bluuebunny/crossref_metadata_2025 huggingface dataset:
Extensions with Abelian Kernels in Protomodular Categories
Authors: Bourn D. , Janelidze G.
Published: February 2021

As observed by J. Beck, and as we know from M. Barr's and his joint work on triple cohomology, the classical isomorphism Opext ≅ 𝐻2 that describes group extensions with abelian kernels, can be deduced from the equivalence between such extensions and torsors (in an appropriate sense). The same is known for many other “group-like” algebraic structures, and now we present a purely-categorical version of that equivalence, essentially by showing that all torsors are extensions with abelian kernels in any pointed protomodular category, and by giving a necessary and sufficient condition for the converse.
Polytopes and 𝐾-Theory
Authors: Bruns W. , Gubeladze J.
Published: February 2021

This is an overview of results from our experiment of merging two seemingly unrelated disciplines – higher algebraic 𝐾-theory of rings and the theory of lattice polytopes. The usual 𝐾-theory is the “theory of a unit simplex”. A conjecture is proposed on the structure of higher polyhedral 𝐾-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.
Generalized Heisenberg Groups and Shtern's Question
Authors: Megrelishvili M.
Published: February 2021

Let 𝐻(𝑋) := (ℝ × 𝑋) ⋋ 𝑋* be the generalized Heisenberg group induced by a normed space 𝑋. We prove that 𝑋 and 𝑋* are relatively minimal subgroups of 𝐻(𝑋). We show that the group 𝐺 := 𝐻(𝐿4[0, 1]) is reflexively representable but weakly continuous unitary representations of 𝐺 in Hilbert spaces do not separate points of 𝐺. This answers the question of A. Shtern.
Weighted Estimates for Operators Generated by Maximal Functions on Nonhomogeneous Spaces
Authors: Komori Yasuo
Published: February 2021

We consider weighted weak type estimates for the modified Hardy–Littlewood maximal functions on a nonhomogeneous space. We use the new covering lemma by Sawano.
On Some Matrix Clifford Algebras
Authors: Chantladze Tamaz , Kandelaki Nodar , Ugulava Douglas
Published: February 2021

A sequence of matrices 𝑈1, 𝑈2, . . . , 𝑈𝑚 is constructed, which satisfies the conditions 𝑈𝑖𝑈𝑗 = – 𝑈𝑗𝑈𝑖 (𝑖 ≢ 𝑗), . These matrices are used to construct representations of a Clifford algebra for special quadratic forms.
Integral Inequalities for Littlewood–Paley Operators
Authors: Tan Changmei
Published: February 2021

Let 𝑇𝑓 denote the 𝑔-function 𝑔(𝑓) or the area integral 𝑠(𝑓). We give a characterization of functions Φ for which

where the constant 𝐶 is independent of 𝑓.
Some Algebraic and Geometric Structures on Poisson Manifolds
Authors: Tevdoradze Zaza
Published: February 2021

In this paper we study some algebraic properties of harmonic forms on Poisson manifolds. It is well known that in the classical case (on Riemannian manifolds) the product of harmonic forms is not harmonic. Here we describe the algebraic and analytical mechanisms explaining this fact. We also obtain a condition under which the product of de Rham cohomology classes, which includes harmonic representatives, can be represented by a harmonic form.
Some Approximation Properties for Modified Baskakov Type Operators
Authors: Gupta Vijay
Published: February 2021

We study some direct results for the recently introduced family of modified Baskakov type operators. In particular, we obtain local direct results on ordinary and simultaneous approximation and an estimation of error for linear combinations in terms of higher order modulus of continuity. We have applied the Steklov mean as a tool for the linear approximating method.
On the Boundedness and Compactness of Weighted Hardy Operators in Spaces 𝐿𝑝(𝑥)
Authors: Edmunds David E. , Kokilashvili Vakhtang , Meskhi Alexander
Published: February 2021

Necessary conditions and sufficient conditions for the boundedness/ compactness of weighted Hardy operators are established in generalized Lebesgue spaces 𝐿𝑝(𝑥).
On the Strong Differentiation of Multiple Integrals along Different Frames
Authors: Oniani Giorgi
Published: February 2021

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

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

Let 𝐶 = 𝐶[0, 1] denote the Banach space of continuous real functions on [0, 1] with the sup norm and let 𝐶* denote the topological subspace of 𝐶 consisting of functions with values in [0, 1]. We investigate the preimages of residual sets in 𝐶 under the operation of superposition Φ : 𝐶 × 𝐶* → 𝐶, Φ(𝑓, 𝑔) = 𝑓 ○ 𝑔. Their behaviour can be different. We show examples when the preimages of residual sets are nonresidual of second category, or even nowhere dense, and examples when the preimages of nontrivial residual sets are residual.
Semimartingale Local Time and the American Put Option
Authors: Babilua Petre
Published: February 2021

A new result is obtained on the vanishing of the local time of a non-negative continuous semimartingale at zero. Based on this result, an early exercise premium representation of a value function of the American put option is obtained in a one-dimensional general diffusion model.
Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
Authors: Belarbi Abdelkader , Benchohra Mouffak , Dhage Bapurao C.
Published: February 2021

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

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

We rephrase Fridli's result [Fridli, Acta Math. Hungar. 45: 393–396, 1985] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [Gát, Acta Math. Acad. Paedagog. Nyhzi. (N.S.) 17: 161–169, 2001] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.
Representation of Numbers by Quadratic Forms. Main Results of the Research Done in Georgia
Authors: Lomadze George
Published: February 2021

This is a survey of the main results obtained by the mathematicians of Georgia on the representation of natural numbers by integral quadratic forms before 2000.
On BVPS for Strongly Elliptic Systems with Higher Order Boundary Conditions
Authors: Lanzara Flavia
Published: February 2021

We consider BVPs for strongly elliptic systems of order 2𝑙 with the boundary conditions of order 𝑙 + 𝑛, 𝑛 ⩾ 0. By representing the solution by means of a simple layer potential of order 𝑛 and by imposing the boundary conditions, we get a singular integral system which is of regular type if and only if the boundary operator satisfies the Lopatinskiĭ condition and which can be solved if suitable compatibility conditions are satisfied. An explicit formula for computing the index of the BVP is given.
Bounded Solutions of Some Second Order Difference Equations
Authors: Mawhin Jean
Published: February 2021

We give some existence results for bounded solutions of linear and nonlinear second order difference equations. In particular, a method of lower and upper solutions for bounded solutions of some nonlinear second order difference equations is obtained, and applied to Duffing-type difference equations.
Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance
Authors: Sadyrbaev Felix
Published: February 2021

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

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

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

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

Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions.

One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.
A Modified Quasi-Reversibility Method for a Class of Ill-Posed Cauchy Problems
Authors: Boussetila Nadjib , Rebbani Faouzia
Published: February 2021

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

We study the pointwise convergence of Walsh–Fourier series on the class of functions of generalized 𝑝-bounded fluctuation.
Corrigenda to “On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces”
Authors: Oniani Giorgi
Published: February 2021

Corrections to [Oniani, Georgian Math. J. 13: 501–514, 2006] are listed.
Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients
Authors: Cialdea Alberto
Published: February 2021

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

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

We prove the boundedness of the Hardy–Littlewood maximal operator on variable Morrey spaces 𝐿𝑝(·), λ(·)(Ω) over a bounded open set Ω ⊂ ℝ𝑛 and a Sobolev type 𝐿𝑝(·), λ(·) → 𝐿𝑞(·), λ(·)-theorem for potential operators 𝐼
α(·), also of variable order. In the case of constant α, the limiting case is also studied when the potential operator 𝐼
α
acts into BMO space.
An Analytic Proof of the Matrix Spectral Factorization Theorem
Authors: Ephremidze Lasha , Janashia Gigla , Lagvilava Edem
Published: February 2021

An analytic proof of Wiener's theorem on factorization of positive definite matrix-functions is proposed.
On Estimating the Approximation of Locally Summable Functions by Gegenbauer Singular Integrals
Authors: Guliyev Vagif S. , Ibrahimov Elman J.
Published: February 2021

Using the generalized shift operator (GSO) generated by the Gegenbauer differential operator we introduce the notion of a Lebesgue–Gegenbauer (L-G)-point of a summable function 𝑓 on the interval [1,∞) and prove that almost all points of this interval are (L-G)-points of 𝑓. Furthermore, we give an exact (by order) estimation of the approximation of locally summable functions by singular integrals generated by GSO (Gegenbauer singular integrals).
Sobolev Spaces with Muckenhoupt Weights, Singularities and Inequalities
Authors: Haroske Dorothee D.
Published: February 2021

We use the recently introduced concept of growth envelopes to characterize weighted spaces of type , where 𝑤 belongs to some Muckenhoupt 𝐴𝑝 class, and discuss some applications.
Wavelets and Modular Inequalities in Variable 𝐿𝑝 Spaces
Authors: Izuki Mitsuo
Published: February 2021

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

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

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

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

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

For the two-dimensional linear differential system

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

For the second order nonlinear singular differential equation

𝑢″ + 𝑓(𝑡, 𝑢, 𝑢′) = 0,

the unimprovable sufficient conditions for the solvability of the problem with the condition at infinity

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

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

Let (ξ
𝑘)𝑘 ≥ 1 be a sequence of independent, identically distributed second order mean zero random elements in a separable Hilbert space 𝐻 and 𝐴 be an element of a certain class of linear continuous operators 𝐻 → 𝐻 such that ‖𝐴‖ < 1. Denote . We prove that if ‖𝐼 – 𝐴‖ tends to zero, where 𝐼 is the identity operator, then the normalized sum (𝐼 – 𝐴2)1/2
η
𝐴 converges in distribution to a Gaussian random element.
On Automorphism Groups of ω-Trees
Authors: Kipiani Archil
Published: February 2021

We give a characterization of all cardinal numbers representable as the cardinality of the group of all automorphisms of an ω-tree. As a consequence, we obtain some statements., in terms of ω-trees and their automorphisms, which are related to the continuum hypothesis.
Singular 2D Behaviors: Fornasini–Marchesini and Givone–Roesser Models
Authors: Lomadze Vakhtang , Rogers Eric , Wood Jeffrey
Published: February 2021

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

In [Category-theoretic models for intuitionistic set theory, 1985] D. Scott showed how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fourman, J. Pure Appl. Algebra 19: 91–101, 1980, Hayashi, On set theories in toposes, Springer, 1981].
On Divergence of Fourier Series with Respect to Multiplicative Systems on the Sets of Measure Zero
Authors: Bitsadze Kakha
Published: February 2021

For any multiplicative system of bounded type and any set of measure zero there exists a bounded measurable function whose Fourier series with respect to this system diverges on this set.
Rate of Approximation for Certain Szasz–Mirakyan–Durrmeyer Operators
Authors: Dubey Deepak Kumar , Gangwar Ravindra Kumar , Jain Shipra
Published: February 2021

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

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

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

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

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

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

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

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

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

The paper considers the lattice of fully invariant subgroups of the cotorsion hull of a countable direct sum of torsion-complete p-groups. It is shown that this lattice is isomorphic to the lattice of dual ideals of a semilattice made up of infinite matrices.
A finite dimensional 𝐴∞ algebra example
Authors: Allocca Michael P. , Lada Tom
Published: February 2021

We construct an example of an 𝐴∞ algebra structure defined over a finite dimensional graded vector space.
Higher order track categories and the algebra of higher order cohomology operations
Authors: Baues Hans-Joachim
Published: February 2021

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

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

Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv.
35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A
∞-algebra structure on the homology of a dg-algebra.

In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A
∞-algebra structure after a finite amount of computational work.
On equivariant disconnected rational homotopy theory
Authors: Golasiński Marek
Published: February 2021

An equivariant disconnected Sullivan–de Rham equivalence is developed using Kan's result on diagram categories. Given a finite Hamiltonian group G, let X be a G-simplicial set. It is shown that the associated system of algebras indexed by the category 𝒪(G) of a canonical orbit can be “approximated” (up to a weak equivalence) by such a system ℳ
X
with the properties required by nonequivariant minimal algebras.
On the operad of associative algebras with derivation
Authors: Loday Jean-Louis
Published: February 2021

We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to the operad of “moulds”. It provides an efficient environment for doing integro-differential calculus. Interesting variations are obtained by using formal group laws. The preceding case corresponds to the additive formal group law. We unravel the notion of homotopy associative algebra with derivation in the spirit of Kadeishvili's work.
Distortion of the Grötzsch–Belinskii type for generalized quasiconformal mappings
Authors: Golberg Anatoly
Published: February 2021

The geometric properties of quasiconformal mappings and generalized quasiconformal mappings are studied. Inequalities of the Grötzsch–Belinskii type are established to estimate the distortion of p-moduli of ring domains for these classes of mappings.
Coincidence and fixed points for hybrid tangential maps
Authors: Kamran Tayyab , Kiran Quanita
Published: February 2021

In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.
Asymptotic efficiency of exponentiality tests based on order statistics characterization
Authors: Nikitin Ya. Yu. , Volkova Ksenia Yu.
Published: February 2021

We propose new scale-invariant tests for exponentiality based on the characterization in terms of order statistics. Limiting distributions and large deviations of new statistics are described and their local Bahadur efficiency for common alternatives is calculated.
An operator version of Abel's continuity theorem
Authors: Tarieladze Vaja
Published: February 2021

For a Banach space X let 𝔄 be the set of continuous linear operators A : X → X with ‖A‖ < 1, I be the identity operator and

𝔄
c
≔ {A ∈ 𝔄 : ‖I – A‖ ≤ c(1 – ‖A‖)},

where c ≥ 1 is a constant. Let, moreover, (xk
)
k≥0 be a sequence in X such that the series converges and ƒ : 𝔄 ∪ {I} → X be the mapping defined by the equality

It is shown that ƒ is continuous on 𝔄 and for every c ≥ 1 the restriction of ƒ to 𝔄
c
∪ {I} is continuous at I.
Mazur–Ulam theorem for Riesz spaces
Authors: Çelik Cesim , Ercan Zafer
Published: February 2021

We give a Mazur–Ulam type theorem for Riesz spaces. In particular, a generalization of the Mazur–Ulam theorem is given in terms of a lattice normed space.
On a relationship between the measurability and continuity of real-valued functions
Authors: Kharazishvili Alexander
Published: February 2021

We discuss certain relationships between the following fundamental concepts of analysis: measurability and continuity. Some examples are presented, which underline deep connections between measurable and continuous real-valued functions. In particular, a variant of Luzin's C-property is formulated for a class of measures significantly wider than the class of Borel measures. In this context, absolutely nonmeasurable functions and Sierpiński–Zygmund type functions are considered and compared.
On the statistical estimation of the logarithmic derivative of a measure in a Hilbert space
Authors: Nadaraya Elizbar , Sokhadze Grigol
Published: February 2021

We consider the problem of statistical estimation of the logarithmic derivative of a measure in an infinite-dimensional Hilbert space. It is shown that an approximating sequence of finite-dimensional estimates can be constructed for the unknown logarithmic derivative using independent observation data.
On the equivalence of a strong symmetrical and a strong complete differentiation basis
Authors: Zerekidze Tamaz
Published: February 2021

It is proved that – different from the case of binary differentiation bases – in the case of strong differentiation bases a symmetrical and a complete differentiation basis are equivalent throughout the space of locally integrable functions.
A note on the existence of three positive periodic solutions of functional difference equation
Authors: Chen Shengping
Published: February 2021

It is shown that, under certain assumptions, the functional difference equations have at least three positive periodic solutions. Applications are given to illustrate the main results.
Function classes and convergence almost everywhere
Authors: Tsagareishvili Vakhtang
Published: February 2021

For a certain class of orthonormal systems (ONS) on [0, 1] there exists a family of functions from L
2(0, 1), independent from that class, such that the Fourier series with respect to each ONS of the class converges a.e. for any member of the family. Similar result holds for the summability of Fourier integrals.
Electromagnetic scattering by cylindrical orthotropic waveguide irises
Authors: Castro Luis P. , Duduchava Roland , Kapanadze David
Published: February 2021

The paper is devoted to the mathematical analysis of scattered time-harmonic electromagnetic waves by an infinitely long cylindrical orthotropic waveguide iris. This is modeled by an orthotropic Maxwell system in a cylindrical waveguide iris for plane waves propagating in the x
3-direction, imbedded in an isotropic infinite medium. The problem is equivalently reduced to a 2-dimensional boundary-contact problem with the operator div M grad+k
2 inside the domain and the (Helmholtz) operator Δ+k
2 = div grad+k
2 outside the domain. Here M is a 2 × 2 positive definite, symmetric matrix with constant, real valued entries. The unique solvability of the appropriate boundary value problems is proved and the regularity of solutions is established in Bessel potential spaces.
A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities
Authors: Partsvania Nino
Published: February 2021

A priori estimates of solutions of two-point boundary value problems for two-dimensional systems of differential inequalities with singular coefficients are established.
Screen slant lightlike submanifolds of indefinite cosymplectic manifolds
Authors: Gupta Ram Shankar
Published: February 2021

In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite cosymplectic manifold. We provide a characterization theorem for the existence of a screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of and prove some characterization theorems.
Boundedness of linear operators via atoms on Hardy spaces with non-doubling measures
Authors: Yang Dachun , Yang Dongyong
Published: February 2021

Let μ be a non-negative Radon measure on which satisfies only the polynomial growth condition. Let 𝒴 be a Banach space and H
1(μ) be the Hardy space of Tolsa. In this paper, the authors prove that a linear operator T is bounded from H
1(μ) to 𝒴 if and only if T maps all (p, γ)-atomic blocks into uniformly bounded elements of 𝒴; moreover, the authors prove that for a sublinear operator T bounded from L
1(μ) to L
1, ∞(μ), if T maps all (p, γ)-atomic blocks with p ∈ (1, ∞) and γ ∈ ℕ into uniformly bounded elements of L
1(μ), then T extends to a bounded sublinear operator from H
1(μ) to L
1(μ). For the localized atomic Hardy space h
1(μ), the corresponding results are also presented. Finally, these results are applied to Calderón–Zygmund operators, Riesz potentials and multilinear commutators generated by Calderón–Zygmund operators or fractional integral operators with Lipschitz functions to simplify the existing proofs in the related papers.
Normality and shared values concerning differential polynomial
Authors: Lei Chunlin L. , Yang Degui G. , Zeng Cuiping P.
Published: February 2021

Let ℱ be a family of meromorphic functions in a domain D; let k ≥ 2 be a positive integer; and let a, b and c be complex numbers such that b ≠ 0 and a ≠ c. If, for each ƒ ∈ ℱ, all zeros of ƒ have multiplicity at least k, ƒ(z) = a ⇔ D(ƒ) = b, and D(ƒ) = 0 ⇒ ƒ(z) = c, where D(ƒ) is the differential polynomial of ƒ(z), then ℱ is normal in D.
On a relationship between absolutely nonmeasurable functions and Sierpiński–Zygmund functions
Authors: Kharazishvili Alexander
Published: February 2021

For a given topological space E, some properties of absolutely nonmeasurable real-valued functions, with respect to a certain class of measures on E, are considered. These functions are compared with Sierpiński–Zygmund type real-valued functions on E which have the property that they are discontinuous on every uncountable subset of E.
Graded primal ideals
Authors: Atani Shahabaddin Ebrahimi , Darani Ahmad Yousefian
Published: February 2021

Let R be a graded commutative ring. This paper is devoted to study some properties of graded primal ideals of R. In particular we show that there is a one-to-one correspondence between the graded P-primal ideals of R and the graded PS
-primal ideals of RS
, where S is a multiplicatively closed subset of homogeneous elements of R and P is a graded prime ideal of R with P ∩ S = ø.
Choquet integrals, weighted Hausdorff content and maximal operators
Authors: Tang Lin
Published: February 2021

The boundedness of maximal operators on the weighted Choquet space and the Choquet–Morrey space is established. These results are used to study Carleson embeddings for weighted Sobolev spaces.
DURABLE RESISTANCE TO BROOMRAPE (Orobanche cumana Wallr. / Orobanche cernua Loefl.) IN SUNFLOWER / RESISTENCIA CONSTANTE A LA OROBANCA (Orobanche cumana Wallr./Orobanche cernua Loefl.) EN EL GIRASOL / RÉSISTANCE DURABLE À L’OROBANCHE (Orobanche cumana Wallr./Orobanche cernua Loefl.) CHEZ LE TOURNESOL
Authors: Venkov Ventsislav , Shindrova Pepa
Published: February 2021

Six cultivars and one hybrid were evaluated for resistance to broomrape in the period 1988-1999. It was found that the resistance varied in the range from 0 to 100%. The evaluation was carried out under greenhouse conditions. Infestations were induced by mixed broomrape populations collected from different regions in Bulgaria. Different lines obtained from three cultivars, Progress, Oktjabr (Russia) and Vega (Bulgaria), and the hybrid Sorem 80 (Romania) showed stable resistance (80-100%) after ten years of evaluation, in spite of the occurrence and distribution of new races (D+E) of the parasite in Bulgaria.
Processing and Characterization of CrB2-Based Novel Composites
Authors: Bedse R. D. , Sonber J. K. , Sairam K. , Murthy T. S. R. Ch. , Hubli R. C.
Published: February 2021

This paper presents the results of investigations carried out on processing and characterization of CrB2-based novel composites. Niobium metal powder was used as additive to form new composites. Hardness and fracture toughness of chromium boride increased by addition of niobium. CrB2 composites were prepared by addition of 2.5, 10 and 20 wt.% Nb. Density of higher than 95% ρ
th was achieved in all the samples. Hot pressed samples were analyzed to contain reaction products of NbB2, Cr2B3 and Cr3B4 phases along with CrB2. Hardness of CrB2 composite was increased from 18.46 GPa to 21.89 GPa by increasing the Nb content from 2.5 to 10 wt.%. Fracture toughness of composites prepared by addition of 2.5 and 10% was measured as 3.11 and 3.38 MPa.m1/2 respectively. Addition of 20% Nb resulted in increased fracture toughness of 4.32 MPa.m1/2
.
A Characterization of Hot Flow Behaviors Involving Different Softening Mechanisms by ANN for As-Forged Ti-10V-2Fe-3Al Alloy
Authors: Quan Guo-zheng , Zou Zhen-yu , Wen Hai-rong , Pu Shi-ao , Lv Wen-quan
Published: February 2021

The isothermal compressions of as-forged Ti-10V-2Fe-3Al alloy at the deformation temperature range of 948–1,123 K and the strain rates in the range of 0.001–10 s−1 with a height reduction of 60% were conducted on a Gleeble-3500 thermo-mechanical simulator. The flow behaviors show nonlinear sensitivity to strain, strain rate and temperature. Based on the experimental data, an artificial neural network (ANN) with back-propagation algorithm was developed to deal with the complex deformation behavior characteristics. In the present ANN model, strain, strain rate and temperature were taken as inputs, and flow stress as output. A comparative study on the constitutive relationships based on regression and ANN methods was conducted. According to the predicted and experimental results, the predictabilities of the two models have been evaluated in terms of correlation coefficient (R) and average absolute relative error (AARE). The R-value and the AARE-value at strain of 0.5 from the ANN model is 0.9998 and 0.572%, respectively, better than 0.9902 and 6.583% from the regression model. The predicted strain–stress curves outside of experimental conditions indicate similar characteristics with experimental curves. The results have sufficiently articulated that the well-trained ANN model with back-propagation algorithm has excellent capability to deal with the complex flow behaviors of as-forged Ti-10V-2Fe-3Al alloy.
(In)Security and Self-Government: Lessons from the Mexican Experience
Authors: Correa Catalina Pérez , Xochitiotzi Carlos De la Rosa
Published: February 2021

Using the Mexican experience in the centralization of public security, this paper proposes federalism as a model of a vertical control of powers and, more importantly, a way of promoting self-governance, citizen participation and, through them, local security. We argue that while federalism as an organizational model of the State does not guarantee self-governance or citizen participation, it can help promote them and through their enhancement, improve security at the community level. Since 2006, the Mexican government has implemented a security strategy that has increasingly centralized public security decisions. The strategy relies on the deployment of federal security forces (Army, Navy and Federal Police) across the country, to replace or support state and local police. The results have been mostly negative. On one hand, there has been an exacerbation of violence in the country, including many incidents in which violence was used disproportionately or illegally by state officials against civilians. On the other, the use of federal forces has undermined the federalist regime which serves as a check on the exercise of power by federal authorities, thus undermining state and local institutional capacities. The lessons from the Mexican case can be useful for other federal systems responding to organized crime.
Effects of Air-Impingement Jet Drying on Drying Kinetics, Nutrient Retention and Rehydration Characteristics of Onion (Allium cepa) Slices
Authors: Li Wenfeng , Wang Moyi , Xulin Xiao  , Zhang Baoshan , Yang Xingbin
Published: February 2021

This study is designed to investigate drying kinetics, nutrient retention and rehydration ratio of onion slices under air-impingement jet drying (AIJD) with different drying temperatures (40, 50 and 60°C), air velocities (11, 12 and 13 m/s), and the distance between jet nozzles and material box (0, 40 and 80 mm). Additionally, the influence of AIJD and hot air drying (HAD) on drying efficiency and product quality of onion slices was comparatively investigated. It was found that the moisture effective diffusivity of onion slices under AIJD ranged from 3.51 × 10−10to 5.51 × 10−10m2/s, and the activation energy (Ea) of onion determined from Arrhenius equation was 14.73 kJ/mol, and ascorbic acid content (AAC), total phenolic content (TPC) and DPPH (1,1-diphenyl-2-picrylhydrazyl) scavenging activity (DSA) significantly decreased in the dried onions compared to that in fresh onion. In addition, the results suggest that the Modified Page model provides the best fit for AIJD curves. Furthermore, AIJD product is better than HAD both in decreasing drying time and enhancing drying rate, AAC, TPC, DSA and rehydration ratio. Accordingly, the AIJD method has advantages in drying time and quality of products, indicating that this technology can be widely applied to food drying process.
Study on photocatalytic activity based on different pH values of AgBr/Ag2CO3 heterojunction
Authors: Li Fengfeng , Zhang Mingxi , Wang Jin , Cai Yongfeng , Zhao Dushao , Guo Mingyue , Wang Luyi , Shen Yi
Published: February 2021

In this work, we fabricate a highly efficient photocatalytic AgBr/Ag2CO3 heterojunction through the co-precipitation method. The obtained samples were characterized by means of X-ray diffraction, scanning electron microscopy, transmission electron microscopy, ultraviolet-visible diffuse reflectance spectra and X-ray photoelectron spectroscopy. The photocatalytic activities of obtained samples can be assessed by visible light (λ ≥ 400 nm) degradation of rhodamine B solution. X-ray diffraction revealed that the crystallinity of the AgBr/Ag2CO3heterojunction was significantly higher than pure AgBr and Ag2CO3. Moreover, the AgBr/ Ag2CO3 heterojunction prepared at pH = 6 has the best photocatalytic performance, it can raise the degradation degree of rhodamine B over 95% at 20 min. Finally, a possible photocatalytic mechanism is discussed.
Assessing knowledge of genomic concepts among Canadian nursing students and faculty
Authors: Dewell Sarah , Benzies Karen , Ginn Carla , Seneviratne Cydnee
Published: February 2021

Objectives

Contemporary nurses require genomic literacy to engage in genomics-informed health care. Little is known about the genomic literacy of undergraduate nursing students and faculty in many countries. Concept inventories can be used to assess levels of knowledge and inform curriculum development.

Methods

The 31-item Genomic Nursing Concept Inventory (GNCI) was administered to undergraduate nursing students (n=207) and faculty (n=13) in a school of nursing with two sites in western Canada.

Results

Scores on the GNCI were low and comparable to those of US students and faculty. Six student characteristics were associated with total score on the GNCI.

Conclusions

Both students and faculty need to increase their knowledge of genomics. Mandates from national nursing organizations and international collaboration are needed to develop and implement foundational genomics content for undergraduate curricula to enable graduates to engage in genomics-informed health care.