bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Some Properties of Multiple Conjugate Trigonometric Series
Authors: Leladze D. 
Published: February 2021

Abstract
We have obtained the estimate in the terms of partial and mixed moduli of continuity of deviation of Cesáro (C, ) means of the sequence of rectangular partial sums of n-multiple (n > 1) conjugate trigonometric series from n-multiple truncated conjugate function. This estimate implies the result on the -convergence (⋋ ≥ 1) of (C, ) means , provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown, that the -convergence cannot be replaced by ordinary convergence.
On Optimal Stopping of Inhomogeneous Standard Markov Processes
Authors: Dochviri B. 
Published: February 2021

Abstract
The connection between the optimal stopping problems for inhomogeneous standard Markov process and the corresponding homogeneous Markov process constructed in the extended state space is established. An excessive characterization of the value-function and the limit procedure for its construction in the problem of optimal stopping of an inhomogeneous standard Markov process is given. The form of ε-optimal (optimal) stopping times is also found.
On Some Properties of Solutions of Second Order Linear Functional
Differential Equations
Authors: Kiguradze I. 
Published: February 2021

Abstract
The properties of solutions of the equation
u″(t) =
p
1
(t)u(τ
1(t))
+
p
2(t)u′(
τ

2(t)) are investigated where
pi
: [a,
+∞[→ R (i
= 1, 2) are locally summable functions,
τ
1 : [a,
+∞[→ R is a measurable
function and τ
2 :
[a, +∞[→
R is a nondecreasing locally absolutely continuous one.
Moreover, τ

i
(t) ≥ t (i
= 1, 2), p
1 (t) ≥
0, ,
ε = const > 0 and
. In particular, it is
proved that solutions whose derivatives are square integrable on
[a, +∞ [ form a
one-dimensional linear space and for any such solution to vanish at infinity it
is necessary and sufficient that .
On Some Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)
Authors: Lomadze G. 
Published: February 2021

Abstract
Two entire modular forms of weight 5 and two of weight 6 for the congruence subgroup Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 10 and 12 variables.
Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels
Authors: Genebashvili I. , Gogatishvili A. , Kokilashvili V. 
Published: February 2021

Abstract
Necessary and sufficient conditions are derived in order that an inequality of the form

be fulfilled for some positive c independent of λ and a ν-measurable nonnegative function ƒ : X → R
1, where

k : X × X × [0, ∞) → R
1 is a nonnegative measurable kernel, (X, d, μ) is a homogeneous type space, φη and ψ are quasiconvex functions, ψ ∈ Δ2, and t
–α

θ(t) is a decreasing function for some α, 0 < α < 1.
A similar problem was solved in Lorentz spaces with weights.
The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries
Authors: Chkadua O. 
Published: February 2021

Abstract
The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.
Fractional Integrodifferentiation in Hölder Classes of Arbitrary Order
Authors: Karapetyants N. K. , Ginzburg A. I. 
Published: February 2021

Abstract
Hölder classes of variable order μ(x) are introduced and it is shown that the fractional integral has Hölder order μ(x) + α (0 < α, μ
+, α + μ
+ < 1, μ
+ = sup μ(x)).
Geometry of Poisson Structures
Authors: Giunashvili Z. 
Published: February 2021

Abstract
The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields. Further, we shall touch upon the dualism between bivector fields and differential 2-forms.
Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. II
Authors: Gogatishvili A. , Kokilashvili V. 
Published: February 2021

Abstract
This paper continues the investigation of weight problems in Orlicz classes for maximal functions and singular integrals defined on homogeneous type spaces considered in [Gogatishvili and Kokilashvili, Georguian Math. J. 2: 361–384, 1995].
The Skorokhod Oblique Reflection Problem in a Convex Polyhedron
Authors: Shashiashvili M. 
Published: February 2021

Abstract
The Skorokhod oblique reflection problem is studied in the case of n-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to construct in a direct way the reflected (in a convex polyhedral domain) diffusion processes possessing the nice properties.
Oscillatory Criteria for Nonlinear nth-Order Differential Equations with Quasiderivatives
Authors: Bartušek Miroslav 
Published: February 2021

Abstract
Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L
0
y, . . . , L

n–1
y) under the validity of the sign condition f(t, x
1, . . . , xn
)x
1 ≤ 0, f(t, 0, x
2, . . . , xn
) = 0 on .
Combinatorial Invariance of Stanley–Reisner Rings
Authors: Bruns W. , Gubeladze J. 
Published: February 2021

Abstract
In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application” in combinatorics [Hibi, Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, 1992, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.
On the Solvability of a Darboux Type Non-Characteristic Spatial Problem for the Wave Equation
Authors: Kharibegashvili S. 
Published: February 2021

Abstract
The question of the correct formulation of a Darboux type non-characteristic spatial problem for the wave equation is investigated. The correct solvability of the problem is proved in the Sobolev space for surfaces of the temporal type on which Darboux type boundary conditions are given.
On Oscillation of Solutions of Second-Order Systems of Deviated Differential Equations
Authors: Partsvania N. 
Published: February 2021

Abstract
Sufficient conditions are found for the oscillation of proper solutions of the system of differential equations

where fi
: R
+ × R
2m
→ R (i = 1, 2) satisfy the local Carathéodory conditions and σi
, τi
: R
+ → R (i = 1, . . . , m) are continuous functions such that σi
(t) ≤ t for t ∈ R
+, .
On Strong Maximal Operators Corresponding to Different Frames
Authors: Oniani G. 
Published: February 2021

Abstract
The problem is posed and solved whether the conditions and sup
θ∈[0,π/2) ∫{M
2, θ
(ƒ) > 1}
M
2, θ
(ƒ) < ∞ are equivalent for functions (where M
2, θ
denotes the strong maximal operator corresponding to the frame {OXθ, OYθ
}).
The results obtained represent a general solution of M. de Guzmán's problem that was previously studied by various authors.
Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator
Authors: Tetruashvili M. 
Published: February 2021

Abstract
We consider the quantifier-free set theory MLSUn containing the symbols U, \, =, ∈, Un. Un(p) is interpreted as the union of all members of the set p. It is proved that there exists an algorithm which for any formula Q of the MLSUn theory containing at most one occurrence of the symbol Un decides whether Q is true or not using the space cn
3 log2
n (n is the length of Q).
On the Solution of the Dirichlet Problem for an Elliptic Equation Degenerating on the Boundary
Authors: Jvarsheishvili A. 
Published: February 2021

Abstract
The Dirichlet problem for the equation

yΔW + αWy
= –F

is studied in the semi-circle x
2 + y
2 < 1, y > 0. The restrictions on F are established under which the problem is uniquely solvable in the definite generalized sense.
The Hörmander and Maslov Classes and Fomenko's Conjecture
Authors: Tevdoradze Z. 
Published: February 2021

Abstract
Some functorial properties are studied for the Hörmander classes defined for symplectic bundles. The behavior of the Chern first form on a Lagrangian submanifold in an almost Hermitian manifold is also studied, and Fomenko's conjecture about the behavior of a Maslov class on minimal Lagrangian submanifolds is considered.
Analogues of the Kolosov–Muskhelishvili General Representation Formulas and Cauchy–Riemann Conditions in the Theory of Elastic Mixtures
Authors: Basheleishvili M. 
Published: February 2021

Abstract
Analogues of the well-known Kolosov–Muskhelishvili formulas of general representations are obtained for nonhomogeneous equations of statics in the case of the theory of elastic mixtures. It is shown that in this theory the displacement and stress vector components, as well as the stress tensor components, are represented through four arbitrary analytic functions.
The usual Cauchy–Riemann conditions are generalized for homogeneous equations of statics in the theory of elastic mixtures.
On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation
Authors: Kharibegashvili S. 
Published: February 2021

Abstract
A multidimensional version of the first Darboux problem is considered for a model second order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.
Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions
Authors: Brykalov S. A. 
Published: February 2021

Abstract
Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.
Bounds for the Characteristic Functions of the System of Monomials in Random Variables and of Its Trigonometric Analogue
Authors: Shervashidze T. 
Published: February 2021

Abstract
Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in and of the system
(cos j
1πξ
1 . . . cos j

s
πξ

s
, 0 ≤ j
1, . . . , j

s
≤ k, j
1 + . . . + j

s
≥ 1),
where (ξ
1, . . . , ξ

s
) is uniformly distributed in [0; 1]
s
.
Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
Authors: Ashordia M. 
Published: February 2021

Abstract
Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem

dx
(t) = dA(t) · f(t, x(t)),

xi
(ti
) = ϕi
(x) (i = 1, . . . , n),
where , A : [a, b] → Rn×n
is a matrix-function with bounded variation components, f : [a; b] × Rn
→ Rn
is a vector-function belonging to the Carathéodory class corresponding to A; t
1, . . . , tn
∈ [a, b] and ϕ
1, . . . , ϕn
are the continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.
On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order
Authors: Jokhadze O. 
Published: February 2021

Abstract
Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.
To the Problem of A Strong Differentiability of Integrals Along Different Directions
Authors: Lepsveridze G. 
Published: February 2021

Abstract
It is proved that for any given sequence (σ
n
, n ∈ ℕ) = Γ0 ⊂ Γ, where Γ is the set of all directions in (i.e., pairs of orthogonal straight lines) there exists a locally integrable function f on such that: (1) for almost all directions σ ∈ Γ\Γ0 the integral ∫ f is differentiable with respect to the family B
2σ of open rectangles with sides parallel to the straight lines from σ; (2) for every direction σ
n
∈ Γ0 the upper derivative of ∫ f with respect to B
2σn
equals +∞; (3) for every direction σ ∈ Γ the upper derivative of ∫ |f | with respect to B
2σ equals +∞.
Oscillatory Properties of Solutions of Impulsive Differential Equations with Several Retarded Arguments
Authors: Bainov D. D. , Dimitrova M. B. , Petrov V. A. 
Published: February 2021

Abstract
The impulsive differential equation

with several retarded arguments is considered, where pi
(t) ≥ 0, 1 + bk
> 0 for i = 1, . . . , m, t ≥ 0, k ∈ ℕ. Sufficient conditions for the oscillation of all solutions of this equation are found.
Allied Integrals, Functions, and Series for the Unit Sphere
Authors: Dzagnidze O. 
Published: February 2021

Abstract
Among the functions defined on the two-dimensional unit sphere we distinguish functions generalizing the conjugate integral, the conjugate function, and the conjugate series which depend on one variable. We establish the properties of these functions whose structures essentially differ from those of integrals, functions, and series based on the theory of analytic functions of two complex variables.
Commutativity for a Certain Class of Rings
Authors: Abujabal H. A. S. , Khan M. A. 
Published: February 2021

Abstract
We first establish the commutativity for the semiprime ring satisfying [xn, y]xr
= ±ys
[x, ym
]yt
for all x, y in R, where m, n, r, s and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital.
On a Class of Covariance Operators
Authors: Chantladze T. , Kandelaki N. 
Published: February 2021

Abstract
This paper is the continuation of [Vakhania and Kandelaki, Teoriya Veroyatnost. i Primenen 41: 31–52, 1996] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra.
Homotopy Classes of Elliptic Transmission Problems Over C*-Algebras
Authors: Khimshiashvili G. 
Published: February 2021

Abstract
The topological aspects of B.Bojarski's approach to Riemann–Hilbert problems are developed in terms of infinite-dimensional grassmanians and generalized to the case of transmission problems over C*-algebras. In particular, the homotopy groups of certain grassmanians related to elliptic transmission problems are expressed through K-groups of the basic algebra. Also, it is shown that the considered grassmanians are homogeneous spaces of appropriate operator groups. Several specific applications of the obtained results to singular operators are given, and further perspectives of our approach are outlined.
Numerical Solutions to the Darboux Problem with the Functional Dependence
Authors: Kamont Z. , Leszczyński H. 
Published: February 2021

Abstract
The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(
x, y
)) where z
(x, y) is a function defined by z(
x, y
)(t, s) = z(x + t, y+ s), (t, s) ∈ [–a
0, 0] × [–b
0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means of a comparison method; moreover we give an error estimate. The convergence of explicit difference schemes is proved under a general assumption that given functions satisfy nonlinear estimates of the Perron type. Our results are illustrated by a numerical example.
On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
Authors: Khosroshvili D. 
Published: February 2021

Abstract
A general formula is derived for the number of representations r(n; f) of a natural number n by diagonal quadratic forms f with five variables of level 16. For f belonging to one-class series, r(n; f) coincides with the sum of a singular series, while in the case of a many-class series an additional term is required, for which the generalized theta-function introduced by T. V. Vepkhvadze [Vepkhvadze, Acta Arithmetica 53: 433–990] is used.
Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures
Authors: Basheleishvili M. 
Published: February 2021

Abstract
The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [Basheleishvili, Georgian Math. J. 4: 223–242, 1997], these problems can be splitted and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.
On the Vector Process Obtained by Iterated Integration of the Telegraph Signal
Authors: Orsingher Enzo 
Published: February 2021

Abstract
We analyse the vector process (𝑋0(𝑡),𝑋1(𝑡), . . . , 𝑋𝑛(𝑡), 𝑡 > 0) where , 𝑘 = 1, . . . , 𝑛, and 𝑋0(𝑡) is the two-valued telegraph process.
In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed.
Special care is given to the case of the process (𝑋0(𝑡),𝑋1(𝑡),𝑋2(𝑡), 𝑡 > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.
Oscillatory Behaviour of Solutions of two-Dimensional Differential Systems with Deviated Arguments
Authors: Koplatadze R. , Partsvania N. 
Published: February 2021

Abstract
Sufficient conditions are established for the oscillation of proper solutions of the system

where satisfy the local Carathéodory conditions and τ𝑖
, σ𝑖
: ℝ+ → ℝ+ (𝑖 = 1, . . . , 𝑚) are continuous functions such that σ𝑖
(𝑡) ≤ 𝑡 for 𝑡 ∈ ℝ+, , .
On the Approximation of Functions on Locally Compact Abelian Groups
Authors: Ugulava D. 
Published: February 2021

Abstract
Questions of approximative nature are considered for a space of functions 𝐿𝑝(𝐺, μ), 1 ≤ 𝑝 ≤ ∞, defined on a locally compact abelian Hausdorff group 𝐺 with Haar measure μ. The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.
Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems
Authors: Davis John M. , Eloe Paul W. , Henderson Johnny 
Published: February 2021

Abstract
For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.
A Problem with Nonlocal Boundary Conditions for a Quasilinear Parabolic Equation
Authors: Dzhuraev T. D. , Takhirov J. O. 
Published: February 2021

Abstract
The solvability of the nonlocal boundary value problem
𝑢𝑡 = 𝑎(𝑡, 𝑥, 𝑢, 𝑢𝑥)𝑢𝑥𝑥 + 𝑏(𝑡, 𝑥, 𝑢, 𝑢𝑥), 0 ≤ 𝑡 ≤ 𝑇, |𝑥| ≤ 𝑙, 𝑢(0, 𝑥) = 0, 𝑢(𝑡, –𝑙) = 𝑢(𝑡, 𝑙), 𝑢𝑥(𝑡, –𝑙) = 𝑢𝑥(𝑡, 𝑙)
in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.
Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure
Authors: Kharazishvili A. 
Published: February 2021

Abstract
We consider some subsets of the Euclidean plane 𝐑2, having small linear sections (in all directions), and investigate those sets from the point of view of measurability with respect to certain invariant extensions of the classical Lebesgue measure on 𝐑2.
On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations
Authors: Kiguradze T. 
Published: February 2021

Abstract
It is proved that the Dirichlet problem is correct in the characteristic rectangle 𝐷𝑎𝑏 = [0, 𝑎] × [0, 𝑏] for the linear hyperbolic equation

with the summable in 𝐷𝑎𝑏 coefficients 𝑝0, 𝑝1, 𝑝2, 𝑝3 and 𝑞 if and only if the corresponding homogeneous problem has only the trivial solution. The effective and optimal in some sense restrictions on 𝑝0, 𝑝1, 𝑝2 and 𝑝3 guaranteeing the correctness of the Dirichlet problem are established.
Limit Distribution of the Mean Square Deviation of the Gasser–Müller Nonparametric Estimate of the Regression Function
Authors: Absava R. , Nadaraya E. 
Published: February 2021

Abstract
Asymptotic distribution of the mean square deviation of the Gasser–Müller estimate of the regression curve is investigated. The testing of hypotheses on regression function is considered. The asymptotic behaviour of the power of the proposed criteria under contiguous alternatives is studed.
Entropy Numbers of Certain Summation Operators
Authors: Creutzig J. , Linde W. 
Published: February 2021

Abstract
Given nonnegative real sequences and we study the generated summation operator

regarded as a mapping from ℓ
p
(ℤ) to ℓ
q
(ℤ). We give necessary and sufficient conditions for the boundedness of S
𝑎, 𝑏 and prove optimal estimates for its entropy numbers relative to the summation properties of 𝑎 and 𝑏. Our results are applied to the investigation of the behaviour of

as ε → 0, where is some nondecreasing sequence in [0, ∞) and (W(t))
t ≥ 0 denotes the Wiener process.
Entropy Numbers of Diagonal Operators of Logarithmic Type
Authors: Kühn Thomas 
Published: February 2021

Abstract
We determine the asymptotic behaviour (as 𝑘 → ∞, up to multiplicative constants not depending on k) of the entropy numbers 𝑒𝑘 (D

σ
: l

p
→ l

q
), 1 ≤ p ≤ q ≤ ∞, of diagonal operators generated by logarithmically decreasing sequences σ = (σ

n
). This complements earlier results by Carl [J. Approx. Theory 32: 135–150, 1981] who investigated the case of power-like decay of the diagonal.
Hölder Versions of Banach Space Valued Random Fields
Authors: Račkauskas Alfredas , Suquet Charles 
Published: February 2021

Abstract
For rather general moduli of smoothness ρ, like ρ(ℎ)=ℎ
α
ln
β
(𝑐/ℎ), we consider the Hölder spaces H

ρ
(B) of functions [0,1]
d
→ B is a separable Banach space. We establish an isomorphism between H

ρ
(B) and some sequence Banach space. With this analytical tool, we follow a very natural way to study, in terms of second differences, the existence of a version in H

ρ
(B) for a given random field.