相关论文: Roots of real-valued zero mean maps: Compositions …

We provide a necessary and sufficient condition for existence of Gaussian cubature formulas. It consists of checking whether some overdetermined linear system has a solution and so complements Mysovskikh's theorem which requires computing…

It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…

We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…

The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support…

Structures of multilinear maps are characterized by invariants. In this paper we introduce two invariants, named the isotropy index and the completeness index. These invariants capture the tensorial structure of the kernel of a multilinear…

This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…

The tubal tensor framework provides a clean and effective algebraic setting for tensor computations, supporting matrix-mimetic features like Singular Value Decomposition and Eckart-Young-like optimality results. Underlying the tubal tensor…

The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…

A. Ya. Zaslavskii's results on the existence of a linear (affine) selection for a linear (affine) or superlinear (convex) map $\Phi : K \to 2^Y$ defined on a convex cone (convex set) $K$ having the interpolation property are extended. We…

The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems from recent models in biology and phylogenetics, where…

In the present paper, we prove the existence of universal polynomials which express multi-singularity loci classes of prescribed types for proper morphisms between smooth schemes over an algebraically closed field of characteristic zero --…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…

We develop the theory of halving spaces to obtain lower bounds in real enumerative geometry. Halving spaces are topological spaces with an action of a Lie group $\Gamma$ with additional cohomological properties. For $\Gamma=\mathbb{Z}_2$ we…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we…