Ordering of operators is purely combinatorial task involving a number of commutators shuffling components of operator expression to desired form. Here we show how it can be illustrated by simple urn models in which normal ...

We address optimization of nonlinear functions of the form $f(W_x)$ , where $f : \mathbb{R}^d \to \mathbb{R}$ is a nonlinear function, $W$ is a $d \times n$ matrix, and feasible $x$ are in some large finite set $\mathcal{F}$ ...

We determine the precise asymptotics of the logarithmic upper tail probability of the total intersection local time of $p$ independent random walks in $\mathbb{Z}^d$ under the assumption $p(d-2)>d$. Our approach allows a ...

We construct closed sets S of arbitrarily small measure with the property: given any discrete set L, every l-function on L can be interpolated by an L-function with spectrum on F. This should be contrasted against ...

We prove that for a polynomial $f \in k[x, y, z]$ equivalent are: (1)$f$ is a $k[z]$-coordinate of $k[z][x,y]$, and (2) $k[x, y, z]/(f)\cong k^[2]$ and $f(x,y,a)$ is a coordinate in $k[x,y]$ for some $a \in k$. This solves ...

We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a one-to-one correspondence between formal ribbons on curves plus some ...

In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished ...

Preconditioning methods via approximate block factorization for block tridiagonal matrices are studied. Bounds for the resulting condition numbers are given, and two methods for the recursive construction of the approximate ...

Conway’s second largest simple group, $Co_2$, is characterized by the centralizer of an element of order 3 and certain fusion data.

A polynomial automorphism $F$ is called shifted linearizable if there exists a linear map $L$ such that $LF$ is linearizable. We prove that the Nagata automorphism $N:= (X-Y\Delta-Z\Delta^2,Y+Z\Delta,Z)$ where $\Delta=XZ+Y^2$ ...