# Siberian Advances in Mathematics

## Current impact factor: 0.00

## Impact Factor Rankings

## Additional details

5-year impact | 0.00 |
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Cited half-life | 0.00 |

Immediacy index | 0.00 |

Eigenfactor | 0.00 |

Article influence | 0.00 |

Other titles | Siberian advances in mathematics (Online), Siberian advances in mathematics |

ISSN | 1934-8126 |

OCLC | 76708366 |

Material type | Document, Periodical, Internet resource |

Document type | Internet Resource, Computer File, Journal / Magazine / Newspaper |

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- Author's pre-print on pre-print servers such as arXiv.org
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- Classificationgreen

## Publications in this journal

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**ABSTRACT:**We find the lower boundary for the essential spectrum of a Fredholm type partial integral operator H. We also obtain an estimate for the number of eigenvalues below this boundary. - [Show abstract] [Hide abstract]

**ABSTRACT:**In nonhomogeneous Hölder spaces, we prove continuity of integral operators with kernels from a special class and indicate simplest properties of this class. A parametrix of new type is constructed in a half-space for second order elliptic operators. We establish that, in local Hölder norms, it admits more exact estimate than that for a parametrix close to the Levi function. - [Show abstract] [Hide abstract]

**ABSTRACT:**For countable infinite structures, two definitions of the small index property are known. One of them contains the words “at most ω,” while the other reads “less than 2ω .” In the present article, we explain in what sense there is no big difference between the two definitions and suggest a generalization to arbitrary infinite structures. - [Show abstract] [Hide abstract]

**ABSTRACT:**On a unidimensional lattice, the Hamiltonian of a system of three arbitrary particles is considered (with dispersion relations), where the particles interact pairwise via zero-range (contact) attractive potentials.We prove that the discrete spectrum of the corresponding Schrödinger operator is finite for all values of the total quasimomentum if the masses of two particles are finite. We also prove that the discrete spectrum of the Schrödinger operator is infinite if the masses of two particles in a three-particle system are infinite. - [Show abstract] [Hide abstract]

**ABSTRACT:**We deduce an analog of the Ito-Venttsel formula for an Ito system of generalized stochastic differential equations (GSDE) with noncentered measure on the basis of a stochastic kernel of an integral invariant. We construct a system of GSDE whose solution is a kernel of an integral invariant connected with a solution to GSDE with noncentered measure. We introduce the notion of a stochastic first integral of a system of GSDE with noncentered measure and find conditions under which a random function is a first integral of a given system of GSDE. - [Show abstract] [Hide abstract]

**ABSTRACT:**We prove a formula for the area of a trihedral on a hyperbolic plane H^ of positive curvature via the angles at its vertices. - [Show abstract] [Hide abstract]

**ABSTRACT:**We establish an invertible characteristic of the boundary behavior of functions from Sobolev spaces defined on a space domain having a vertex of exterior peak on the boundary. The boundary is assumed sufficiently smooth in a neighborhood of the peak vertex. The description of the traces on the boundary is given with the use of weighted Besov spaces. -
##### Article: C-minimality and model companions

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**ABSTRACT:**We study the question on existence of a model companion of the theory of a C-minimal structure with a distinguished automorphism of a special form. - [Show abstract] [Hide abstract]

**ABSTRACT:**Various theorems on convergence of general spatial homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q-homeomorphisms are obtained. In particular, it is established that a family of all ring Q-homeomorphisms f in ℝn fixing two points is compact provided that the function Q is of finite mean oscillation. The corresponding applications have been given to mappings in the Sobolev classes W loc1,p for the case p > n − 1. -
##### Article: On a problem by V. A. Toponogov

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**ABSTRACT:**We give the positive solution of a problem formulated by V. A. Toponogov and discuss some of its natural generalizations. -
##### Article: An integral representation and boundary behavior of functions defined in a domain with a peak

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**ABSTRACT:**We establish an invertible characteristic of boundary behavior of functions in Sobolev spaces defined in a space domain with a vertex of a peak on the boundary. - [Show abstract] [Hide abstract]

**ABSTRACT:**We obtain two new equivalent quasinorms for unweighted isotropic Besov and Lizorkin-Triebel spaces in the epigraph of a Lipschitz function. The question on the straightening is studied, i. e., the question on the existence of a diffeomorphism taking the epigraph into a halfspace which preserves the Lizorkin-Triebel spaces of the same indices. A criterion for the straightening is established in terms of dyadic weighted inequality where oscillations of a given function on stretched dyadic cubes are involved. -
##### Article: On a semilattice of numberings

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**ABSTRACT:**We study some properties of a $$ \mathfrak{c} $$-universal semilattice $$ \mathfrak{A} $$ with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be also $$ \mathfrak{c} $$-universal. In addition, there exists an isomorphism $$ \mathfrak{A} $$ such that $$ {\mathfrak{A} \mathord{\left/ {\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right. \kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}} $$ will be also $$ \mathfrak{c} $$-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice, the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $$ L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)} $$ on the hereditarily finite superstructure $$ \mathbb{H}\mathbb{F} $$(S) over a countable set S will be a $$ \mathfrak{c} $$-universal semilattice with the cardinality of the continuum. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let Ω1, Ω2 ⊂ ℝν be compact sets. In the Hilbert space L 2(Ω1 × Ω2), we study the spectral properties of selfadjoint partially integral operators T 1, T 2, and T 1 + T 2, with $$ \begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered} $$ whose kernels depend on three variables. We prove a theorem describing properties of the essential and discrete spectra of the partially integral operator T 1 + T 2. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let Ω = [a, b]ν and let T be a partially integral operator defined in L 2(Ω2) as follows: $$ (Tf)(x,y) = \int_\Omega {q(x,s,y)f(s,y)} d\mu (s). $$ In the article, we study the solvability of the partially integral Fredholm equations f − ℵTf = g, where g ∈ L 2(Ω2) is a given function and ℵ ∈ ℂ. The notion of determinant (which is a measurable function on Ω) is introduced for the operator E − ℵT, with E is the identity operator in L 2(Ω2). Some theorems on the spectrum of a bounded operator T are proven. -
##### Article: An analytic representation of the L 0 -valued homomorphisms in the Orlicz-Kantorovich modules

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**ABSTRACT:**We consider the Orlicz-Kantorovich modules L M (∇,m) associated with a complete Boolean algebra ∇, an N-function M, and a measure m defined on ∇ and taking values in the algebra L 0 of all measurable real functions. We obtain an analytic representation of the continuous L 0-valued homomorphisms defined on such modules. - [Show abstract] [Hide abstract]

**ABSTRACT:**We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let a piece of the boundary of a Lipschitz domain be parameterized conventionally and let the traces of functions in the Sobolev space W p 2 be written out through this parameter. In this space, we propose a discrete (diadic) norm generalizing A. Kamont’s norm in the plane case. We study the conditions when the space of traces coincides with the corresponding space for the plane boundary. -
##### Article: Superlarge deviations for sums of random variables with arithmetical super-exponential distributions

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**ABSTRACT:**Local limit theorems are obtained for superlarge deviations of sums S(n) = ξ(1) + ... + ξ(n) of independent identically distributed random variables having an arithmetical distribution with the right-hand tail decreasing faster that that of a Gaussian law. The distribution of ξ has the form ℙ(ξ = k) = $$ e^{ - k^\beta L(k)} $$, where β > 2, k ∈ ℤ (ℤ is the set of all integers), and L(t) is a slowly varying function as t → ∞ which satisfies some regularity conditions. These theorems describing an asymptotic behavior of the probabilities ℙ(S(n) = k) as k/n → ∞, complement the results on superlarge deviations in [4, 5].

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