All Questions
7
questions with no upvoted or accepted answers
3
votes
1
answer
91
views
An inequality involving a quasiconvex function with binomial and power terms
The question is as follows.
Let us consider a positive integer number $x \in \{1,2,3,...\}$ and a positive real number $q \in [1,x]$. Show that
\begin{equation}
\sum_{m=0}^{x-1} \left( \frac{x+2-q}{m+...
- 109
3
votes
0
answers
222
views
Two-leg games in Elo rating for football teams
Do you know Elo rating for association football? It is a numerical estimation of strength of football clubs using simple mathematical formula based past results allowing predictions for the future.
...
- 777
2
votes
0
answers
49
views
Prove that $(f+g)(x)<t$ ($t\in\mathbb{R}$) holds if and only if there is a rational number $r$ such that $f(x)<r$ and $g(x)<t-r$.
I got stuck on this question:
Prove that $(f+g)(x)<t$, $t\in\mathbb{R}$, holds if and only if there is a rational number $r$ such that $f(x)<r$ and $g(x)<t-r$.
I think one direction is ...
- 2,493
2
votes
0
answers
94
views
Which assumptions on $f$ and $T$ make $\int_0^T f(x) dx \le \int_0^T |f(x)|^2 dx\implies 1\le \int_0^T |f(x)| dx$ true?
Let $T>0$ be fixed and let $f$ be a real valued function such that
$$\|f\|_{\infty}\le T,$$
where $\|\cdot\|_{\infty}$ denotes the sup-norm.
My question is the following: if
$$\int_0^T f(x) dx \le \...
user603537
1
vote
0
answers
78
views
Lower bounds for holomorphic functions on annuli with explicit bounds on their power series
Let $f$ be a holomorphic function on $\mathbf{C}$ and consider its restriction to the annulus $X=B(0,1) - B(0,3/4)$ in the complex plane. (Here $B(0,r)$ is the open disc with radius $r$ around $0$.) ...
- 221
0
votes
0
answers
51
views
Gravitational potential energy (explanation)
Hello to you dear person reading, I need your help to please explain me this :
$${\displaystyle \Phi (P)={\frac {-GmM}{\|OP\|}}+K}{\displaystyle \Phi (P)={\frac {-GmM}{\|OP\|}}+K}$$
(I haven't learned ...
- 1
0
votes
1
answer
61
views
Show that the function $f(x)=\frac{1}{x}-\left(\frac{d}{2x+2}\right)^d$ is always positive for $x\geq 2$ and $d \in \{2,3,4,5\}$?
My first instinct was to show that the derivative is always negative for the conditions above and with the limit $=0$ it should follow that it is always positive but it is way to complicated for me. ...
- 1