<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>

# Questions tagged [inequalities]

for questions involving inequalities.

884 questions
35 views

### On the relation between elementary symmetric polynomial inequalities and $p$-norms

Let $x, y \in \mathbb{R}^n_+$, and let $e_k$ denote the $k$th elementary symmetric polynomial. It is known (see e.g. [1]) that if \begin{align} e_1(x) &= e_1(y),\tag{1}\\ e_k (x) &\leq e_k (y)...
174 views

50 views

$$c_n=1-2t_n+2t_{n-1}-...\pm2t_1~,~b_n=1-2t_j+2t_{j-1}-...~,~~~~~~$$ $$a_n=1-2t_i+2t_{i-1}-...$$ $0<t_1<t_2<t_3....<t_n<1$ and $j\in J$ and $i\in I$ and $I\cup J=\{1,2,3,...,n\}$ and $I\... 1answer 99 views ### Moment generating function of random unit vector Let$X$be uniformly distributed on the unit sphere$S^{n-1}$. Is there any result concerning the calculation or bound (particularly lower bound) of $$\mathbb{E}[\exp(X^Tv)]$$ for any$v$? 0answers 66 views ### Gagliardo-Nirenberg inequality for periodic functions? I am interested in Gagliardo-Nirenberg type inequality (see https://en.m.wikipedia.org/wiki/Gagliardo%E2%80%93Nirenberg_interpolation_inequality) for functions in the space $$H^1_T(\mathbb{R}^n)=\... 0answers 51 views ### Ratio of exponentially weighted Selberg integrals I'm interested in bounding the following ratio of integral:$$\frac{\int_{0<x_k<...<x_1<1}\prod_{i=1}^kx_i^{m-\frac{k+1}{2}}\prod_{i<j}(x_i-x_j)\exp(-\sum_{i=1}^kw_ix_i)}{\int_{0<x_k&... 1answer 143 views ### Relation between two different functionals:$\lVert p^{-\max}_{-\varepsilon}\rVert$and$\kappa_{p}^{-1}(1-\varepsilon)$Given a non-negative sequence$p=(p_i)_{i\in\mathbb{N}}\in \ell_1$such that$\lVert p\rVert_1 = 1$,we define the two following quantities, for every$\varepsilon \in (0,1]$. Assuming, without loss ... 1answer 81 views ### a simple functional inequation Is there some general solution to the functional inequality: f(x*y) <= y*f(x) + x*f(y) Where x and y are in [0,1]? I can find many particular solutions ... 1answer 115 views ### When does the spectral radius strictly increase? For bounded linear operators$A$and$B$on a Banach space$X$, I'm looking for results which imply that$r(A) < r(A+B)$(note the strict inequality), where$r(A)$denotes the spectral radius of$A$... 0answers 58 views ### Is there a software to solve functional inequalities? Suppose I have some inequalities that my function (say$\mathbb R\to \mathbb R$) needs to satisfy, like$\forall x,y\; f(x)+f(y)\le f(x+y)$and$f(1)=0$. Is there some software that can find solutions/... 1answer 140 views ### Inequalities for moments of a certain integral Let$X(t)$be a stationary Gaussian process,$EX(t)=0$, the correlation function$R(\tau)$is given. What bounds from above can be given for the$p$-th moment ($p>0, p \in \mathbb{R}\$) of the ...

15 30 50 per page
山西福彩快乐十分钟

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>