Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Том 216, № 7 (2025)
- Жылы: 2025
- Мақалалар: 5
- URL: https://journals.rcsi.science/0368-8666/issue/view/20350
On partial derivatives of Bernstein-–Stancu polynomials for functions of several variables
Аннотация
The aim of the paper is to prove that mixed second-order derivatives of a function of several variables can be approximated in the $L_1$ norm by similar derivatives of modified Bernstein-–Stancu polynomials in the case of the minimal possible smoothness.
3-27
Lower bound for cyclicity of hyperbolic polycycles
Аннотация
Consider a monodromic hyperbolic polycycle formed by $n$ saddles and $n$ separatrix connections. Let the product of the characteristic numbers of these saddles be equal to $1$. It is shown that for any $n$, in a perturbation of this polycycle in a generic $(n+1)$-parameter family at least $n+1$ limit cycles appear.
28-77
Secondary staircase complexes on isotropic Grassmannians
Аннотация
We introduce a class of equivariant vector bundles on the isotropic symplectic Grassmannians $\mathrm{IGr}(k,2n)$ defined as appropriate truncations of staircase complexes, and we show that these bundles can be assembled into a number of complexes quasi-isomorphic to symplectic wedge powers of the symplectic bundle on $\mathrm{IGr}(k,2n)$. We are planning to use these secondary staircase complexes to study the fullness of exceptional collections in the derived categories of isotropic Grassmannians and Lefschetz exceptional collections on $\mathrm{IGr}(3,2n)$.
78-95
A remark on constructive covering of a ball of finite dimensional Banach space
Аннотация
We discuss construction of coverings of the unit ball of a finite-dimensional Banach space. The well-known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of a good covering. Here we study incoherent systems and apply them to the construction of good coverings. We use the following strategy. First, we build a good covering by balls of radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We provide a greedy-type algorithm for such constructions.
96-108
Distribution of zeros of entire functions with subharmonic majorants
Аннотация
Restrictions on the distribution of the zeros of entire functions $f\ne0$ on the complex plane are established under upper bounds $\ln |f|\leqslant M$ by subharmonic functions $M$ on $\mathbb C$. These bounds make up a broad scale of inequalities for various characteristics of the distribution of the zeros of $f$ in terms of relevant characteristics of the distribution of the Riesz masses of the subharmonic function $M$. Various classes of generalized convex functions of the argument ($p$-trigonometrically convex functions) or modulus ($p$-power convex functions) of the complex variable are used as test objects in these integral inequalities. From the restrictions obtained uniqueness theorems are deduced, from which all similar results that are known in the case when no additional special restrictions are imposed on the distribution of the zeros can be derived. The results are sharp in the sense of their sensitivity to the addition or removal of a single zero. Subharmonic versions of these results are also obtained for functions on a disc.
109-152