bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Strong Differentiation of Multiple Integrals along Different Frames
Authors: Oniani Giorgi 
Published: February 2021

Abstract
Let 𝐸 be a set consisting of rectangular frames in . The following question connected with one problem of A. Zygmund is studied in the paper: Does there exists a function the integral of which is: 1) non-differentiable almost everywhere in a strong sense along every frame from 𝐸, and 2) strongly differentiable along every frame not belonging to 𝐸? In particular, the question is solved on the existence of a non-empty set 𝐸 different from the set of all rectangular frames for which there is a function with the properties 1) and 2).
Wavelet Frames for Distributions in Anisotropic Besov Spaces
Authors: Haroske Dorothee D. , Tamási Erika 
Published: February 2021

Abstract
This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].
Preimages of Residual Sets of Continuous Functions under Operation of Superposition
Authors: Wachowicz Artur 
Published: February 2021

Abstract
Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets in 𝐶 under the operation of superposition Φ : 𝐶 × 𝐶* → 𝐶, Φ(𝑓, 𝑔) = 𝑓 ○ 𝑔. Their behaviour can be different. We show examples when the preimages of residual sets are nonresidual of second category, or even nowhere dense, and examples when the preimages of nontrivial residual sets are residual.
Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
Authors: Belarbi Abdelkader , Benchohra Mouffak , Dhage Bapurao C. 
Published: February 2021

Abstract
In this paper, the existence of solutions and extremal solutions for a second order perturbed nonlinear boundary value problem with integral boundary conditions is proved under the mixed generalized Lipschitz and Carathéodory conditions.
On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)
Authors: Galewski Marek 
Published: February 2021

Abstract
We provide a generalized sufficient condition for the continuity of the Nemytskij operator between 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋). An example is given.
Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
Authors: Mező István 
Published: February 2021

Abstract
We rephrase Fridli's result [Fridli, Acta Math. Hungar. 45: 393–396, 1985] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [Gát, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 17: 161–169, 2001] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.
On BVPS for Strongly Elliptic Systems with Higher Order Boundary Conditions
Authors: Lanzara Flavia 
Published: February 2021

Abstract
We consider BVPs for strongly elliptic systems of order 2𝑙 with the boundary conditions of order 𝑙 + 𝑛, 𝑛 ⩾ 0. By representing the solution by means of a simple layer potential of order 𝑛 and by imposing the boundary conditions, we get a singular integral system which is of regular type if and only if the boundary operator satisfies the Lopatinskiĭ condition and which can be solved if suitable compatibility conditions are satisfied. An explicit formula for computing the index of the BVP is given.
Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance
Authors: Sadyrbaev Felix 
Published: February 2021

Abstract
Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.
Finite Dimensional Grading of the Virasoro Algebra
Authors: Hidalgo Rubén A. , Markina Irina , Vasil'ev Alexander 
Published: February 2021

Abstract
The Virasoro algebra is a central extension of the Witt algebra, the complexified Lie algebra of the sense preserving diffeomorphism group of the circle Diff 𝑆1. It appears in Quantum Field Theories as an infinite dimensional algebra generated by the coefficients of the Laurent expansion of the analytic component of the momentum-energy tensor, Virasoro generators. The background for the construction of the theory of unitary representations of Diff 𝑆1 is found in the study of Kirillov's manifold Diff 𝑆1=𝑆1. It possesses a natural Kählerian embedding into the universal Teichmüller space with the projection into the moduli space realized as an infinite-dimensional body of the coefficients of univalent quasiconformally extendable functions. The differential of this embedding leads to an analytic representation of the Virasoro algebra based on Kirillov's operators. In this paper we overview several interesting connections between the Virasoro algebra, Teichmüller theory, Löwner representation of univalent functions, and propose a finite-dimensional grading of the Virasoro algebra such that the grades form a hierarchy of finite dimensional algebras which, in their turn, are the first integrals of Liouville partially integrable systems for coefficients of univalent functions.
Complex Geometry of the Universal Teichmüller Space. II
Authors: Krushkal Samuel 
Published: February 2021

Abstract
We give an alternate and simpler proof of the important theorem stating that all invariant distances on the universal Teichmüller space 𝐓 coincide, and solve for 𝐓 the problem of Kra on isometric embeddings of a disk into Teichmüller spaces.
Stagnation Zones of 𝐴-Solutions
Authors: Miklyukov Vladimir M. 
Published: February 2021

Abstract
We investigate stagnation zones of solutions of partial differential elliptic equations. With the domain width being much less than its length and special boundary conditions, these solutions can be almost constant over large subdomains. Such domains are called stagnation zones (𝑠-zones). We estimate the size, the location of these 𝑠-zones and study the behavior of solutions on 𝑠-zones.
Generalized Analytic Functions in Higher Dimensions
Authors: Tutschke Wolfgang 
Published: February 2021

Abstract
Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions.
One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.
A Modified Quasi-Reversibility Method for a Class of Ill-Posed Cauchy Problems
Authors: Boussetila Nadjib , Rebbani Faouzia 
Published: February 2021

Abstract
The goal of this paper is to present some extensions of the method of quasi-reversibility applied to an ill-posed Cauchy problem associated with an unbounded linear operator in a Hilbert space. The key point to our proof is the use of a new perturbation to construct a family of regularizing operators for the considered problem. We show the convergence of this method, and we estimate the convergence rate under a priori regularity assumptions on the problem data.
Convergence of Walsh–Fourier Series of a Class 𝐵𝑂(𝑝(𝑛) ↑ ∞)
Authors: Goginava Ushangi , Toledo Rodolfo 
Published: February 2021

Abstract
We study the pointwise convergence of Walsh–Fourier series on the class of functions of generalized 𝑝-bounded fluctuation.
Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
Authors: Cialdea Alberto 
Published: February 2021

Abstract
Let {ω𝑘
} be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚
aα
𝐷
α
𝑢 = 0, aα
being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.
A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers
Authors: Zireh Ahmad 
Published: February 2021

Abstract
We use a commutative generalization of complex numbers called bicomplex numbers to introduce the bicomplex dynamics of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑤) = 𝑤(𝑤 + 𝑐)𝑑. Rochon [Fractals 8: 355–368, 2000] proved that the Mandelbrot set of quadratic polynomials in bicomplex numbers of the form 𝑤2 + 𝑐 is connected. We prove that our generalized Mandelbrot set of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑤) = 𝑤(𝑤 + 𝑐)𝑑, is connected.
Maximal and Potential Operators in Variable Exponent Morrey Spaces
Authors: Almeida Alexandre , Hasanov Javanshir , Samko Stefan 
Published: February 2021

Abstract
We prove the boundedness of the Hardy–Littlewood maximal operator on variable Morrey spaces 𝐿𝑝(·), λ(·)(Ω) over a bounded open set Ω ⊂ ℝ𝑛 and a Sobolev type 𝐿𝑝(·), λ(·) → 𝐿𝑞(·), λ(·)-theorem for potential operators 𝐼
α(·), also of variable order. In the case of constant α, the limiting case is also studied when the potential operator 𝐼
α
acts into BMO space.
On Estimating the Approximation of Locally Summable Functions by Gegenbauer Singular Integrals
Authors: Guliyev Vagif S. , Ibrahimov Elman J. 
Published: February 2021

Abstract
Using the generalized shift operator (GSO) generated by the Gegenbauer differential operator we introduce the notion of a Lebesgue–Gegenbauer (L-G)-point of a summable function 𝑓 on the interval [1,∞) and prove that almost all points of this interval are (L-G)-points of 𝑓. Furthermore, we give an exact (by order) estimation of the approximation of locally summable functions by singular integrals generated by GSO (Gegenbauer singular integrals).
Wavelets and Modular Inequalities in Variable 𝐿𝑝 Spaces
Authors: Izuki Mitsuo 
Published: February 2021

Abstract
The aim of this paper is to characterize variable 𝐿𝑝 spaces 𝐿𝑝(·)() using wavelets with proper smoothness and decay. We obtain conditions for the wavelet characterizations of 𝐿𝑝(·)() with respect to the norm estimates and modular inequalities.
On Absolutely Nonmeasurable Sets and Functions
Authors: Kharazishvili Alexander 
Published: February 2021

Abstract
We consider some properties of sets and functions which are measurable (or nonmeasurable) with respect to certain classes of measures. In this context, the notion of an absolutely nonmeasurable set (function) is examined. Sierpiński-Zygmund type functions are constructed having additional properties closely connected with the above-mentioned notion. Also, some small subsets of uncountable commutative groups are discussed whose algebraic sum turns out to be an absolutely nonmeasurable set.
Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
Authors: Avalos George , Lasiecka Irena , Triggiani Roberto 
Published: February 2021

Abstract
This paper considers an established model of a parabolic-hyperbolic coupled system of two PDEs, which arises when an elastic structure is immersed in a fluid. Coupling occurs at the interface between the two media. Semigroup well-posedness on the space of finite energy for {𝑤, 𝑤𝑡, 𝑢} was established in [Contemp. Math. 440: 15–54, 2007]. Here, [𝑤, 𝑤𝑡] are the displacement and the velocity of the structure, while 𝑢 is the velocity of the fluid. The domain D(A) of the generator A does not carry any smoothing in the 𝑤-variable (its resolvent 𝑅(λ, A) is not compact on this component space). This raises the issue of higher regularity of solutions. This paper then shows that the mechanical displacement, fluid velocity, and pressure terms do enjoy a greater regularity if, in addition to the I.C. {𝑤0, 𝑤1, 𝑢0} ∈ D(A), one also has 𝑤0 in (𝐻2(Ω𝑠))𝑑.
Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary
Authors: Hamouda Makram , Temam Roger 
Published: February 2021

Abstract
We prove the existence of a strong corrector for the linearized incompressible Navier–Stokes solution on a domain with characteristic boundary. This case is different from the noncharacteristic case considered in [Hamouda and Temam, Some singular perturbation problems related to the Navier–Stokes equations: Springer Verlag, 2006] and somehow physically more relevant. More precisely, we show that the linearized Navier–Stokes solutions behave like the Euler solutions except in a thin region, close to the boundary, where a certain heat equation solution is added (the corrector). Here, the Navier–Stokes equations are considered in an infinite channel of but our results still hold for more general bounded domains.
Existence and Uniqueness of Weak Solution for a Class of Elliptic Reaction-Diffusion Systems
Authors: Bouziani Abdelfatah , Mounir Ilham 
Published: February 2021

Abstract
We present a simple proof of the existence and uniqueness of a weak solution for a class of quasilinear elliptic reaction-diffusion systems. The proof is based on an iterative process and on some a priori estimates.
Beurling–Borg Type Theorem for Two-Dimensional Linear Differential Systems
Authors: Kiguradze Ivan 
Published: February 2021

Abstract
For the two-dimensional linear differential system

with Lebesgue integrable coefficients 𝑝𝑖𝑘 : [𝑎, 𝑏] → ℝ (𝑖 = 1, 2), a Beurling–Borg type theorem is proved on an upper estimate of the number of zeros of an arbitrary non-trivial solution.
On One Problem with the Condition at Infinity for Second Order Singular Ordinary Differential Equations
Authors: Partsvania Nino 
Published: February 2021

Abstract
For the second order nonlinear singular differential equation
𝑢″ + 𝑓(𝑡, 𝑢, 𝑢′) = 0,
the unimprovable sufficient conditions for the solvability of the problem with the condition at infinity

are established.
Compact Composition Operators on Generalized Hardy Spaces
Authors: Sharma Ajay K. 
Published: February 2021

Abstract
We investigate compact composition operators acting on generalized Hardy spaces 𝐻𝑤. In fact, we prove that if 𝑤 is a differentiable, subharmonic and strictly increasing function defined on [0, ∞), then 𝐶
φ
is compact on the generalized Hardy spaces if and only if it is compact on the Hardy space 𝐻2.
CLT for Operator Abel Sums of Random Elements
Authors: Shervashidze Tengiz , Tarieladze Vaja 
Published: February 2021

Abstract
Let (ξ
𝑘)𝑘 ≥ 1 be a sequence of independent, identically distributed second order mean zero random elements in a separable Hilbert space 𝐻 and 𝐴 be an element of a certain class of linear continuous operators 𝐻 → 𝐻 such that ‖𝐴‖ < 1. Denote . We prove that if ‖𝐼 – 𝐴‖ tends to zero, where 𝐼 is the identity operator, then the normalized sum (𝐼 – 𝐴2)1/2
η
𝐴 converges in distribution to a Gaussian random element.
Singular 2D Behaviors: Fornasini–Marchesini and Givone–Roesser Models
Authors: Lomadze Vakhtang , Rogers Eric , Wood Jeffrey 
Published: February 2021

Abstract
In this paper we study 2D Fornasini–Marchesini and 2D Givone–Roesser models from the viewpoint developed in our recent paper [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008]. We give necessary and sufficient conditions for a behavior to be expressable in Fornasini–Marchesini or Givone–Roesser form, and a canonical realization when the conditions are met. We also study the regularity, controllability and autonomy of these models. In particular, we provide the concepts of controllability in the sense of Kalman for each model, and show that they agree with the behavioral controllability as defined in [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008].
Forcing for IZF in Sheaf Toposes
Authors: Streicher Thomas 
Published: February 2021

Abstract
In [Category-theoretic models for intuitionistic set theory, 1985] D. Scott showed how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fourman, J. Pure Appl. Algebra 19: 91–101, 1980, Hayashi, On set theories in toposes, Springer, 1981].
Rate of Approximation for Certain Szasz–Mirakyan–Durrmeyer Operators
Authors: Dubey Deepak Kumar , Gangwar Ravindra Kumar , Jain Shipra 
Published: February 2021

Abstract
We study a certain integral modification of the well known Szasz–Mirakyan operators with a weight function of a general Baskakov basis function. We establish some direct results on a simultaneous approximation for these new operators.
Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series
Authors: Goginava Ushangi 
Published: February 2021

Abstract
The main aim of this paper is to prove that the partial sums of double Vilenkin–Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of 𝐿ln+ 𝐿, the set of functions whose quadratic partial sums of double Vilenkin–Fourier series converge in measure is of first Baire category.
On the Exponential Uniform Strong Summability of Multiple Trigonometric Fourier Series
Authors: Gogoladze Larry 
Published: February 2021

Abstract
In the paper, in particular, it is proved that the 𝑠-dimensional trigonometric Fourier series of the 2π-periodic continuous on [–π, π]𝑠 function 𝑓 is uniformly strong summable to the function 𝑓 exponentially in the power . Moreover, it is proved that this result is best possible.
On the Integrability and Uniform Convergence of Multiplicative Fourier Transforms
Authors: Golubov Boris I. , Volosivets Sergey S. 
Published: February 2021

Abstract
Analogues of two Hardy–Littlewood theorems are proved for a multiplicative Fourier transform. A Szasz type condition for a multiplicative Fourier transform is given and its nonimprovability is proved. Besides, an analogue of Ul'yanov's theorem on the uniform convergence of a trigonometric series and an analogue of Konyuškov–Stechkin's embedding theorem are obtained by means of a Nikol'skii type inequality of various metrics.
A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
Authors: Hakl Robert , Mukhigulashvili Sulkhan 
Published: February 2021

Abstract
On the interval [0,ω], consider the periodic boundary value problem

where 𝑛 ≥ 2, 𝑙𝑖 : 𝐶([0,ω];𝑅) → 𝐿([0,ω];𝑅) (𝑖 = 0,…,𝑛 – 1) are linear bounded operators, 𝑞 ∈ 𝐿([0,ω];𝑅), 𝑐𝑗 ∈ 𝑅 (𝑗 = 0,…,𝑛 – 1). The effective sufficient conditions guaranteeing the unique solvability of the considered problem are established.
On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant
Authors: Karsli Harun , Pych-Taberska Paulina 
Published: February 2021

Abstract
We consider the Bézier variant of Chlodovsky–Durrmeyer operators 𝐷𝑛,α
for functions 𝑓 measurable and locally bounded on the interval [0,∞). By using the Chanturia modulus of variation we estimate the rate of pointwise convergence of (𝐷𝑛,α
𝑓) (𝑥) at those 𝑥 > 0 at which the one-sided limits 𝑓(𝑥+), 𝑓(𝑥–) exist. In the special case α = 1 the recent result of [Ibikli, Karsli, J. Inequal. Pure Appl. Math. 6: 12, 2005] concerning the Chlodovsky–Durrmeyer operators 𝐷𝑛 is essentially improved and extended to more general classes of functions.
On Nonmeasurable Functions of Two Variables and Iterated Integrals
Authors: Kharazishvili Alexander 
Published: February 2021

Abstract
Following the paper of Pkhakadze [Trudy Tbiliss. Mat. Inst. Razmadze 20: 167–209, 1954], we consider some properties of real-valued functions of two variables, which are not assumed to be measurable with respect to the two-dimensional Lebesgue measure on the plane 𝐑2, but for which the corresponding iterated integrals exist and are equal to each other. Close connections of these properties with certain set-theoretical axioms are emphasized.
On Solutions of a Singular Viscoelastic Equation with an Integral Condition
Authors: Mecheri Hacene , Mesloub Said , Messaoudi Salim A. 
Published: February 2021

Abstract
In this work, we use a functional analysis approach to prove the well posedness of a mixed problem with a nonclassical condition for a viscoelastic equation with dissipation. The proof is mainly based on some a priori bounds and on some density arguments.
The Lattice of Fully Invariant Subgroups of a Cotorsion Hull
Authors: Kemoklidze Tariel 
Published: February 2021

Abstract
The paper considers the lattice of fully invariant subgroups of the cotorsion hull of a countable direct sum of torsion-complete p-groups. It is shown that this lattice is isomorphic to the lattice of dual ideals of a semilattice made up of infinite matrices.
Higher order track categories and the algebra of higher order cohomology operations
Authors: Baues Hans-Joachim 
Published: February 2021

Abstract
We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an 𝑛-th order track category suitable for studying higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also, differential algebras give rise to higher order track categories.
On the construction of 𝐴∞-structures
Authors: Huebschmann Johannes 
Published: February 2021

Abstract
We relate a construction of Kadeishvili's establishing an 𝐴∞-structure on the homology of a differential graded algebra or, more generally, of an 𝐴∞-algebra with certain constructions of Chen and Gugenheim. Thereafter we establish the links of these constructions with subsequent developments.
Blackbox computation of A
∞-algebras
Authors: Vejdemo-Johansson Mikael 
Published: February 2021

Abstract
Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv.
35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A
∞-algebra structure on the homology of a dg-algebra.
In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A
∞-algebra structure after a finite amount of computational work.
On equivariant disconnected rational homotopy theory
Authors: Golasiński Marek 
Published: February 2021

Abstract
An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ
X
with the properties required by nonequivariant minimal algebras.