144,352 reputation
592238
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 9 months
seen 5 hours ago

I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


9h
revised $x^TAx-b^Tx\leq 0\Rightarrow\|x\|_2\leq\|A^{-1}b\|_2$?
added 294 characters in body
10h
comment Hitting time of Brownian Motion on a line
Use coordinates so the orthogonal projection is $(x,y,z) \to (x,y)$. The coordinates of an $n$-dimensional Wiener process are independent $1$-dimensional Wiener processes. Depending on which definition you use, this is either a definition or a theorem.
13h
answered $x^TAx-b^Tx\leq 0\Rightarrow\|x\|_2\leq\|A^{-1}b\|_2$?
13h
answered Hitting time of Brownian Motion on a line
13h
answered Is there an analytic function that takes on every value apart from 3 numbers?
14h
answered Is Information Theory Mathematics?
1d
comment What's difference between spectrum and eigenvectors of an operator
If $\text{ker}\; T = \{0\}$, $\text{ran}\; T$ is closed iff the map $Tv \to v$ is bounded (use the Open Mapping Theorem).
1d
revised What's difference between spectrum and eigenvectors of an operator
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1d
answered What's difference between spectrum and eigenvectors of an operator
1d
answered (some errors are corrected)Can $\int_0^T{\frac{e^{at}}{(1+t)^b}} \leq \frac{Ce^{aT}}{(1+T)^b}$ where $a,b>0$?
1d
comment Uniqueness of a positive solution to an integral equation
More prosaically, use $$u^3 \ge \overline{u}^3 + 3 \overline{u}^2 (u - \overline{u}) = 3 \overline{u}^2 u - 2 \overline{u}^3$$ for $u \ge 0$, with equality only when $u = \overline{u}$.
1d
revised Uniqueness of a positive solution to an integral equation
edited body
1d
comment Difficult Functional Equation Problem, Non-Standard Type
For $n=1$, it's $3 f(1) f(2\cdot 1 + 1) = f(2\cdot 1)(3 f(1)+1)$ and $f(1) = 1$ so it's $3 f(3) = 4 f(2)$. Yes, $f(2) < 6 f(1)$, but $f(1) = 1$.
1d
answered Do there exist nontrivial global solutions of the PDE $ u_x - 2xy^2 u_y = 0 $?
1d
comment Why is $\cos(x/2)+2\sin(x/2)=\sqrt5 \sin(x/2+\tan^{-1}(1/2))$ true?
... and more generally $$\sin(x + \arctan(r)) = \cos(\arctan(r)) \sin(x) + \sin(\arctan(r))\cos(x) = \dfrac{1}{\sqrt{1+r^2}} \sin(x) + \dfrac{r}{\sqrt{1+r^2}} \cos(x)$$
1d
answered Why do I get $0.098765432098765432…$ when I divide $8$ by $81$?
1d
answered Difficult Functional Equation Problem, Non-Standard Type
1d
comment trace identities for the functional calculus
Yes, but the equation in question has $f$'s in it.
2d
revised Correct definition of convolution of distributions?
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2d
comment what is word problem at group theory
en.wikipedia.org/wiki/Word_problem_for_groups