Robert Israel
Reputation
397/400 score
 54m answered Square root of a matrix as it relates to the identity 59m answered Series that converges to $1$ slowly 2h answered What does P(X=Y) mean? 2h comment Independence and expected value Or if you want $X$ and $Y$ to be non-negative as well, take $X$ uniform on $[0,2]$ and $Y = (X-1)^2$. 4h answered Prove that if a function has an isolated singularity at $z_0$, then its derivative also has an isolated singularity at $z_0$ 4h answered Find the number of vertices n of the tree? 4h comment Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$ See Wikipedia. 4h answered Functional Equation: $f(x^2-y^2)=xf(x)-yf(y)$ 5h revised Let $f(x)=x^3-3x+1$.Find the number of distinct real roots of $f(f(f(x)))=3$ added 438 characters in body 6h answered Let $f(x)=x^3-3x+1$.Find the number of distinct real roots of $f(f(f(x)))=3$ 16h answered Under what condition on matrix $Q$ we have $tr(AQ)=tr(BQ)$ 17h answered Is there a graph that has 7 vertices and each vertex has a degree of $2,2,3,5,5,5,6$? 18h answered Have any property of square to make below problem reasonable? 18h comment Definition of ordered ring flawed? But it doesn't satisfy the first property: $1 \le 2$ but $1+1 > 2+1$. 22h answered Differential Equation - Where does the solution end? 22h comment Closed-Form solution for system of simple nonlinear equations Also, if you're really interested in $N \approx 10,000$, algebraic methods are likely to be essentially useless. 22h revised Closed-Form solution for system of simple nonlinear equations added 250 characters in body 23h comment Closed-Form solution for system of simple nonlinear equations I suspect this might not be well-received at MO. First of all, "analytical" or "analytic" is not the right word. To a mathematician, "analytic" means "locally given by a convergent Taylor series". What you mean is more like "closed form", but that's still ambiguous: exactly what kinds of special functions are you going to allow? For example, some high-order polynomials can be solved by generalized hypergeometric functions, theta functions, etc. Would you be happy with that? 1d comment Solving equation of form $x = -a/ln(bx)$ I mean that you made a mistake. The solution to the equation you wrote is $-a/W(-ab)$, not $-a/W(-a/b)$. 1d answered Solving equation of form $x = -a/ln(bx)$