10 problems

Let $K(Gamma,R,g)$ denote the class of functions on $Gamma$ that are convex, where $Gamma$ and the operators $L_n^2$ are as defined in the paper. Eventual domination and monotonici…

Let $S$ be the simplex domain, let $B_n$ be the Bernstein operator on the space of polynomials of total degree at most $n$, and let $A_n^{(k)}$ be its partial inverse of order $k$.…

For each positive integer $n$, let $b_n(u)$ denote the factorially normalized Bernoulli polynomial of degree $n$, and consider the polynomial probability density $1-2^n b_n(u)$ on…

Let $(\beta,p)\in\mathcal E_d$, let $\Lambda\in\mathcal M_f([0,1])$, and let $L_t$ be the number of leaves in the associated ancestral selection graph at time $t$. Let $P_t$ be its…

Let $d:[0,1]\to\bash$ be continuous with $d(0)=d(1)=0$. An infinite selection decomposition (SD) is a pair $(\beta,p)$ with coefficients $\beta_\ell$ and colouring probabilities…

Exact minimum conjecture.

Let $d$ be fixed, let $\mathcal I_d$ be the set of weak $3$-compositions of $d$, and for every nonempty subset $\Gamma\subset\mathcal I_d$ let $M_\Gamma$ be the corresponding Berns…

The principal-minor positivity conjecture. For every such $\Gamma$, the matrix $M_\Gamma$ is nonsingular and

Let $f$ be a polynomial, let the poles of its $p$-adic zeta function be considered, and let $b_f(s)$ be the Bernstein polynomial of $f$. Stronger form of Igusa's conjecture. The re…

Let $f\function C[0,1]$, let $B_n$ be the Bernstein operator, and let $\omega^2_\varphi(f,t)_{C[0,1]}$ denote the second Ditzian–Totik modulus with $\varphi(x)=\sqrt{x(1-x)}$. The…