bluuebunny/crossref_metadata_2025_split huggingface dataset:
Iterating the Bar Construction
Authors: Kadeishvili T. , Saneblidze S. 
Published: February 2021

Abstract
For a 1-connected space X Adams's bar construction B(C*(X)) describes H*(ΩX) only as a graded module and gives no information about the multiplicative structure. Thus it is not possible to iterate the bar construction in order to determine the cohomology of iterated loop spaces Ω
iX. In this paper for an n-connected pointed space X a sequence of A(∞)-algebra structures , k = 1, 2, . . . , n, is constructed, such that for each k ≤ n there exists an isomorphism of graded algebras
Crossed Semimodules and Schreier Internal Categories in the Category of Monoids
Authors: Patchkoria A. 
Published: February 2021

Abstract
We introduce the notion of a Schreier internal category in the category of monoids and prove that the category of Schreier internal categories in the category of monoids is equivalent to the category of crossed semimodules. This extends a well-known equivalence of categories between the category of internal categories in the category of groups and the category of crossed modules.
Markov Dilation of Diffusion Type Processes and its Application to the Financial Mathematics
Authors: Tevzadze R. 
Published: February 2021

Abstract
The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.
On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations
Authors: Kiguradze T. 
Published: February 2021

Abstract
In the rectangle 𝐷 = (0, 𝑎) × (0, 𝑏) with the boundary Γ the Dirichlet problem

𝑢(𝑥, 𝑦) = 0 for (𝑥, 𝑦) ∈ Γ
is considered, where 𝑝 and 𝑞 : 𝐷 → ℝ are locally summable functions and may have nonintegrable singularities on Γ. The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbations of the coefficients of the equation under consideration are established.
Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
Authors: Kokilashvili V. , Meskhi A. 
Published: February 2021

Abstract
The optimal sufficient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces defined on homogeneous groups. In some particular case the found conditions are necessary for the corresponding inequalities to be valid. Also, the necessary and sufficient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces defined on homogeneous groups.
On the Absolute Summability of Series with Respect to Block-Orthonormal Systems
Authors: Nadibaidze G. 
Published: February 2021

Abstract
Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {ω(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {Nk
} such that {ω(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the Δ
k
-orthonormal systems.
Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
Authors: Soltani A. R. , Shishebor Z. 
Published: February 2021

Abstract
Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {An
} ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An
} by a positive measure μ and a number T of -valued functions a
0, . . . , a

T–1; in the spectral form , where and Φ is an -valued Borel set function on [0, 2π) such that
(Φ(Δ)x, Φ(Δ′)x′)
Y
= (x, x′)
X μ(Δ ∩ Δ′).
Topological Spaces with the Strong Skorokhod Property
Authors: Banakh T. O. , Bogachev V. I. , Kolesnikov A. V. 
Published: February 2021

Abstract
We study topological spaces with the strong Skorokhod property, i.e., spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measure on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost everywhere convergent sequences of mappings. We construct nonmetrizable spaces with such a property and investigate the relations between the Skorokhod and Prokhorov properties. It is also shown that a dyadic compact has the strong Skorokhod property precisely when it is metrizable.
On a Characterisation of Inner Product Spaces
Authors: Chelidze G. 
Published: February 2021

Abstract
It is well known that for the Hilbert space H the minimum value of the functional F

μ
(f) = ∫
H
‖f – g‖2
dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner product that generates the norm.
On the Tail Estimation of the Norm of Rademacher Sums
Authors: Chobanyan S. , Salehi H. 
Published: February 2021

Abstract
The main aim of this paper is to prove a bilateral inequality for , where t > 0, (𝑎𝑘) are elements of a normed space, while (𝑟𝑘) are Rademacher functions. Then this inequality is applied for estimation of . As another corollary we give a maximal inequality for exchangeable random variables that recently has been published in [Pruss, Proc. Amer. Math. Soc. 126: 1811–1819, 1998].
Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
Authors: Kawabe Jun 
Published: February 2021

Abstract
We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam's criterion for real measures and applies to cases which are not covered by März–Shortt's criterion for Banach space valued vector measures.
Representations of Conditional Means
Authors: Rao M. M. 
Published: February 2021

Abstract
A unified treatment of integral representations of conditional expectations, in terms of Bochner integrals, with specializations to Gaussian conditioning, is given. The integrals in the latter have deterministic kernels. Difficulties in actual calculations of (even regular) conditional probabilities, and the inadequacy of methods related to L'Hospital's procedures, are exemplified. Limitations of the methods used and some new problems for investigation are indicated.
On Accuracy of Improved χ
2-Approximations
Authors: Ulyanov V. V. , Fujikoshi Y. 
Published: February 2021

Abstract
For a statistic S whose distribution can be approximated by χ
2-distributions, there is a considerable interest in constructing improved χ
2-approximations. A typical approach is to consider a transformation T = T(S) based on the Bartlett correction or a Bartlett type correction. In this paper we consider two cases in which S is expressed as a scale mixture of a χ
2-variate or the distribution of S allows an asymptotic expansion in terms of χ
2-distributions. For these statistics, we give sufficient conditions for T to have an improved χ
2-approximation. Furthermore, we present a method for obtaining its error bound.
Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
Authors: Woźniakowski Henryk 
Published: February 2021

Abstract
We study tractability in the worst case setting of tensor product linear operators defined over weighted tensor product Hilbert spaces. Tractability means that the minimal number of evaluations needed to reduce the initial error by a factor of ε in the d-dimensional case has a polynomial bound in both ε
–1 and d. By one evaluation we mean the computation of an arbitrary continuous linear functional, and the initial error is the norm of the linear operator S

d
specifying the d-dimensional problem.
We prove that nontrivial problems are tractable iff the dimension of the image under S
1 (the one-dimensional version of S

d
) of the unweighted part of the Hilbert space is one, and the weights of the Hilbert spaces, as well as the singular values of the linear operator S
1, go to zero polynomially fast with their indices.
Weighted Exponential Inequalities
Authors: Heinig H. P. , Kerman R. , Krbec M. 
Published: February 2021

Abstract
Necessary and sufficient conditions on weight pairs are found for the validity of a class of weighted exponential inequalities involving certain classical operators. Among the operators considered are the Hardy averaging operator and its variants in one and two dimensions, as well as the Laplace transform. Discrete analogues yield characterizations of weighted forms of Carleman's inequality.
Global Geometric Aspects of Riemann–Hilbert Problems
Authors: Bojarski B. , Khimshiashvili G. 
Published: February 2021

Abstract
We discuss some global properties of an abstract geometric model for Riemann–Hilbert problems introduced by the first author. In particular, we compute the homotopy groups of elliptic Riemann–Hilbert problems and describe some connections with the theory of Fredholm structures which enable one to introduce more subtle geometrical and topological invariants for families of such problems.
On the Product of Separable Metric Spaces
Authors: Kighuradze D. 
Published: February 2021

Abstract
Some properties of the dimension function dim on the class of separable metric spaces are studied by means of geometric construction which can be realized in Euclidean spaces. In particular, we prove that if dim(𝑋 × 𝙔) = dim 𝑋 + dim 𝙔 for separable metric spaces 𝑋 and 𝙔, then there exists a pair of maps , , 𝑠 = dim 𝑋 + dim 𝙔, with stable intersections.
On Singular Boundary Value Problems for Functional Differential Equations of Higher Order
Authors: Kiguradze I. , Půža B. , Stavroulakis I. P. 
Published: February 2021

Abstract
Sufficient conditions are established for the solvability of the boundary value problem
𝑥(𝑛) (𝑡) = 𝑓(𝑥)(𝑡), ℎ𝑖(𝑥) = 0 (𝑖 = 1, . . . , 𝑛),
where 𝑓 is an operator (ℎ𝑖 (𝑖 = 1, . . . , 𝑛) are operators) acting from some subspace of the space of (𝑛 – 1)-times differentiable on the interval ]𝑎, 𝑏[ 𝑚-dimensional vector functions into the space of locally integrable on ]𝑎, 𝑏[ 𝑚-dimensional vector functions (into the space ).
The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices
Authors: Matsak Ivan , Plichko Anatolij 
Published: February 2021

Abstract
A Bochner mean square deviation for random elements of 2-convex Banach lattices is introduced and investigated. Results, analogous to the law of large numbers for squares of random elements are proved in some classes of Köthe function spaces.
A Strong Solution of an Evolution Problem with Integral Conditions
Authors: Mesloub S. , Bouziani A. , Kechkar N. 
Published: February 2021

Abstract
The paper is devoted to proving the existence and uniqueness of a strong solution of a mixed problem with integral boundary conditions for a certain singular parabolic equation. A functional analysis method is used. The proof is based on an energy inequality and on the density of the range of the operator generated by the studied problem.
A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure. Correction
Authors: Mania M. , Tevzadze R. 
Published: February 2021

Abstract
Corrections are given for [Mania and Tevzadze, Georgian Math. J. 7: 765–792, 2000], most of which consist in replacing “ess sup” by “ess inf” in all the exposed formulas.
On the Theory of Functional-Differential Inclusion of Neutral Type
Authors: Bulgakov A. I. , Vasilyev V. V. 
Published: February 2021

Abstract
A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.
Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation
Authors: Jangveladze T. , Kiguradze Z. 
Published: February 2021

Abstract
The asymptotic behavior as 𝑡 → ∞ of solutions of a nonlinear integro-differential equation is studied. The equation arises as a model describing the penetration of the electromagnetic field in to a substance.
Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Authors: Zhou Haiyun , Agarwal Ravi P. , Cho Yeol Je , Kim Yong Soo 
Published: February 2021

Abstract
In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors.
Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
Authors: Khomasuridze N. 
Published: February 2021

Abstract
Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ
0 < ρ < ρ
1, α
0 < α < α
1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ
ρ
= ℎ
α
= ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.
A Unified Characterization of 𝑞-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
Authors: Mania M. , Tevzadze R. 
Published: February 2021

Abstract
We give a unified characterization of 𝑞-optimal martingale measures for 𝑞 ∈ [0, ∞) in an incomplete market model, where the dynamics of asset prices are described by a continuous semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases 𝑞 = 2, 𝑞 = 1 and 𝑞 = 0 respectively. Under assumption that the Reverse Hölder condition is satisfied, the continuity (in 𝐿1 and in entropy) of densities of 𝑞-optimal martingale measures with respect to 𝑞 is proved.
Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions
Authors: Dattoli Giuseppe , Ricci Paolo E. 
Published: February 2021

Abstract
Some classes of entire functions which are eigenfunctions of generalizations of the Laguerre derivative operator are considered.
Since this property is an analog of the one characterizing the exponential function, we refer to such functions as Laguerre-type exponentials, or shortly 𝐿-exponentials. The definition of 𝐿-circular and 𝐿-hyperbolic functions easily follows.
Applications in the framework of generalized evolution problems are also mentioned.
The Superstability of the Generalized D'alembert Functional Equation
Authors: Elqorachi Elhoucien , Akkouchi Mohamed 
Published: February 2021

Abstract
We generalize the well-known Baker's superstability result for the d'Alembert functional equation with values in the field of complex numbers to the case of the integral equation

where 𝐺 is a locally compact group, μ is a generalized Gelfand measure and σ is a continuous involution of 𝐺.
On the Solvability of a Nonlocal Problem Arising in Dynamics of Moisture Transfer
Authors: Bouziani Abdelfatah 
Published: February 2021

Abstract
In the recent years, evolution problems with an integral term in the boundary conditions have received a great deal of attention. Such problems, in general, are nonself-adjoint, and this poses the basic source of difficulty, which can considerably complicate the application of standard functional and numerical techniques. To avoid these complications, we have introduced a nonclassical function space to establish a priori estimates without any additional complication as compared to the classical evolution problems. As an example of the applicability of this way of solving problems of this type, we investigate an initial-boundary value problem for a pseudoparabolic equation which combines Neumann and integral conditions.
Oscillation Criteria for Second-Order Nonlinear Differential Equations with Damping Term
Authors: Wang Qi-Ru 
Published: February 2021

Abstract
By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrate the importance of our results are included.
The Bellman Equation Related to the Minimal Entropy Martingale Measure
Authors: Mania M. , Santacroce M. , Tevzadze R. 
Published: February 2021

Abstract
We derive a backward stochastic differential equation and a Bellman equation characterizing the minimal entropy martingale measure for market models, where asset prices are driven by Markov diffusion processes. A relation between these equations is established.
A Recursion Formula for the Coefficients of Entire Functions Satisfying an ODE with Polynomial Coefficients
Authors: Belingeri C. 
Published: February 2021

Abstract
A recursion formula for the coefficients of entire functions which are solutions of linear differential equations with polynomial coefficients is derived. Some explicit examples are developed.
The Newton sum rules for the powers of zeros of a class of entire functions are constructed in terms of Bell polynomials.
On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane
Authors: Kharazishvili A. 
Published: February 2021

Abstract
The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.
Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates
Authors: Khomasuridze N. 
Published: February 2021

Abstract
A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ
0 < ρ < ρ
1, α
0 < α < α
1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly transversally isotropic if its nine elastic and thermal characteristics are correlated by one or several conditions) and non-homogeneous with respect to 𝑧.
Particular Solutions for a Class of ODE Related to the L-Exponential Functions
Authors: Bretti Gabriella , Natalini Pierpaolo 
Published: February 2021

Abstract
Particular solutions of a class of higher order ordinary differential equations, with non-constant coefficients, are determined by using the properties of the Laguerre exponentials functions introduced by G. Dattoli and P. E. Ricci in [Georgian Math. J. 10: 481–494, 2003]
Extensions with Abelian Kernels in Protomodular Categories
Authors: Bourn D. , Janelidze G. 
Published: February 2021

Abstract
As observed by J. Beck, and as we know from M. Barr's and his joint work on triple cohomology, the classical isomorphism Opext ≅ 𝐻2 that describes group extensions with abelian kernels, can be deduced from the equivalence between such extensions and torsors (in an appropriate sense). The same is known for many other “group-like” algebraic structures, and now we present a purely-categorical version of that equivalence, essentially by showing that all torsors are extensions with abelian kernels in any pointed protomodular category, and by giving a necessary and sufficient condition for the converse.
Polytopes and 𝐾-Theory
Authors: Bruns W. , Gubeladze J. 
Published: February 2021

Abstract
This is an overview of results from our experiment of merging two seemingly unrelated disciplines – higher algebraic 𝐾-theory of rings and the theory of lattice polytopes. The usual 𝐾-theory is the “theory of a unit simplex”. A conjecture is proposed on the structure of higher polyhedral 𝐾-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.
Generalized Heisenberg Groups and Shtern's Question
Authors: Megrelishvili M. 
Published: February 2021

Abstract
Let 𝐻(𝑋) := (ℝ × 𝑋) ⋋ 𝑋* be the generalized Heisenberg group induced by a normed space 𝑋. We prove that 𝑋 and 𝑋* are relatively minimal subgroups of 𝐻(𝑋). We show that the group 𝐺 := 𝐻(𝐿4[0, 1]) is reflexively representable but weakly continuous unitary representations of 𝐺 in Hilbert spaces do not separate points of 𝐺. This answers the question of A. Shtern.
On Some Matrix Clifford Algebras
Authors: Chantladze Tamaz , Kandelaki Nodar , Ugulava Douglas 
Published: February 2021

Abstract
A sequence of matrices 𝑈1, 𝑈2, . . . , 𝑈𝑚 is constructed, which satisfies the conditions 𝑈𝑖𝑈𝑗 = – 𝑈𝑗𝑈𝑖 (𝑖 ≢ 𝑗), . These matrices are used to construct representations of a Clifford algebra for special quadratic forms.
Integral Inequalities for Littlewood–Paley Operators
Authors: Tan Changmei 
Published: February 2021

Abstract
Let 𝑇𝑓 denote the 𝑔-function 𝑔(𝑓) or the area integral 𝑠(𝑓). We give a characterization of functions Φ for which

where the constant 𝐶 is independent of 𝑓.
Some Algebraic and Geometric Structures on Poisson Manifolds
Authors: Tevdoradze Zaza 
Published: February 2021

Abstract
In this paper we study some algebraic properties of harmonic forms on Poisson manifolds. It is well known that in the classical case (on Riemannian manifolds) the product of harmonic forms is not harmonic. Here we describe the algebraic and analytical mechanisms explaining this fact. We also obtain a condition under which the product of de Rham cohomology classes, which includes harmonic representatives, can be represented by a harmonic form.
Some Approximation Properties for Modified Baskakov Type Operators
Authors: Gupta Vijay 
Published: February 2021

Abstract
We study some direct results for the recently introduced family of modified Baskakov type operators. In particular, we obtain local direct results on ordinary and simultaneous approximation and an estimation of error for linear combinations in terms of higher order modulus of continuity. We have applied the Steklov mean as a tool for the linear approximating method.
On the Boundedness and Compactness of Weighted Hardy Operators in Spaces 𝐿𝑝(𝑥)
Authors: Edmunds David E. , Kokilashvili Vakhtang , Meskhi Alexander 
Published: February 2021

Abstract
Necessary conditions and sufficient conditions for the boundedness/ compactness of weighted Hardy operators are established in generalized Lebesgue spaces 𝐿𝑝(𝑥).