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).

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Noncommutative Jordan superalgebras of degree n > 2

We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a ""nodal"" case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0.

DJKM ALGEBRAS I: THEIR UNIVERSAL CENTRAL EXTENSION

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g circle times C[t, t(-1), u vertical bar u(2) = (t(2) - b(2))(t(2) - c(2))], appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from the Landau-Lifshitz differential equation.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Percutaneous central venous catheterization through the external jugular vein in children: improved success rate with body maneuvers and fluoroscopy assistance

Background/Purpose: Central venous catheterization is among the most common procedures performed by pediatric surgeons. Significant morbidity and even mortality can ensue from the widespread approach to the deep veins of the neck and femoral region. The external jugular vein (EJV) is a low-morbidity alternative for percutaneous catheterization in children, but it has yielded a low success rate in previous reports The authors show an improved success rate with this option. Methods: We performed an analysis of 33 patients` charts in which central venous catheterization using Seldinger technique through the EJV was attempted in 2005. Age, diagnosis, maneuvers used for success, fluoroscopy usefulness, and types of inserted catheters were evaluated. Results: The procedure was successful in 26 (78.8%) patients without complications. Diagnosis was neoplasia in almost half of the patients (42%). In half of the successful cases, body maneuvers were used, namely, twisting the head of the patient to the side of the vein and stretching the ipsilateral arm and shoulder. All but one procedure were completed under fluoroscopic guidance. In 6 (23%) patients, a long-term catheter was inserted. Conclusions: The EJV is an excellent option for central venous catheterization in children. The execution of simple maneuvers along with fluoroscopic assistance might allow for an improved success rate not only for short-term but also for long-term catheter insertion. (C) 2008 Elsevier Inc. All rights reserved.

Decay chain differential equations: Solution through matrix algebra

A matricial method to solve the decay chain differential equations system is presented. The quantity of each nuclide in the chain at a time t may be evaluated by analytical expressions obtained in a simple way using recurrence relations. This method may be applied to problems of radioactive buildup and decay and can be easily implemented computationally. (C) 2009 Elsevier B.V. All rights reserved.

Multilevel analysis of hepatitis A infection in children and adolescents: a household survey in the Northeast and Central-west regions of Brazil

Background The objectives were to estimate the prevalence of hepatitis A among children and adolescents from the Northeast and Midwest regions and the Federal District of Brazil and to identify individual-, household- and area-levels factors associated with hepatitis A infection. Methods This population-based survey was conducted in 20042005 and covered individuals aged between 5 and 19 years. A stratified multistage cluster sampling technique with probability proportional to size was used to select 1937 individuals aged between 5 and 19 years living in the Federal capital and in the State capitals of 12 states in the study regions. The sample was stratified according to age (59 and 10- to 19-years-old) and capital within each region. Individual- and household-level data were collected by interview at the home of the individual. Variables related to the area were retrieved from census tract data. The outcome was total antibodies to hepatitis A virus detected using commercial EIA. The age distribution of the susceptible population was estimated using a simple catalytic model. The associations between HAV infection and independent variables were assessed using the odds ratio and corrected for the random design effect and sampling weight. Multilevel analysis was performed by GLLAMM using Stata 9.2. Results The prevalence of hepatitis A infection in the 59 and 1019 age-group was 41.5 and 57.4, respectively for the Northeast, 32.3 and 56.0, respectively for the Midwest and 33.8 and 65.1 for the Federal District. A trend for the prevalence of HAV infection to increase according to age was detected in all sites. By the age of 5, 31.5 of the children had already been infected with HAV in the Northeast region compared with 20.0 in the other sites. By the age of 19 years, seropositivity was 70 in all areas. The curves of susceptible populations differed from one area to another. Multilevel modeling showed that variables relating to different levels of education were associated with HAV infection in all sites. Conclusion The study sites were classified as areas with intermediate endemicity area for hepatitis A infection. Differences in age trends of infection were detected among settings. This multilevel model allowed for quantification of contextual predictors of hepatitis A infection in urban areas.

The smallest simple Moufang loop

We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

Simple components of the center of FG/J(FG)

Let G be a finite group, F a field, FG the group ring of G over F, and J(FG) the Jacobson radical of FG. Using a result of Berman and Witt, we give a method to determine the structure of the center of FG/J(FG), provided that F satisfies a field theoretical condition.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

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.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.