bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Remarks on Fractals Generated by a Sequence of Finite Systems of Contractions
Authors: Follo Giorgio 
Published: February 2021

Abstract
We generalize some results shown by J. E. Hutchinson in [Indiana Univ. Math. J. 30: 713–747, 1981].
Let be finite systems of contractions on a complete metric space; then, under some conditions on (𝔉𝑛), there exists a unique non-empty compact set 𝐾 such that the sequence defined by ((𝔉1 ○ 𝔉2 ○ ⋯ ○ 𝔉𝑛)(𝐶)) converges to 𝐾 in the Hausdorff metric for every non-empty closed and bounded set 𝐶.
If the metric space is also separable and for every there are real numbers strictly between 0 and 1, satisfying the condition , then there exists a unique probability Radon measure μ
𝐾 such that the sequence

weakly converges to μ
𝐾 for every probability Borel regular measure ν with bounded support (where by we denote the image measure of ν under a contraction 𝑓). Moreover, 𝐾 is the support of μ
𝐾.
On Homomorphisms, Open Operators and their Adjoints
Authors: Zarnadze D. 
Published: February 2021

Abstract
The well-known A. Grothendieck's theorem on a homomorphism between locally convex spaces is generalized to the case of topologies which are incompatible with dualities. On the basis of this theorem, necessary and sufficient conditions are obtained for a weak homomorphism (resp. its adjoint operator, resp. its double adjoint operator) to be again a homomorphism in various topologies of the initial (resp. dual, resp. bidual) spaces. Some new classes of pairs of locally convex spaces satisfying these conditions are established. The results obtained have enabled us to reveal new properties of frequently encountered homomorphisms and weakly open operators, as well as to strengthen and generalize some well-known results.
Characteristic Functions and s-Orthogonality Properties of Chebyshev Polynomials of Third and Fourth Kind
Authors: Martinelli Maria Renata 
Published: February 2021

Abstract
The properties of two families of s-orthogonal polynomials, which are connected with Chebyshev polynomials of third and fourth kind, are studied. Evaluations of the remainders are given and asymptotic formulae are calculated for the corresponding hyper-Gaussian formulae used for an approximate estimation of integrals.
Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence
Authors: Bychowska A. 
Published: February 2021

Abstract
We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.
Holomorphic Framings for Projections in A Banach Algebra
Authors: Dupré Maurice J. , Glazebrook James F. 
Published: February 2021

Abstract
Given a complex Banach algebra, we consider the Stiefel bundle relative to the similarity class of a fixed projection. In the holomorphic category the Stiefel bundle is a holomorphic locally trivial principal bundle over a certain Grassmann manifold. Our main application concerns the holomorphic parametrization of framings for projections. In the spatial case this amounts to a holomorphic parametrization of framings for a corresponding complex Banach space.
On A Multiplicativity up to Homotopy of the Gugenheim Map
Authors: Kharebava Z. 
Published: February 2021

Abstract
In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ
𝑖} : 𝐴* → 𝐶* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐵𝐴*, dBA
, Δ,) and (𝐵𝐶*, dBC*
, Δ,) carry multiplications. We show that the Gugenheim's map
𝐵{ρ
𝑖} : (𝐵𝐴*, dBA*
, Δ,) → (𝐵𝐶*, dBC*
, Δ,)
is multiplicative up to homotopy with respect to these structures.
On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
Authors: Bakhia I. 
Published: February 2021

Abstract
Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.
On the Uniform Convergence and 𝐿-Convergence of Double Fourier Series with Respect to the Walsh–Kaczmarz System
Authors: Goginava U. 
Published: February 2021

Abstract
In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces 𝐶 and 𝐿. From our results we obtain different criteria of the uniform convergence and 𝐿-convergence of a double Fourier–Kaczmarz series.
General 𝑀-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique
Authors: Lazrieva N. , Toronjadze T. 
Published: February 2021

Abstract
A multidimensional parametric filtered statistical model is considered, the notions of the regularity and ergodicity of the model, as well as the notion of a general 𝑀-estimator are studied. A skew projection technique is proposed, by which we construct an 𝑀-estimator of the parameter of interest in the presence of nuisance parameters, which is asymptotically normal with the zero mean and the same covariance matrix as the corresponding block of the asymptotic covariance matrix of the full parameter's 𝑀-estimator.
On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
Authors: Shervashidze T. 
Published: February 2021

Abstract
We discuss an application of an inequality for the modulus of the characteristic function of a system of monomials in random variables to the convergence of the density of the corresponding system of the sample mixed moments. Also, we consider the behavior of constants in the inequality for the characteristic function of a trigonometric analogue of the above-mentioned system when the random variables are independent and uniformly distributed. Both inequalities were derived earlier by the author from a multidimensional analogue of Vinogradov's inequality for a trigonometric integral. As a byproduct the lower bound for the spectrum of is obtained, where 𝐴𝑘 is the matrix of coefficients of the first 𝑘 + 1 Chebyshev polynomials of first kind.
Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data
Authors: Chudinovich Igor , Constanda Christian 
Published: February 2021

Abstract
The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.
The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
Authors: Kokilashvili V. , Paatashvili V. 
Published: February 2021

Abstract
We investigate the Dirichlet problem in domains with nonsmooth boundaries when a boundary function belongs to functional classes of the Zygmund class type. A complete picture of solvability is established also in the case of existence of solutions for which explicit expressions are found.
On the Embedding Waterman, Chanturia and Generalized Wiener Classes in the Classes
Authors: Goginava U. 
Published: February 2021

Abstract
Chanturia, Wang and Akhobadze proved sufficient conditions for the inclusion of Chanturia, Waterman and Generalized Wiener classes, respectively, in the classes . In this paper we prove that these conditions are necessary for this inclusion to hold.
Nonlocal and Initial Problems for Quasilinear, Nonstrictly Hyperbolic Equations with General Solutions Represented by Superposition of Arbitrary Functions
Authors: Gvazava J. 
Published: February 2021

Abstract
We have selected a class of hyperbolic quasilinear equations of second order, admitting parabolic degeneracy by the following criterion: they have a general solution represented by superposition of two arbitrary functions. For equations of this class we consider the initial Cauchy problem and nonlocal characteristic problems for which sufficient conditions are established for the solution solvability and uniquness; the domains of solution definition are described.
On Superfluous Subsemimodules
Authors: Tuyen Nguyen Xuan , Thang Ho Xuan 
Published: February 2021

Abstract
This paper considers superfluous subsemimodules and some applications of them to projective covers of semimodules. The following notions are introduced: a superfluous ∧-subsemimodule, a 𝑘-quasiregular homomorphism, a radical of a ∧-semimodule, a projective cover, and a semiring satisfying the condition 0–1. We present some characteristic properties of superfluous subsemimodules and give some applications of them to projective covers of semimodules, analogous to applications of superfluous submodules to projective covers of modules.
On Entire Modular Forms of Half-Integral Weight on the Congruence Subgroup Γ0(4N)
Authors: Lomadze G. 
Published: February 2021

Abstract
Some entire modular forms of weight on the congruence subgroup Γ0(4N) are constructed if s is odd > 11. The constructed type of entire modular forms is useful for revealing the arithmetical meaning of additional terms in formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients if the number s of variables is odd > 11.
On the Equivalence between Ch and The Existence of Certain I-Luzin Subsets of ℝ
Authors: Zoli Enrico 
Published: February 2021

Abstract
We extend Rothberger's theorem (on the equivalence between CH and the existence of Luzin and Sierpiński-sets having power 𝔠) and certain paradoxical constructions due to Erdös. More precisely, by employing a suitable σ-ideal associated to the (α, β)-games introduced by Schmidt, we prove that the Continuum Hypothesis holds if and only if there exist subgroups of (ℝ, +) having power 𝔠 and intersecting every “absolutely losing” (respectively, every meager and null) set in at most countably many points.
Projective Bundles on Infinite-Dimensional Complex Spaces
Authors: Ballico E. 
Published: February 2021

Abstract
Let V be a complex localizing Banach space with countable unconditional basis and E a rank r holomorphic vector bundle on P(V). Here we study the holomorphic embeddings of P(E) into products of projective spaces and the holomorphic line bundles on P(E). In particular we prove that if r ≥ 3, then H
1(P(E), L) = 0 for every holomorphic line bundle L on P(E).
Strong Homology Theories as Localizations
Authors: Bauer F. W. 
Published: February 2021

Abstract
Let 𝔎 be a category of pairs of spaces, 𝔏 ⊂ 𝔎 the category of pairs of ANRs or CW-spaces, 𝐴∗ a chain functor (e.g., one associated with a spectrum). Then the derived homology 𝑠ℎ∗ of the 𝔏-localization of 𝐴∗ is the strong homology theory on 𝔎 which is up to an isomorphism uniquely determined by the fact that 𝑠ℎ∗ | 𝔏 agrees with the derived homology of 𝐴∗ on 𝔏. This establishes a relationship between localization theory and strong homology theory (e.g., Steenrod–Sitnikov homology theory, whenever all pairs are compact metric).
Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
Authors: Huang Jui-Chi 
Published: February 2021

Abstract
Let 𝐸 be a uniformly convex Banach space which satisfies Opial's condition or its dual 𝐸* has the Kadec–Klee property, 𝐶 a nonempty closed convex subset of 𝐸, and 𝑇𝑗 : 𝐶 → 𝐶 an asymptotically nonexpansive mapping for each 𝑗 = 1, 2, . . . , 𝑟. Suppose {𝑥𝑛} is generated iteratively by

where 𝑈𝑛(0) = 𝐼, 𝐼 is the identity map and {α
𝑛(𝑗)} is a suitable sequence in [0, 1]. If the set of common fixed points of is nonempty, then weak convergence of {𝑥𝑛} to some is obtained.
Integrability and L
1-Convergence of Modified Sine Sums
Authors: Kaur Kulwinder , Bhatia S. S. , Ram Babu 
Published: February 2021

Abstract
New modified sine sums are introduced and a criterion for the L
1-convergence of these modified sine sums under a new class K is obtained. Also a necessary and sufficient condition for the L
1-convergence of the cosine series is deduced as a corollary.
The Non-Vanishing of First Cohomology Groups for Certain Infinite-Dimensional Complex Manifolds
Authors: Ballico E. 
Published: February 2021

Abstract
Here, using the ideas of an old paper by S. Dineen (An. Acad. Brasil. Ci. 48: 11–12, 1976), we give large classes of pairs (𝑋, 𝐸) such that 𝑋 is an infinite-dimensional complex space very far from a Banach manifold, 𝐸 is a holomorphic vector bundle on 𝑋 and 𝐻1(𝑋,𝐸) is infinite-dimensional.
Postnikov “Invariants” in 2004
Authors: Rubio Julio , Sergeraert Francis 
Published: February 2021

Abstract
The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the Postnikov “invariants” will be actual invariants only when an arithmetical decision problem – currently open – will be solved; it is even possible this problem is undecidable.
On a Boundary Value Problem for 𝑛-th Order Linear Functional Differential Systems
Authors: Hakl Robert , Mukhigulashvili Sulkhan 
Published: February 2021

Abstract
In this paper, theorems on the Fredholm alternative and wellposedness of the linear boundary value problem
𝑢′(𝑡) = ℓ(𝑢)(𝑡) + 𝑞(𝑡), ℎ(𝑢) = 𝑐,
where ℓ : 𝐶([𝑎, 𝑏]; 𝑅𝑛) → 𝐿([𝑎, 𝑏]; 𝑅𝑛) and ℎ : 𝐶([𝑎, 𝑏]; 𝑅𝑛) → 𝑅𝑛 are linear bounded operators, 𝑞 ∈ 𝐿([𝑎, 𝑏]; 𝑅𝑛), and 𝑐 ∈ 𝑅𝑛, are established even when ℓ is not a strongly bounded operator.
Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium
Authors: Kumar Rajneesh , Choudhary Suman 
Published: February 2021

Abstract
The present study is concerned with the plane strain problem in homogeneous orthotropic micropolar viscoelastic solid. The disturbance due to the time harmonic concentrated source is investigated by employing the eigenvalue approach. Integral transforms have been inverted by a numerical technique to obtain the components of displacement, force stress and couple stress in the physical domain. The results obtained are given and illustrated graphically.
Boundary Regularity for Capillary Surfaces
Authors: Liang Fei-Tsen 
Published: February 2021

Abstract
For solutions of capillarity problems with the boundary contact angle being bounded away from 0 and π and the mean curvature being bounded from above and below, we show the Lipschitz continuity of a solution up to the boundary locally in any neighborhood in which the solution is bounded and ∂Ω is 𝐶2; the Lipschitz norm is determined completely by the upper bound of | cos θ|, together with the lower and upper bounds of 𝐻, the upper bound of the absolute value of the principal curvatures of ∂Ω and the dimension 𝑛.
On a Generalized Wilson Functional Equation
Authors: Badora Roman 
Published: February 2021

Abstract
We solve the functional equation

where 𝐺 is a locally compact Abelian group, {𝑘0 = 𝑖𝑑𝐺, 𝑘1, . . . , 𝑘𝑁–1} is a finite group of continuous automorphisms of 𝐺, 𝑓 is a bounded continuous complex-valued function on 𝐺 and 𝑔 is an almost periodic function on 𝐺.
Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
Authors: Dinu Teodora-Liliana 
Published: February 2021

Abstract
We establish the existence of an entire solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof is based on the critical point theory in the sense of Clarke and we apply the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz [Z. Angew. Math. Phys. 43: 270–291, 1992] on the existence of entire solutions of the nonlinear Schrödinger equation.
Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
Authors: Henderson Johnny , Ma Ding 
Published: February 2021

Abstract
Uniqueness implies existence results are obtained for solutions of the fourth order ordinary differential equation, 𝑦(4) = 𝑓(𝑥, 𝑦, 𝑦′, 𝑦″, 𝑦‴), satisfying 5-point, 4-point and 3-point nonlocal boundary conditions.
New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
Authors: Hytönen Tuomas , Kaiser Cornelia 
Published: February 2021

Abstract
We give a new proof of the 𝑇(1) theorem for reflexive homogeneous Triebel–Lizorkin spaces , which uses neither maximal functions nor atomic decompositions. The substitute tool is an estimate on translations in the 𝐿𝑝(ℓ𝑞) spaces.
Fourier Series with Small Gaps
Authors: Vyas Rajendra G. 
Published: February 2021

Abstract
Let 𝑓 be a 2π-periodic function in 𝐿1[–π, π] and be its lacunary Fourier series with small gaps. We have estimated Fourier coefficients of 𝑓 if it is of φ∧ 𝐵𝑉 locally. We have also obtained a precise interconnection between the lacunarity in such series and the localness of the hypothesis to be satisfied by the generic function which allows us to the interpolate the results concerning lacunary series and non-lacunary series.
Finitely Generated Modules and Connectivity
Authors: Ansari-Toroghy Habibollah , Ovlyaee-Sarmazdeh Reza 
Published: February 2021

Abstract
Let 𝑅 be a commutative Noetherian ring and let 𝑀 be a finitely generated 𝑅-module. Let 𝑋 = Spec𝑅(𝑀) be the topological space with Zariski topology. Our main goal in this paper is to describe the connectedness dimension of 𝑅 in terms of Krull dimension of some quotient of 𝑀 and prove that 𝑐(Spec𝑅(𝑀)) = 𝑐(Supp(𝑀)).
New Estimates of the Singular Series Corresponding to Positive Quaternary Quadratic Forms
Authors: Gogishvili Guram 
Published: February 2021

Abstract
Let 𝑚 ∈ ℕ, 𝑓 be a positive definite, integral, primitive, quaternary quadratic form of the determinant 𝑑 and let ρ(𝑓,𝑚) be the corresponding singular series.
When studying the best estimates for ρ(𝑓,𝑚) with respect to 𝑑 and 𝑚 we proved in [Gogishvili, Trudy Tbiliss. Univ. 346: 72–77, 2004] that

where 𝑏(𝑘) is the product of distinct prime factors of 16𝑘 if 𝑘 ≠ 1 and 𝑏(𝑘) = 3 if 𝑘 = 1.
The present paper proves a more precise estimate

where 𝑑 = 𝑑0𝑑1, if 𝑝 > 2; 𝑕(2) ⩾ –4.
The last estimate for ρ(𝑓,𝑚) as a general result for quaternary quadratic forms of the above-mentioned type is unimprovable in a certain sense.
Quadratic Envelope of the Category of Class Two Nilpotent Groups
Authors: Jibladze Mamuka , Pirashvili Teimuraz 
Published: February 2021

Abstract
Using quadratic maps we define a category Niq with objects class two nilpotent groups. Hom's in this category are groups and we investigate functoriality properties of this group. The classification problem in Niq is reduced to a certain linear problem.
On the Eisenstein Series Corresponding to Quadratic Forms of Certain Type
Authors: Kachakhidze Nikoloz 
Published: February 2021

Abstract
The Eisenstein series corresponding to quadratic forms of type (𝑓/2, 4𝑁, χ) (𝑁 is a square-free natural number) are constructed using the bases of the spaces of Eisenstein series given in [Kachakhidze, Georgian Math. J. 13: 55–78, 2006].
Some Properties of the Inversion Counting Function
Authors: Robbins Neville 
Published: February 2021

Abstract
Let 𝑕, 𝑘 be integers such that 0 < 𝑕 < 𝑘 and (𝑕, 𝑘) = 1. If 1 ≤ 𝑖 ≤ 𝑘 – 1, let 𝑟𝑖 be the least positive residue (mod 𝑘) of 𝑕𝑖. Let the permutation

For 1 ≤ 𝑖 < 𝑗 ≤ 𝑘 – 1, if 𝑟𝑖 > 𝑟𝑗, this is called an inversion of σ
𝑕, 𝑘. Let 𝐼(𝑕, 𝑘) denote the total number of inversions of σ
𝑕, 𝑘. In this note, we prove several identities concerning 𝐼(𝑕, 𝑘).
The Cauchy Transform for the Hodge/De Rham System and Some of its Properties
Authors: Abreu-Blaya Ricardo , Bory-Reyes Juan , Shapiro Michael 
Published: February 2021

Abstract
We study the analogue of the Cauchy transform for the theory of solutions of the Hodge/de Rham system in the case of a rectifiable surface of integration which additionally satisfies an Ahlfors/David regularity condition and we prove the Cauchy integral formula, the Plemelj/Privalov theorem and the Sokhotski/Plemelj theorem for it, as well as the necessary and sufficient condition for the possibility to extend a given 𝑘-form from such a surface to a harmonic 𝑘-form in the domain. A formula for the square of the singular Cauchy transform is given. The proofs of all these facts are based on a close relation between algebra-valued null-solutions of the Dirac operator in the Euclidean space and hyperholomorphic functions of Clifford analysis.
An Example of Fractal Singular Homogenization
Authors: Mosco Umberto , Vivaldi Maria Agostina 
Published: February 2021

Abstract
We construct a sequence of quadratic weighted energy forms in an open domain of the plane, that 𝑀-converges to an energy form with a singular fractal term. The weights belong to the Muckenoupt class 𝐴2 and have pointwise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.
Explicit Bounds for Composition Operators Preserving BMO(ℝ)
Authors: Alberico Teresa , Corporente Rossella , Sbordone Carlo 
Published: February 2021

Abstract
We improve a recent result of Y. Gotoh [Pacific J. Math 201: 289-307, 2001] who has established a precise relation between the constants in P. W. Jones theorem [Ark. Mat. 21: 229-231, 1983] about homeomorphisms of the line preserving BMO. We also give an explicit bound for a distance to L
∞ after composition.
The Growth Condition Guaranteeing Small Solutions for a Linear Oscillator with an Increasing Elasticity Coefficient
Authors: Hatvani László 
Published: February 2021

Abstract
The second order linear differential equation

is considered, where 𝑞 : [0, ∞) → (0, ∞) is continuous, piecewise continuously differentiable, non-decreasing, and lim𝑡→∞ 𝑞(𝑡) = ∞. A solution 𝑥0 is called small if lim𝑡→∞ 𝑥0(𝑡) = 0. It is known that the equation always has at least one nontrivial small solution, but, in general, it can have also solutions not small. The Armellini–Tonelli–Sansone Theorem says that if the function 𝑞 grows “regularly” in some sense, then all solutions are small. A generalization of this growth condition is given in terms only of the integral of 𝑞 and . It is proved that the result is a real generalization of the earlier theorems.
On Wiener's Criterion for an Elliptic Equation with Nonuniform Degeneration
Authors: Amanov Rabil A. , Mamedov Farman I. 
Published: February 2021

Abstract
For some class of nonuniformly degenerated elliptic equations of second order, a necessary and sufficient condition for boundary points to be regular is found. This condition is an analogue of Wiener's criterion for the Laplace equation.
Positive Solutions for Neutral Difference Equations with Continuous Arguments
Authors: Li Xianyi 
Published: February 2021

Abstract
Some “sharp” conditions are established for a kind of linear neutral difference equations with continuous arguments not to possess eventually positive solutions. The existence and asymptotic behavior are obtained for positive solutions of the kind of equations. The results for linear cases are further extended to nonlinear ones. A comparison principle, which is a necessary and sufficient condition, for linear equations not to possess eventually positive solutions is also presented.