127,610 reputation
584218
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 5 months
seen 5 mins ago

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


1h
answered Open, closed, neither or both in $\mathbb R^2$?
1h
comment Is it possible to make a 3dimensional parametric plot of this equation that looks like a UFO?
You could at least type out the equation rather than showing us an image with tiny type.
2h
answered What is negation of the following sentence?
2h
answered Probabilistic method in coloring of graph
2h
comment Prove that $\int_0^{\pi/2}\ln^2(\cos x)\,dx=\frac{\pi}{2}\ln^2 2+\frac{\pi^3}{24}$
OK, I added some details.
2h
revised Prove that $\int_0^{\pi/2}\ln^2(\cos x)\,dx=\frac{\pi}{2}\ln^2 2+\frac{\pi^3}{24}$
added 82 characters in body
2h
answered Prove that $\int_0^{\pi/2}\ln^2(\cos x)\,dx=\frac{\pi}{2}\ln^2 2+\frac{\pi^3}{24}$
12h
answered Series of points in a bounded sector of a complex half-plane
15h
comment Unusual closed form for an indefinite integral
Once you know $$ \dfrac{1}{P(x)} = \sum_{j=1}^n \dfrac{c_j}{x-\omega_j}$$ just multiply both sides by $x - \omega_j$ and take the limit as $x \to \omega_j$, using l'Hospital's rule on the left.
16h
answered Unusual closed form for an indefinite integral
19h
comment How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
$k$? There is no $k$ in the problem. And your second question is apparently unrelated to the first.
19h
answered Coefficients of a polynomial representation of factorials
1d
answered Intersection of nested closed balls in a normed linear space
1d
answered Prove that if $y= 2x+\sin(y-2x)$, then $\frac{dy}{dx}$ is equal to $2$ using implicit differentiation
1d
comment Finding a probability density function of a function of three dependent random variables
Where do you see $U = f(V,W)$?
2d
comment Newtons Method for approximation of absolute maximum
It's hard to tell what you're doing wrong without seeing more of what you did. What was the iteration function you used? If you did it right, this would converge very quickly: $x_1$ is already within about $2.8 \times 10^{-8}$ of the correct solution.
2d
comment Relationship between Primes and Fibonacci Sequence
@you-sir-33433 : see latest edit.
2d
revised Relationship between Primes and Fibonacci Sequence
added 670 characters in body
2d
comment Avoiding initial guess in Newton Method for nonlinear systems
Reinventing the wheel is usually not a good idea, except maybe as an academic exercise. Good libraries of numerical methods exist. If you don't have access to one in Java, then Java may be a bad choice of language to use. How about python?
Aug
29
answered Relationship between Primes and Fibonacci Sequence