Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

The Limit Theorems for Transportation Networks

2000 Mathematics Subject Classi cation: 60K25 (primary); 60F05, 37A50 (secondary)

Limit Theorems for Maxima of Heavy-Tailed Terms with Random Dependent Weights

2000 Mathematics Subject Classification: Primary 60F17, 60G52, 60G70 secondary 60E07, 62E20.

Limit Theorems for Non-Critical Branching Processes with Continuous State Space

2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).

Free Resolutions from Involutive Bases

We show that the theory of involutive bases can be combined with discrete algebraic Morse Theory. For a graded k[x0 ...,xn]-module M, this yields a free resolution G, which in general is not minimal. We see that G is isomorphic to the resolution induced by an involutive basis. It is possible to identify involutive bases inside the resolution G. The shape of G is given by a concrete description. Regarding the differential dG, several rules are established for its computation, which are based on the fact that in the computation of dG certain patterns appear at several positions. In particular, it is possible to compute the constants independent of the remainder of the differential. This allows us, starting from G, to determine the Betti numbers of M without computing a minimal free resolution: Thus we obtain a new algorithm to compute Betti numbers. This algorithm has been implemented in CoCoALib by Mario Albert. This way, in comparison to some other computer algebra system, Betti numbers can be computed faster in most of the examples we have considered. For Veronese subrings S(d), we have found a Pommaret basis, which yields new proofs for some known properties of these rings. Via the theoretical statements found for G, we can identify some generators of modules in G where no constants appear. As a direct consequence, some non-vanishing Betti numbers of S(d) can be given. Finally, we give a proof of the Hyperplane Restriction Theorem with the help of Pommaret bases. This part is largely independent of the other parts of this work.

What can be learned from failed proofs of non-theorems?

This paper reports an investigation into the link between failed proofs and non-theorems. It seeks to answer the question of whether anything more can be learned from a failed proof attempt than can be discovered from a counter-example. We suggest that the branch of the proof in which failure occurs can be mapped back to the segments of code that are the culprit, helping to locate the error. This process of tracing provides finer grained isolation of the offending code fragments than is possible from the inspection of counter-examples. We also discuss ideas for how such a process could be automated.

About a Vanishing Viscosity-Capillarity Method

We consider a class of nonlinear dissipative-dispersive perturbations of the scalar conservation law @tu + div f (u) = 01 and we study the convergence of the approximated solutions to its entropy solution. In particular, we obtain conditions under which the balance between dissipation and dispersion gives rise to the convergence (by DiPerna's measure-valued solution technique).

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Ichthyofauna of Rio Jurubatuba, Santos, São Paulo: a high diversity refuge in impacted lands

Ichthyofaunistic surveys in the Atlantic Rainforest have been published in relatively few works, in spite of the major biological importance of this once vast biome which is rapidly vanishing due to disordered human population growth and natural resources overexploitation. The present study aimed to access the fish fauna of a relatively well preserved basin between the cities of Santos and Cubatão (SP), an area highly modified by human activities where recent ichthyofaunistic surveys are still missing. Collections were made during three field trips in Rio Jurubatuba, a medium sized costal river, and Riacho Sabão, one of its main tributaries. A total of 2773 specimens were sampled, representing 25 species from 14 families. Six species were primary marine using the upper reaches of Rio Jurubatuba. Twelve of the 19 freshwater species are endemic of the Atlantic Rainforest and four are present in regional lists of endangered species. Only five species occurred in both Rio Jurubatuba and Riacho Sabão. The most diverse family was Characidae, followed by Poeciliidae, Rivulidae and Heptapteridae. Phalloceros caudimaculatus was the most abundant species, followed by Poecilia vivipara and Geophagus brasiliensis. The study area is considered well preserved and due to its critical location, urges for conservation policies to protect its fish diversity.