﻿ oipapio

### inequality - Plotting inequalities domain comb-style with JSXGraph

I want to draw axis line with comb-styled selection of inequality domain, like in this picture:Is it possible with JSXGraph?...Read more

### inequality - Prove that $\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$

$a,b,c$ are positive reals with $abc = 1$. Prove that $$\frac{1}{a^3(b+c)}+\frac{1}{b^3(a+c)}+\frac{1}{c^3(a+b)}\ge \frac32$$I try to use AM $\ge$ HM.$$\frac{\dfrac{1}{a^3(b+c)}+\dfrac{1}{b^3(a+c)}+\dfrac{1}{c^3(a+b)}}3\ge \frac{3}{a^3(b+c)+b^3(a+c)+c^3(a+b)}$$Then how I proceed....Read more

### inequality - Comparing the relative entropies of some stochastically ordered distributions

Motivation of this question:This question is related to the expected stopping time of a stochastic process under two hypotheses. Especially, it answers the question "how many more samples are required such that a sequential test stops when there is a model missmatch compared to the case when there is no missmatch". I found that the ratio is ${D(f_0,f_1)}/{D(g_0,g_1)}$ if the null hypothesis is correct and ${D(f_1,f_0)}/{D(g_1,g_0)}$ if the alternative hypothesis is correct. I know that both should be greater than $1$ because $g_0$ and $g_1$ are...Read more

### inequality - Finding maxima of a 3-variable function.

Let $x,y,z$ be positive real number satisfy $x+y+z=3$Find the maximum value of $P=\frac{2}{3+xy+yz+zx}+(\frac{xyz}{(x+1)(y+1)(z+1)})^\frac{1}{3}$...Read more

### inequality - How to prove $\sqrt { \frac {s(c-a-b)}{2∆} }$ is equal to i?

Consider a right angles triangle. Let, c be it's hypotenuse and a,b it's other sides.Then prove,$\sqrt { \frac {s(c-a-b)}{2∆} }$ is complex.Where ∆= area of the triangle and s is semi perimeter.I am not able to tackle this questions second part which is the above fraction can be proven equal to i.Proving it is complex is easy by the triangle equality. But how to prove that it is equal to i. Also, is there any other way to prove that the above fraction is complex.Edit- Including the other method, there are basically 2 ways for proving it is ...Read more