POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

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.

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.

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.

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.

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).

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Partial projective representations and partial actions

The concept of a partial projective representation of a group is introduced and studied. The interaction with partial actions is explored. It is shown that the factor sets of partial projective representations over a field K are exactly the K-valued twistings of crossed products by partial actions. (C) 2009 Elsevier B.V. All rights reserved.

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.