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

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 ...

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 ...

The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles ...

It is well-known that an element of the linear group $GL_n(\mathbb{C})$ is semisimple if and only if its conjugacy class is Zariski closed. The aim of this paper is to show that the same result holds for the group of complex ...

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 $\Delta=XZ+Y^2$ ...

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 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 ...

We consider a model of frequency-dependent selection, to which we refer as the Wildcard Model, that accommodates as particular cases a number of diverse models of biologically specific situations. Two very different ...

We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution ...