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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
27
comment An integral problem related to matrix determinant
I would be very surprised if this had a simple closed form in general. Do you have any reason to think it does? Or are you just looking for whether it converges?
Jun
27
revised Another integral from Apostol
added 2 characters in body
Jun
27
answered Another integral from Apostol
Jun
26
awarded  Enlightened
Jun
26
awarded  Nice Answer
Jun
26
answered Differential equations of the form $\frac{dy}{dt}=ky\left(1-\frac{y}{N(t)}\right)$
Jun
26
awarded  real-analysis
Jun
26
comment I have a special solution for the Lane-Emden equation. Can I use it to find the general solution?
Probably not, since the general solution is not likely to be expressible in closed form.
Jun
26
answered Can a marginal p.m.f. ever be exactly equal to the joint p.m.f.
Jun
25
answered Approximate continuous function that vanishes at origin by odd powers polynomial
Jun
25
comment Approximate continuous function that vanishes at origin by odd powers polynomial
You left out the condition on $f(0)$.
Jun
25
comment Algebraic manipulation of floors and ceilings
If so, get rid of the $\lceil \rceil$ by splitting into the two cases $i$ even and $i$ odd.
Jun
25
comment Algebraic manipulation of floors and ceilings
Do you really mean what you wrote, or should that be $\lceil \dfrac{i-2}{2}\rceil$ instead of $\lceil \dfrac{n-2}{2}\rceil$?
Jun
25
answered A problem on complex polynomials
Jun
25
comment Probability of winning given pair probabilities
Once you get the $\mu_j$ and $\sigma_j$, competitor $i$ wins if $T_i < T_j$ for all $j \ne i$. So if $f_j$ and $F_j$ are the pdf and cdf for $T_j$, $$P(i\text{ wins}) = \int_{-\infty}^\infty f_i(x) \prod_{j\ne i} (1 - F_j(x))\; dx$$ This won't have a closed form, but you can use numerical methods.
Jun
25
answered how to show the image under $T$ of the unit ball in $L^p[0,1]$ has compact closure in $C[0,1]$.
Jun
24
answered Perturbation of complex polynomials
Jun
24
comment Do modulus and absolute value operations use the same sign?
The absolute value of a real number is the same as its modulus as a complex number, so there is no confusion. The fact that $|a| = \sqrt{a^2}$ for real numbers is, from this point of view, an accident, and is not to be taken as the definition of absolute value.
Jun
24
answered Fourier coefficients of a measure and absolute continuity
Jun
24
answered Simplifying the expression of a product of inner products