenetic characterization of the strongly electric Amazonian eel, Electrophorus electricus (Teleostei, Gymnotiformes), from the Brazilian rivers Amazon and Araguaia

A karyotype analysis of the electric eel, Electrophorus electricus (Teleostei, Gymnotiformes), a strongly electric fish from northern South America, is presented. Two female specimens were analyzed, one from the Amazon River and one from the Araguaia River. The specimens had a chromosomal number of 2n = 52 (42M-SM + 10A). C-bands were present in a centromeric and pericentromeric position on part of the chromosomes; some interstitial C-bands were also present. Heteromorphic nucleolus organizer regions (NORs) were detected in two chromosome pairs of the specimen from the Amazon River. The chromosome number and karyotype characteristics are similar to those of other Gymnotidae species. The genera Electrophorus and Gymnotus are positioned as the basal lineages in the Gymnotiformes phylogeny.

Self-disclosure of HIV diagnosis to sexual partners by heterosexual and bisexual men: a challenge for HIV/AIDS care and prevention

This study investigated the disclosure of HIV-positive serostatus to sexual partners by heterosexual and bisexual men, selected in centers for HIV/AIDS care. In 250 interviews, we investigated disclosure of serostatus to partners, correlating disclosure to characteristics of relationships. The focus group further explored barriers to maintenance/establishment of partnerships and their association with disclosure and condom use. Fear of rejection led to isolation and distress, thus hindering disclosure to current and new partners. Disclosure requires trust and was more frequent to steady partners, to partners who were HIV-positive themselves, to female partners, and by heterosexuals, occurring less frequently with commercial sex workers. Most interviewees reported consistent condom use. Unprotected sex was more frequent with seropositive partners. Suggestions to enhance comprehensive care for HIV-positive men included stigma management, group activities, and human rights-based approaches involving professional education in care for sexual health, disclosure, and care of "persons living with HIV".

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Comparison of C-reactive protein and serum amyloid A protein in septic shock patients

Septic shock is a severe inflammatory state caused by an infectious agent. Our purpose was to investigate serum amyloid A (SAA) protein and C-reactive protein (CRP) as inflammatory markers of septic shock patients. Here we evaluate 29 patients in postoperative period, with septic shock, in a prospective study developed in a surgical intensive care unit. All eligible patients were monitored over a 7-day period by sequential organ failure assessment (SOFA) score, daily CRP, SAA, and lactate measurements. CRP and SAA strongly correlated up to the fifth day of observation but were not good predictors of mortality in septic shock. Copyright (C) 2008.

BALB/c Mice Infected with Antimony Treatment Refractory Isolate of Leishmania braziliensis Present Severe Lesions due to IL-4 Production

Background: Leishmania braziliensis is the main causative agent of cutaneous leishmaniasis in Brazil. Protection against infection is related to development of Th1 responses, but the mechanisms that mediate susceptibility are still poorly understood. Murine models have been the most important tools in understanding the immunopathogenesis of L. major infection and have shown that Th2 responses favor parasite survival. In contrast, L. braziliensis-infected mice develop strong Th1 responses and easily resolve the infection, thus making the study of factors affecting susceptibility to this parasite difficult. Methodology/Principal Findings: Here, we describe an experimental model for the evaluation of the mechanisms mediating susceptibility to L. braziliensis infection. BALB/c mice were inoculated with stationary phase promastigotes of L. braziliensis, isolates LTCP393(R) and LTCP15171(S), which are resistant and susceptible to antimony and nitric oxide (NO), respectively. Mice inoculated with LTCP393(R) presented larger lesions that healed more slowly and contained higher parasite loads than lesions caused by LTCP15171(S). Inflammatory infiltrates in the lesions and production of IFN-gamma, TNF-alpha, IL-10 and TGF-beta were similar in mice inoculated with either isolate, indicating that these factors did not contribute to the different disease manifestations observed. In contrast, IL-4 production was strongly increased in LTCP393(R)-inoculated animals and also arginase I (Arg I) expression. Moreover, anti-IL-4 monoclonal antibody (mAb) treatment resulted in decreased lesion thickness and parasite burden in animals inoculated with LTCP393(R), but not in those inoculated with LTCP15171(S). Conclusion/Significance: We conclude that the ability of L. braziliensis isolates to induce Th2 responses affects the susceptibility to infection with these isolates and contributes to the increased virulence and severity of disease associated with them. Since these data reflect what happens in human infection, this model could be useful to study the pathogenesis of the L. braziliensis infection, as well as to design new strategies of therapeutic intervention.

Multistability and Self-Similarity in the Parameter-Space of a Vibro-Impact System

The dynamics of a dissipative vibro-impact system called impact-pair is investigated. This system is similar to Fermi-Ulam accelerator model and consists of an oscillating one-dimensional box containing a point mass moving freely between successive inelastic collisions with the rigid walls of the box. In our numerical simulations, we observed multistable regimes, for which the corresponding basins of attraction present a quite complicated structure with smooth boundary. In addition, we characterize the system in a two-dimensional parameter space by using the largest Lyapunov exponents, identifying self-similar periodic sets. Copyright (C) 2009 Silvio L.T. de Souza et al.

Accurate prediction of the Si/SiO(2) interface band offset using the self-consistent ab initio DFT/LDA-1/2 method

We use the density functional theory/local-density approximation (DFT/LDA)-1/2 method [L. G. Ferreira , Phys. Rev. B 78, 125116 (2008)], which attempts to fix the electron self-energy deficiency of DFT/LDA by half-ionizing the whole Bloch band of the crystal, to calculate the band offsets of two Si/SiO(2) interface models. Our results are similar to those obtained with a ""state-of-the-art"" GW approach [R. Shaltaf , Phys. Rev. Lett. 100, 186401 (2008)], with the advantage of being as computationally inexpensive as the usual DFT/LDA. Our band gap and band offset predictions are in excellent agreement with experiments.

Dispersion of electron g-factor with optical transition energy in (In,Ga)As/GaAs self-assembled quantum dots

The electron spin precession about an external magnetic field was studied by Faraday rotation on an inhomogeneous ensemble of singly charged, self-assembled (In,Ga)As/GaAs quantum dots. From the data the dependence of electron g-factor on optical transition energy was derived. A comparison with literature reports shows that the electron g-factors are quite similar for quantum dots with very different geometrical parameters, and their change with transition energy is almost identical. (C) 2011 American Institute of Physics. [doi:10.1063/1.3588413]

Possible hyperdeformed band in (36)Ar observed in (12)C+(24)Mg elastic scattering

Fifteen strongly oscillating angular distributions of the elastic scattering of (12)C + (24)Mg at energies around the Coulomb barrier (E(c.m). = 10.67-16.00 MeV) are reproduced by adding five Breit-Wigner resonance terms to the l = 2, 4, 6, 7, and 8 elastic S matrix. The nonresonant, background elastic scattering S matrix S(l)(0) is calculated using the Sao Paulo potential. The J = 2, 4, 6, 7, and 8 (h) over bar molecular resonances fit well into a rotational molecular band, together with other higher lying resonances observed in the (16)O + (20)Ne elastic scattering. We propose that the presently observed, largely deformed molecular band corresponds to the hyperdeformed band, which has been found previously in alpha-cluster calculations, as well as in a new Nilsson model calculation. Systematic study of its possible clusterizations predicts the preference of the (12)C + (24)Mg and (16)O + (20)Ne molecular structure, in accordance with our present results.

Higher charges and regularized quantum trace identities in su(1,1) Landau-Lifshitz model

We solve the operator ordering problem for the quantum continuous integrable su(1,1) Landau-Lifshitz model, and give a prescription to obtain the quantum trace identities, and the spectrum for the higher-order local charges. We also show that this method, based on operator regularization and renormalization, which guarantees quantum integrability, as well as the construction of self-adjoint extensions, can be used as an alternative to the discretization procedure, and unlike the latter, is based only on integrable representations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3509374]