Bulletin of the Brazilian Mathematical Society, New Series最新文献

Given a group G and a partial factor set (sigma ) of G, we introduce the twisted partial group algebra ({kappa }_{textrm{par}}^sigma G,) which governs the partial projective (sigma )-representations of G into algebras over a field (kappa .) Using the relation between partial projective representations and twisted partial actions we endow ({kappa }_{textrm{par}}^sigma G) with the structure of a crossed product by a twisted partial action of G on a commutative subalgebra of ({kappa }_{textrm{par}}^sigma G.) Then, we use twisted partial group algebras to obtain a first quadrant Grothendieck spectral sequence converging to the Hochschild homology of the crossed product (A*_{Theta } G,) involving the Hochschild homology of A and the partial homology of G, where ({Theta }) is a unital twisted partial action of G on a (kappa )-algebra A with a (kappa )-based twist. An analogous third quadrant cohomological spectral sequence is also obtained.

In this work, it is presented a characterization of star property for a (C^1) vector field based on Lyapunov functions. It is also obtained conditions to strong homogeneity for singular sets by using the notion of infinitesimal Lyapunov functions. As an application, we obtain some results related to singular hyperbolic sets for flows.

In the present paper, we propose a new approach to solving a class of generalized split problems. This approach will open some new directions for research to solve the other split problems, for instance, the split common zero point problem and the split common fixed point problem. More precisely, we study the split common solution problem for monotone operator equations in real Hilbert spaces. To find a solution to this problem, we propose and establish the strong convergence of the two new iterative methods by using the Tikhonov regularization method. Meantime, we also study the stability of the iterative methods. Finally, two numerical examples are also given to illustrate the effectiveness of the proposed methods.

In this paper we consider (C^1) surface diffeomorphisms and study the existence of phase transitions, here expressed by the non-analiticity of the pressure function associated to smooth and geometric-type potentials. We prove that the space of (C^1)-surface diffeomorphisms admitting phase transitions is a (C^1)-Baire generic subset of the space of non-Anosov diffeomorphisms. In particular, if S is a compact surface which is not homeomorphic to the 2-torus then a (C^1)-generic diffeomorphism on S has phase transitions. We obtain similar statements in the context of (C^1)-volume preserving diffeomorphisms. Finally, we prove that a (C^2)-surface diffeomorphism exhibiting a dominated splitting admits phase transitions if and only if has some non-hyperbolic periodic point.

In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and fatness, the SRB measure is indeed absolutely continuous with respect to the Lebesgue measure.

We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.

We prove that mean multiplicities in the length spectrum of a non-compact arithmetic hyperbolic orbifold of dimension (n geqslant 4) have exponential growth rate

extending the analogous result for even dimensions of Belolipetsky, Lalín, Murillo and Thompson. Our proof is based on the study of (square-rootable) Salem numbers. As a counterpart, we also prove an asymptotic formula for the distribution of square-rootable Salem numbers by adapting the argument of Götze and Gusakova. It shows that one can not obtain a better estimate on mean multiplicities using our approach.

The investigation of Ricci solitons is the focus of this work. We have proved triviality results for compact gradient Ricci soliton under certain restriction. Later, a rigidity result is derived for a compact gradient shrinking Ricci soliton. Also, we have estimated the conjugate radius for non-compact gradient shrinking Ricci soliton with superharmonic potential. Moreover, an upper bound for the conjugate radius of Ricci soliton with concircular potential vector field is determined. Finally, it is proved that a non-compact gradient Ricci soliton with a pole and non-negative Ricci curvature is non-shrinking.