Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

The identity of Mygale brunnipes CL Koch 1842 (Araneae, Theraphosidae), with a redescription of the species and the description of a new genus

We describe Kochiana new genus to accommodate a small Brazilian theraphosine species described originally as Mygale brunnipes by Koch (1842), resulting in Kochiana brunnipes new combination. Recently, specimens were rediscovered in northeastern Brazilian Atlantic rainforest. A preliminary cladistic analysis using equal weights parsimony and implied weights, was carried out to examine its phylogenetic placement. Kochiana new genus was monophyletic in all trees regardless of weighting scheme or concavity used. There is preliminary evidence for Kochiana new genus monophyly and weak evidence for its placement as sister group of Plesiopelma. Kochiana new genus can be characterized by the presence of a hornshaped spermatheca in females and males with a palpal bulb having prolateral accessory keels and a well developed medial crest on the embolus apex.

Revalidation of Pterinopelma Pocock 1901 with description of a new species and the female of Pterinopelma vitiosum (Keyserling 1891) (Araneae: Theraphosidae: Theraphosinae)

We revalidate the theraphosid genus Pterinopelma Pocock 1901, describe the female of P. vitiosum for first time and Pterinopelma sazimai sp. nov. from Brazil. These two species were included in a matrix with 35 characters and 32 taxa and were analyzed both with all characters having same weight and with implied weights. Searches considering all characters non-additive or some additive were also carried out. The preferred tree, obtained with implied weights, concavity 6 and all characters non-additive shows that Pterinopelma is a monophyletic genus sister to the clade Lasiodora (Vitalius + Nhandu). The presence of denticles on the prolateral inferior male palpal bulb keel is a synapomorphy of the genus.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.