148,560 reputation
593245
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 10 months
seen 58 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


20h
answered “Multivariable” version of this lemma about showing analytically that a number is irrational.
20h
comment Study the convergence of $\int_1^\infty \frac{x\ln x}{x^4-1} dx$
How do you know it's monotonic?
23h
answered Study the convergence of $\int_1^\infty \frac{x\ln x}{x^4-1} dx$
23h
answered False equations with Euler's Identity
1d
comment Evaluate $S=\left|\sum_{n=1}^{\infty} \frac{\sin n}{i^n \cdot n}\right|$
aDo you know series for $\ln(1+z)$?
1d
answered Reversible modular exponent in cryptography
1d
answered Why is a linear autonomous system asymptotically stable iff for all eigenvalues $\lambda$ of $A$, $Re(\lambda) < 0$
1d
answered What is true for rank of a $5\times5$ matrix
1d
comment Diffusion equation problem
Hint: The total amount of heat at time $t$ can be taken to be $\int_0^\ell u(x,t)\; dx$.
1d
comment Diffusion equation problem
The boundaries are insulated, which means $\dfrac{\partial u}{\partial x} =0$ at $x=0$ and $x=\ell$.
1d
answered Show that between any two real roots of the equation $e^x \cos{x}+1=0$, there is a root of the equation $e^x \sin{x}+1=0$
1d
answered Show if $k$ is an integer, then $\sqrt[n]{k}$ is rational if and only if it is an integer.
2d
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.
2d
answered Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$
2d
comment Using $\ln (\cos x)=\frac{-x^2}{2}-\frac{x^4}{12}+…$, approximate $\ln 2$ in terms of $\pi$
Approximate what?
2d
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.