As part of a different problem, I came across the following simplified question, for which I cannot exhibit a proof nor a counterexample. Note that the assumptions of smoothness an …

Does anyone know of any tight upper/lower bound for incomplete Gamma functions? i.e either of the following functions: $$ \Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t …

Hello Is it possible to decide whether a given or calculated lower bound is the optimal solution for a problem, like a Arc Routing Problem? If yes, when is a lower bound the optim …

I am trying to understand a proof by G.Wagner in his paper "On Means on Distances on the Surface of a Sphere (Lower Bounds)": http://projecteuclid.org/DPubS/Repository/1.0/Dissemin …

Suppose a bipartite graph $G=(V_1 \cup V_2, E)$ is given, and one is interested in matching vertices $V_1$ to vertices $V_2$. Assume Hall's condition does not hold, so a perfect ma …

The $n$-th Bell number $B_n$ represents the number of distinct partitions of a set with $n$ distinguished elements. It can be expressed as the infinite sum $B_n = (1/e)\sum_{k=1}^{ …

I recently came across an interesting expression: $$f = \frac{X\cdot b\cdot\left(\frac{a}{a+b}\right)^X}{a}$$ Where we have the following constraints: $0 < (a,b) < 1$, $(a …

Let $ L_{d}^{(1)}(x)$ denote the generalized Laguerre polynomial of degree $d$ and order $\alpha=1$. Clearly, since all the roots $r_1,\dots,r_d$ of $L_{d}^{(1)}$ are simple, there …

Suppose we have $N$ independent random variables $X_1$, $\ldots$, $X_N$ with finite means $\mu_1 \leq \ldots \leq \mu_N$ and variances $\sigma_1^2$, $\ldots$, $\sigma_N^2$. I am lo …

Let $f$ be a monic polynomial with bounded integer coefficients and such that all zeros are (in absolute value) greater than $1$. How close can the zeros of $f$ reach $1$ (in ab …

Are there tight upper and lower bounds on the density of the sum of $n$ i.i.d laplace random variables that depend on $n$ and the individual laplacian densities?

I am confused by the Zonrn's lemma and Least Upper Bound axiom: (1) Least upper bound axiom: every subset of real number if has an upper bound then has a least upper bound. (2) Z …

Hi is there any lower bound for $\Re\zeta(1+it)$. I did try with computer until some ordinate and I saw $\Re\zeta(1+it)>0$. If it is true, is there any reference to prove it. t …

I am trying to find a good lower bound for chromatic number of one family of graphs. I'm curious what are the known lower bounds for chromatic number. There are two obvious: $\chi( …

Assume the following: • $L\leq K$ . • $\Gamma\in M_{K,L}$ is a $L$ rank ${ 0,1} $ matrix, without identical rows or the zeros row. • $N\in M_{K,K}$ is a diagonal matrix, whose …