143,680 reputation
592238
bio website math.ubc.ca/~israel
location Richmond, Canada
age
visits member for 3 years, 9 months
seen 6 hours 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


6h
comment Function with zero description
All these are different expressions for the same function.
12h
comment Arithmetic functions of particular type
For example, the sum of the primes $\le x$?
1d
comment Find the sum of digits of m?
This is not a matter of checking. It is finding the condition for a number $z$ to be expressible in this way in terms of the congruence class of $z \mod 4$.
1d
comment Diophantine equation : two products of linear factors differ by a constant
Certainly it can't be "only a few", because if $p(X) = (X-a)(X-b)(X-c)$ is a solution (for a given $k$), then so is $p(X + m)$ for any integer $m$. So either no solutions or infinitely many.
2d
comment Are the poll results likely to be valid if they are based on only those subjects who agree to respond?
There was a time when having Gallup call you up and ask your opinion was a novelty, and people were happy to participate. Now it's just an annoyance. Why should I provide valuable data to a commercial enterprise for free?
2d
comment Determining a radius convergence of a power series
Differentiate term-by-term...
2d
comment sum of infinte series with exponential and factorial terms
There is probably no closed form for the sum (when it converges). What do you really need?
2d
comment Is the simplest form of a quadratic equation factored form or standard form?
Simplicity, like beauty, is in the eye of the beholder.
2d
comment Why does the set of an hermitian operator's eigenfunctions spans the functions space
Actually, physical applications tend to deal with unbounded self-adjoint operators.
2d
comment Should I Put My Lifesavings into the Lottery?
See en.wikipedia.org/wiki/Utility
2d
comment What is the “cost” of computation of two special CAS algorithms
en.wikipedia.org/wiki/…
2d
comment Is there a formula telling if number is prime?
What is the difference for you between a function and an algorithm?
2d
comment How to define the 'error'
You might look up en.wikipedia.org/wiki/Approximation_error
2d
comment What is the “cost” of computation of two special CAS algorithms
You might start by looking up "factorization" on Wikipedia.
Dec
19
comment Probability of the sum of exponentials being greater than a number
The number of occurrences of a Poisson process of rate $r$ in an interval of length $L$ is a Poisson random variable with parameter $rL$.
Dec
19
comment Probability of the sum of exponentials being greater than a number
... and your $X_i$ must be assumed to be independent.
Dec
19
comment Probability of the sum of exponentials being greater than a number
Presumably your $1/5$ should be $1/3$, or else your $1/3$ should be $1/5$.
Dec
18
comment Determine the probability distribution of a ratio of two random variables?
1. Check the CDF. 2. Not geometric, exponential. The time to the next occurrence in a Poisson process of rate $r$ is an exponential random variable of rate $r$.
Dec
18
comment Questionable Power Series for $1/x$ about $x=0$
I know that, you know that, but does Wolfram Alpha?
Dec
18
comment Can anyone tell me how to factor this expression?
A side splitting theorem? What's so funny?