Reputation
Next tag badge:
975/1000 score
446/200 answers
Badges
6 105 285
Newest
 Nice Answer
Impact
~2.1m people reached

Jul
27
comment Conditional Expectation for IIDs
What is $E[X+Y \mid X + Y]$?
Jul
27
comment Help with Euler Equations
The second derivative part is a bit tricky. You want to think of $\dfrac{d^2y}{dt^2} = \dfrac{d}{dt} \dfrac{dy}{dt}$. You already know how to write the "inner" $dy/dt$ in terms of $dy/dx$ and $t$. Use the product rule on this, and then again $\dfrac{d}{dt} = \dfrac{dx}{dt} \dfrac{d}{dx}$.
Jul
27
comment Help with Euler Equations
It's not a nonlinearity: the Euler equation is as linear as they come. What it removes is the presence of non-constant coefficients.
Jul
27
answered Conditional Expectation for IIDs
Jul
27
answered $A$ be a convex subset and $D$ be dense in a real NLS ; then for every non-empty open subset $U$ of the NLS , $U\cap D\cap V \ne \phi$?
Jul
27
comment Interesting Combinatorics question relating the coefficients of variables in Pascal's Triangle
If $b \ge 1$, it suffices to have $a \ge 3 b$.
Jul
27
comment System of equations to solve this nested radical.
The point is that there isn't anything special about this. You have a target number $1.74793$ and a function $f(A)$, and you found a value of $A$ such that $f(A) = 1.74793$.
Jul
27
comment System of equations to solve this nested radical.
If $f$ is a continuous function on $[a,b]$ with $f(a) < c < f(b)$, the Intermediate Value Theorem says there is some $x \in (a,b)$ with $f(x) = c$. You seem to have found that $x$ in the case $f(A) = \sqrt{1/A} \sqrt{A + 2 \sqrt{A + 2\sqrt{A + \ldots}}}$ and $c = 1.75793$.
Jul
27
comment Does this function achieve a maximum or minimum?
That's part of it.
Jul
26
answered Does this function achieve a maximum or minimum?
Jul
26
answered How to find median from a probability distribution?
Jul
26
answered Choose initial values such that sequence always has integer values
Jul
26
comment On Period of Linear Recurring Sequences modulo $P^e$
Don't confuse the integers mod $p^e$ with the finite field $\mathbb F_{p^e}$. They are quite different.
Jul
26
comment Interesting Combinatorics question relating the coefficients of variables in Pascal's Triangle
Because if $b$ is small and $a$ is large, ${a \choose b} > {a+1 \choose b-1}$.
Jul
26
comment Interesting Combinatorics question relating the coefficients of variables in Pascal's Triangle
What's the question? You can't prove something that isn't true.
Jul
26
answered Interesting Combinatorics question relating the coefficients of variables in Pascal's Triangle
Jul
26
revised Ordering : Ranges
added 504 characters in body
Jul
25
comment Can we embed unital Banach algebras into semi-simple ones?
I meant nilpotent in the algebraic sense. So if $B$ contains a nonzero nilpotent element, you can't embed it in an abelian semi-simple Banach algebra.
Jul
24
comment How to solve the paradox in the negation to definition of limit?
Yes, the book made a mistake. They are not equivalent. For example, it might be that $f(u_n) - f(v_n) = 1$ for even $n$ and $0$ for odd $n$. Then with $\epsilon = 1$, $\forall N \in {\mathbb N}: \exists n \ge N: |f(u_n) - f(v_n)| \ge \epsilon$ is true, but the book's version with $\forall n \in \mathbb N$ is false.
Jul
24
comment Replacing pinv with inv in MATLAB
There's no way around the fact that your system has rank $< n$. But if you adopt the criterion that you want ${\bf A x}$ to be as close as possible to $\bf y$ and (subject to that) ${\bf x}$ should be as close as possible to $0$, then you do have a unique answer, which is exactly what the pseudoinverse gives you.