Consider functions $f(x)$ defined and real-analytic for $x>0$ , such that
for all real $x,y > 0$ and integer $n > 0$ :
$$ sign (\frac{d^n }{d^n x} f(x) ) = sign (\frac{d^n}{d^n x} f(x+y) ) $$
In other words ; the signs of the derivatives do not change over the positive reals.
Some trivial exa...
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Here $p$ is an odd prime, $n$ is uniform on $[0, 2^\lambda]$, and $\lambda$ is a constant. We define distribution $\mathcal{D}$ by:
$$x \xleftarrow{\$} p-2^\lambda n$$
Assume $p \approx 2^{4\lambda}$, $\lambda \in \{128, 256\}$, and $0 \leq k \leq \log_2 \lambda$. Do a non-negligible fraction of...
I have to answer the following two questions:
Using Zorn's Lemma, one could try to give a "proof" of the following statement: Every subgroup $H$ of a group $G$ such that $H \neq G$ is contained in a maximal subgroup of $G$. Explain why this argument does not work.
Is it true that any group has ...
What I tried was I took $$\tan^{-1}(x) =t $$ ,but I got terms like $$\cos(\tan(t))$$ which I don't know what to do with,,,
So please guide me into solving this..
