2019
Том 71
№ 7

### All Issues

Article (Russian)

### Clark representation for local times of self-intersection of Gaussian integrators

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1587-1614

We prove the existence of a multiple local time of self-intersection for a class of Gaussian integrators generated by operators with finite-dimensional kernel, describe its Ito – Wiener expansion and establish the Clark representation.

Article (Ukrainian)

### Limit distributions of conflict dynamical system with point spectra

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1615-1624

We construct a model of conflict dynamical system whose limit states are associated with singular distributions. We prove that a criterion for appearance of a point spectrum in the limit distribution is the strategy of fixed priority. In all other cases, the limit distributions are pure singular continuous.

Article (English)

### Simple transitive 2-representations for two non-fiat 2-categories of projective functors

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1625-1649

We show that any simple transitive 2-representation of the 2-category of projective endofunctors for the quiver algebra of $\mathbb{k}(\bullet \rightarrow \bullet )$ and for the quiver algebra of $\mathbb{k}(\bullet \rightarrow \bullet \rightarrow \bullet )$ is equivalent to a cell 2-representation.

Article (English)

### On generalized ideal asymptotically statistical equivalent of order $α$ for functions

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1650-1659

We introduce new definitions related to the notions of asymptotically $\mathcal{I}_{\lambda}$ -statistical equivalent of order \alpha to multiple L and strongly $\mathcal{I}_{\lambda}$ -asymptotically equivalent of order $\alpha$ to multiple $L$ by using two nonnegative real-valued Lebesque measurable functions in the interval $(1,\infty )$ instead of sequences. In addition, we also present some inclusion theorems.

Article (Ukrainian)

### Theory of multidimensional Delsarte – Lions transmutation operators. I

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1660-1695

We present a brief review of the original results obtained by the authors in the theory of Delsarte –Lions transmutations of multidimensional spectral differential ope rators based on the classical works by Yu. M. Berezansky, V. A. Marchenko, B. M. Levitan, and R. G. Newton, on the well-known L. D. Faddeev’s survey, the book by L. P. Nyzhnyk, and the generalized De-Rham – Hodge theory suggested by I. V. Skrypnik and developed by the authors for the differential-operator complexes. The operator structure of Delsarte – Lions transformations and the properties of their Volterra factorizations are analyzed in detail. In particular, we study the differential-geometric and topological structures of the spectral properties of the Delsarte – Lions transmutations within the framework of the generalized De-Rham – Hodge theory.

Article (English)

### On the generalization of some Hermite – Hadamard inequalities for functions with convex absolute values of the second derivatives via fractional integrals

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1696-1706

We provide a unified approach to getting Hermite – Hadamard inequalities for functions with convex absolute values of the second derivatives via the Riemann – Liouville integrals. Some particular inequalities generalizing the classical results, such as the trapezoid inequality, Simpson’s inequality, and midpoint inequality are also presented.

Article (Russian)

### On $\Sigma_t^{σ}$ -closed classes of finite groups

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1707-1716

All analyzed groups are finite. Let $\sigma = \{ \sigma_i| i \in I\}$ be a partition of the set of all primes $\mathbb{P}$. If $n$ is an integer, then the symbol $\sigma (n)$ denotes a set $\{\sigma_i| \sigma_i \cap \pi (n) \not = \emptyset\}$. Integers $n$ and $m$ are called $\sigma$ -coprime if $\sigma (n) \cap \sigma (m) = \emptyset$.
Let $t > 1$ be a natural number and let $\mathfrak{F}$ be a class of groups. Then we say that $\mathfrak{F}$ is $\Sigma^{\sigma}_ t$ -closed provided $\mathfrak{F}$ contains each group $G$ with subgroups $A_1, ... ,A_t \in \mathfrak{F}$ whose indices $| G : A_1| ,..., | G : A_t|$ are pairwise $\sigma$ -coprime. We study $\Sigma_t^{σ}$ -closed classes of finite groups.

Brief Communications (Russian)

### Trotter – Daletskii formula for nonlinear disturbance

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1717-1722

For a semilinear parabolic equation, we prove a relation generalizing the Trotter – Daletskii formula.

Index (Ukrainian)

### Index of volume 70 of „Ukrainian Mathematical Journal”

Ukr. Mat. Zh. - 2018νmber=1. - 70, № 12. - pp. 1723-1728