Immersions in the metastable dimension range via the normal bordism approach

Let f : M --> N be a continuous map between two closed n-manifolds such that f(*): H-*(M, Z(2)) --> H-* (N, Z(2)) is an isomorphism. Suppose that M immerses in Rn+k for 5 less than or equal to n < 2k. Then N also immerses in Rn+k. We use techniques of normal bordism theory to prove this result and we show that for a large family of spaces we can replace the homolog condition by the corresponding one in homotopy. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Uranium distribution and radon exhalation from Brazilian dimension stones

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A multimetric index based on fish fauna for the evaluation of the biotic integrity of streams at a mesohabitat scale

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

Effect of tegument integrity on the light sensitivity in seeds of Cucumis anguria L

Cucumis anguria present dark germinating seeds at 25 degrees C. Seeds without the tegument are photosensitive germinating better in darkness than under continuous white light. However, pre-incubation at 40 degrees C for 48 hours allows the seeds to germinate under continuous white light and the incubation of naked seeds at -0.6MPa restored the light inhibition of seed germination. Our results suggest that the tegument interact with the phytochrome in the control of seed germination in part of the population of seed of C. anguria.

Characterization of hobo element copy number and integrity in Brasilian populations of Drosophila melanogaster

We have determined the copy number and the presence of full-size hobo transposable elements in eight Brasilian strains of Drosophila melanogaster. Genomic DNA was digested with AvaII and XhoI restriction enzymes, respectively, and probed with a 963 bp sequence of the hobo element. Variable numbers of full-sized and defective elements were detected in all strains. The range of the copy number was 22.13 +/- 4.52. Blots showed the presence of a 2.6 kb fragment, corresponding to the complete element, in all strains exception of one and the 1.0 kb sequence, correponding to the Th1 and Th2 repressor elements. There was neither association among copy numbers of hobo elements and latitude nor the mean annual temperatures in the original geographical region of each strain.

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.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

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.

Self-bound droplet of Bose and Fermi atoms in one dimension: Collective properties in mean-field and Tonks-Girardeau regimes

We investigate a dilute mixture of bosons and spin-polarized fermions in one dimension. With an attractive Bose-Fermi scattering length the ground state is a self-bound droplet, i.e., a Bose-Fermi bright soliton where the Bose and Fermi clouds are superimposed. We find that the quantum fluctuations stabilize the Bose-Fermi soliton such that the one-dimensional bright soliton exists for any finite attractive Bose-Fermi scattering length. We study density profile and collective excitations of the atomic bright soliton showing that they depend on the bosonic regime involved: mean-field or Tonks-Girardeau.

Temperature dependence of fractal dimension of grain boundary region in SnO2 based ceramics

Fractal dimensions of grain boundary region in doped SnO2 ceramics were determined based on previously derived fractal model. This model considers fractal dimension as a measure of homogeneity of distribution of charge carriers. Application of the derived fractal model enables calculation of fractal dimension using results of impedance spectroscopy. The model was verified by experimentally determined temperature dependence of the fractal dimension of SnO2 ceramics. Obtained results confirm that the non-Debye response of the grain boundary region is connected with distribution of defects and consequently with a homogeneity of a distribution of the charge carriers. Also, it was found that C-T-1 function has maximum at temperature at which the change in dominant type of defects takes place. This effect could be considered as a third-order transition.

Effects of milling condition on the surface integrity of hot forged steel

This paper presents a study on the influence of milling condition on workpiece surface integrity focusing on hardness and roughness. The experimental work was carried out on a CNC machining center considering roughing and finishing operations. A 25 mm diameter endmill with two cemented carbide inserts coated with TiN layer were used for end milling operation. Low carbon alloyed steel Cr-Mo forged at 1200 degrees C was used as workpiece on the tests. Two kinds of workpiece conditions were considered, i.e. cur cooled after hot forging and normalized at 950 degrees C for 2 h. The results showed that finishing operation was able to significantly decrease the roughness by at least 46% without changing the hardness. on the other hand, roughing operation caused an increase in hardness statistically significant by about 6%. The machined surface presented deformed regions within feed marks, which directly affected the roughness. Surface finish behavior seems to correlate to the chip ratio given the decrease of 25% for roughing condition, which damaged the chip formation. The material removal rate for finishing operation 41% greater than roughing condition demonstrated to be favorable to the heat dissipation and minimized the effect on material hardness.