Topological equivalence of complex polynomials

The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions $f_s \colon \mathbb{C}^n \to \mathbb{C}$ with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant in the family.Comment: 14 pages, revised text for final versio

Report on the Sewage Problem of the City of Los Angeles with Conclusions and Recommendations

No Abstract

Maps with Locally Flat Singular Sets

A map f : M → N is topologically equivalent tog: X → Y if there exist homeomorphisms α: M → X and β: N → Y such that βfα–1 = g. At x ∊ M, f is locally topologically equivalent to g if, for every neighbourhood W ⊂ M of x, there exist neighbourhoods U ⊂ W of x and V of f(x) such that f|U: U → V is topologically equivalent to g.1.1. Definition. Given a map f: M → N and x ∊ M, let F be the component of f–1(f(x)) containing x. The singular set Af is defined as follows: x ∊ M – Af if and only if there are neighbourhoods U of F and V of f(x) such that f| U: U → F is topologically equivalent to the product projection map of V × F onto V.</jats:p

A Comparison between Cross-Tolerance and Cross-Reaction Induced by Bovine γ-Globulin

Summary The effect of neonatal injection of BGG on subsequent production of anti-BGG, anti-BSA and anti-HGG was studied in the rabbit. The magnitude of cross-tolerance was compared with the degree of cross-reaction between anti-BGG and BSA and HGG. Injection of 60 mgs of BGG into neonatal rabbits resulted in: a) 95% suppression of anti-BGG when the rabbits were challenged at 4 and 5 months of age; b) 70 to 90% suppression of anti-HGG production in comparison with noninjected littermate controls tested at 4 and 5 months of age; and c) 70% suppression of anti-BSA at 5 months of age. Anti-BSA production at 4 months of age was not significantly affected. Rabbit anti-BGG cross-reacted with BSA (6%) and with HGG (3%). The high degree of specificity of anti-BGG produced in normal adult rabbits is in contrast with the relatively low specificity of immunological tolerance induced by the same antigen in neonatal rabbits.</jats:p