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.

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).

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.

Effect of salivary stimulation on erosion of human and bovine enamel subjected or not to subsequent abrasion: An in situ/ex vivo study

This in situ/ex vivo study evaluated whether saliva stimulated by chewing gum could prevent or reduce the wear and the percent change in microhardness (%SMH) of bovine and human enamel submitted to erosion followed by brushing abrasion immediately or after 1 h. During 2 experimental 7-day crossover phases, 9 previously selected volunteers wore intraoral palatal devices, with 12 enamel specimens (6 human and 6 bovine). In the first phase, the volunteers immersed the device for 5 min in 150 ml of cola drink, 4 times per day (at 8, 12, 16 and 20 h). Immediately after the immersions, no treatment was performed in 4 specimens, 4 other specimens were immediately brushed (0 min) using a fluoride dentifrice, and the device was replaced into the mouth. After 60 min, the remaining 4 specimens were brushed. In the second phase, the procedures were repeated, but after the immersions, the volunteers stimulated the salivary flow rate by chewing a sugar-free gum for 30 min. Changes in wear and %SMH were measured. ANOVA and Tukey's test showed statistical differences (p < 0.05) for the following comparisons. The chewing gum promoted less wear and %SMH. A decreasing %SMH and an increasing enamel wear were observed in the following conditions: erosion only, 60 min and 0 min. The human enamel presented greater %SMH and less wear compared to bovine enamel. The data suggest that the salivary stimulation after an erosive or erosive/abrasive attack can reduce the dental wear and the %SMH.

Titanium surface topography after brushing with fluoride and fluoride-free toothpaste simulating 10 years of use

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scanning electron microscopic study of the in situ effect of salivary stimulation on erosion and abrasion in human and bovine enamel

This in situ study investigated, using scanning electron microscopy, the effect of stimulated saliva on the enamel surface of bovine and human substrates submitted to erosion followed by brushing abrasion immediately or after one hour. During 2 experimental 7-day crossover phases, 9 previously selected volunteers wore intraoral palatal devices, with 12 enamel specimens (6 human and 6 bovine). In the first phase, the volunteers immersed the device for 5 minutes in 150 ml of a cola drink, 4 times a day (8h00, 12h00, 16h00 and 20h00). Immediately after the immersions, no treatment was performed in 4 specimens (ERO), 4 other specimens were immediately brushed (0 min) using a fluoride dentifrice and the device was replaced into the mouth. After 60 min, the other 4 specimens were brushed. In the second phase, the procedures were repeated but, after the immersions, the volunteers stimulated the salivary flow rate by chewing a sugar-free gum for 30 min. Enamel superficial alterations of all specimens were then evaluated using a scanning electron microscope. Enamel prism core dissolution was seen on the surfaces submitted to erosion, while on those submitted to erosion and to abrasion (both at 0 and 60 min) a more homogeneous enamel surface was observed, probably due to the removal of the altered superficial prism layer. For all the other variables - enamel substrate and salivary stimulation the microscopic pattern of the enamel specimens was similar.

Remarks on the normal bordism forgetful homomorphism

Assume that X is an oriented smooth (n+k)-manifold. Then the kernel of the forgetful map F considered in this work consists of immersions f: Mn → X nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, we present a homological characterization of the kernel of the forgetful map F. Also, we prove that Ωi(X, εs - ηs and Hi(X,Z) are -isomorphic for i≤3 and C2-isomorphic for i≤2, where C2,3 (resp. C2 is the class of abelian groups whose elements have order 2p. 3q (resp. 2p), and ηs is an orientable stable vector bundle over X. © 2009 Pushpa Publishing House.

Aspectos biológicos de Quesada gigas (Olivier, 1790) (Hemiptera: Cicadidae) em cafeeiro

Pós-graduação em Agronomia (Entomologia Agrícola) - FCAV

Determinação da fração lábil de mercúrio em águas fluviais

Pós-graduação em Geociências e Meio Ambiente - IGCE

Influência do acabamento e polimento na estabilidade de cor e na rugosidade superficial de uma resina composta submetida a diferentes soluções fluoretadas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influência de métodos de limpeza de próteses sobre a rugosidade, dureza e quantificação de candida albicans de uma resina para reembasamento

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

Estudo da degradação de resinas compostas pela ação de bebidas alcoólicas: análise de fluorescência e rugosidade superficial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influência de soluções fluoretadas na estabilidade de cor, rugosidade e dureza superficial de resinas compostas em função do tempo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Topografia superficial e aderência de Streptococcus mutans no titânio após imersão e escovação com dentifrícios fluoretado e não-fluoretado simulando 10 anos de uso

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reduced graphene oxide multilayers for gas and liquid phases chemical sensing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)