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

We give an example of a regular 1-dimensional foliation along a genus 3 curve whose Ueda type is one and normal bundle is of order two.

We study the singularities of commuting vector fields of a real submanifold of a Kähler manifold Z.

Abstract

As is well-known, numerical experiments show that Napoleon’s Theorem for planar triangles does not extend to a similar statement for triangles on the unit sphere (S^2) . Spherical triangles for which an extension of Napoleon’s Theorem holds are called Napoleonic, and until now the only known examples have been equilateral. In this paper we determine all Napoleonic spherical triangles, including a class corresponding to points on a 2-dimensional ellipsoid, whose Napoleonisations are all congruent. Other new classes of examples are also found, according to different versions of Napoleon’s Theorem for the sphere. The classification follows from successive simplifications of a complicated original algebraic condition, exploiting geometric symmetries and algebraic factorisations.

Abstract

We consider some local entropy properties of dynamical systems under the assumption of shadowing. In the first part, we give necessary and sufficient conditions for shadowable points to be certain entropy points. In the second part, we give some necessary and sufficient conditions for (non) h-expansiveness under the assumption of shadowing and chain transitivity; and use the result to present a counter-example for a question raised by Artigue et al. (Proc Am Math Soc 150:3369–3378, 2022).

The generalized three dimensional Navier–Stokes equations with damping are considered. Firstly, existence and uniqueness of strong solutions in the periodic domain ({mathbb {T}}^{3}) are proved for (frac{1}{2}<alpha <1,~~ beta +1ge frac{6alpha }{2alpha -1}in (6,+infty )). Then, in the whole space (R^3,) if the critical situation (beta +1= frac{6alpha }{2alpha -1}) and if (u_{0}in H^{1}(R^{3}) bigcap {dot{H}}^{-s}(R^{3})) with (sin [0,1/2]), the decay rate of solution has been established. We give proofs of these two results, based on energy estimates and a series of interpolation inequalities, the key of this paper is to give an explanation for that on the premise of increasing damping term, the well-posedness and decay can still preserve at low dissipation (alpha <1,) and the relationship between dissipation and damping is given.

In this work we study evaluation codes defined on the points of a subset (mathcal {X}) of an affine space over a finite field, whose vanishing ideal admits a Gröbner basis of a certain type, which occurs for subsets considered in several well-known examples of evaluation codes, like Reed-Solomon codes, Reed-Muller codes and affine cartesian codes. We determine properties of the polynomials in this basis which allow the determination of the footprint of the vanishing ideal and the explicit construction of indicator functions for the points of (mathcal {X}). We then consider generalized monomial evaluation codes and find information on their duals, and the dimension of their hulls. We present several examples of applications of the results we found.

This paper is concerned with the existence and concentration of ground state solutions for the following class of elliptic Kirchhoff–Boussinesq type problems given by

where (2< p< 4,) (fin C( {mathbb {R}}, {mathbb {R}})) is a nonlinearity which has subcritical or critical exponential growth at infinity and (Vin C({mathbb {R}}^4,{mathbb {R}})) is a potential that vanishes on a bounded domain (Omega subset {mathbb {R}}^4.) Using variational methods, we show the existence of ground state solutions, which concentrates on a ground state solution of a Kirchhoff–Boussinesq type equation in (Omega .)

We characterise the numerical semigroups with a monotone Apéry set (MANS-semigroups for short). Moreover, we describe the families of MANS-semigroups when we fix the multiplicity and the ratio.

The invariant subspace problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operators (in the sense of Rota) the ISP can be solved by proving that every minimal invariant subspace of a universal operator is one dimensional. In this work, we obtain conditions for (T^{*}_{varphi }|_{M}) to have a non-trivial subspace where (Msubset H^{2}({mathbb {D}}^{2})) is an invariant subspace of the Toeplitz operator (T_{varphi }^{*}) on the Hardy space over the bidisk (H^{2}({mathbb {D}}^{2})) induced by the symbol (varphi in H^{infty }({mathbb {D}})). We then use this fact to obtain sufficient conditions for the ISP to be true.

Lattice Lipschitz operators define a new class of nonlinear Banach-lattice-valued maps that can be written as diagonal functions with respect to a certain basis. In the n-dimensional case, such a map can be represented as a vector of size n of real-valued functions of one variable. In this paper we develop a method to approximate almost diagonal maps by means of lattice Lipschitz operators. The proposed technique is based on the approximation properties and error bounds obtained for these operators, together with a pointwise version of the interpolation of McShane and Whitney extension maps that can be applied to almost diagonal functions. In order to get the desired approximation, it is necessary to previously obtain an approximation to the set of eigenvectors of the original function. We focus on the explicit computation of error formulas and on illustrative examples to present our construction.