143,625 reputation
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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
18
comment Can anyone tell me how to factor this expression?
A side splitting theorem? What's so funny?
Dec
18
answered Writing number as sum of reciprocals of factorial
Dec
18
answered Infinite Sum of 1/Polynomial
Dec
17
answered Why do we write $a^n$ instead of $^n\!a$ for exponentiation?
Dec
17
answered Questionable Power Series for $1/x$ about $x=0$
Dec
17
comment How to put the equation $y'' + ky =0$ into Sturm-Liouville form?
It is a Sturm-Liouville equation over any interval. Maybe there's something you're not telling us? Boundary conditions?
Dec
17
comment Mixed strategies in 3x3 game - can strategies be negative?
What bad things? The only thing I can think of is if you require the payoff variable ($z$ above) to be nonnegative. I do not require that. Linear programming can be done perfectly well with some variables unrestricted.
Dec
17
answered Mixed strategies in 3x3 game - can strategies be negative?
Dec
17
answered How to put the equation $y'' + ky =0$ into Sturm-Liouville form?
Dec
17
answered Adding and Subtracting Normal Distributions
Dec
17
answered Why before $e^{x}$,the solution was not possible?
Dec
17
comment Examples of Unitary Matrices with coefficients all having the same amplitude
en.wikipedia.org/wiki/Complex_Hadamard_matrix
Dec
17
answered What is this picture?
Dec
17
comment How is it possible to write $\text {Pr} [M = m]$ where $M$ is random variable defined over a message space $\mathcal M$ and $m \in \mathcal M$.
If you want a metric, use the metric $d(x,y) = 0$ if $x=y$, $1$ otherwise.
Dec
17
comment Selecting n matches from two pockets.
en.wikipedia.org/wiki/Banach%27s_matchbox_problem
Dec
17
comment Phase Portrait of DE's
You might look at math.ubc.ca/~israel/m215/nonlin/nonlin.html
Dec
17
comment Obtaining the Poisson distribution in the calculator.
A better approximation is $$\ln(n!) \approx (\ln(n)-1) n + \dfrac{1}{2}\ln(2 \pi n) + \dfrac{1}{12n} - \dfrac{1}{360 n^3} + \ldots$$ For $n = 100$, the terms shown give $\ln(100!) \approx 363.73937555556341078$ while the correct value is $363.73937555556349014$.
Dec
17
answered Proving that each compact operator is bounded
Dec
17
revised Find all positive integers $a,b,c,d$ with given conditions.
added 754 characters in body
Dec
17
comment How is it possible to write $\text {Pr} [M = m]$ where $M$ is random variable defined over a message space $\mathcal M$ and $m \in \mathcal M$.
No, a topological space in which all subsets are open.