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15h
comment Classify the growth of functions and find a more general growth function
Something's not right. For each fixed $\alpha$, $\sup_{|x|\le \alpha} |f(x) - f(0)|$ is a number, not a function of anything, so what is the variable with respect to which it is supposed to be $L^1$? Do you mean there is a locally $L^1$ function $g(\alpha)$ such that $\sup_{|x|\le \alpha} |f(x) - f(0)| \le g(\alpha)$? It can't be globally $L^1$ if you allow any growth at all.
16h
comment Find all pair of cubic equations
Computer search.
17h
comment Is there a name for this type of expression?
E.g. the example is $a_1 x^{3/12} + a_2 x^{4/12} + a_3 x^{6/12} + a_4 x^{12/12} + a_0 x^{0/12}$.
17h
comment A closed set A and compact set B in a topological vector space.
Continuity of addition in a topological vector space.
19h
comment How to symbolize impossible discrete logarithm?
Use $:$ instead of $\mid$ if you prefer.
19h
comment equation for probability stumper?
You are assuming, without any justification, that all possible pairs of days are equally likely. Ignorance is not the same as equal probability.
1d
comment Proving two domains are not conformally equivalent
The number of zeros of $f(z) - w$ (counted by multiplicity) inside a simple positively oriented closed contour can be expressed as $(2\pi i)^{-1}$ times the integral of $f'/(f-w)$ over the contour, and is constant as long as none of the zeros hits the contour.
1d
comment Has anyone ever explored $(\sin{x})^x$ , $(\cos{x})^x$, etc?
@David : Probably not.
1d
comment Proving two domains are not conformally equivalent
1) $D \backslash [-1/2, 1/2]$ is bounded. 2) Argument principle.
1d
comment I am trying to find where $\sin ( \pi t) e ^{ -t } $ converges via secant method and I keep getting this error below with my code.
Yes, f is a function handle. You defined it as such. So why are you trying to assign a value to f(n+1)?
1d
comment Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
Needed $3 (j/2)$ not to be in $S$.
2d
comment Evaluating definite integral of $e^{i t^2}$
The integral converges as an improper Riemann integral, i.e. $\lim_{M \to -\infty, N \to +\infty} \int_{M}^N e^{it^2}\; dt$.
2d
comment Why should quaternions exist?
The existence of a mathematical object (the quaternions) is not contingent on any aspect of physical reality. Rather, the algebra generated (over the reals) by the $2 \times 2$ matrices $i\sigma_x$, $i \sigma_y$, $i \sigma_z$ is a representation of the Quaternions. The fact that these Pauli matrices can be used in describing certain physical particles is interesting, but not relevant.
2d
comment Cramer, $P(S_n\geqslant na)\sim e^{-n I(a)}$
I don't know if it's possible in general to say in which cases the $o(n)$ is $O(1)$, but the fact that it doesn't happen for the normal distribution makes me guess that this will be extremely rare, if indeed it ever occurs.
2d
comment Cramer, $P(S_n\geqslant na)\sim e^{-n I(a)}$
$|b_n| < n \epsilon$ when $\left| \dfrac{\ln(a_n)}{n} - c \right| < \epsilon$
2d
comment Can this congruence be simplified?
... and those seem to be all the solutions; at least, there are no others with $p+q \le 10^5$
2d
comment Can this congruence be simplified?
Also for consecutive terms in A032908, with $5$ instead of $6$.
2d
comment Can this congruence be simplified?
Here's something interesting: it looks like each pair $(a(n),a(n+1))$ of consecutive terms in OEIS sequence A101265 (oeis.org/A101265) satisfy the condition, with $(p+q)(p+q+1)/(pq) = 6$
2d
comment Can this congruence be simplified?
I suspect there are only finitely many solutions for any fixed $p$, and for most $p$ there will be none. The only solutions for $1 \le p \le q \le 1000$ are $$[p,q] = [1, 1], [1, 2], [2, 2], [2, 3], [2, 6], [3, 6], [6, 14], [6, 21], [14, 35], [21, 77], [35, 90], [90, 234], [77, 286], [234, 611]$$
2d
comment Can this congruence be simplified?
For example, try $p = 6$, $q = 3$, $pq = 18$: $(p+q)(p+q+1) = 90 \equiv 0 \mod 18$, but $18$ doesn't divide either $p+q = 9$ or $p+q+1 = 10$.