On symmetries of singular implicit ODEs

We study implicit ODEs, cubic in derivative, with infinitesimal symmetry at singular points. Cartan showed that even at regular points the existence of nontrivial symmetry imposes restrictions on the ODE. Namely, this algebra has the maximal possible dimension 3 iff the web of solutions is flat. For cubic ODEs with flat 3-web of solutions we establish sufficient conditions for the existence of nontrivial symmetries at singular points and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling is some coordinates. We use this symmetry to find first integrals of the ODE.

Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries

Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.

A note about splittings of groups and commensurability under a cohomological point of view

Let G be a group, let S be a subgroup with infinite index in G and let FSG be a certain Z2G-module. In this paper, using the cohomological invariant E(G, S, FSG) or simply E˜(G, S) (defined in [2]), we analyze some results about splittings of group G over a commensurable with S subgroup which are related with the algebraic obstruction “singG(S)" defined by Kropholler and Roller ([8]. We conclude that E˜(G, S) can substitute the obstruction “singG(S)" in more general way. We also analyze splittings of groups in the case, when G and S satisfy certain duality conditions.

Some considerations about cohomology of finite groups

In this work we present some considerations about cohomology of finite groups. In the first part we use the restriction map in cohomology to obtain some results about subgroups of finite index in a group. In the second part, we use Tate cohomology to present an application of the theory of groups with periodic cohomology in topology.

Quaternion orders over quadratic integer rings from arithmetic fuchsian groups

In this paper we show that the quaternion orders OZ[ √ 2] ≃ ( √ 2, −1)Z[ √ 2] and OZ[ √ 3] ≃ (3 + 2√ 3, −1)Z[ √ 3], appearing in problems related to the coding theory [4], [3], are not maximal orders in the quaternion algebras AQ( √ 2) ≃ ( √ 2, −1)Q( √ 2) and AQ( √ 3) ≃ (3 + 2√ 3, −1)Q( √ 3), respectively. Furthermore, we identify the maximal orders containing these orders.

Chemical reduction of carboxyl groups in heparin abolishes its vasodilatory activity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Controllability of control systems on complex simple lie groups and the topology of flag manifolds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Ecological strategies of Al-accumulating and non-accumulating functional groups from the cerrado sensu stricto

Coordenação de Aperfei çoamento de Pessoal de Nível Superior (CAPES)

Performance and parasite control of different genetic groups of lambs finished in irrigated pasture

The aim of this study was to compare the following four genetic groups of hair sheep: Santa Inês (SI), Morada Nova (MN), Brazilian Somali (BS), and the F1 1/2Dorper x 1/2Morada Nova crossbreed on traits related to growth and parasitic infection. Thirty-three male lambs of the same age and of simple birth, under the same pre-weaning management conditions were used in the experiment. After weaning the animals were housed in a completely randomized design in paddocks made of Panicum maximum cv. Tanzania. Along the course of the research, the performance of the four groups of sheep was observed to be negatively affected by gastrointestinal parasites, but there was a genotype effect to the average daily weight gain (ADWG), where the SI and F1 genotypes presented higher values. The effects of genotype, time and genotype x time interaction were significant in weight and corporal score (CS) measurements. The BS lambs had the highest CS values throughout the experiment despite not presenting greater weight gain when compared to the SI and F1 breeds. There were also significant effects of time and genotype x time interaction for packed cell volume (PCV) and FAMACHA© score (FAM) and only the time effect was significant in the total number of eggs per gram (EPG) and total plasma protein (TPP). The MN lambs showed higher PCV values and unlike the other groups, presented a FAMACHA© score below 3 and PCV above 23% even having a higher EPG tendency, especially in the initial phase, indicating a possible higher resilience to infection caused by gastrointestinal parasites.

Occurrence of periodontal pathogens in ethnic groups from a native Brazilian reservation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Accidental symmetries and massless quarks in the economical 3-3-1 model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pseudospin and spin symmetries in 1+1 dimensions: the case of the Coulomb potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Differential habitat use by demographic groups of the redfinger rubble crab Eriphia gonagra (Fabricius, 1781)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Metacommunity versus Biogeography: a case study of two groups of neotropical vegetation-dwelling arthropods

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)