bluuebunny/crossref_metadata_2025_split huggingface dataset:
Asymptotic Behaviour and Hopf Bifurcation of a Three-Dimensional Nonlinear Autonomous System
Authors: Baráková Lenka 
Published: February 2021

Abstract
A three-dimensional real nonlinear autonomous system of a concrete type is studied. The Hopf bifurcation is analyzed and the existence of a limit cycle is proved. A positively invariant set, which is globally attractive, is found using a suitable Lyapunov-like function. Corollaries for a cubic system are presented. Also, a two-dimensional nonlinear system is studied as a restricted system. An application in economics to the Kodera's model of inflation is presented. In some sense, the model of inflation is an extension of the dynamic version of the neo-keynesian macroeconomic IS-LM model and the presented results correspond to the results for the IS-LM model.
AMD-Numbers, Compactness, Strict Singularity and the Essential Spectrum of Operators
Authors: Castejón A. , Corbacho E. , Tarieladze V. 
Published: February 2021

Abstract
For an operator 𝑇 acting from an infinite-dimensional Hilbert space 𝐻 to a normed space 𝑌 we define the upper AMD-number and the lower AMD-number as the upper and the lower limit of the net (δ(𝑇|𝐸))𝐸∈𝐹𝐷(𝐻), with respect to the family 𝐹𝐷(𝐻) of all finite-dimensional subspaces of 𝐻. When these numbers are equal, the operator is called AMD-regular.
It is shown that if an operator 𝑇 is compact, then and, conversely, this property implies the compactness of 𝑇 provided 𝑌 is of cotype 2, but without this requirement may not imply this. Moreover, it is shown that an operator 𝑇 has the property if and only if it is superstrictly singular. As a consequence, it is established that any superstrictly singular operator from a Hilbert space to a cotype 2 Banach space is compact.
For an operator 𝑇, acting between Hilbert spaces, it is shown that and are respectively the maximal and the minimal elements of the essential spectrum of , and that 𝑇 is AMD-regular if and only if the essential spectrum of |𝑇| consists of a single point.
A Problem of Linear Conjugation for Analytic Functions with Boundary Values from the Zygmund Class
Authors: Kokilashvili V. , Paatashvili V. 
Published: February 2021

Abstract
The solvability conditions are established for a problem of linear conjugation for analytic functions with boundary values from the Zygmund class 𝐿(ln+ 𝐿)
α
when the conjugation coefficient is piecewise-continuous in the Hölder sense. Solutions of the problem are constructed in explicit form.
On Obtaining Dual Sequences Via Quasi-Monomiality
Authors: Cheikh Youssèf Ben 
Published: February 2021

Abstract
In this paper, we introduce a method to obtain the dual sequence of a given polynomial set using the lowering operator associated with the involved polynomials. As application, we derive polynomial expansions of analytic functions. The particular case corresponding to Boas–Buck polynomials allows us to unify many polynomial expansions of analytic functions in the literature. This method can be useful in studying many problems arising in the theory of polynomials as the so-called connection and linearization problems.
Solvability and the Unique Solvability of A Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations
Authors: Hakl R. , Lomtatidze A. , Šremr J. 
Published: February 2021

Abstract
Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem
𝑢′ (𝑡) = 𝐹 (𝑢) (𝑡), 𝑢(𝑎) – λ𝑢(𝑏) = ℎ(𝑢)
are established, where 𝐹 : 𝐶([𝑎, 𝑏]; 𝑅) → 𝐿([𝑎, 𝑏];𝑅) is a continuous operator satisfying the Carathéodory condition, ℎ : 𝐶([𝑎, 𝑏]; 𝑅) → 𝑅 is a continuous functional, and λ ∈ 𝑅+.
Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications
Authors: Yang Dachun 
Published: February 2021

Abstract
The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.
Time-Dependent Barrier Options and Boundary Crossing Probabilities
Authors: Novikov A. , Frishling V. , Kordzakhia N. 
Published: February 2021

Abstract
The problem of pricing of time-dependent barrier options is considered in the case when interest rate and volatility are given functions in Black–Scholes framework. The calculation of the fair price reduces to the calculation of non-linear boundary crossing probabilities for a standard Brownian motion. The proposed method is based on a piecewise-linear approximation for the boundary and repeated integration. The numerical example provided draws attention to the performance of suggested method in comparison to some alternatives.
On the Mathematical Basis of the Linear Sampling Method
Authors: Cakoni Fioralba , Colton David 
Published: February 2021

Abstract
The linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. The method is based on showing that a linear integral equation of first kind has a solution that becomes unbounded as a parameter 𝑧 approaches the boundary of the scatterer 𝐷 from inside 𝐷. However, except for the case of the transmission problem, the case where z is in the exterior of 𝐷 is unresolved. Since for the inverse scattering problem 𝐷 is unknown, this step is crucial for the mathematical justification of the linear sampling method. In this paper we give a mathematical justification of the linear sampling method for arbitrary 𝑧 by using the theory of integral equations of first kind with singular kernels.
About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations
Authors: Domoshnitsky Alexander 
Published: February 2021

Abstract
In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value problem for the heat equation: the maximum principle is not valid, unbounded solutions appear while all solutions of the classical Dirichlet problem tend to zero at infinity, for “narrow enough zones” all solutions oscillate instead of being positive. We establish that the Dirichlet problem for the wave equation with delay can possess unbounded solutions. We estimate zones of positivity of solutions for hyperbolic equations.
On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities
Authors: Mukhigulashvili S. 
Published: February 2021

Abstract
For a differential system

where λ ∈]0, 1[ and ℎ𝑖 :]𝑎, 𝑏[×]0, +∞[×ℝ → [0, +∞[ (𝑖 = 0, 1, 2) are continuous functions, we have established sufficient conditions for the existence of at least one solution satisfying one of the two boundary conditions

and
Analytic Subsets of Products of Infinite-Dimensional Projective Spaces
Authors: Ballico E. 
Published: February 2021

Abstract
Let 𝑉𝑖, 1 ≤ 𝑖 ≤ 𝑠, be complex topological vector spaces with 𝑉1 infinite-dimensional and 𝑌 a closed analytic subset of finite codimension of 𝐏(𝑉1) × . . . × 𝐏(𝑉𝑠). Here we show that 𝑌 is algebraic (at least if each 𝑉𝑖 is a Banach space) and that any two points of 𝑌 may be connected by a chain of 𝑠 + 3 lines contained in 𝑌.
Simplicial Crossed Modules and Mapping Cones
Authors: Conduché D. 
Published: February 2021

Abstract
Given a bisimplicial group 𝐺∗∗ such that 𝑁(𝐺)∗𝑞 = {1} for 𝑞 ⩾ 2, a simplicial group is obtained whose Moore complex is a mapping cone of the chain morphism 𝑁(𝐺)∗1 → 𝑁(𝐺)∗0. This simplicial group is homotopy equivalent to the diagonal of 𝐺∗∗. In the last section a special case is considered.
Badora's Equation on Non-Abelian Locally Compact Groups
Authors: Elqorachi E. , Akkouchi M. , Bakali A. , Bouikhalene B. 
Published: February 2021

Abstract
This paper is mainly concerned with the following functional equation

where 𝐺 is a locally compact group, 𝐾 a compact subgroup of its morphisms, and μ is a generalized Gelfand measure. It is shown that continuous and bounded solutions of this equation can be expressed in terms of μ-spherical functions. This extends the previous results obtained by Badora (Aequationes Math. 43: 72–89, 1992) on locally compact abelian groups. In the case where 𝐺 is a connected Lie group, we characterize solutions of the equation in question as joint eigenfunctions of certain operators associated to the left invariant differential operators.
Convergence of Marcinkiewicz Means of Integrable Functions with Respect to Two-Dimensional Vilenkin Systems
Authors: Gát György 
Published: February 2021

Abstract
We prove that the maximal operator of the Marcinkiewicz mean of integrable two-variable functions is of weak type (1, 1) on bounded two-dimensional Vilenkin groups. Moreover, for any integrable function 𝑓 the Marcinkiewicz mean σ
𝑛𝑓 converges to 𝑓 almost everywhere.
On the Measurability of Functions with Respect to Certain Classes of Measures
Authors: Kharazishvili A. , Kirtadze A. 
Published: February 2021

Abstract
The concept of measurability of real-valued functions with respect to various classes of measures is introduced and the associated notion of an absolutely nonmeasurable function is investigated. A characterization of such functions is given. Also, it is shown that functions produced by the classical Vitali partition of the real line are measurable with respect to the class of all extensions of the Lebesgue measure on this line.
Equicontinuity and Quasi-Uniformities
Authors: Corbacho E. , Tarieladze V. , Vidal R. 
Published: February 2021

Abstract
For topological spaces 𝑋, 𝑌 with a fixed compatible quasi-uniformity 𝑄 in 𝑌 and for a family (𝑓𝑖)𝑖∈𝐼 of mappings from 𝑋 to 𝑌, the notions of even continuity in the sense of Kelley, topological equicontinuity in the sense of Royden and 𝑄-equicontinuity (i.e., equicontinuity with respect to the topology of 𝑋 and 𝑄) are compared. It is shown that 𝑄-equicontinuity implies even continuity, and if 𝑄 is locally symmetric, it implies topological equicontinuity too. It turns out that these notions are equivalent provided 𝑄 is a uniformity compatible with a compact topology, but the equivalence may fail even for a locally symmetric quasi-uniformity 𝑄 compatible with a compact metrizable topology.
Witt's Theorem for Groups with Action and Free Leibniz Algebras
Authors: Datuashvili T. 
Published: February 2021

Abstract
A subcategory of the category of groups with action is determined and it is proved that the functor defined in [Datuashvili, Georgian Math. J. 9: 671–681, 2002] takes free objects from this category to free Leibniz algebras. This result gives a solution to a problem stated by J.-L. Loday [Enseign. Math. 39: 269–293, 1993], [K-Theory, 30: 105–127, 2003] and is an analogue of Witt's theorem for groups and Lie algebras [Witt, J. Reine Angew. Math. 1: 152–160, 1937].
Linearization and Higher Order Nonlinear Oscillation Theorems Using Comparison Methods
Authors: Agarwal Ravi P. , Grace Said R. , O'Regan Donal 
Published: February 2021

Abstract
We establish some new oscillation criteria for higher order nonlinear differential equations. The main idea involves comparing our equation with the related linear second order differential equations so that the known oscillation theorems from the literature can be employed directly.
New Applications of Algebraic Formulae for Topological Invariants
Authors: Khimshiashvili G. 
Published: February 2021

Abstract
Some geometric results are presented which can be derived from algebraic formulae for topological degree and Euler characteristic. In particular, it is shown that Euler characteristics of configuration spaces and work spaces of mechanical linkages can be computed in an algorithmic way. We also find the expected gradient degree of rotation invariant Gaussian random polynomial on an even-dimensional space.
Two-Step Systems for G-H-Relaxed Pseudococoercive Nonlinear Variational Problems Based on Projection Methods
Authors: Agarwal Ravi P. , O'Regan Donal , Verma Ram U. 
Published: February 2021

Abstract
The approximation-solvability of a generalized system of nonlinear variational inequalities (SNVI) involving relaxed pseudococoercive mappings, based on the convergence of a system of projection methods, is presented. The class of relaxed pseudococoercive mappings is more general than classes of strongly monotone and relaxed cocoercive mappings. Let 𝐾1 and 𝐾2 be nonempty closed convex subsets of real Hilbert spaces 𝐻1 and 𝐻2, respectively. The two-step SNVI problem considered here is as follows: find an element (𝑥*, 𝑦*) ∈ 𝐻1 × 𝐻2 such that (𝑔(𝑥*), 𝑔(𝑦*)) ∈ 𝐾1 × 𝐾2 and

where 𝑆 : 𝐻1 × 𝐻2 → 𝐻1, 𝑇 : 𝐻1 × 𝐻2 → 𝐻2, 𝑔 : 𝐻1 → 𝐻1 and ℎ : 𝐻2 → 𝐻2 are nonlinear mappings.
Integrability of the Majorant of the Fourier Series Partial Sums with Respect to Bases
Authors: Tkebuchava George 
Published: February 2021

Abstract
The majorant of Fourier series partial sums with respect to the system of functions formed by the product of 𝐿([0, 1]) space bases is considered. It is proved that in any Orlicz space wider than 𝐿(log+ 𝐿)𝑑([0, 1]𝑑), 𝑑 ≥ 1, the set of functions with such a majorant is integrable on [0, 1]𝑑 and has the first Baire category.
Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations
Authors: Bouikhalene Belaid , Kabbaj Samir 
Published: February 2021

Abstract
We show that Cauchy's, d'Alembert's functional equations and their generalizations are the functional equations for bounded spherical functions associated to some Gel'fand pairs. Our results are very close to the ones obtained by Stetkær in [Aequationes Math. 48: 220–227, 1994].
Interior and Exterior Problems of Couple-Stress and Classical Elastostatics with Given Friction
Authors: Gachechiladze Roland 
Published: February 2021

Abstract
We consider an interior problem of statics of couple-stress elasticity for anisotropic nonhomogeneous media with friction taken into account and the corresponding exterior problem for homogeneous isotropic media. The question of the existence and uniqueness of weak solutions of these problems is studied when friction forces occur along the boundary of an elastic medium or on some part of this boundary.
Some Basic 𝑑-Orthogonal Polynomial Sets
Authors: Zaghouani Ali 
Published: February 2021

Abstract
The purpose of this paper is to study the class of polynomial sets which are at the same time 𝑑-orthogonal and 𝑞-Appell. By a linear change of variable, the resulting set reduces to 𝑞-Al-Salam–Carlitz polynomials, for 𝑑 = 1. Various properties of the obtained polynomials are singled out: a generating function, a recurrence relation of order 𝑑 + 1. We also explicitly express a 𝑑-dimensional functional for which the d-orthogonality holds.
Convergence in Measure of Logarithmic Means of Double Walsh–Fourier Series
Authors: Gát György , Goginava Ushangi , Tkebuchava George 
Published: February 2021

Abstract
The main aim of this paper is to prove that the logarithmic means of the double Walsh–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 𝐿log 𝐿(𝐼2), the set of functions for which quadratic logarithmic means of the double Walsh–Fourier series converge in measure is of first Baire category.
On the Accuracy of Kraft Upper Bound for the 𝐿1-Distance between Gaussian Densities in 𝑅𝑘
Authors: Kvatadze Zurab , Shervashidze Tengiz 
Published: February 2021

Abstract
For a scaled family of centered nonsingular Gaussian measures in 𝑘𝑘 the 𝐿1-distance between any two densities is compared with its Kraft upper bound.
Optimal Control in Bombieri's and Tammi's Conjectures
Authors: Prokhorov Dmitri , Vasil'ev Alexander 
Published: February 2021

Abstract
Let 𝑆 stand for the usual class of univalent regular functions in the unit disk 𝑈 = {𝑧 : |𝑧| < 1} normalized by 𝑓(𝑧) = 𝑧 + 𝑎2𝑧2 + . . . in 𝑈, and let 𝑆𝑀 be its subclass defined by restricting |𝑓(𝑧)| < 𝑀 in 𝑈, 𝑀 ≥ 1. We consider two classical problems: Bombieri's coefficient problem for the class 𝑆 and the sharp estimate of the fourth coefficient of a function from 𝑆𝑀. Using Löwner's parametric representation and the optimal control method we propose a way to finding initial Bombieri's numbers and derive a sharp constant 𝑀0 such that for all 𝑀 ≥ 𝑀0 the Pick function gives the local maximum to |𝑎4|. Numerical approximation is given.
Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
Authors: Gát György , Goginava Ushangi 
Published: February 2021

Abstract
We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞.
Oscillations of Higher Order Functional Differential Equations with Impulses
Authors: Zhang Chaolong , Feng Weizhen 
Published: February 2021

Abstract
A kind of higher order sub-and super-linear FDE with impulses is studied in this paper. Several criteria on the oscillations of solutions are given. In particular, in the case where the coefficients of equations are positive and continuous functions, we find some suitable impulse functions such that all solutions of the equation are oscillatory under the impulse control.
The Dirichlet Problem for Harmonic Functions in the Smirnov Class with Variable Exponent
Authors: Kokilashvili Vakhtang , Paatashvili Vakhtang 
Published: February 2021

Abstract
A solution of the Dirichlet problem for harmonic functions from the Smirnov class is obtained in the framework of functional spaces with a nonstandard growth condition. It is found that the domain boundary geometry influences the character of a problem solution. In the case of solvability, solutions are constructed in explicit form.
Singular Dirichlet Boundary Value Problem for Second Order Ode
Authors: Rachůnková Irena , Stryja Jakub 
Published: February 2021

Abstract
This paper investigates the singular Dirichlet problem
–𝑢″ = 𝑓(𝑡, 𝑢, 𝑢′), 𝑢(0) = 0, 𝑢(𝑇) = 0,
where 𝑓 satisfies the Carathéodory conditions on the set and .
The function 𝑓(𝑡, 𝑥, 𝑦) can have time singularities at 𝑡 = 0 and 𝑡 = 𝑇 and space singularities at 𝑥 = 0 and 𝑦 = 0. The existence principle for the above problem is given and its application is presented here. The paper provides conditions which guarantee the existence of a solution which is positive on (0; T) and which has the absolutely continuous first derivative on [0, 𝑇].
The Robin Function and Its Eigenvalues
Authors: Dittmar Bodo , Hantke Maren 
Published: February 2021

Abstract
The paper deals with the Robin function and eigenvalue problems generated by the Robin operator. First we show that Green's function of an 𝑛-fold connected domain is the Robin function of an appropriate simply connected domain. The main part of the paper deals with eigenvalue problems for the Robin operator: the mixed Stekloff eigenvalue problem and the membrane problem with mixed boundary conditions. Isoperimetric inequalities are proved for the sum of reciprocal eigenvalues.
On a Priori Estimates of Solutions of Systems of Higher Order Nonlinear Functional-Differential Inequalities
Authors: Kiguradze Ivan , Partsvania Nino 
Published: February 2021

Abstract
Systems of higher order nonlinear functional-differential inequalities arising in the theory of boundary value problems as well as in the stability theory are considered on a finite and an infinite interval. On a finite interval, a priori estimates are obtained for solutions of these systems satisfying boundary conditions of periodic type, and on an infinite interval, a priori estimates are established for the derivatives of bounded solutions.
On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak
Authors: Maz'ya Vladimir G. , Poborchi Sergei V. 
Published: February 2021

Abstract
We describe the dual space of the boundary trace space for functions with a finite Dirichlet integral for a domain with a vertex of an isolated cusp at the boundary. This leads to conditions of solvability of the Neumann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for 𝑞 such that the Neumann problem is solvable if the boundary function is in 𝐿𝑞 over the boundary of a domain with an outer peak.
On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations
Authors: Agwo Hassan A. 
Published: February 2021

Abstract
In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation
(𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ
1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ
2)) = 0,
on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation
(𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ
1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ
2)) = 0,
is presented, which improves other conditions and an example is given to illustrate our result.
Vector Measures on Topological Spaces
Authors: Khurana Surjit Singh 
Published: February 2021

Abstract
Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀
τ
(𝑋,𝐸), 𝑀
σ
(𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.
Elusive Examples of Non-Metrizable Continua which Admit a Whitney Map
Authors: Lončar Ivan 
Published: February 2021

Abstract
The main purpose of this paper is to prove that the class of near locally connected continua contains no non-metrizable continuum 𝑋 which admits a Whitney map for 𝐶(𝑋). In particular, each near locally connected continuum 𝑋 which admits a Whitney map for 𝐶(𝑋) is metrizable.
On the Absolute Convergence of Fourier Series of Functions of ∧𝐵𝑉(𝑝) and φ ∧𝐵𝑉
Authors: Vyas Rajendra G. 
Published: February 2021

Abstract
Let 𝑓 be a 2π periodic function in 𝐿1[0,2π] and , be its Fourier coefficients. Extending the classical result of Zygmund, Schramm and Waterman obtained the sufficiency conditions for the absolute convergence of Fourier series of functions of ∧𝐵𝑉(𝑝) and φ ∧𝐵𝑉. Here we have generalized these results by obtaining certain sufficiency conditions for the convergence of the series , where is a strictly increasing sequence of natural numbers and 𝑛–𝑘 = –𝑛𝑘 for all 𝑘, for such functions.
Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems
Authors: Wang Youyu , Ge Weigao 
Published: February 2021

Abstract
In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem:

where

(0,1), 0 < ξ
1 < ξ
2 < ⋯ < ξ
𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.