bluuebunny/crossref_metadata_2025 huggingface dataset:
Rate of Approximation for Certain Durrmeyer Operators
Authors: Gupta Vijay , Shervashidze Tengiz , Craciun Maria
Published: February 2021

In the present note, we study a certain Durrmeyer type integral modification of Bernstein polynomials. We investigate simultaneous approximation and estimate the rate of convergence in simultaneous approximation.
On Decompositions of a Cube into Cubes and Simplexes
Authors: Kharazishvili Alexander
Published: February 2021

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

We give positive answer to Velichko's question in which the quotient and 𝑠-map is replaced by a sequence-covering and 𝑐𝑠-map. In addition, let 𝑋 have a star-countable 𝑘-network, then 𝑋 is a sequence-covering and 𝑐𝑠-image of a locally separable metric space if and only if 𝑋 is a sequencecovering and 𝑐𝑠-image of a metric space.
Corrections to “On a Singular Direction of a Meromorphic Function”
Authors: Wu Zhaojun , Sun Daochun
Published: February 2021

The corrections to our paper [Wu and Sun, Georgian Math J. 12: 551–559, 2005] are made.
Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
Authors: Amroun Nour-Eddine , Benaissa Abbes
Published: February 2021

We consider the nonlinearly damped semilinear Petrovsky equation

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

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

A functor responsible for second obstruction problems is defined and investigated on the category of topological spaces. In terms of this functor we formulate and prove a classification theorem for maps, which is the reformulation of all known classification theorems for the second obstruction.
On the Convergence of Conjugate Trigonometric Polynomials
Authors: Gogoladze Larry
Published: February 2021

Sufficient conditions are found, under which for 𝑓 ∈ 𝐶([–π, π]) or 𝑓 ∈ 𝐿([–π, π]) the convergence of a sequence of trigonometric polynomials in the norms of these spaces implies the convergence of their conjugates in the same norms.
Inversion of Ahlfors and Grunsky Inequalities
Authors: Krushkal Samuel
Published: February 2021

We solve the old Kühnau's problem on the exact lower bound in the inverse inequality estimating the dilatation of a univalent function by its Grunsky norm and in the related Ahlfors inequality for Fredholm eigenvalues.
On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
Authors: Oniani Giorgi
Published: February 2021

A resonance type theorem is proved, where conditions are given, which imply the non-compactness and a certain estimation of the measure of the non-compactness of operators in weighted ideal and symmetric function spaces. The application of the theorem to some concrete classes of operators is discussed.
The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
Authors: Usanetashvili Mikheil
Published: February 2021

The first boundary value problem with weight is investigated for a general-type second order elliptic type equation degenerating on the whole boundary.
Principal Maps in Triangulated Categories and Maps between 2-Stage Spectra
Authors: Baues Hans Joachim
Published: February 2021

Using two natural axioms on track triangles in triangulated track category we show that the mapping cone construction is functorial, i.e., principal maps between mapping cones in a triangulated category can be identified with the homotopy classes of homotopy pairs. This result is applied to obtain an algebraic model of the category of principal maps between 2-stage spectra.
A Local System of Spaces and a Bigraded Model of Fibration
Authors: Berikashvili Nodar
Published: February 2021

On the singular complex of a space, a local system of acyclic spaces is constructed leading, for Serre fibrations, to a bigraded differential model for the chain complex of the total space.
On the Lacunarity of Two-Eta-Products
Authors: Cooper Shaun , Gun Sanoli , Ramakrishnan B.
Published: February 2021

We classify all lacunary modular forms corresponding to the two-eta-products η
𝑟(𝑧)η
𝑠(𝑚𝑧) for 𝑚 = 3, 4, 5, where 𝑟 + 𝑠 is even and 𝑟𝑠 ≠ 0. We show that there are no lacunary non-cusp forms corresponding to the eta-product η
𝑟(𝑧)η
𝑠(𝑚𝑧), 𝑚 ≥ 4.
Sums of Odd Squares
Authors: Peters Meinhard
Published: February 2021

The number of representations of an integer as a sum of 𝑛 odd squares for 𝑛 ≡ 0 mod 4 is expressed by the number of representations as a sum of 𝑛 squares of integers and the number of representations by the lattice .
Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed
Authors: Gilbert Robert , Ou Miao-Jung
Published: February 2021

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

In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive the greater the chosen subset of the function space. The problem is to find an optimal subset leading to a domain of existence for the desired solution being as large as possible. The present paper will discuss this question for a Goursat problem.
On Approximation of the Perturbed Inclusion
Authors: Bulgakov Alexander I. , Grigorenko Anna A. , Korobko Anatoliy I.
Published: February 2021

The paper is concerned with the so-called perturbed inclusion in the space of continuous functions. The right-hand side of the inclusion is represented by an algebraic sum of the values of two multi-valued maps, one of which consists of compacts and the other is not necessarily closed-valued and is a composition of a linear integral operator and multimap convex-valued with respect to switching. For such an inclusion it is proved that approximation in the space of summable functions of the values of a multimap convex-valued with respect to switching is not always a stable process. The necessary and sufficient condition for the closure of the set of approximate solutions to converge to the closure of the set of solutions for perturbed inclusion is derived.
The Exponential Stability and Instability of Differential Systems with Respect to the Linear Coppel–Conti Approximation. Estimation of Characteristic Exponents
Authors: Izobov Nikolai A. , Prokhorova Rimma A.
Published: February 2021

We prove the exponential stability and instability of a trivial solution of perturbed nonlinear differential systems' with various Coppel–Conti linear approximations and perturbations of higher order smallness. We also obtain upper and lower estimates for characteristic exponents of systems of linear approximation and solutions of the considered perturbed systems.
Slowly Varying Solutions of Functional Differential Equations with Retarded and Advanced Arguments
Authors: Kusano Takaŝi , Marić Vojislav
Published: February 2021

Regularity, in the sense of Karamata, (with nonoscillation as a consequence) and the precise asymptotic behaviour of solutions of two functional differential equations are studied.
Duck Trajectories of Three-Dimensional Singularly Perturbed Systems
Authors: Rozov Nikolai Kh.
Published: February 2021

For the singularly perturbed system of three equations with one fast variable and two slow ones the problem of the emergence of duck trajectories is considered in the case with two different slow motion trajectories intersecting in a general manner.
On a Three-Point Boundary Value Problem for Third Order Differential Equations with Singularities in Phase Variables
Authors: Staněk Svatoslav
Published: February 2021

The singular boundary value problem (ϕ(𝑥″))′ = 𝑓(𝑡, 𝑥, 𝑥′, 𝑥″), 𝑥(0) = 𝑥(𝑇1) = 𝑥(𝑇) = 0 is considered. Here 0 < 𝑇1 < 𝑇, ϕ is an increasing homeomorphism from ℝ onto ℝ, positive 𝑓 satisfies the local Carathéodory conditions on [0, 𝑇] × (ℝ \ {0})3 and 𝑓 may be singular at the value 0 of all its phase variables. The conditions guaranteeing the solvability of the above problem are presented. The proofs are based on regularization and sequential techniques and in limit processes a combination of the Fatou theorem and the Lebesgue dominated convergence theorem is used.
Bound Sets and Two-Point Boundary Value Problems for Second Order Differential Equations
Authors: Taddei Valentina , Zanolin Fabio
Published: February 2021

Using Mawhin's continuation principle we obtain a general result on the existence of solutions to a boundary value problem for second order nonlinear vector ODEs. Applications are given to the existence of solutions which are contained in suitable bound sets with possibly non-smooth boundary.
On Nonmeasurable Subgroups of Uncountable Solvable Groups
Authors: Kharazishvili Alexander , Kirtadze Aleks
Published: February 2021

It is shown that any uncountable commutative group (𝐺, +) admits a representation 𝐺 = ∪{𝐺𝑗 : 𝑗 ∈ 𝐽}, where 𝐽 is a countable set, 𝐺𝑗 is a subgroup of 𝐺 for each 𝑗 ∈ 𝐽, and 𝐺/𝐺𝑗 is uncountable. A related fact for uncountable solvable groups is established in terms of invariant (quasiinvariant) measures and an application of the above-mentioned results to the measure extension problem is given.
The Monomiality Approach to Multi-Index Polynomials in Several Variables
Authors: Belingeri Carlo , Dattoli Giuseppe , Ricci Paolo E.
Published: February 2021

The monomiality principle was introduced (see [Dattoli, Hermite–Bessel and Laguerre–Bessel functions: a by-product of the monomiality principle: 147–164, Aracne, 2000] and the references therein) in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. We show a general technique of extending the monomiality approach to multi-index polynomials in several variables. Application of this technique to the case of Hermite, Laguerre-type and mixed-type (i.e., between Laguerre and Hermite) polynomials is given.
On the Global and Local Solution of the Multidimensional Darboux Problem for Some Nonlinear Wave Equations
Authors: Bogveradze Giorgi , Kharibegashvili Sergo
Published: February 2021

We consider a multidimensional analogue of the Darboux problem for wave equations with power nonlinearity. Depending on the spatial dimension of an equation, a power nonlinearity exponent and the sign in front of a nonlinear term, it is proved that the Darboux problem is globally solvable in some cases, but has no global solution in other cases though the local solvability of this problem remains in force.
Some Combinatorial Properties of Finite Line-Systems in the Euclidean Plane
Authors: Kharazishvili Alexander
Published: February 2021

We consider finite systems of straight lines in the Euclidean plane 𝐑2 with some of their combinatorial characteristics. Euler's formula is applied for obtaining results of combinatorial type for such systems. In particular, a lower estimate for the number of two-sided and three-sided domains determined by a given finite line-system in 𝐑2 is presented and it is shown that this estimate is precise in a certain sense.
Rate of Convergence in Recursive Parameter Estimation Procedures
Authors: Sharia Teo
Published: February 2021

This paper is concerned with the rate of convergence of recursive estimation procedures for parameters of discrete time stochastic processes. Applications to estimation of parameters in several models are presented to illustrate the theory.
On Some Properties of the Dirichlet Problem at Resonance
Authors: Lepin Arnold
Published: February 2021

The boundary value problem at resonance

𝑥″ + 𝑥 = 𝑞 sin 𝑡 + 𝑓(𝑡,𝑥,𝑥′), 𝑥(0) = 0, 𝑥(π) = 0,

is considered, where 𝑓 : [0,π] × 𝑹2 → 𝑹 is a bounded Carathéodory function, 𝑞 is a parameter. We state the multiplicity results without assuming that 𝑓 has limits.
Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
Authors: Lezama Oswaldo
Published: February 2021

We present the theory of Gröbner bases for the submodules of the free module 𝐴𝑚, 𝑚 ≥ 1, where 𝐴 = 𝑅[𝑥1,…,𝑥𝑛] and 𝑅 is a Noehterian commutative ring. This generalizes the theory of Gröbner bases for the ideals of 𝐴 and the submodules of (𝐾[𝑥1,…,𝑥𝑛])𝑚, where 𝐾 is a field, see [Möller, J. Symbolic Comput. 6: 345–359, 1988], [Möller, J. Algebra 100: 138–178, 1986] and [Zacharias, Generalized Gröbner bases in commutative polynomial rings, MIT, 1978]. This generalization to the submodules of 𝐴𝑚 was also partially considered in [Rutman, J. Symbolic Comput. 14: 483–503, 1992], however our presentation is more complete and detailed because we have included all algorithms, proofs and examples omitted in [Rutman, J. Symbolic Comput. 14: 483–503, 1992].
Singular 2D Behaviors: Homologies
Authors: Lomadze Vakhtang , Rogers Eric , Wood Jeffrey
Published: February 2021

We present a new definition of a discrete 2D behavior, which generalizes the standard notion by including trajectories from all quarter- and half-planes in ℤ2. Behaviors then admit certain natural homology spaces, which can be used to define controllability and autonomy, and describe finite trajectories. We discuss the regularity, controllability and autonomy of these models, and demonstrate the equivalence of suitable generalizations of controllability in the senses of Willems and of Rosenbrock, and similarly for autonomy.
On Fractional Integrals on the Plane Curves of Finite Length
Authors: Khuskivadze Givi
Published: February 2021

The paper investigates the questions of continuity and boundedness of a fractional integral on the curves of finite length in Lebesgue spaces depending on the geometrical properties of an integration curve.
Mixed and Crack-Type Boundary Value Problems in Mindlin's Theory of Piezoelectricity
Authors: Buchukuri Tengiz , Chkadua Otar
Published: February 2021

We consider mixed boundary value problems for a piezoelectric medium with a crack. The study is based on Mindlin's model of piezoelectricity which takes into account the influence of the polarization gradient. Using the potential methods and the theory of pseudodifferential equations on manifolds with boundary we prove the existence and uniqueness of solutions and establish their regularity properties.
Estimates of the Location of a Free Boundary for the Obstacle and Stefan Problems Obtained by Means of Some Energy Methods
Authors: Díaz Jesús Ildefonso
Published: February 2021

In this paper we use some energy methods to study the location (and formation) of a free boundary arising in some unilateral problems, for instance, in the obstacle problem and the Stefan problem.
Extended Normal Vector Field and the Weingarten Map on Hypersurfaces
Authors: Duduchava Roland , Kapanadze David
Published: February 2021

We present a different method for studying the Weingarten map for a hypersurface in the Euclidean space . Applying the Cartesian coordinates of the ambient space and tangential Günter's derivatives we obtain a simple matrix representation formula for the Weingarten map for implicit hypersurfaces, which can be applied, for example, to calculate the mean and Gauß's curvatures without passing to intrinsic coordinates.
A Measure Theoretical Version of the Aleksandrov Theorem
Authors: Gazor Majid
Published: February 2021

In this paper a theorem analogous to the Aleksandrov theorem is presented in terms of measure theory. Furthermore, we introduce the condensation rank of Hausdorff spaces and prove that any ordinal number is associated with the condensation rank of an appropriate locally compact totally imperfect space. This space is equipped with a probability Borel measure which is outer regular, vanishes at singletons, and is also inner regular in the sense of closed sets.
On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order
Authors: Kiguradze Tariel
Published: February 2021

In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation

𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢)

with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered.

Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.
Uniqueness for Meromorphic Functions Concerning Differential Polynomials
Authors: Meng Chao
Published: February 2021

Using the notion of weighted sharing of values which was introduced by I. Lahiri [Nagoya Math. J. 161: 193–206, 2001], we deal with the uniqueness problem of meromorphic functions concerning differential polynomials and obtain some theorems which not only improve a recent result of W. L. Xiong, W. C. Lin and S. Mori [Sci. Math. Jpn. 62: 305–315, 2005], but also improve and supplement the result of W. C. Lin and H. X. Yi [Complex Var. Theory Appl. 49: 793–806, 2004].
A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
Authors: Kawakami Hajime
Published: February 2021

We conjecture that the Gauss–Bonnet formula gives a necessary and sufficient condition for the existence of a metric deformation to obtain a positive/negative Gaussian curvature on a disk. The conjecture is reduced to a problem of a partial differential inequality with Dirichlet–Neumann boundary condition. We give a partial answer and an example.
Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
Authors: Kumar Devendra
Published: February 2021

We study the growth of functions which are harmonic in any number of variables. The results are expressed in terms of spherical harmonic coefficients as well as by the approximation error of the harmonic function with (𝑝, 𝑞)-growth.
A Conjecture on Homotopy Groups of Spheres, Details on the Algebra of Higher Cohomology Operations
Authors: Baues Hans-Joachim
Published: February 2021

The computation of the algebra of secondary cohomology operations in [Baues, The algebra of secondary cohomology operations, Birkhäuser Verlag, 2006] leads to a conjecture concerning the algebra of higher cohomology operations in general and an Ext-formula for the homotopy groups of spheres. This conjecture is discussed in detail in this paper.
Representation of Quasi-Measure by Henstock–Kurzweil Type Integral on a Compact-Zero Dimensional Metric Space
Authors: Skvortsov Valentin , Tulone Francesco
Published: February 2021

A derivation basis is introduced in a compact zero-dimensional metric space 𝑋. A Henstock–Kurzweil type integral with respect to this basis is defined and used to represent the so-called quasi-measure on 𝑋.
T-Direction and Borel Direction of Algebroid Functions of Finite and Positive Order
Authors: Wu Zhao-Jun
Published: February 2021

In the present paper, the connection between a T-direction and Borel direction of algebroid functions is investigated. Two algebroid functions (not meromorphic) are obtained to prove that T-directions and Borel directions are two different classes of singular directions for algebroid functions. The existence of an algebroid function (not meromorphic) with a given Borel direction is proved.
Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
Authors: Jin Chuhua , Luo Jiaowan
Published: February 2021

We study the stability of the zero solution of nonlinear delay difference equations by fixed point theory. An example is given to illustrate our theory.
Fixpoint Objects Need Not be Ω-Discrete
Authors: Johnstone Peter
Published: February 2021

We show by an example that a fixpoint object in a topos need not be Ω-discrete, though it does share with the polymorphic types studied by Pitts [Non-trivial power types can't be subtypes of polymorphic types, 6-13, 1989] the property that no nontrivial power-object can be embedded in it.
A twisted tale of cochains and connections
Authors: Stasheff Jim
Published: February 2021

Early in the history of higher homotopy algebra [Stasheff, Trans. Am. Math. Soc. 108: 293–312, 1963], it was realized that Massey products are homotopy invariants in a special sense, but it was the work of Tornike Kadeishvili that showed they were but a shadow of an 𝐴∞-structure on the homology of a differential graded algebra. Here we relate his work to that of Victor Gugenheim [J. Pure Appl. Algebra 25: 197–205, 1982] and K. T. (Chester) Chen [Ann. of Math. (2) 97: 217–246, 1973]. This paper is a personal tribute to Tornike and the Georgian school of homotopy theory as well as to Gugenheim and Chen, who unfortunately are not with us to appreciate this convergence.
A boundary value problem on the whole line to second order nonlinear differential equations
Authors: Philos Christos G. , Purnaras Ioannis K.
Published: February 2021

Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of second order linear ordinary differential equations, respectively.
The optimal forecasting for the multinomial scheme with disorder
Authors: Glonti Omar
Published: February 2021

Stochastic processes with discrete time are considered which are described by one multinomial scheme until the random disorder moment and by another one, after the disorder moment. The problems of optimal in mean square sense filtering and interpolation of disorder moment are investigated and the forecasting estimate for this process is found.
Some nonlocal problems for second order strictly hyperbolic systems on the plane
Authors: Kharibegashvili Sergo , Midodashvili Bidzina
Published: February 2021

Some nonlocal problems for one class of second order strictly hyperbolic systems in a strip on the plane are considered in weighted functional spaces. Proceeding from the structure of solutions of hyperbolic systems and using the methods of complex analysis conditions are found for weight exponents of functional spaces which ensure well-posedness of considered problems.
Complete anti-analytic continuation of analytic functions
Authors: Kühnau Reiner
Published: February 2021

We seek for closed Jordan curves C, for which there exists a pair of analytic functions ƒ, F, where ƒ is analytic in the interior of C, while F in the exterior, except for a given singularity, and with at C.
On a problem concerning quaternion valued Gaussian random variables
Authors: Chelidze George , Vakhania Nicholas
Published: February 2021

In the present paper we construct an example of a quaternion random variable such that Polya's type characterization theorem of Gaussian distributions does not hold. The matter is that in the linear form, consisting of the independent copies of quaternion random variables, a part of the quaternion coefficients is written on the right hand side and the other part on the left-hand side. This gives a negative answer to the question posed in [Vakhania and Chelidze, Teor. Veroyatnost. i Primenen. 54: 337–344, 2009].
Recursive parameter estimation in the trend coefficient of a diffusion process
Authors: Lazrieva Nanuli , Toronjadze Teimuraz
Published: February 2021

The recursive estimation problem of a one-dimensional parameter in the trend coefficient of a diffusion process is considered. The asymptotic properties of recursive estimators are derived, based on the results on the asymptotic behaviour of a Robbins–Monro type SDE. Various special cases are considered.
Proof of the Zalcman conjecture for initial coefficients
Authors: Krushkal Samuel L.
Published: February 2021

The well-known Zalcman conjecture, which implies the Bieberbach conjecture, states that the coefficients of univalent functions on the unit disk satisfy the inequality for all n > 2, with the equality only for the Koebe function. This conjecture remained open for n > 3.

We provide here the proof of this inequality for n = 4, 5, 6. It relies on the holomorphic homotopy of univalent functions and comparison of generated singular conformal metrics in the disk. The extremality of Koebe's function follows from hyperbolic properties.
A weak type inequality for the two-dimensional diagonal Sunouchi operator on the Hardy space
Authors: Goginava Ushangi
Published: February 2021

Define the two dimensional diagonal Sunouchi operator

where S
2
n
, 2
n

ƒ and σ
2
n

ƒ are the (2
n
, 2
n
)th cubic-partial sums and 2
n
th Marcinkiewicz–Fejér means of a two-dimensional Walsh–Fourier series. The main aim of this paper is to prove that the operator is bounded from the Hardy space H
1/2 to the weak L
1/2 space and is not bounded from the Hardy space H
1/2 to the space L
1/2.
A note on Muckenhoupt type weight classes on nondoubling measure spaces
Authors: Komori-Furuya Yasuo
Published: February 2021

We consider some Muckenhoupt type weight classes on nondoubling measure space (, μ) and give an example of measure μ such that where α
1 ≠ α
2.
(σ, τ)-amenability of C*-algebras
Authors: Mirzavaziri Madjid , Moslehian Mohammad Sal
Published: February 2021

Suppose that is an algebra, σ, τ : → are two linear mappings such that both σ() and τ() are subalgebras of and 𝒳 is a (τ(), σ())-bimodule. A linear mapping D : → 𝒳 is called a (σ, τ)-derivation if D(ab) = D(a) · σ(b) + τ(a) · D(b) (a, b ∈ ). A (σ, τ)-derivation D is called a (σ, τ)-inner derivation if there exists an x ∈ 𝒳 such that D is of the form either or . A Banach algebra is called (σ, τ)-amenable if every (σ, τ)-derivation from into a dual Banach (τ(), σ())-bimodule is (σ, τ)-inner.

Studying some general algebraic aspects of (σ, τ)-derivations, we investigate the relation between the amenability and the (σ, τ)-amenability of Banach algebras in the case where σ, τ are homomorphisms. We prove that if 𝔄 is a C*-algebra and σ, τ are *-homomorphisms with ker(σ) = ker(τ), then 𝔄 is (σ, τ)-amenable if and only if σ(𝔄) is amenable.
Attractivity results for a nonlinear functional integral equation
Authors: Agarwal Ravi P. , Banaś Józef , Dhage Bapurao C. , Sarkate Sidharth D.
Published: February 2021

In this paper two existence results concerning the global attractivity and global asymptotic attractivity for a certain functional nonlinear integral equation are proved. Our existence results include several existence and attractivity results obtained earlier by Darwish and Hu–Yan as special cases under weaker conditions. A fixed point theorem of Dhage is used in formulating our main results and the characterizations of solutions are obtained in the space of functions defined, continuous and bounded on unbounded intervals.
About some geometric characteristics of the generalized Möbius–Listing surfaces
Authors: Ricci Paolo Emilio , Tavkhelidze Ilia
Published: February 2021

We consider the cutting process of the generalized Möbius–Listing surface along some closed line which is parallel to its border line. We show connections of the resulting mathematical objects with the set of knots and links. In some cases we count the indices of the corresponding objects according to the known classification.
On the logarithmic summability of Fourier series
Authors: Gát György , Nagy Károly
Published: February 2021

In 2005, Tkebuchava constructed a set of logarithmic summation methods which includes Riesz and Nörlund logarithmic summation methods as limit cases. He gave estimates for the kernels of a trigonometric system and also some consequences with respect to the convergence of the means of a Fourier series. Here we give such good estimates for the kernels with respect to Walsh and Walsh–Kaczmarz systems as Tkebuchava did.
A generalization of the Euler beta function and applications
Authors: Lomidze Ilia
Published: February 2021

A generalization of the Euler beta function to the case of a multi-dimensional variable is defined. In this context, the original beta function is a function of a two-dimensional variable. An analogue of the Euler formula for this new function is derived for the case of a three-dimensional variable. Based on the derived formula, a number of relations for the Gauss hypergeometrical function are obtained. Moreover, the analytic formulae for some new integrals of special functions are obtained.
The growth of entire solutions of some algebraic differential equations
Authors: Gu Rongmei , Li Zhirong , Yuan Wenjun
Published: February 2021

In this paper, we estimate the growth order of entire solutions of some algebraic differential equations and improve the related result of Bergweiler, Barsegian and others. We also give some examples to show that our result is sharp in special cases.
A note on Lorentz–Zygmund spaces
Authors: Oba Hiroto , Sato Enji , Sato Yuichi
Published: February 2021

Let 1 ≤ q < p < ∞, and ℝ be the real line. Hörmander showed that any bounded linear translation invariant operator from Lp
(ℝ) to Lq
(ℝ) is trivial. Blozinski obtained an analogy to Hörmander in Lorentz spaces on the real line. In this paper, we generalize Blozinski's result in Lorentz–Zygmund spaces. Also, Bochkarev proved an inequality related to the Hausdorff–Young–Riesz theorem in Lorentz spaces, and the sharpness of the inequality. We improve Bochkarev's inequality in Lorentz–Zygmund spaces, and prove the sharpness of our inequality.
INTENSIVE SUNFLOWER CULTIVATION FROM IMMATURE SEEDS / CULTIVO INTENSO DEL GIRASOL A PARTIR DE SEMILLAS NO COMPLETAMENTE MADURAS / CULTURE INTENSIVE DE TOURNESOL À PARTIR DE GRAINES IMMATURES
Authors: I.V. Marin
Published: February 2021

Experiments were laid out to investigate the germination ability of immature sunflower seeds. Seeds of different age after fertilization were planted directly into bags filled with soil mixture. The experiments, conducted in the period 1984-1986, proved the possibility of sunflower cultivation with immature seeds directly in soil, without artificial nutritive media. Seeds are removed from a head 10 or 12 days after fertilization and immediately planted (do not permit them to dry) into bags with soil mixture. Our method is simple and easy. It does not demand special equipment, tools and specially prepared nutritive media and allows getting six vegetative cycles per year. It permits to obtain different line analogues in a single year instead of 6 or 7 years.
HETEROSIS IN TOP-CROSS HYBRIDS OF DIVERSE CYTOSTERILE SOURCES OF SUNFLOWER (Helianthus annuus L.) / HETEROSIS EN LOS HIBRIDOS TOP-CROSS DEL GIRASOL CREADOS DE DIVERSAS FUENTES CITOESTERILES / HÉTEROSIS DANS LES HYBRIDES TOP-CROSS DE TOURNESOL (Helianthus annuus L.) OBTENUS DE DIVERSES SOURCES CYTOSTÉRILES
Authors: Rajanna M.P. , Seetharam A. , Virupakshappa K. , Ramesh S.
Published: February 2021

Standard heterosis was estimated for eight quantitative traits in top-cross hybrids of three diverse cytoplasmic male sterile (CMS) sources of sunflower viz., Helianthus petiolaris (CMS-PET1), Helianthus petiolaris ssp. fallax (CMS-PEF1) and Helianthus annuus ssp. lenticularis (CMS-ANL2) maintained under different nuclear backgrounds. The top-cross hybrids were derived by crossing the above three CMS sources with 12 male parents in a line x tester design. Significant heterosis over two standard checks in the desirable direction was observed for all traits. All three sources under study advanced the maturity in most of the hybrids. CMS-PET1 was found to be the best compared with the other sources as far as oil content was concerned. Mean performance of the hybrids for achene yield and other economically important characteristics indicated that the hybrids derived in the cytoplasmic background of CMSANL2 were the best followed by CMS-PET1 and CMS-PEF1 suggesting that CMS diversification in heterosis breeding programs would be rewarding in sunflower.
Dry Sliding Wear Behaviours of Valve Seat Inserts Produced from High Chromium White Iron
Authors: Kalyon Ali , Özyürek Dursun , Günay Mustafa , Aztekin Hasan
Published: February 2021

In this present study, wear behaviours of high chromium white iron valve seat inserts and tappets used in the automotive sector were investigated. Wear behaviours of three different rates of high chromium white cast irons (containing 10, 12 and 14% chromium) were examined under heavy service conditions. For that purpose, the produced valve seat inserts were characterized through Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDS), X-ray diffraction (XRD) and hardness measurements. They were tested at a sliding speed of 1 ms−1, under 120 N load and for six different sliding distances (500, 1000, 1500, 2000, 2500, 3000 m) by using a standard wear apparatus (pin-on-disk type). The result showed that as the amount of Cr increased in the alloys, their hardness decreased. The decrease in the hardness were considered to be as the result of transformation of M7C3 carbides into M23C6 carbides in the structure. This decrease in hardness with increasing chromium content also increased the weight loss. Thus, it was determined that the white iron with 14% Cr (which had a greater amount of M23C6 carbides) was subjected to the highest wear.
Austrian Constitutional Court: The Annulment of the Run-off for the Presidency
Authors: Frank Stefan Leo
Published: February 2021

In this judgment the Austrian Constitutional Court pronouned that the runoff election of the Federal President had to be repeated in its entirety in all of Austria. It held that the system of postal voting is in conformity with the constitutional principles of voting in person and secrecy of ballots. However, votes may only be handled and counted by the collegiate election boards, the representative composition of which is seen as a specific guarantee for a transparent and impartial carrying out of elections. If state authorities transmit results of the vote count prior to the closing of the election, this runs counter to the principle of freedom of voting. A challenge to an election must be allowed if proven infringements of legal provisions aiming to prevent manipulations affect a decisive number of votes, regardless of whether or not manipulations have actually occurred.
Austrian Constitutional Court: Presidential Election – Violation of the Principle of Free Elections
Authors: Friedrichkeit-Lebmann Julia
Published: February 2021

One reason for the annulment of the Presidential Election was the violation of the principle of free elections enshrined in the Austrian Federal Constitutional Law (cf VfGH 1.7.2016, W I 6/2016, paras 511 ff). This can be seen as a consistent further development of former case-law by the Constitutional Court.
Austrian Constitutional Court: Presidential Election – Counterevidence and Influence of New Media
Authors: Matti Emanuel
Published: February 2021

In the course of the annulment of the run-off election of the Federal President by the Austrian Constitutional Court in 2016 formal unlawfulness became evident. This contribution argues that the Constitutional Court did not sufficiently consider if the proven illegalities actually had an effect on the election result. Furthermore, it discusses if the jurisprudence concerning electoral freedom needs to be interpreted more extensively in times of new media.
Parental perception of developmental vulnerability after inter-country adoption: a 10-year follow-up study: longitudinal study after inter-country adoption
Authors: Diamond Gary , Senecky Yehuda , Reichman Hadar , Inbar Dov , Chodick Gabriel
Published: February 2021

Background: The goal of the study was to identify developmental disabilities in internationally adopted children and evaluate the utility of pre-adoption screening.

Methods: Parents of 191 adopted children (80.93%) completed the Parents’ Evaluation of Developmental Status (PEDS) questionnaire. Responses were analyzed for the reported presence of developmental dysfunction in the children.

Results: For 137 children, parental response rates ranged from 55% to 74.4% at different junctures. The cumulative incidence of reported concerns over developmental and behavioral disabilities at 12 years post-adoption was 79%. Children adopted after 1-year-old had more behavioral problems than those adopted earlier (relative risk=4.62; 95% confidence interval: 0.97–22.07).

Conclusions: Parents perceive international adoption as being associated with a substantial risk for developmental problems. Even meticulous pre-adoption screening cannot preclude developmental problems that may appear in later childhood.
Development of Markov Chain-Based Queuing Model and Wireless Infrastructure for EV to Smart Meter Communication in V2G
Authors: Santoshkumar  , Udaykumar R. Y.
Published: February 2021

The electrical vehicles (EVs) can be connected to the grid for power transaction. The vehicle-to-grid (V2G) supports the grid requirements and helps in maintaining the load demands. The grid control center (GCC), aggregator and EV are three key entities in V2G communication. The GCC sends the information about power requirements to the aggregator. The aggregator after receiving the information from the GCC sends the information to the EVs. Based on the information, the interested EV owners participate in power transaction with the grid. The aggregator facilitates the EVs by providing the parking and charging slot. In this paper the queuing model for EVs connected to the grid and development of wireless infrastructure for the EV to Smart Meter communication is proposed. The queuing model is developed and simulated. The path loss models for WiMAX are analyzed and compared. Also, the physical layer of WiMAX protocol is modeled and simulated for the EV to Smart Meter communication in V2G.
Preparation of silicon boride SiBx (x = 3, 4, 5, 6) powders by chemical oven self-propagating combustion synthesis
Authors: Liu W. , Feng P. , Ren X. , Zhu L.
Published: February 2021

A new method was developed for quickly preparing a highemissivity silicon boride compound of SiBx (x = 3, 4, 5, 6) by highly exothermic Ti-TiO2-Si-Al chemical oven preheating. The SiBx combustion synthesis process and adiabatic combustion temperature were investigated. A large exothermic reaction occurred at the combustion temperature of 1 700 K. X-ray diffraction results indicate that an SiBx phase and a substantial amount of unreacted Si were identified in the products. By increasing the boron content until the Si-B ratio reached to 1 : 6, the diffraction peaks primarily indicated SiB6, SiB4, and Si11B33 in the final product. According to the spectra and quantitative results, the atomic chemical composition ratio of Si and B was close to the nominal composition. Thus, this method offers an efficient way to produce Si-B compounds with less time and energy consumption than current methods.
Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions
Authors: Suarez Pablo , Johnson Stephen , Biswas Anjan
Published: February 2021

This article studies the numerical solution of the two-dimensional sine-Gordon equation (SGE) using a split-step Chebyshev Spectral Method. In our method we split the 2D SGE by considering one dimension at a time, first along x and then along y. In each fractional step we solve a 1D SGE. Time integration is handled by a finite difference scheme. The numerical solution is then compared with many of the known numerical solutions found throughout the literature. Our method is simple to implement and second order accurate in time and has spectral convergence. Our method is both fast and accurate.
Vapor Films under Influence of High Heat Fluxes: Nongravity Surface Waves and Film Explosive Disintegration
Authors: Sinkevich O. A. , Glazkov V. V. , Ivochkin Yu. P. , Kireeva A. N.
Published: February 2021

Linear and non-linear stability analysis of the interface between a thin vapor film and a layer of liquid in the presence of a steady heat flux from a metal surface heated to a high temperature, to the vapor film and then from vapor to the subcooled liquid is investigated. The temperature dependence of saturation pressure is taken into account. Boundary conditions on the vapor–liquid interface that generalizes the known correlations on the free surface of liquid in the gravity field are derived. The thermal processes on the phase boundary lead to the generation of weakly decaying periodic surface waves of low amplitude and may cause small length waves (ripple), which are not capillary ones. Thermal processes on the phase interface are capable to provide the stability of a film of lights vapor under a layer of heavy liquid in the gravity field. The explosive instability may arise in the non-linear stage due to a weak variation of the film thickness or superheating of liquids.
Adaptive Synchronization of Filippov Systems with Unknown Parameters via Sliding Mode Control
Authors: Fu Shihui , Li Ke
Published: February 2021

In this paper, adaptive synchronization of Filippov systems with unknown parameters is investigated via sliding mode control. In order to obtain smooth error systems, Filippov systems are redesigned by the Generalized Hamiltonian system. The sliding mode control is applied to the error systems and stabilizes their zero solutions. Adaptive synchronization of chaotic systems via sliding mode control is investigated with the applications to Chua's system and the Duffing Oscillator with dry friction. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.
A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines
Authors: Corvaro Sara , Brocchini Maurizio
Published: February 2021

A novel mechanistic two-fluid model (CB model) similar, in spirit, to the Taitel and Dukler [1, 2] (TD model), for the identification of possible multiple solutions of a multi-phase (gas-liquid) stratified flow in slightly inclined pipelines, is proposed. While Blasius-type closures are used in the TD model to represent the wall friction coefficients, the newly-implemented CB model makes use of Colebrook-White-type closures. Moreover, different closures for the interfacial shear are also employed in the CB models. The predictive capabilities of the CB model have been tested by using several experimental data, finding a better agreement between measured and calculated data than that existing when the TD model is used. The region of multiple solutions is influenced by the closures in use, such a dependence is more evident when different interfacial friction factors are used. Moreover, for the CB model also the fluid mixture in use influences the boundaries of the non-uniqueness region, while by using the TD model the multiple-solution region is unchanged. The choice of closures for the interfacial friction strongly influences the holdups, the Andritsos and Hanratty [10] correlation significantly shifting the non-uniqueness region to small values of the inclination parameter. Such a behaviour is more and more significant with the increase of the superficial gas velocity, even if for values of the inclination parameter within the range of inclinations for stratified flows (i.e. less than about 30° from the horizontal [11]), multiple solutions were not found. Finally, for the fluid mixture and flow conditions analyzed, multivalued solutions are obtained only for upward flows. Moreover, the portion of multiple-solution region interested by co-current flow (that occurs for slightly upward and downward pipes) is rather small, so that the operational point unlikely falls within such a region in the case of the studied hydrocarbon gas-liquid mixture.
Self-adaptive inertial subgradient extragradient scheme for pseudomonotone variational inequality problem
Authors: Abubakar Jamilu , Kumam Poom , Rehman Habib ur
Published: February 2021

In this article, we propose a self-adaptive inertial subgradient extragradient algorithm for solving variational inequality problems involving pseudomonotone operator. The scheme uses a variable step sizes and inertial extrapolation step. The step size is self-adaptive, which does not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we prove the weak convergence of the sequence generated by the proposed algorithm to a solution of the considered problem. We give numerical experiments to illustrate the inertial-effect and the computational performance of our proposed algorithm in comparison with the existing state of the art algorithms.
A Spherical Cavity Expansion Penetration Model for Concrete Based on Hoek–Brown Strength Criterion
Authors: Xu H. , Wen H. M.
Published: February 2021

A spherical cavity expansion model for concrete is first proposed by using an elastic-brittle-plastic material law with Hoek–Brown strength criterion. The constitutive model can capture the basic features of the mechanical response of concrete materials including the effects of strain-softening and pressure hardening (pressure-dependent shear strength) and all the parameters used in the model can be determined from material tests. The forcing function obtained from the spherical cavity expansion analysis is then employed to construct a penetration model for concrete targets struck by ogival-nosed projectiles. It transpires that the present model predictions are in good agreement with experimental observations in terms of penetration depth and ballistic limits/residual velocities in the case of perforation.