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bio website math.ubc.ca/~israel
location Richmond, Canada
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visits member for 3 years, 9 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


Dec
16
comment Is there a proof that $\int \frac {dx}{x}=\ln |x|+c$?
The simple way to test an alleged antiderivative is to take its derivative.
Dec
16
revised Orthogonality of remaining non-intersecting basis
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Dec
16
answered Orthogonality of remaining non-intersecting basis
Dec
16
revised Solve $x''(t)-\frac{x^2(t)}{\sin t}=\frac{\sin\left( (t-1)^2\right)}{\sin t}$.
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Dec
16
answered Solve $x''(t)-\frac{x^2(t)}{\sin t}=\frac{\sin\left( (t-1)^2\right)}{\sin t}$.
Dec
16
comment first order equation problem
Have you tried the method of characteristics?
Dec
16
comment Las Vegas Algorithms
Each time you run it (on a given input), independently of what has happened before, the algorithm will have probability $\ge 1/2$ of finishing with an output other than '?'. So with probability 1 it will eventually do this. If on some input the algorithm always outputs '?', it doesn't satisfy your assumption.
Dec
16
answered Double solutions and plotting transcendental equations
Dec
16
answered Create a non-linear first order differential equation which can be used using the method of separation.
Dec
16
answered Analytic continuation of holomorphic function along clockwise/counterclockwise path
Dec
16
answered Is it possible to find the closed-form expression for $\int_{\alpha}^{\infty} \frac{e^{-At}}{\left(1+ Bt\right)t^m}dt$?
Dec
16
answered Las Vegas Algorithms
Dec
16
answered Antiderivative of $\frac{1}{\ln(x)}$?
Dec
16
comment Arnold ODE Problem
$\lim_{t\to \infty} e^t |x_1(t) - x_2(t)| = 0$ is just exponentially, and would be easy: take $x' = -2x$. For "faster than exponentially", you want $\lim_{t\to \infty} e^{rt} |x_1(t) - x_2(t)| = 0$ for all constants $r$.
Dec
16
comment How many numbers less than $x$ have a prime factor that is not $2$ or $3$
I don't immediately see the relevance of Baker's theorem here. $\log(n) - x \log(2) - y \log(3)$ for nonnegative integers $x, y, n$ can be $0$ (if $n = 2^x 3^y$), or if positive it's at least $\log(n/(n-1))$ (with equality if $n = 2^x 3^y + 1$).
Dec
16
revised How many numbers less than $x$ have a prime factor that is not $2$ or $3$
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Dec
16
answered How many numbers less than $x$ have a prime factor that is not $2$ or $3$
Dec
16
answered Why is it differential equations exist on an interval instead of a domain?
Dec
16
comment Proof of this theorem: $ tr(A^-)=\sum_{i=1}^r \lambda_i^{-1} $
If that's all you require, then the result will be false. For example, if $A$ is diagonal it doesn't restrict $A^-_{i,i}$ when $A_{i,i} = 0$.
Dec
15
awarded  Nice Answer