Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

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.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Electronic Structure and Chemical Bonding in the Ground and Low-Lying Electronic States of Ta(2)

The electronic structure and chemical bonding of the ground and low-lying Lambda - S and Omega states of Ta(2) were investigated at the multiconfiguration second-order perturbation theory (CASSCF//CASPT2) level. The ground state of Ta(2) is computed to be a X(3)Sigma(-)(g) state (R(e) = 2.120 angstrom, omega(e) = 323 cm(-1), and D(e) = 4.65 eV), with two low-lying singlet states close to it (a(1) Sigma(+)(g) : T(e) = 409 cm(-1), R(e) = 2.131 angstrom, and omega(e) = 313 cm(-1); b(1) Gamma(g): T(e) = 1, 038 cm(-1), R(e) = 2.127 angstrom, and omega(e) = 316 cm(-1)). These electronic states are derived from the same electronic configuration: vertical bar 13 sigma(2)(g)14 sigma(2)(g)7 delta(2)(g)13 pi(4)(u)>. The effective bond order of the X(3) Sigma(-)(g) state is 4.52, which indicates that the Ta atoms are bound by a quintuple chemical bond. The a(1) Sigma(+)(g) state interacts strongly with the X(3)Sigma(-)(g) g ground state by a second-order spin-orbit interaction, giving rise to the (1)0(g)(+) (ground state) (dominated by the X(3)Sigma(-)(g) Lambda - S ground state) and (9)0(g)(+) (dominated by the a(1) Sigma(+)(g) Lambda - S state) Omega states. These results are in line with those reported for the group 5B homonuclear transition metal diatomics. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 1306-1315, 2011

Adsorption of 4-aminopyridine on Co and Ag electrodes probed by SERS

The adsorption of 4-aminopyridine (4-AP) on Co and Ag electrodes in acid or alkaline solutions of KCl and KI electrolyte salts were monitored by the Surface-enhanced Raman Spectroscopy (SERS) technique. The SERS intensity for the Ag electrode was in 2 orders of magnitude higher than for the Co electrode, due to the enhancement of the Raman cross-section on Ag by the surface-plasmon excitation. In acidic chloride medium (pH 4), the SERS results for Ag electrodes indicate that the protonated form of 4-AP (4-APH(+)) adsorbs in the potential range of -0.1 to -0.6 V (Ag broken vertical bar AgCl broken vertical bar KCl sat) through hydrogen-bonding between 4-APH(+) and Cl(-) adsorbed on the electrode surface: at more negative potentials the neutral form 4-AP is the predominant adsorbed species. For Co electrode in the same medium, only bands due to neutral 4-AP were observed in the spectra at -0.8 and -0.9 V. For more negative potentials bands assigned to both 4-AP and 4-AP surface complex are observed, with the lasts being enhanced, as the potentials are turned more negative. In alkaline chloride medium (pH 13), for less negative potentials the bands assigned to free 4-AP were observed in the spectra of both Ag and Co surfaces. For more negative potentials, only bands assigned to the 4-AP surface complex were observed. For 0.1 mol L(-1) KI acidic or alkaline solutions, bands assigned to 4-AP and 4-APH(+) were observed in a wider potential range than in chloride solutions. An adsorption scheme of 4-AP on Ag and Co is proposed for acidic and alkaline solutions. (C) 2010 Elsevier B.V. All rights reserved.

Development and Application of a Highly Selective Biomimetic Sensor for Detection of Captopril, an Important Ally in Hypertension Control

A biomimetic sensor is proposed as a promising new analytical method for determination of captopril in different classes of samples. The sensor was prepared by modifying a carbon paste electrode with iron (II) phthalocyanine bis(pyridine) [FePe(dipy)] complex. Amperometric measurements in a batch analytical mode were first carried out in order to optimize the sensor response. An applied potential lower than 0.2 V vs Ag vertical bar AgCl in 0.1 mol L(-1) of TRIS buffer at pH 8.0 provided the best response, with a linear range of 2.5 x 10(-5) to 1.7 x 10(-4) mol L(-1). A detailed investigation of the selectivity of the sensor, employing seventeen other drugs, was also performed. Recovery studies were carried out using biological and environment samples in order to evaluate the sensor`s potential for use with these sample classes. Finally, the performance of the biomimetic sensor was optimized in a flow injection (FIA) system using a wall jet electrochemical cell. Under optimized flow conditions, a broad linear response range, from 5.0 x 10(-4) to 2.5 x 10(-2) mol L(-1), was obtained for captopril, with a sensitivity of 210 +/- 1 mu A L mol(-1).

Sample stacking in CZE using dynamic thermal junctions I. Analytes with low dpK(a)/dT crossing a single thermally induced pH junction in a BGE with high dpH/dT

The possibility to compress analyte bands at the beginning of CE runs has many advantages. Analytes at low concentration can be analyzed with high signal-to-noise ratios by using the so-called sample stacking methods. Moreover, sample injections with very narrow initial band widths (small initial standard deviations) are sometimes useful, especially if high resolutions among the bands are required in the shortest run time. In the present work, a method of sample stacking is proposed and demonstrated. It is based on BGEs with high thermal sensitive pHs (high dpH/dT) and analytes with low dpK(a)/dT. High thermal sensitivity means that the working pK(a) of the BGE has a high dpK(a)/dT in modulus. For instance, Tris and Ethanolamine have dpH/dT = -0.028/degrees C and -0.029/degrees C, respectively, whereas carboxylic acids have low dpK(a)/dT values, i.e. in the -0.002/degrees C to+0.002/degrees C range. The action of cooling and heating sections along the capillary during the runs affects also the local viscosity, conductivity, and electric field strength. The effect of these variables on electrophoretic velocity and band compression is theoretically calculated using a simple model. Finally, this stacking method was demonstrated for amino acids derivatized with naphthalene-2,3-dicarboxaldehyde and fluorescamine using a temperature difference of 70 degrees C between two neighbor sections and Tris as separation buffer. In this case, the BGE has a high pH thermal coefficient whereas the carboxylic groups of the analytes have low pK(a) thermal coefficients. The application of these dynamic thermal gradients increased peak height by a factor of two (and decreased the standard deviations of peaks by a factor of two) of aspartic acid and glutamic acid derivatized with naphthalene-2,3-dicarboxaldehyde and serine derivatized with fluorescamine. The effect of thermal compression of bands was not observed when runs were accomplished using phosphate buffer at pH 7 (negative control). Phosphate has a low dpH/dT in this pH range, similar to the dK(a)/dT of analytes. It is shown that vertical bar dK(a)/dT-dpH/dT vertical bar >> 0 is one determinant factor to have significant stacking produced by dynamic thermal junctions.

The role of HBF(4) in electro-catalysis: Arsenic contamination and anion adsorption

We present in this work a comprehensive investigation of the role played by dissolved tetrafluoroboric acid on the electrochemical response of a polycrystalline platinum electrode in acidic media. HBF(4) from two different suppliers was employed and characterized in terms of the amount of arsenic contamination by Inductively Coupled Plasma-Optical Emission Spectroscopy. The effect of different amounts of HBF(4) on the voltammetric profile of the Pt vertical bar HClO(4)(aq) interface was investigated by means of electrochemical quartz crystal nanobalance (EQCN). Despite the comparable cyclic voltammograms, the presence of arsenic in one of the two HBF(4) used resulted in dramatic variations in the mass change profile, which evidences the deposition/dissolution of arsenic prior to the surface oxidation. For the arsenic-free HBF(4), its effect on the mass change profile was mainly associated to anion adsorption. The impact of dissolved HBF(4) on the electro-oxidation of formic acid was rationalized in terms of two contributions: current enhancement at low potentials due to the arsenic-assisted formic acid electro-oxidation and inhibition at high potentials due to anion adsorption. (C) 2011 Elsevier B.V. All rights reserved.

Correlation between vertical misfits and stresses transmitted to implants from metal frameworks

An inappropriate prosthetic fit could cause stress over the interface implant/bone. The objective of this study was to compare stresses transmitted to implants from frameworks cast using different materials and to investigate a possible correlation between vertical misfits and these stresses. Fifteen one-piece cast frameworks simulating bars for fixed prosthesis in a model with five implants were fabricated and arranged into three different groups according to the material used for casting: CP Ti (commercially pure titanium), Co-Cr (cobalt-chromium) or Ni-Cr-Ti (nickel-chromium-titanium) alloys. Each framework was installed over the metal model with all screws tightened to a 10 N cm torque and then, vertical misfits were measured using an optical microscope. The stresses transmitted to implants were measured using quantitative photoelastic analysis in values of maximum shear stress (T), when each framework was tightened to the photoelastic model to a 10 N cm standardized torque. Stress data were statistically analyzed using one-way ANOVA and Tukey`s test and correlation tests were performed using Pearson`s rank correlation (alpha = 0.05). Mean and standard deviation values of vertical misfit are presented for CP Ti (22.40 +/- 9.05 mu m), Co-Cr (66.41 +/- 35.47 mu m) and Ni-Cr-Ti (32.20 +/- 24.47 mu m). Stresses generated by Co-Cr alloy (tau = 7.70 +/- 2.16 kPa) were significantly higher than those generated by CP Ti (tau = 5.86 +/- 1.55 kPa, p = 0.018) and Ni-Cr-Ti alloy (tau =5.74 +/- 3.05 kPa, p = 0.011), which were similar (p = 0.982). Correlations between vertical misfits and stresses around the implants were not significant as for any evaluated materials. (C) 2011 Elsevier Ltd. All rights reserved.