The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Computing the dimension of a semi-algebraic set.”

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

Similarity:

Given integers D > 0 , n > 1 , 0 < r < n and a constant C > 0 , consider the space of r -tuples P → = ( P 1 ... P r ) of real polynomials in n variables of degree ≤ D , whose coefficients are ≤ C in absolute value, and satisfying det ∂ P i ∂ x i ( 0 ) 1 ≤ i , j ≤ r = 1 . We study the family { f | V } of algebraic functions, where f is a polynomial, and V = { | x | ≤ δ , P → ( x ) = 0 } , δ > 0 being a constant depending only on n , D , C . The main result is a quantitative extension theorem for these functions which is uniform in P → . This is used to prove Bernstein-type inequalities which are again uniform with respect to P → . ...

On some global semianalytic sets

Abdelhafed Elkhadiri (2013)

Annales de l’institut Fourier

Similarity:

We give some structures without quantifier elimination but in which the closure, and hence the interior and the boundary, of a quantifier free definable set is also a quantifier free definable set.