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 ...

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 ...

Noncommutative topological entropy estimates are obtained for ‘finite range’ endomorphisms of Cuntz algebras,generalising known results for the canonical shift endomorphisms. Exact values are computed for a class of ...

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ...

For each fixed number $\varepsilon$ in $(0, 1)$ we construct a bounded linear operator on the Banach space $\ell_1$ having a certain orbit which intersects every cone of aperture $\varepsilon$, but with every orbit avoiding ...

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 ...

It has been shown recently that, under an appropriate integrability condition, densities of functions of independent and identically distributed random variables can be estimated at the parametric rate by a local U-statistic, ...

We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ...

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 ...

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture ...