On codimensions k immersions of m-manifolds for k=1 and k=m-2

Let us consider M a closed smooth connected m-manifold, N a smooth ( 2m-2)-manifold and f: M -> N a continuous map, with m equivalent to 1( 4). We prove that if f*: H(1)(M; Z(2)) -> H(1)(f(M); Z(2)) is injective, then f is homotopic to an immersion. Also we give conditions to a map between manifolds of codimension one to be homotopic to an immersion. This work complements some results of Biasi et al. (Manu. Math. 104, 97-110, 2001; Koschorke in The singularity method and immersions of m-manifolds into manifolds of dimensions 2m-2, 2m-3 and 2m-4. Lecture Notes in Mathematics, vol. 1350. Springer, Heidelberg, 1988; Li and Li in Math. Proc. Camb. Phil. Soc. 112, 281-285, 1992).

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regularization of discontinuous vector fields on R-3 via singular perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of' sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Remarks on immersions in the metastable dimension range

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that if h : M-n --> Xn+k, 5 less than or equal to n < 2k, is a continuous map between two manifolds and g : M-n --> BO is the classifying map of the stable normal bundle of h such that (h, g)(*) : H-i (M, Z(2)) --> H-i (X x BO, Z(2)) is an isomorphism for i < n - k and an epimorphism for i = n - k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Goncalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.

Partial hyperbolicity for symplectic diffeomorphisms

We prove that every robustly transitive and every stably ergodic symplectic diffeomorphism on a compact manifold admits a dominated splitting. In fact, these diffeomorphisms are partially hyperbolic. (c) 2005 Elsevier SAS. All rights reserved.

Optimum design of microirrigation systems in sloping lands

When an area to be irrigated has a high slope gradient in the manifold line direction, an option is to use a tapered pipeline to economize on pipe costs and to keep pressure head variations within desired limits. The objective of this paper is to develop a linear optimization model to design a microirrigation system with tapered, downhill manifold lines, minimizing the equivalent annual cost of the hydraulic network and the annual pumping cost, and maximizing the emission uniformity previously established to the subunit. The input data are irrigation system layout, cost of all hydraulic network components, and electricity price. The output data are equivalent annual cost, pipeline diameter in each line of the system, pressure head in each node, and total operating pressure head. To illustrate its capability, the model is applied in a citrus orchard in Sao, Paulo State, Brazil, considering slopes of 3, 6, and 9%. The model proved to be efficient in the design of the irrigation system in terms of the emission uniformity desired.

CLOSED SPACES IN COSMOLOGY

This paper deals with two aspects of relativistic cosmologies with closed spatial sections. These spacetimes are based on the theory of general relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a three-dimensional closed Riemannian manifold. The topics discussed are: (i) a comparison, previously obtained, between Thurston geometries and Bianchi-Kantowski-Sachs metrics for such three-manifolds is here clarified and developed; and (ii) the implications of global inhomogeneity for locally homogeneous three-spaces of constant curvature are analyzed from an observational viewpoint.

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

Bound state solution of the grassmannian nonlinear sigma model with fermions

We construct the S-matrix for bound state (gauge-invariant) scattering for nonlinear sigma models defined on the manifold SU(n) S(U(p)⊗U(n-p)) with fermions. It is not possible to compute gauge non-singlet matrix elements. In the present language, constraints from higher conservation laws determine the bound state solution. An alternative derivation is also presented. © 1988.

Higher spin symmetries and w∞ algebra in the conformal affine Toda model

As recently shown the conformal affine Toda models can be obtained via hamiltonian reduction from a two-loop Kac-Moody algebra. In this paper we propose a systematic procedure to analyze the higher spin symmetries of the conformal affine Toda models. The method is based on an explicit construction of infinite towers of extended conformal symmetry generators. Two fundamental building blocks of this construction are special spin-one and -two primary fields characterizing the conformal structure of these models. The connection to the algebra of area preserving diffeomorphisms on a two-manifold (w∞ algebra) is established.

Electrodynamics of helium with retardation and self-interaction effects

We show that an extra constant of motion with an analytic form can exist in the neighborhood of some discrete circular orbits of helium when one includes retardation and self-interaction effects. The energies of these discrete stable circular orbits are in the correct atomic magnitude. The highest frequency in the stable manifold of one such orbit agrees with the highest frequency sharp line of parahelium to within 2%. The generic term of the frequency in the stable manifold to higher orbits is also in agreement with the asymptotic form of quantum mechanics for helium.

Design of microirrigation systems in sloping lands using linear programming

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

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.