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bio website math.ubc.ca/~israel
location Vancouver BC
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Associate Professor Emeritus, University of British Columbia, and Optimization Algorithms Researcher, D-Wave Systems, Burnaby BC

1d
comment For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds
Already asked on MSE: math.stackexchange.com/questions/1300048/…
1d
comment Numerical equality testing
Caution: Maple's testeq can quite unreliable. For example: testeq(exp(2 * Pi * I * x)=1); $$ true$$
May
22
revised What methods do we have to understand the spectrum of matrices with restricted entries?
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May
21
revised What methods do we have to understand the spectrum of matrices with restricted entries?
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May
21
comment What methods do we have to understand the spectrum of matrices with restricted entries?
Yes, this is with entries from $\{0,1,-1\}$. Since $M$ and $M^T$ have the same spectrum, it's true for columns as well.
May
21
answered What methods do we have to understand the spectrum of matrices with restricted entries?
May
21
comment Are these inequalities for primes equivalent?
There are least two cases of $p_{n+1} < a b$, namely $p_{4} = 7 < 4 \times 2$ and $p_{9} = 23 < 6 \times 4$. Of course these are not counterexamples to the OP: $p_4^2 - p_3 p_5 = -6$ and $p_9^2 - p_8 p_{10} = -22$.
May
21
comment Specifying $L^p$ norms of derivatives
For a finite set of $a_n$, consider linear combinations of a finite set of basis functions and try to solve a nonlinear system of equations in the coefficients.
May
20
answered Expressing a convex Polytope as a sublevel set of a function
May
20
comment Reference for measures of commutativity needed
Trace of the commutator is always $0$, so that's not useful... If you want something that's nonzero whenever the commutator is nonzero and zero whenever the commutator is zero, a norm would seem to be the obvious choice.
May
20
answered Specifying $L^p$ norms of derivatives
May
20
revised Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent (“weakly”)?
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May
20
comment complexity of eigenvalue decomposition
The OP was asking about unitary matrices. Note that if $U$ is unitary and $|\omega|=1$ with $\omega \notin \sigma(U)$, $i (U+\omega I)(U-\omega I)^{-1}$ is hermitian, so solving the unitary problem is essentially like solving the hermitian problem.
May
20
comment Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent (“weakly”)?
As $x \to 0$, $\ln(1-\cos(x)) \sim 2\ln|x|$, which is an integrable singularity.
May
19
comment Multiple convex sets hyperplane separations
What kind of condition are you looking for? In case (2), the three convex sets $X_1$, $X_2$, $Y$ are disjoint, and so you can separate any two of them by hyperplanes.
May
19
comment Specifying $L^p$ norms of derivatives
In the case $p=2$, integration by parts gives you $\|f'\|_2^2 = - \int f f'' \; dx \le \|f\|_2 \|f''\|_2$.
May
19
answered Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent (“weakly”)?
May
19
answered How can two random variables are continuous infers that their jointly random variable is continuous
May
17
comment Proof that image of a polynomial map is a cone
We may assume $y_3 \ne 0$. The point is that $t^2 y_3 - t y_2 + y_1 = (t x_{22} - x_{21})(t x_{12}-x_{11})$ has real roots, and therefore its discriminant is nonnegative.
May
15
comment Explicit formula for the moment problem with Carleman's conditions
Carleman's is a sufficient condition for uniqueness. It is not a condition for existence. For that you need positive definiteness.