bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Radial Derivative with Boundary Values of the Spherical Poisson Integral
Authors: Dzagnidze O. 
Published: February 2021

Abstract
A formula of a radial derivative is obtained with the aid of derivatives with respect to θ and to φ of the functions closely connected with the spherical Poisson integral 𝑢f
(r, θ, φ) and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates , and .
On Some Entire Modular Forms of an Integral Weight for the Congruence Subgroup Γ0(4𝑁)
Authors: Lomadze G. 
Published: February 2021

Abstract
Four types of entire modular forms of weight are constructed for the congruence subgroup Γ0(4𝑁) when 𝑠 is even. One can find these forms helpful in revealing the arithmetical meaning of additional terms in the formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients in an even number of variables.
The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary
Authors: Basheleishvili M. 
Published: February 2021

Abstract
The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary value problem is proved for the split equation.
Proper Moving Average Representations and Outer Functions in Two Variables
Authors: Gawarecki L. , Mandrekar V. , Richard P. 
Published: February 2021

Abstract
In this work, we consider the problem of moving average representations for random fields. As in the Kolmogorov–Wiener case, such representations lead to interesting questions in harmonic analysis in the polydisc. In particular, we study outer functions with respect to half-space, semigroup and quarterplane and their interrelations.
Probability Measures with Big Kernels
Authors: Tien Nguyen Duy , Tarieladze V. 
Published: February 2021

Abstract
It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [Kernel associated with a cylindrical measure, Springer-Verlag, 1981, p. 69] is solved by proving that the annihilator of the kernel of a measure μ coincides with the annihilator of μ if and only if the topology of μ-convergence in the dual space is essentially dually separated.
On the ξ-Exponentially Asymptotic Stability of Linear Systems of Generalized Ordinary Differential Equations
Authors: Ashordia M. , Kekelia N. 
Published: February 2021

Abstract
Necessary and sufficient conditions and effective sufficient conditions are established for the so-called ξ-exponentially asymptotic stability of the linear system
𝑑𝑥(𝑡) = 𝑑𝘈(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡),
where and are respectively matrix- and vector-functions with bounded variation components, on every closed interval from [0, +∞[ and ξ : [0, +∞[ → [0, +∞[ is a nondecreasing function such that .
Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity
Authors: Bitsadze L. 
Published: February 2021

Abstract
The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary value problems of electroelasticity are proved and the symbolic matrix is calculated. The uniqueness and existence theorem for the basic BVPs of electroelasticity are given.
Existence and Properties of ℎ-Sets
Authors: Bricchi Michele 
Published: February 2021

Abstract
In this note we shall consider the following problem: which conditions should satisfy a function ℎ : (0, 1) → ℝ in order to guarantee the existence of a (regular) measure μ in with compact support and

for some positive constants 𝑐2, and 𝑐2 independent of γ ∈ Γ and 𝑟 ∈ (0,1)? The theory of self-similar fractals provides outstanding examples of sets fulfilling (♡) with ℎ(𝑟) = 𝑟𝑑, 0 ≤ 𝑑 ≤ 𝑛, and a suitable measure μ. Analogously, we shall rely on some recent techniques for the construction of pseudo self-similar fractals in order to deal with our more general task.
Solution of a Linear Integral Equation of Third Kind
Authors: Shulaia D. 
Published: February 2021

Abstract
The aim of this paper is to study, in the class of Hölder functions, a nonhomogeneous linear integral equation with coefficient cos 𝑥. Necessary and sufficient conditions for the solvability of this equation are given under some assumptions on its kernel. The solution is constructed analytically, using the Fredholm theory and the theory of singular integral equations.
On an Optimal Decomposition in Zygmund Spaces
Authors: Fiorenza Alberto , Krbec Miroslav 
Published: February 2021

Abstract
An optimal decomposition formula for the norm in the Orlicz space 𝐿(log 𝐿)
α
is given. New proofs of some results involving 𝐿(log 𝐿)
α
spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes.
On A Generalization of the Dirichlet Integral
Authors: Chantladze T. , Kandelaki N. , Lomtatidze A. , Ugulava D. 
Published: February 2021

Abstract
Using the theory of spline functions, we investigate the problem of minimization of a generalized Dirichlet integral

where Ω is a bounded domain of an 𝑛-dimensional Euclidean space 𝑅𝑛, λ ≥ 0 is a fixed number, and 𝑢𝑥𝒊
is a generalized according to Sobolev with respect to 𝑥𝒊 derivative of the function 𝑢 defined on Ω. Minimization is realized with respect to the functions 𝑢 whose boundary values on Γ form a preassigned function, and for them 𝐹λ(𝑢) is finite.
On Ideals with Projective Bases
Authors: Cichoń J. , Kharazishvili A. 
Published: February 2021

Abstract
A theorem concerning some descriptive properties of σ-ideals and generalizing the main result of [Brzuchowski, Cichoń, Grzegorek, and Ryll-Nardzewski, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27: 447–448, 1979] is proved. Various applications of this theorem are also presented.
On Intersections of Small Perfect Sets
Authors: Fast H. 
Published: February 2021

Abstract
For a not empty perfect subset of the unit circle C there is a perfect subset of C measure zero which being rotated to every position intersects the first set on a nonempty perfect set. This result may be stated in terms of set of distances between pairs of points from these two sets.
A generalization of this result to a product of tori is suggested.
Cesàro Means of Trigonometric Fourier Series
Authors: Goginava U. 
Published: February 2021

Abstract
L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿𝑝-deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛
α
𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.
On the Uniqueness Property for Products of Symmetric Invariant Probability Measures
Authors: Kharazishvili A. 
Published: February 2021

Abstract
Two symmetric invariant probability measures μ
1 and μ
2 are constructed such that each of them possesses the strong uniqueness property but their product μ
1 × μ
2 turns out to be a symmetric invariant probability measure without the uniqueness property.
Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
Authors: Chkadua O. 
Published: February 2021

Abstract
Spatial boundary value problems of statics of couple-stress elasticity for anisotropic homogeneous media (with contact on a part of the boundary) with an open crack are studied supposing that one medium has a smooth boundary and the other one has an open crack.
Using the method of the potential theory and the theory of pseudodifferential equations on manifolds with boundary, the existence and uniqueness theorems are proved in Besov and Bessel-potential spaces. The smoothness and a complete asymptotics of solutions near the contact boundaries and near crack edge are studied.
Properties of exponents of the first terms of the asymptotic expansion of solutions are established. Classes of isotropic, transversally-isotropic and anisotropic bodies are found, where oscillation vanishes.
First Order Partial Functional Differential Equations with Unbounded Delay
Authors: Kamont Z. , Kozieł S. 
Published: February 2021

Abstract
The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.
On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
Authors: Kondrat'ev V. A. , Nikishkin V. A. 
Published: February 2021

Abstract
Two terms of asymptotics near crack are obtained for solutions of the Dirichlet boundary value problem for second-order elliptic equations in divergent form. The front of a crack is from 𝐶1+𝑠 and the coefficients of the equations belong to 𝐶𝑠 (0.5 < 𝑠 < 1).
On Faces of a Convex Polyhedron in 𝐑3 With a Small Number of Sides
Authors: Kharazishvili A. 
Published: February 2021

Abstract
For any convex polyhedron 𝑃 ⊂ 𝐑3 and for any natural number 𝑘, let 𝐹𝑘(𝑃) denote the number of all faces of 𝑃 with exactly 𝑘 sides. It is well known that 𝐹𝑘(𝑃) ≥ 2 for at least one 𝑘. We consider the question whether 𝐹𝑘(𝑃) ≥ 3, for at least one 𝑘, and present a solution to it. Some related questions are also discussed.
Investigation of a Basic Plane Interface Problem of Statics for Elastic Mixtures
Authors: Svanadze K. 
Published: February 2021

Abstract
The two-dimensional interface problem of statics of elastic mixtures is investigated when differences between displacement vectors and stress vectors are given on the contact curve.
For this problem special potentials with complex densities are constructed and by means of them the contact problem is reduced to a system of integral equations of Fredholm type. Analysis of the equations obtained is given.
On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with 𝑝-Orthogonal Summands. Correction
Authors: Rosalsky Andrew , Volodin Andrei I. 
Published: February 2021

Abstract
A result by Móricz, Su, and Taylor from Acta Math. Hungar.
65(1994), 1–16, was misstated in the authors' paper in Georgian Math. J.
8(2001), No. 2, 377–388, where due to this misstatement the invalid formulation and proof of a corollary is given. In this correction note, the needed result is correctly stated and a corrected version of the invalid corollary is proved.
On Homogeneous Coverings of Euclidean Spaces
Authors: Kharazishvili A. 
Published: February 2021

Abstract
The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction.
Multiplication Operators and Dynamical Systems on Weighted Locally Convex Spaces of Holomorphic Functions
Authors: Manhas J. S. 
Published: February 2021

Abstract
Let 𝐺 be an open subset of ℂ and let 𝑉 be an arbitrary system of weights on 𝐺. Let 𝐻𝑉𝑏(𝐺) and 𝐻𝑉0(𝐺) be the weighted locally convex spaces of holomorphic functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present article, we characterize the analytic functions inducing multiplication operators and invertible multiplication operators on the spaces 𝐻𝑉𝑏(𝐺) and 𝐻𝑉0(𝐺) for different systems of weights 𝑉 on 𝐺. A (linear) dynamical system induced by multiplication operators on these spaces is obtained as an application of the theory of multiplication operators.
Asymptotic Behavior of Generalized Nonexpansive Sequences and Mean Points
Authors: Pathak H. K. , O'Regan D. , Khan M. S. , Agarwal R. P. 
Published: February 2021

Abstract
Let 𝐸 be a real Banach space with norm ‖ · ‖ and let {𝑥𝑛}𝑛≥0 be a generalized nonexpansive sequence in 𝐸 (i.e., ‖ 𝑥𝑖+1 – 𝑥𝑗+1 ‖2 ≤ ‖𝑥𝑖 – 𝑥𝑗‖2 + (ε(𝑖+1, 𝑗+1) – ε(𝑖, 𝑗))2 for all 𝑖, 𝑗 ≥ 0, where the series of nonnegative terms is convergent). Let . We deal with the mean point of concerning a Banach limit μ. If 𝐸 is reflexive and 𝑑 = 𝑑(0, 𝐾), then we show that and there exists a point 𝑧0 with ‖ 𝑧0 ‖= 𝑑 such that . In the sequel, this result is applied to obtain the weak and strong convergence of .
On Nonnegative Solutions of a Certain Nonlocal Boundary Value Problem for Second Order Linear Functional Differential Equations
Authors: Vodstrčil P. 
Published: February 2021

Abstract
On the interval [𝑎, 𝑏], we consider the boundary value problem

where ℓ : 𝐶([𝑎, 𝑏]; ℝ) → 𝐿([𝑎, 𝑏]; ℝ), 𝑞 ∈ 𝐿([𝑎, 𝑏]; ℝ), and 𝑡0 ∈]𝑎, 𝑏[.
The question on the existence and uniqueness of a nonnegative solution of this problem is studied.
Mappings Confluent over Locally Connected Continua
Authors: Charatonik J. J. 
Published: February 2021

Abstract
A mapping is said to be confluent over locally connected continua if for each locally connected subcontinuum 𝑄 of the range each component of its preimage is mapped onto 𝑄. For mappings of compact spaces this class is a very natural generalization of locally confluent mappings. Various properties of these mappings are systematically studied in the paper.
On Hyers–Ulam Stability of Cauchy and Wilson Equations
Authors: Elqorachi Elhoucien , Akkouchi Mohamed 
Published: February 2021

Abstract
We study the Hyers–Ulam stability problem for the Cauchy and Wilson integral equations

where 𝐺 is a topological group, 𝑓, 𝑔 : 𝐺 → ℂ are continuous functions, μ is a complex measure with compact support and σ is a continuous involution of 𝐺. The result obtained in this paper are natural extensions of the previous works concerning the Hyers–Ulam stability of the Cauchy and Wilson functional equations done in the particular case of μ=δe
: The Dirac measure concentrated at the identity element of 𝐺.
Minimal Free Multi-Models for Chain Algebras
Authors: Huebschmann J. 
Published: February 2021

Abstract
Let 𝑅 be a local ring and 𝐴 a connected differential graded algebra over 𝑅 which is free as a graded 𝑅-module. Using homological perturbation theory techniques, we construct a minimal free multi-model for 𝐴 having properties similar to those of an ordinary minimal model over a field; in particular the model is unique up to isomorphism of multialgebras. The attribute ‘multi’ refers to the category of multicomplexes.
On the Method of Direct Products in the Theory of Quasi-Invariant Measures
Authors: Kirtadze A. 
Published: February 2021

Abstract
For invariant (quasi-invariant) σ-finite measures on an uncountable group (𝐺, ·), the behaviour of small sets with respect to the operation “·” is studied. Some classes of non-commutative groups (𝐺, ·) are discussed especially, by using a representation of the original group in the form of a direct product of its two subgroups, one of which is commutative.
On Absolutely Negligible Sets in Uncountable Solvable Groups
Authors: Kharazishvili Alexander 
Published: February 2021

Abstract
Absolutely negligible sets in uncountable groups are considered in connection with the measure extension problem (for σ-finite invariant or quasi-invariant measures). In particular, it is proved that, for any uncountable solvable group (𝐺, ·), there exists a countable covering of 𝐺 consisting of 𝐺-absolutely negligible sets.
On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
Authors: Padhi Seshadev 
Published: February 2021

Abstract
Sufficient conditions in terms of coefficient functions have been obtained so that all nonoscillatory solutions along with their first and second derivatives of the third order delay differential equation
𝑦‴(𝑡) + 𝑎(𝑡)𝑦″(𝑡) + 𝑏(𝑡)𝑦′(𝑡) + 𝑐(𝑡)𝑦(𝑔(𝑡)) = 0
tend to zero as 𝑡 → ∞.
Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains
Authors: Hussain Nawab , O'Regan Donal , Agarwal Ravi P. 
Published: February 2021

Abstract
We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.
Generalized Derivation and Double Operator Integrals
Authors: Mecheri Salah 
Published: February 2021

Abstract
Let 𝐻 be a separable infinite dimensional complex Hilbert space, and let 𝔹(𝐻) denote the algebra of all bounded linear operators on 𝐻. Let 𝐴, 𝐵 be operators in 𝔹(𝐻). We define the generalized derivation δ
𝐴, 𝐵 : 𝔹(𝐻) ↦ 𝔹(𝐻) by δ
𝐴, 𝐵(𝑋) = 𝐴𝑋 – 𝑋𝐵. In this paper we consider the question posed by Turnsek [Publ. Math. Debrecen 63: 293–304, 2003], when ? We prove that this holds in the case where 𝐴 and 𝐵 satisfy the Fuglede–Putnam theorem. Finally, we apply the obtained results to double operator integrals.
Oscillation and Nonoscillation Theorems for Superlinear Emden–Fowler Equations of even Order
Authors: Wong James S. W. , Ou C. H. 
Published: February 2021

Abstract
We study the existence of oscillatory solutions of the even order superlinear ordinary differential equations

where 𝑛 is an even integer ≥ 2, α > 1 and 𝑝(𝑡) ∈ 𝐶[𝑡0, ∞), 𝑡0 > 0 and 𝑝(𝑡) > 0. When 𝑛 = 2, our results reduce to those of Jasny and Kurzweil, and Erbe and Muldowney for (). When 𝑛 = 4, our result becomes that of Kura for equation (). We present here new techniques suitable for the study of oscillation and nonoscillation of solutions of the general equations of even order () and ().
On Decompositions of a Cube into Cubes and Simplexes
Authors: Kharazishvili Alexander 
Published: February 2021

Abstract
Some combinatorial results concerning finite decompositions (dissections) of a 𝑘-dimensional cube into cubes (respectively, simplexes) of the same dimension are presented in the paper. In connection with such decompositions, the notion of a decomposability number is introduced and the problem of description of all these numbers is discussed.
A Positive Answer to Velichko's Question
Authors: Li Jinjin , Li Zhaowen 
Published: February 2021

Abstract
We give positive answer to Velichko's question in which the quotient and 𝑠-map is replaced by a sequence-covering and 𝑐𝑠-map. In addition, let 𝑋 have a star-countable 𝑘-network, then 𝑋 is a sequence-covering and 𝑐𝑠-image of a locally separable metric space if and only if 𝑋 is a sequencecovering and 𝑐𝑠-image of a metric space.
Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
Authors: Amroun Nour-Eddine , Benaissa Abbes 
Published: February 2021

Abstract
We consider the nonlinearly damped semilinear Petrovsky equation

and prove the global existence of its solutions by means of the stable set method in combined with the Faedo–Galerkin procedure. Furthermore, we study the asymptotic behavior of solutions when the nonlinear dissipative term 𝑔 does not necessarily have a polynomial growth near the origin.
Curves with Two Pencils and Associated Maps to Projective Spaces
Authors: Ballico Edoardo 
Published: February 2021

Abstract
Let 𝑋 be a smooth and connected projective curve. Assume the existence of spanned 𝐿 ∈ Pic𝑎(𝑋), 𝑅 ∈ Pic𝑏(𝑋) such that ℎ0(𝑋, 𝐿) = ℎ0(𝑋, 𝑅) = 2 and the induced map ϕ
𝐿,𝑅 : 𝑋 → 𝐏1 × 𝐏1 is birational onto its image. Here we study the following question. What can be said about the morphisms β : 𝑋 → 𝐏𝑅 induced by a complete linear system |𝐿⊗𝑢⊗𝑅⊗𝑣| for some positive 𝑢, 𝑣? We study the homogeneous ideal and the minimal free resolution of the curve β(𝑋).
On the Convergence of Conjugate Trigonometric Polynomials
Authors: Gogoladze Larry 
Published: February 2021

Abstract
Sufficient conditions are found, under which for 𝑓 ∈ 𝐶([–π, π]) or 𝑓 ∈ 𝐿([–π, π]) the convergence of a sequence of trigonometric polynomials in the norms of these spaces implies the convergence of their conjugates in the same norms.
Principal Maps in Triangulated Categories and Maps between 2-Stage Spectra
Authors: Baues Hans Joachim 
Published: February 2021

Abstract
Using two natural axioms on track triangles in triangulated track category we show that the mapping cone construction is functorial, i.e., principal maps between mapping cones in a triangulated category can be identified with the homotopy classes of homotopy pairs. This result is applied to obtain an algebraic model of the category of principal maps between 2-stage spectra.
On the Lacunarity of Two-Eta-Products
Authors: Cooper Shaun , Gun Sanoli , Ramakrishnan B. 
Published: February 2021

Abstract
We classify all lacunary modular forms corresponding to the two-eta-products η
𝑟(𝑧)η
𝑠(𝑚𝑧) for 𝑚 = 3, 4, 5, where 𝑟 + 𝑠 is even and 𝑟𝑠 ≠ 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product η
𝑟(𝑧)η
𝑠(𝑚𝑧), 𝑚 ≥ 4.
Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
Authors: Gilbert Robert , Ou Miao-Jung 
Published: February 2021

Abstract
In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller [Exact and asymptotic representations of the sound field in a stratified ocean, Springer, 1977]. The relation between the constructed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be generalized for an N-layer waveguide.
Solution of a Goursat Problem in Optimal Domains
Authors: Tutschke Wolfgang 
Published: February 2021

Abstract
In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive the greater the chosen subset of the function space. The problem is to find an optimal subset leading to a domain of existence for the desired solution being as large as possible. The present paper will discuss this question for a Goursat problem.