bio | website | |
---|---|---|
location | Israel | |
age | ||
visits | member for | 1 year, 5 months |
seen | Mar 29 at 0:15 | |
stats | profile views | 117 |
Hi,
Please forgive me if sometimes my questions seems a bit simple.
I'm only self taught and researching by myself. But I did manage to derive some new published material, and my questions are real research questions. I just don't have anyone else to ask.
Jan 12 |
comment |
RFC for definite integral connection to second derivative
Thanks Gerald I appreciate your help |
Jan 12 |
accepted | RFC for definite integral connection to second derivative |
Jan 12 |
comment |
RFC for definite integral connection to second derivative
I got $-min(x,t)$ |
Jan 12 |
comment |
RFC for definite integral connection to second derivative
can you express it in terms of max/min? |
Jan 12 |
comment |
RFC for definite integral connection to second derivative
I dont understand where $f$ comes into the picture |
Jan 12 |
comment |
RFC for definite integral connection to second derivative
so maybe I didn't get it.. doesn't Dirac and Heavyside discontinuous? |
Jan 12 |
awarded | Critic |
Jan 12 |
comment |
RFC for definite integral connection to second derivative
Hint: $g$ is continuous. |
Jan 12 |
revised |
RFC for definite integral connection to second derivative
edited body |
Jan 12 |
asked | RFC for definite integral connection to second derivative |
Jan 9 |
revised |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
deleted 139 characters in body; deleted 252 characters in body |
Jan 9 |
revised |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
added 51 characters in body |
Jan 9 |
revised |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
added 254 characters in body; added 88 characters in body |
Jan 9 |
accepted | Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$ |
Jan 9 |
comment |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
now it really works :) |
Jan 9 |
comment |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
Thanks for your help! Unfortunatly, this doesn't work as well. Here's my code: #include <iostream> #include <cmath> using namespace std; long double phi(long double x, long double n, long double t = 2) { static long double pi = acos((long double)-1); return sin((n+.5)*pi*x/t)*sqrt(t*2.)/(pi*(n+.5)); } int main(int, char**) { long double sum = 0, x=.8,y=.3; for (long double n = 1;n< 100000;n++) { sum += phi(x,n)*phi(y,n); if (((int)n)%1000) cout<<n<<' '<<sum<<endl; } return 0; } |
Jan 8 |
comment |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
here's my code: ## #include <iostream> #include <cmath> using namespace std; long double phi(double x, double n) { return sin(n*x)/n; } int main(int, char**) { long double sum = 0, x=8,y=1; for (long double n = 1;n< 100000;n++) { sum += phi(x,n)*phi(y,n); if (((int)n)%1000) cout<<n<<' '<<sum<<endl; } return 0; } ## |
Jan 8 |
comment |
Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$
wow that's amazing. you actually got $ \min(x,y)=\sum_{n=1}^\infty n^{-2}\sin nx\sin ny$? |
Jan 8 |
asked | Elaborating Mercer's theorem (RKHS) on Cameron-Martin space $k(x,y)=\min(x,y)$ |
Jan 2 |
comment |
Injective with Finite Discontinuities Mapping from $\mathbb R^n$ to $[0,1]$
yes, I do understand now, many thanks!! btw when I practically want to use what we learnt here (especially in the previous question), I encounter a problem that $f(x)$ for some $x\in\mathbb R^n$ requires $nd$ digits to be represented numerically, when $d$ is the maximum number of digits in the elements of $x$. so this can be numerically unstable. I'm now trying to find such injective&integrable function that would be more numerically stable for computers. |