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5h
answered How to describe the transformation that changes French flag to Russian flag?
9h
awarded  Fanatic
9h
accepted Diophantine equation $(x+y)(x+y+1) - kxy = 0$
14h
comment Disprove Officer's account - Velocity / Distance / Time
It takes about $18.7$ seconds to travel $270$ metres at $52\ km/h$. The officer could easily have taken $15$ seconds to make a safe left turn into your lane and then be noticed by you. Then it takes another few seconds to slow down and pull over. There's nothing here to exonerate you.
16h
asked Diophantine equation $(x+y)(x+y+1) - kxy = 0$
19h
answered Difficult Differential Equation ($2^{nd}$ order ODE)
20h
revised A question on numerical range
added 83 characters in body
20h
comment Can someone give me real world example of uniform distribution [0,1] of a continuous random variable.
The probability of each outcome (i.e. each real number in the interval $[0,1]$) is $0$. The PDF value is a density, not a probability. If you graph it, probability corresponds to area under the curve. For a uniform distribution on $[0,360]$ the PDF would be $f(x) = 1/360$ for $0 \le x \le 360$: corresponding to the area of a rectangle of width $360$ and height $1/360$ is $1$.
20h
comment Proving uniform convergence on disk within radius of convergence
If $|c_k| r_1^k \le M$, then $|c_k| |z|^k \le M |r/r_1|^k$ for $|z| \le r$.
20h
awarded  complex-analysis
1d
awarded  Good Answer
1d
answered Why does WolframAlpha's expression for $\int\frac{dx}{x\sqrt{x^4-4}}$ disagree with my own?
1d
answered Families of subsets whose union is the whole set
1d
answered Proving uniform convergence on disk within radius of convergence
1d
comment Finding generators for products of ideals
This is for a commutative ring, I presume. Then of course, if $A$ is a set of generators of $I$ and $B$ a set of generators of $J$, $AB = \{ab \; : \; a \in A,\; b \in B\}$ is a set of generators of $IJ$.
1d
comment Name of the probability distribution
Variance of $X^3$ (when mean of $X^3$ is $0$) is $E[X^6]$. For standard normal, the even-numbered moments are $1, 1, 3, 15, 105, 945, 10395, \ldots$ (the "double factorials", oeis.org/A001147 ).
1d
answered If $A,B \in \mathcal{M}_n$ and $AB=BA=\mathbb{O}_n$ prove that $(A+B)^ν = Α^ν + Β^ν$.
1d
comment Minimal Polynomial Properties
$\alpha$ would have a minimal polynomial, but not a monic minimal polynomial. For example, the minimal polynomial of $\sqrt{2}/2$ **over $\mathbb Z$** is $2 X^2 - 1$. The minimal polynomial over $\mathbb Q$ is $X^2 - 1/2$, but that has a coefficient that is not in $\mathbb Z$.
1d
answered A question on numerical range
1d
comment A question on numerical range
Do you mean $A, B \in \mathbb C^{n \times n}$? And $v^* v = 1$ rather than $v v^*$?