109 citations · 213 across the 16 of their papers we have counts for
17 papers
Correction to : The Kuo condition, an inequality of Thom's type and (c)-regularity
Karim Bekka, Satoshi Koike
We correct a statement of a theorem on characterisation of the (c)-regularity we gave in Topology 37 (1998), 45--62. This theorem was used in the paper in the proof of two theorems…
On finiteness theorems of polynomial functions
Satoshi Koike, Laurentiu Paunescu
Let d be a positive integer. We show a finiteness theorem for semialgebraic RL triviality of a Nash family of Nash functions defined on a Nash manifold, generalising Benedetti-Shio…
Stabilisation of geometric directional bundle for a subanalytic set
Satoshi Koike, Laurentiu Paunescu
In a previous paper we have introduced the notion of geometric directional bundle of a singular space, in order to introduce global bi-Lipschitz invariants. Then we have posed the…
On the relative Kuo condition and the second relative Kuo condition
Karim Bekka, Satoshi Koike
The Kuo condition and the the second Kuo condition are known as criteria for an r-jet to be V-sufficient in C^r mappings and C^{r+1} mappings, respectively. In a previous paper we…
Equivalence of Kuo and Thom quantities for analytic functions
Karim Bekka, Satoshi Koike
Sufficiency of jets is a very important notion introduced by Rene Thom in order to establish the structural stability theory. The criteria for some sufficiency of jets are known as…
Characterisations of V-sufficiency and C^0-sufficiency of relative jets
Karim Bekka, Satoshi Koike
We consider the problems of sufficiency of jets relative to a given closed set. In the non-relative case, criteria for r-jets to be V-sufficient and C^0-sufficient in C^r mappings…