12 нояб. 2012 г. · The quickest way is to convolve the characteristic function of another interval with a smooth bump function. Let Φ(x)=cexp(1/(1−x2))χ(−1,1) ...

5 нояб. 2018 г. · Consider an indicator function χ[a,b] on an interval [a,b]. My question - is there a decreasing sequence fδ∈C1(V) (where [a,b]⊂V and V is open), ...

3 мар. 2024 г. · Constructing a smooth function such that the measure of critical points of f is a given positive real number x.

12 авг. 2020 г. · I need to show that for each a∈R,δ>0 that there exists a smooth function g which is 1 if x≤a and 0 when x>a+δ, which means having all its derivatives being 0

30 мар. 2013 г. · Let U be an open bounded set of Rn. Is it possible to approximate χU as almost everywhere limit of increasing sequence of smooth functions?

31 июл. 2014 г. · The short answer is that you don't differentiate an indicator function. An indicator function is not smooth: it jumps at certain values in the domain.

12 апр. 2016 г. · The indicartor function is used to compute approximatively the surface area by implicitly assuming it to be smooth and calculating its derivative.

21 сент. 2015 г. · The weak gradient of the characteristic function of a domain Ω with a smooth boundary is the vector-valued measure ν(x)dσ(x) where ν(x) is the ...

5 мая 2016 г. · I am trying to determine a continuously differentiable approximation of the indicator function of an interval [a,b] given by: I(x)={1,x∈[a,b]0, ...

6 февр. 2019 г. · Given a function f(x) does there exist a sequence of smooth functions that fn(x)→f(x) as n→0? I am currently trying to smooth out a kink for ...