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bio website math.ubc.ca/~israel
location Richmond, Canada
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visits member for 3 years, 4 months
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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


Jun
20
comment Set defined by $xy-zw=1$
I used Maple...
Jun
20
revised Set defined by $xy-zw=1$
added 1 characters in body
Jun
20
answered Set defined by $xy-zw=1$
Jun
20
answered Exhaustive (?) list of cases giving $\sigma(n) \equiv 0 \pmod 4$ whenever $n$ is odd
Jun
20
answered Consecutive non square free numbers
Jun
19
answered Conditions stronger than differentiability or weaker than integrability
Jun
19
comment Trignometric shifting in ODE. Wolframalpha gives different answer?
Your $t$ and $x$ should be the same variable. I don't know why @AndréNicolas wants the cot in front.
Jun
19
answered Continued fraction question
Jun
19
answered Complex Analysis Book
Jun
19
answered Totally Uni-modular Matrices
Jun
18
comment Calculation of atan2
They were calculated by Maple's minimax function, which uses the Remez algorithm. en.wikipedia.org/wiki/Remez_algorithm
Jun
18
comment Calculation of atan2
There is nothing special to arctan here, except that it is a continuous function and is odd (i.e. $\arctan(-x) = -\arctan(x)$).
Jun
18
comment Calculation of atan2
Yes, minimax in the numapprox package.
Jun
18
revised Calculation of atan2
added 106 characters in body
Jun
18
answered Calculation of atan2
Jun
18
answered Operator norm is not induced by a scalar product
Jun
17
comment Evaluation of $\Xi(z)=\sum_{t=1}^{\infty}\frac{t^z}{e^t}$
Sorry, I left out a factor $(-1)^z$. $$\dfrac{1}{e^s-1} = 1 - \dfrac{e^s}{e^s-1} = 1 - \dfrac{1}{1-e^{-s}} = \sum_{j=1}^\infty e^{-js}$$ So $$\dfrac{d^z}{ds^z} \dfrac{1}{e^s-1} = \sum_{j=1}^\infty (-j)^z e^{-js}$$
Jun
17
comment Implication injective holomorphic function on the zeroes of derivative
To be clear: the interesting parts that don't require $f$ to be polynomial are that if $f$ is holomorphic and injective, $f'$ is never $0$, and that $f$ has exactly one zero (obviously there can't be more than one since $f$ is injective).
Jun
17
comment Evaluation of $\Xi(z)=\sum_{t=1}^{\infty}\frac{t^z}{e^t}$
If $z$ is a positive integer, $\Xi(z) = \left.\dfrac{d^z}{ds^z} \dfrac{1}{e^s-1} \right|_{s=1}$.
Jun
17
comment How to define the transform?
You can write your curve $y = f(x)$ as $y - y_1 = f(x_1 + (x - x_1)) - y_1$. After rotation by angle $\theta$, this becomes $(y - y_1) \cos(\theta) + (x - x_1) \sin(\theta) = f(x_1 + (x - x_1) \cos(\theta) - (y - y_1) \sin(\theta)) - y_1$.