149,355 reputation
595247
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 10 months
seen 36 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


Jan
25
answered “Multivariable” version of this lemma about showing analytically that a number is irrational.
Jan
25
comment Study the convergence of $\int_1^\infty \frac{x\ln x}{x^4-1} dx$
How do you know it's monotonic?
Jan
25
answered Study the convergence of $\int_1^\infty \frac{x\ln x}{x^4-1} dx$
Jan
25
answered False equations with Euler's Identity
Jan
25
comment Evaluate $S=\left|\sum_{n=1}^{\infty} \frac{\sin n}{i^n \cdot n}\right|$
aDo you know series for $\ln(1+z)$?
Jan
25
answered Reversible modular exponent in cryptography
Jan
25
answered Why is a linear autonomous system asymptotically stable iff for all eigenvalues $\lambda$ of $A$, $Re(\lambda) < 0$
Jan
25
answered What is true for rank of a $5\times5$ matrix
Jan
25
comment Diffusion equation problem
Hint: The total amount of heat at time $t$ can be taken to be $\int_0^\ell u(x,t)\; dx$.
Jan
25
comment Diffusion equation problem
The boundaries are insulated, which means $\dfrac{\partial u}{\partial x} =0$ at $x=0$ and $x=\ell$.
Jan
25
answered Show that between any two real roots of the equation $e^x \cos{x}+1=0$, there is a root of the equation $e^x \sin{x}+1=0$
Jan
25
answered Show if $k$ is an integer, then $\sqrt[n]{k}$ is rational if and only if it is an integer.
Jan
23
comment Polynomial $(x − a)^2(x − b)^2 + 1$ is not the product of two polynomials with integral coefficients
... of two nonconstant polynomials ..... Note that $1$ is a polynomial with integer coefficients.
Jan
23
answered Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$
Jan
23
comment Using $\ln (\cos x)=\frac{-x^2}{2}-\frac{x^4}{12}+…$, approximate $\ln 2$ in terms of $\pi$
Approximate what?
Jan
23
comment Commutativity of the square root of matrices
It's obvious. If $A$ commutes with $B$, then so does $A^n$ for all positive integers $n$, and then so does any linear combination of these.
Jan
23
answered Commutativity of the square root of matrices
Jan
23
comment Bounded operator
See Young's inequality for convolutions.
Jan
23
comment Finding the largest factorial of only three digits
Thus $5!$, $6!$ and $7!$ qualify.
Jan
23
comment Finding the largest factorial of only three digits
Presumably "composed of only 3 digits" means the decimal representation contains only 3 of the digits 0,1,2,3,4,5,6,7,8,9.