bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures
Authors: Basheleishvili M.
Published: February 2021

The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [Basheleishvili, Georgian Math. J. 4: 223–242, 1997], these problems can be splitted and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.
Kan Extensions of Internal Functors. Algebraic Approach
Authors: Datuashvili T.
Published: February 2021

We investigate the question of the Kan extension in the case when all categories and functors are internal in the category of groups. Under certain assumptions we establish the necessary and sufficient conditions for the existence of internal Kan extensions. Questions related to this problem are also discussed.
On the Vector Process Obtained by Iterated Integration of the Telegraph Signal
Authors: Orsingher Enzo
Published: February 2021

We analyse the vector process (𝑋0(𝑡),𝑋1(𝑡), . . . , 𝑋𝑛(𝑡), 𝑡 > 0) where , 𝑘 = 1, . . . , 𝑛, and 𝑋0(𝑡) is the two-valued telegraph process.

In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed.

Special care is given to the case of the process (𝑋0(𝑡),𝑋1(𝑡),𝑋2(𝑡), 𝑡 > 0) representing a randomly accelerated motion where some explicit results on the probability distribution are derived.
Oscillatory Behaviour of Solutions of two-Dimensional Differential Systems with Deviated Arguments
Authors: Koplatadze R. , Partsvania N.
Published: February 2021

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

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

Questions of approximative nature are considered for a space of functions 𝐿𝑝(𝐺, μ), 1 ≤ 𝑝 ≤ ∞, defined on a locally compact abelian Hausdorff group 𝐺 with Haar measure μ. The approximating subspaces which are analogs of the space of exponential type entire functions are introduced.
On the Dirichlet Problem for a Second Order Elliptic System with Degeneration on the Entire Domain Boundary
Authors: Usanetashvili M.
Published: February 2021

The solvability of the first boundary value problem is investigated for a second order elliptic system with degeneration on the entire domain boundary.
Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems
Authors: Davis John M. , Eloe Paul W. , Henderson Johnny
Published: February 2021

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

The solvability of the nonlocal boundary value problem

𝑢𝑡 = 𝑎(𝑡, 𝑥, 𝑢, 𝑢𝑥)𝑢𝑥𝑥 + 𝑏(𝑡, 𝑥, 𝑢, 𝑢𝑥), 0 ≤ 𝑡 ≤ 𝑇, |𝑥| ≤ 𝑙, 𝑢(0, 𝑥) = 0, 𝑢(𝑡, –𝑙) = 𝑢(𝑡, 𝑙), 𝑢𝑥(𝑡, –𝑙) = 𝑢𝑥(𝑡, 𝑙)

in a class of functions is investigated for a quasilinear parabolic equation. The solution uniqueness follows from the maximum principle.
Subsets of the Plane with Small Linear Sections and Invariant Extensions of the Two-Dimensional Lebesgue Measure
Authors: Kharazishvili A.
Published: February 2021

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

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

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

Asymptotic distribution of the mean square deviation of the Gasser–Müller estimate of the regression curve is investigated. The testing of hypotheses on regression function is considered. The asymptotic behaviour of the power of the proposed criteria under contiguous alternatives is studed.
On the Prandtl Equation
Authors: Duduchava R. , Kapanadze D.
Published: February 2021

The unique solvability of the airfoil (Prandtl) integro-differential equation on the semi-axis is proved in the Sobolev space and Bessel potential spaces under certain restrictions on 𝑝 and 𝑠.
Entropy Numbers of Certain Summation Operators
Authors: Creutzig J. , Linde W.
Published: February 2021

Given nonnegative real sequences and we study the generated summation operator

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

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

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

σ
: l

p
→ l

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

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

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

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

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

ρ
(B) for a given random field.
Some Remarks on Fractals Generated by a Sequence of Finite Systems of Contractions
Authors: Follo Giorgio
Published: February 2021

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

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.
On the Dimension of Some Spaces of Generalized Ternary Theta-Series
Authors: Shavgulidze K.
Published: February 2021

The upper bound of dimension of vector spaces of generalized theta-series corresponding to some ternary quadratic forms is established. In a number of cases, the dimension of vector spaces of generalized theta-series is established and bases of these spaces are constructed.
Ordinary Differential Equations with Nonlinear Boundary Conditions
Authors: Jankowski Tadeusz
Published: February 2021

The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.
Characteristic Functions and s-Orthogonality Properties of Chebyshev Polynomials of Third and Fourth Kind
Authors: Martinelli Maria Renata
Published: February 2021

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.
Some Uniqueness Results for Impulsive Semilinear Neutral Functional Differential Equations
Authors: Benchohra M. , Ouahabi A.
Published: February 2021

The Banach contraction principle is used to investigate the existence and uniqueness of solutions for first and second order impulsive semilinear neutral functional differential equations in Banach spaces.
Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence
Authors: Bychowska A.
Published: February 2021

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

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

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 ARU-Resolutions of Uniform Spaces
Authors: Baladze V.
Published: February 2021

In this paper theorems which give conditions for a uniform space to have an ARU-resolution are proved. In particular, a finitistic uniform space admits an ARU-resolution if and only if it has trivial uniform shape or it is an absolute uniform shape retract.
On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
Authors: Bakhia I.
Published: February 2021

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

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

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.
Oscillation Theorems of Nonlinear Difference Equations of Second Order
Authors: Saker S. H.
Published: February 2021

Using the Riccati transformation techniques, we establish some new oscillation criteria for the second-order nonlinear difference equation

Some comparison between our theorems and the previously known results in special cases are indicated. Some examples are given to illustrate the relevance of our results.
On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
Authors: Shervashidze T.
Published: February 2021

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

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

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

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

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.
Continuity for Multilinear Marcinkiewicz Operators on Certain Hardy Spaces
Authors: Liu Lanzhe
Published: February 2021

In this paper, the continuity of multilinear Marcinkiewicz operators on certain Hardy and Herz–Hardy spaces is obtained.
On Superfluous Subsemimodules
Authors: Tuyen Nguyen Xuan , Thang Ho Xuan
Published: February 2021

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.
Oscillation of Second Order Half-Linear Differential Equations with Damping
Authors: Yang Qigui , Cheng Sui Sun
Published: February 2021

This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results.
Some Integral Operators which Preserve a Subclass of Uniformly Quasiconvex Functions
Authors: Acu Mugur
Published: February 2021

In this paper we define a subclass of uniformly quasiconvex functions and show that this class is preserved under the Alexander and Bernardi integral operators.
On Entire Modular Forms of Half-Integral Weight on the Congruence Subgroup Γ0(4N)
Authors: Lomadze G.
Published: February 2021

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

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

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

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).
On Generalized Step-Functions and Superposition Operators
Authors: Kharazishvili A.
Published: February 2021

For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.
On the Shape of Regularly Movable Compacta
Authors: Mardešić S.
Published: February 2021

It is proved that every regularly movable metric compactum has the shape of the inverse limit of an inverse sequence consisting of compact polyhedra and retractions.
Common Fixed Points Iteration Processes for a Finite Family of Asymptotically Nonexpansive Mappings
Authors: Huang Jui-Chi
Published: February 2021

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

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

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

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

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

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

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.
Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
Authors: Liu Lanzhe
Published: February 2021

In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces.
Mapping Properties of Integral Operators of Levy Type
Authors: Runst Thomas , Youssfi Abdellah
Published: February 2021

We study the boundedness and compactness of a special class of integral operators defined on generalized Sobolev spaces.
On the Uniqueness of the Two-Sided Ergodic Maximal Function
Authors: Ephremidze Lasha
Published: February 2021

It is proved that the two-sided ergodic maximal operator is one-to-one.
On a Generalized Wilson Functional Equation
Authors: Badora Roman
Published: February 2021

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.
Monadic 𝐵𝐿-Algebras
Authors: Grigolia Revaz
Published: February 2021

We define and study monadic 𝐵𝐿-algebras as a pair of 𝐵𝐿-algebras one of which is a special case of relatively complete subalgebra.
Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
Authors: Dinu Teodora-Liliana
Published: February 2021

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

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

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

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

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

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

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

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

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).
On Cusp Forms of Weight 9/2
Authors: Vepkhvadze Teimuraz
Published: February 2021

The modular properties of general theta-functions with characteristics are used to build a cusp form of weight 9/2.
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

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

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

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

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

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.
Rate of Convergence for the Bézier Variant of the MKZD Operators
Authors: Gupta Vijay , Karsli Harun
Published: February 2021

We estimate the rate of convergence of the Bézier variant of Durrmeyer type Meyer–König and Zeller operators for functions with derivatives of bounded variation defined on [0, 1].
Positive Solutions for Neutral Difference Equations with Continuous Arguments
Authors: Li Xianyi
Published: February 2021

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.
Stability of Finite Difference Schemes on Irregular Meshes for Von Foerster-Type 1-D Equations
Authors: Zwierkowski Piotr
Published: February 2021

We consider a generalized von Foerster equation in one dimensional spatial variable and construct finite difference schemes for the initial value problem. The stability of finite difference schemes on irregular meshes generated by characteristics is studied.
Turbulence of Real Functions
Authors: Barsegian Grigor A.
Published: February 2021

The concept of 𝐴-level sets of real functions 𝑢(𝑥, 𝑦) (i.e., the solutions of 𝑢(𝑥, 𝑦) = 𝐴 = const) in a given domain admits numerous interpretations in applied sciences: level sets are potential lines, streamlines in hydrodynamics, meteorology and electromagnetics, isobars in gas-dynamics, isotherms in thermodynamics, etc. In fact, the level sets of 𝑢 considered for all values 𝐴 make the “map” of this function and their interpretations in different sciences make the “maps” of the corresponding processes.

In this paper we study the geometry of these maps for broad classes of functions and arbitrary values 𝐴. In particular, we study how much twisted or, speaking in general, how turbulent these maps are.

The concepts and results admit some immediate interpretations and can be stated in terms of flow rotation and turbulence. The study gives a new, in fact a geometric description of these applied phenomena.
A Note on Maximal Operator on 𝐿𝑝(𝑡) (Ω)Spaces
Authors: Kapanadze Ekaterine , Kopaliani Tengiz
Published: February 2021

We study the Hardy–Littlewood maximal operator 𝑀 on 𝐿𝑝(·) (Ω), where Ω ∈ is an open bounded domain with a Lipschitz boundary. Under the assumption that the exponent 𝑝 satisfies 1 < inf 𝑝(𝑥) ≤ sup 𝑝(𝑥) < ∞ and 𝑝 ∈ 𝑉𝑀𝑂1/|log|(Ω), we prove that 𝑀 is bounded on 𝐿𝑝(·) (Ω).
The Boundedness of Maximal Functions in Orlicz–Campanato Spaces of Homogeneous Type
Authors: Tao Xiangxing , Chen Qinqin
Published: February 2021

Let (𝑋,𝑑,μ) be a normal space of homogeneous type, 𝑋+ be the upper half-space equipped with a Carleson measure β, and let Φ be an N-function and φ a suitable function satisfying the doubling property. We prove that the generalized Hardy–Littlewood maximal operator 𝑀 is bounded from the Orlicz–Campanato space 𝐿Φ,φ
(𝑋,μ) to 𝐿Φ,φ
(𝑋+,β).
Impulse Control in Discrete Time
Authors: Bensoussan Alain
Published: February 2021

We present here impulse control theory in discrete time. We show the connection between quasi-variational inequalities (QVI) in this context, with the standard formulation of dynamic programming. We show that the QVI formulation brings many interesting features, completing the standard formulation of dynamic programming. We study applications to inventory control in discrete time.
Capacity Induced by a Nonlinear Operator and Applications
Authors: Galaktionov Victor A. , Mitidieri Enzo , Pohozaev Stanislav I.
Published: February 2021

We consider the application of the concept of nonlinear capacity induced by nonlinear operators to blow-up problems for various types of nonlinear partial differential equations involving equations with nonlocal nonlinearities.
On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part
Authors: Kharibegashvili Sergo , Midodashvili Bidzina
Published: February 2021

One boundary value problem for a hyperbolic equation with power nonlinearity and the iterated wave operator in the principal part is considered in a conical domain. Depending on the index of nonlinearity and spatial dimensionality of the equation the question on the existence and uniqueness of a solution of a boundary value problem is investigated. The question as to the absence of a solution of this problem is also considered.
On Dynamical Three-Dimensional Fluid-Solid Interaction Problem
Authors: Avalishvili Gia , Avalishvili Mariam , Gordeziani David
Published: February 2021

The present paper is devoted to the investigation of one dynamical three-dimensional mathematical model of the fluid-solid interaction. The variational formulation of the corresponding initial boundary problem is considered and a problem for abstract second order evolution equation is formulated, which is a generalization of the three-dimensional initial boundary value problem. For the stated abstract problem the existence and uniqueness of solution, and the energy equality are proved, which yield the corresponding result for the dynamical three-dimensional problem of fluid-solid interaction.
Dual Variational Method for a Fourth Order Dirichlet Problem
Authors: Galewski Marek
Published: February 2021

We obtain the existence and stability results for a fourth order Dirichlet problems with nonlinearity being convex in a certain interval. A dual variational method is introduced, which relies on investigating the primal and dual action functionals on certain subsets of their domains. The dependence on a functional parameter for a fourth order Dirichlet problem is considered as a consequence of stability.
The Maximal Operator in Weighted Variable Exponent Spaces on Metric Spaces
Authors: Kokilashvili Vakhtang , Samko Stefan
Published: February 2021

We study the boundedness of the maximal operator in the weighted variable exponent spaces 𝐿𝑝(·)(𝑋, ϱ) on a doubling measure metric space 𝑋. When 𝑋 is bounded, the weight belongs to a version of a Muckenhoupt-type class, which is narrower than the expected Muckenhoupt condition for a variable exponent, but coincides with the usual Muckenhoupt class 𝐴𝑝 in the case of a constant 𝑝. For the bounded 𝑋 we also consider the class of weights of the form , where the functions 𝑤𝑘(𝑟) have finite upper and lower indices 𝑚(𝑤) and 𝑀(𝑤) satisfying the condition , where 𝔡𝔦𝔪(𝑋) is a version of lower dimension of the space 𝑋. In the case of unbounded 𝑋 we admit weights of the form .

Some of the results are new even in the case of a constant 𝑝. We also deal with some new notions of upper and lower local dimensions of measure metric spaces.
On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
Authors: Karsli Harun
Published: February 2021

In the present paper we obtain both the pointwise convergence and the rate of pointwise convergence theorems of a class of operators defined by

as (𝑥,λ) → (𝑥0,λ
0) in 𝐿1 〈𝑎,𝑏〉, where 〈𝑎,𝑏〉 is an arbitrary interval in 𝑅. Here λ ∈ Λ and Λ is a nonempty set of indices.
On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series
Authors: Akhobadze Teimuraz
Published: February 2021

The behavior of generalized Cesàro (𝐶, α
𝑛)-means (α
𝑛 ∈ (–1, 0), 𝑛 = 1, 2, . . .) of conjugate trigonometric Fourier series of 𝐻𝑤 classes in the space of continuous functions is studied.
Necessary Conditions for Integrability of the Fourier Transform
Authors: Liflyand Elijah
Published: February 2021

We prove the necessary conditions for the integrability of the Fourier transform. The result is a generalization, on one hand, of the well known necessary condition for absolutely convergent Fourier series and, on the other hand, of an earlier multidimensional result of Trigub.
The Diagonal Mapping in Bmoa-Type Spaces of Analytic Functions on the Polydisk
Authors: Shamoyan Romi F.
Published: February 2021

For any holomorphic function 𝑓 on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag 𝑓(𝑧) = 𝑓(𝑧, . . . , 𝑧) and prove that the diagonal map Diag maps the space of the polydisk onto the space of the unit disk.
The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
Authors: Kokilashvili Vakhtang , Paatashvili Vakhtang
Published: February 2021

The Riemann–Hilbert problem for an analytic function is solved in weighted classes of Cauchy type integrals in a simply connected domain not containing 𝑧 = ∞ and having a density from variable exponent Lebesgue spaces. It is assumed that the domain boundary is a piecewise smooth curve. The solvability conditions are established and solutions are constructed. The solution is found to essentially depend on the coefficients from the boundary condition, the weight, space exponent values at the angular points of the boundary curve and also on the angle values. The non-Fredholmian case is investigated. An application of the obtained results to the Neumann problem is given.
On the Representation of Numbers by Some Quadratic Forms of Level 12
Authors: Kachakhidze Nikoloz
Published: February 2021

Formulas are obtained for the number of representations of positive integers by quadratic forms .
The existence and boundedness of square functions on generalized Orlicz–Campanato spaces
Authors: Zhang Songyan
Published: February 2021

Let T(ƒ) denote the Littlewood–Paley square operators, including the g-function g(ƒ), Luzin area function S(ƒ) and Stein's function , on the generalized Orlicz–Campanato spaces , where Φ is a N-function satisfying the Δ2 condition and φ a positive function satisfying the doubling property. It is proved that if T(ƒ)(x
0) < ∞ for a single point
, then T(ƒ)(x) exists almost everywhere in , and T(ƒ) is bounded on the spaces .
Backward stochastic PDEs related to the utility maximization problem
Authors: Mania Michael , Tevzadze Revaz
Published: February 2021

We study utility maximization problem for general utility functions using the dynamic programming approach. An incomplete financial market model is considered, where the dynamics of asset prices is described by an -valued continuous semimartingale. Under some regularity assumptions, we derive the backward stochastic partial differential equation related directly to the primal problem and show that the strategy is optimal if and only if the corresponding wealth process satisfies a certain forward stochastic differential equation. The cases of power, exponential and logarithmic utilities are considered as examples.
Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth
Authors: Akgün Ramazan
Published: February 2021

This work deals with basic approximation problems such as direct, inverse and simultaneous theorems of trigonometric approximation of functions of weighted Lebesgue spaces with a variable exponent on weights satisfying a variable Muckenhoupt A

p(·) type condition. Several applications of these results help us transfer the approximation results for weighted variable Smirnov spaces of functions defined on sufficiently smooth finite domains of complex plane ℂ.
AGRONOMIC ASPECTS OF THE SUNFLOWER 7-HYDROXYLATED SIMPLE COUMARINS / ASPECTOS AGRONÓMICOS DE LAS CUMARINAS SIMPLES 7- HIDROXILADAS EN GIRASOL / ASPECTS AGRONOMIQUES DE 7 COUMARINES HYDROXYLES SIMPLES CHEZ LE TOURNESOL
Authors: Prats-Perez Elena , Bazzalo María Eugenia , León Alberto , Novo Jesús V. Jorrín
Published: February 2021

Sunflower and other Helianthus ssp. produced, among other secondary metabolites, the coumarins scopoletin, scopolin and ayapin. In the most general sense they can be defined as stress metabolites, their synthesis being induced in response to adverse environmental condition, both biotic and abiotic. The pattern of coumarin synthesis and accumulation depends on plant variety, it is tissue dependent and developmentally regulated. Coumarin synthesis in sunflower seems to be part of the defence strategy against microorganisms, insect and parasitic plants. From an agricultural point of view the defensive potential of these compounds can be exploited in order to develop resistant varieties (either by classical plant breeding or by biotechnology) or crop protection strategies involving the use of chemicals which induced coumarin synthesis.