126,195 reputation
583217
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 5 months
seen 12 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


Aug
17
answered Is Adobe Acrobat's icon a special function?
Aug
17
answered $2p-2$ as the sum of consecutive prime numbers
Aug
16
awarded  Enlightened
Aug
16
awarded  Nice Answer
Aug
16
awarded  diophantine-equations
Aug
15
comment Uniqueness of solution for a system of differential equations
By $y_1(y_2)$ do you mean $y_1 \circ y_2$? But $y_1$ is only defined on $X$, and $y_2$ maps $X$ into $\mathbb R$, not into $X$.
Aug
15
answered How to evaluate $\sum_{k=1}^n\ln\left(2\cos\left(\frac{2\pi\cdot3^k}{3^n+1}\right)+1\right)$
Aug
15
answered Moment-determinacy in multivariate case
Aug
15
comment how can I find Integer solutions for the two variables equation?
What do you mean by "without searching factors"? A solution provides a factorization of $50437$ where one factor is congruent to $7 \mod 30$ and the other to $1 \mod 30$.
Aug
15
comment How to express $x^5$ as a telescoping series
You mean like $x^5 = (x^5 - x^4) + (x^4 - x^3) + (x^3 - x^2) + (x^2 - x) + (x - 1) + 1$?
Aug
15
answered how can I find Integer solutions for the two variables equation?
Aug
15
answered When to Taylor expand in a differential equation
Aug
15
comment Conditions for the commutator of two operators on a Hilbert space to not be a nonzero scalar operator
You might also look at en.wikipedia.org/wiki/Canonical_commutation_relation and en.wikipedia.org/wiki/Stone%E2%80%93von_Neumann_theorem
Aug
15
comment Conditions for the commutator of two operators on a Hilbert space to not be a nonzero scalar operator
In the result I referred to, $A$ and $B$ are densely defined.
Aug
15
comment Conditions for the commutator of two operators on a Hilbert space to not be a nonzero scalar operator
$\text{Dom}(A) \cap \text{Dom}(B) = \{0\}$ is a very real possibility; in some situations it can even be "generic". See e.g. math.ubc.ca/~israel/papers/is.ps
Aug
15
comment Conditions for the commutator of two operators on a Hilbert space to not be a nonzero scalar operator
If the domains are not the whole space, what does it mean for $[A,B]$ to be a scalar multiple of the identity? It might not be defined anywhere except $0$.
Aug
15
comment How to solve $(x-3)\left(\frac{\mathrm dy}{\mathrm dx}\right)+y=6e^x, x>0$
Then you should. Look up "differential equations" in your textbook.
Aug
15
comment Relation between eigenvectors after transforming a nonsymmetric matrix to symmetric?
You copied some signs wrong, I think: $.71008...$ should be $-.71008...$ and $.725005...$ should be $-.725005...$. But your final result is correct. These are eigenvectors of $AB$. They don't have the same scaling as the ones you got directly, but a nonzero scalar multiple of an eigenvector is an eigenvector.
Aug
15
comment $f: \mathbb{R}^2 \to \mathbb{R}$ is a continuously differentiable function (of class $C^1$). Show that mapping f can not be one-to-one mapping.
Nothing to do with local homeomorphism. If $f: X \to Y$ is continuous and $C \subseteq X$ is connected, then $f(C)$ is also connected. If $f(C) \backslash \{y\}$ is disconnected, and $f^{-1}(y)$ consists of a single point $x$ of $X$, then $C \backslash \{x\}$ must be disconnected.
Aug
15
revised Growth Rate of Alternating Sign Matrices
added 263 characters in body