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.

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.

Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q-algebra and Gamma subset of A a Z-order. We classify those A with the property that Z(2) negated right arrow U(Gamma) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q(root-d). A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup. (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.

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.

HYPERBOLICITY OF SEMIGROUP ALGEBRAS II

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose rational semigroup algebra contains a Z-order with hyperbolic unit group. In this paper, we complete this classification and give an easy proof that deals with all finite semigroups.

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.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Effect of laser welding on the titanium composite tensile bond strength

The aim of this study was to analyze the shear bond strength between commercially pure titanium, with and without laser welding, after airbone-particle abrasion (Al2O3) and 2 indirect composites. Sixty-four specimens were cast and divided into 2 groups with and without laser welding. Each group was divided in 4 subgroups, related to Al2O3 grain size: A - 250 µm; B - 180 µm; C- 110 µm; and D - 50 µm. Composite rings were formed around the rods and light polymerized using UniXS unit. Specimens were invested and their shear bond strength at failure was measured with a universal testing machine at a crosshead speed of 2.0 mm/min. Statistical analysis was carried out with ANOVA and Tukey's test (α=0.05). The highest bond strength means were recorded in 250 µm group without laser welding. The lowest shear bond strength means were recorded in 50 µm group with laser welding. Statistically significant differences (p<0.05) were found between all groups. In conclusion, airborne particle abrasion yielded significantly lower bond strength as the Al2O3 particle size decreased. Shear bond strength decreased in the laser welded specimens.

A revision of the Neotropical Solenopsidini ant genus Oxyepoecus Santschi, 1926 (Hymenoptera: Formicidae: Myrmicinae): 2. Final. Key for species and revision of the Rastratus species-group

In the first paper of this series (Albuquerque & Brandão, 2004) we revised the Vezenyii species group of the exclusively Neotropical solenopsidine (Myrmicinae) ant genus Oxyepoecus. In this closing paper we update distribution information on the Vezenyii group species and revise the other Oxyepoecus species-group (Rastratus). We describe two species (Oxyepoecus myops n. sp. and O. rosai n. sp.) and redescribe previously known species of the group [O. daguerrei (Santschi, 1933), O. mandibularis (Emery, 1913), O. plaumanni Kempf, 1974, O. rastratus Mayr, 1887, and O. reticulatus Kempf, 1974], adding locality records and comments on the meagre biological data of these species. We also present an identification key to Oxyepoecus species based on workers.

Two new species of the Hypostomus cochliodon group (Siluriformes: Loricariidae) from the rio Negro basin in Brazil

Two new species of Hypostomus are described from the middle and upper rio Negro in Brazil. They are assigned to the Hypostomus cochliodon group (sensu Armbruster, 2003) by possessing few spoon-shaped teeth, and dentary angle averaging less than 80º. Hypostomus kopeyaka is described from the rio Tiquié, a tributary of the rio Uaupés, upper rio Negro basin, presents a unique color pattern among the Hypostomus species belonging to the Hypostomus cochliodon group, consisting of conspicuously horizontally elongated, closely-set black spots over the entire dorsal and lateral surfaces of the body. Hypostomus weberi is described from the middle rio Negro and can be distinguished from all remaining Hypostomus species belonging to the Hypostomus cochliodon group by possessing a unique color pattern consisting in large, rounded, widelyspaced black spots over body and fins.

Alluvial-eolian interaction in a Cambrian rift margin: the Pedra das Torrinhas and Pedra Pintada formations (Guaritas Group, RS)

This work presents a study of selected outcrops from the Pedra das Torrinhas Formation of the Guaritas Group (Cambrian, Camaquã Basin), near the basin bordering Encantadas Fault Zone. The studied succession includes alluvial fan deposits that pass laterally into eolian deposits. Sedimentary facies and architectural element analysis were performed, followed by sedimentary petrography and microscopic porosity analysis, aiming to characterize the porosity of the deposits and its spatial distribution. The main objective was to contribute to a better understanding of the porosity spatial distribution in depositional systems characterized by the interaction between alluvial and eolian processes, with special reference to deposits formed prior to the development of terrestrial plants. Porosity values are related to depositional processes, with higher porosities associated to eolian dune deposits (mean of 8.4%), and lower porosity related to interdunes (mean of 3.4%) and alluvial fans (mean of 4.3%). Architectural elements analysis revealed the spatial relationships of these deposits, a response to the interplay of the eolian and alluvial processes. The integration of porosity data reveals that the interaction of alluvial and eolian processes results in heterogeneous distribution of porosity at the facies association scale. Eolian reworking of alluvial facies increases porosity whereas sheet-flood and other alluvial processes in the interdune areas reduce porosity.

Neuromodulation approaches for the treatment of major depression: challenges and recommendations from a working group meeting

The use of neuromodulation as a treatment for major depressive disorder (MDD) has recently attracted renewed interest due to development of other non-pharmacological therapies besides electroconvulsive therapy (ECT) such as transcranial magnetic stimulation (TMS), transcranial direct current stimulation (tDCS), deep brain stimulation (DBS), and vagus nerve stimulation (VNS). METHOD: We convened a working group of researchers to discuss the updates and key challenges of neuromodulation use for the treatment of MDD. RESULTS: The state-of-art of neuromodulation techniques was reviewed and discussed in four sections: [1] epidemiology and pathophysiology of MDD; [2] a comprehensive overview of the neuromodulation techniques; [3] using neuromodulation techniques in MDD associated with non-psychiatric conditions; [4] the main challenges of neuromodulation research and alternatives to overcome them. DISCUSSION: ECT is the first-line treatment for severe depression. TMS and tDCS are strategies with a relative benign profile of side effects; however, while TMS effects are comparable to antidepressant drugs for treating MDD; further research is needed to establish the role of tDCS. DBS and VNS are invasive strategies with a possible role in treatment-resistant depression. In summary, MDD is a chronic and incapacitating condition with a high prevalence; therefore clinicians should consider all the treatment options including invasive and non-invasive neuromodulation approaches.

Revision of the Neotropical trahiras of the Hoplias lacerdae species-group (Ostariophysi: Characiformes: Erythrinidae) with descriptions of two new species

Hoplias lacerdae was originally described from the rio Ribeira de Iguape, Iporanga, São Paulo State. The Hoplias lacerdae group is defined as containing generally large trahiras with the medial margins of dentaries running parallel to each other and lacking teeth on the basihyal compared to the H. malabaricus group in which the medial margins of the dentaries converge towards the mandibular symphysis and which have teeth on the basihyal. A taxonomic revision of the group based on meristic and morphometric data identified five distinct species: H. lacerdae distributed in the rio Ribeira de Iguape and rio Uruguai; H. intermedius from the rio São Francisco, upper rio Paraná basin, and rio Doce; H. brasiliensis from rivers of the Atlantic Coastal drainage from the rio Paraguaçu to the rio Jequitinhonha; H. australis new species, endemic to the rio Uruguai; and H. curupira new species present in northern South America, including the rios Negro, Trombetas, Tapajós, Xingu, Tocantins and Capim in the Amazon basin, upper rio Orinoco near the rio Casiquiare (Venezuela), and coastal rivers of Guyana and Suriname. A lectotype for Hoplias intermedius and a neotype for H. brasiliensis are designated.