On the number of singularities in generic deformations of map germs

Let f:C-n, 0 --> C-p, 0 be a K-finite map germ, and let i = (i(1),..., i(k)) be a Boardman symbol such that Sigma(i) has codimension n in the corresponding jet space J(k)(n, p). When its iterated successors have codimension larger than n, the paper gives a list of situations in which the number of Sigma(i) points that appear in a generic deformation of f can be computed algebraically by means of Jacobian ideals of f. This list can be summarised in the following way: f must have rank n - i(1) and, in addition, in the case p = 6, f must be a singularity of type Sigma(i2.i2).

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Organization of the cysts in bee (Hymenoptera, Apidae) testis: number of spermatozoa per cyst

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

A new species of Urostreptus (Diplopoda, Spirostreptidae): description and chromossome number

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Description and chromosome number of a species of Pseudonannolene Silvestri (Arthropoda, Diplopoda, Pseudonannolenidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Number of ovarioles in workers descendent from crossings between Africanized and Italian honeybees, Apis mellifera L.: comparison among backcrosses and ancestors colonies

Comparou-se o número de ovaríolos de operárias de abelhas Apis mellifera L. de 36 colônias de retrocruzamentos (Africanizadas e Italianas) e operárias de colônias ancestrais parentais, endocruzadas e híbridas (F1). Não houve diferença no número de ovaríolos dos ovários direito e esquerdo das operárias. As abelhas híbridas da geração F1 apresentaram de 2 a 31 ovaríolos. O número de ovaríolos nas operárias dos retrocruzamentos africanizados variou de 2 a 56 e nos retrocruzamentos italianos de 2 a 117. A grande variação no número de ovaríolos das abelhas dos retrocruzamentos deveu-se a variabilidade observada na geração parental (abelhas africanizadas: 2 - 16; italianas: 6 - 26) e no F1 (2 - 31).