A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

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.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

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.

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.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

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.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

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.

Fluorimetric determination of intra- and extracellular free amino acids in the microalgae Tetraselmis gracilis (Prasinophyceae) using monolithic column in reversed phase mode

This paper describes the development and application of an RP HPLC method using a C(18) monolithic stationary phase for the separation and quantification of extra- and intracellular amino acids in a batch cultivation of the marine alga Tetraselmis gracilis. Fluorimetric detection was made after separation of the o-phthaldialdehyde 2-mercaptoethanol (OPA-2MCE) derivatives using a binary gradient elution. Separation of 19 amino acids was achieved with resolution >1.5 in about 39 min at a flow rate of 1.5 mL/min. RSD of analyses in seawater medium ranged from 0.36% for Orn (0.50 mu mol/L) to 12% for Ile (0.10 mu mol/L). The main constituents of the intracellular dissolved free amino acids (DFAAs) in the exponential growth phase were arginine (Arg), asparagine (Asn), alanine (Ala), aspartic acid (Asp), glutamic acid (Glu), serine (Ser), glycine (Gly), glutamine (Gln), and leucine (Leu). The major amino acids excreted to the media were valine (Val), Ala, Ser, and Gly. The monolithic phase facilitates the analysis by shortening the separation time and saving solvents and instrumentation costs (indeed conventional HPLC instrumentation can be used, running at lower pressures than those ones used with packed particle columns).

Superoxide radical protects liposome-contained cytochrome c against oxidative damage promoted by peroxynitrite and free radicals

The effects of nitrosative species on cyt c structure and peroxidase activity were investigated here in the presence of O(2)(center dot-) and anionic and zwitterionic vesicles. Nitrosative species were generated by 3-morpholinesydnonymine (SIN1) decomposition, using cyt c heme iron and/or molecular oxygen as electron acceptor. Far-and near-UV CD spectra of SIN1-treated cyt c revealed respectively a slight decrease of a-helix content (from 39 to 34%) and changes in the tryptophan structure accompanied by increased fluorescence. The Soret CD spectra displayed a significant decrease of the positive signal at 403 nm. EPR spectra revealed the presence of a low-spin cyt c form (S = 1/2) with g(1) = 2.736, g(2) = 2.465, and g(3) = 2.058 after incubation with SIN1. These data suggest that the concomitant presence of NO(center dot) and O(2)(center dot-) generated from dissolved oxygen, in a system containing cyt c and liposomes, promotes chemical and conformational modi. cations in cyt c, resulting in a hypothetical bis-histidine hexacoordinated heme iron. We also show that, paradoxically, O(2)(center dot-) prevents not only membrane lipoperoxidation by peroxide-derived radicals but also oxidation of cyt c itself due to the ability of O(2)(center dot-) to reduce heme iron. Finally, lipoperoxidation measurements showed that, although it is a more efficient peroxidase, SIN1-treated cyt c is not more effective than native cyt c in promoting damage to anionic liposomes in the presence of tert-ButylOOH, probably due to loss of affinity with negatively charged lipids. (C) 2009 Elsevier Inc. All rights reserved.

Total phenolic content and free radical scavenging activities of methanolic extract powders of tropical fruit residues

Methanolic extract powders of acerola, passion fruit and pineapple industrial residues, including pulp, seeds and peel, altogether (except for acerola) devoid of seeds, were screened for antioxidant capacity. The total phenolic contents (TPCs) of the extract powders were compared with their radical-scavenging activities (RSA) against both DPPH(center dot) and superoxide anion (O(2)(center dot-)) radicals, and their protective effect against liposome peroxidation, triggered by peroxyl radical. Lipid peroxidation was followed by the fluorescence decay of the probe, 4,4-difluoro-5-(4-phenyl-1,3-butadienyl)-4-bora-3a,4a-diaza-s-indacene-3-undecanoic acid (C(11)-BODIPY(581/591)). The TPCs of acerola, passion fruit and pineapple extract powders were (94.6 +/- 7.4); (41.2 +/- 4.2) and (9.1 +/- 1.3) mg of gallic acid equivalents g(-1) of dry extract, respectively. Acerola showed the best RSA-DPPH(center dot) scores, whereas passion fruit was more protective on the RSA-O(2)(center dot-) system. Together with the protective effects against lipid peroxidation (rate of BODIPY decay) which, were similar for acerola and passion fruit extracts, these data suggest that the methanolic extracts of acerola and passion fruit residues may be useful as antioxidant supplements, particularly the acerola extract, due to its high phenolic content. (C) 2008 Elsevier Ltd. All rights reserved

New material for orthopedic implants: Electrochemical study of nickel free P558 stainless steel in minimum essential medium

Nickel, a component of stainless steels (SS) applied in orthopedic implants may cause allergic processes in human tissues P558 nickel free SS was studied to verify its viability as a substitute for stainless steel containing nickel Its performance is compared to ISO 5832-9 and F138 most used nowadays grades in implants fabrications, in minimum essential medium. MEM, at 37 degrees C. Potentiodynamic polarization curves, electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM) and ""in vitro"" cytotoxicity were used as techniques. From the electrochemical point of view P558 SS is comparable to ISO 5832-9 SS in MEM It remains passivated until the transpassivation potential, above which generalized corrosion occurs F138 presents pitting corrosion at 370 mV/SCE. The cytotoxicity results showed that P558. ISO 5832-9 and F138 do not present cytotoxic character Therefore, these results suggest that P558 SS can be applied in orthopedic implants (C) 2010 Elsevier BV All rights reserved