bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Approximation of the Perturbed Inclusion
Authors: Bulgakov Alexander I. , Grigorenko Anna A. , Korobko Anatoliy I. 
Published: February 2021

Abstract
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

Abstract
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.
On a Three-Point Boundary Value Problem for Third Order Differential Equations with Singularities in Phase Variables
Authors: Staněk Svatoslav 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
On Some Properties of the Dirichlet Problem at Resonance
Authors: Lepin Arnold 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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.
Mixed and Crack-Type Boundary Value Problems in Mindlin's Theory of Piezoelectricity
Authors: Buchukuri Tengiz , Chkadua Otar 
Published: February 2021

Abstract
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.
Extended Normal Vector Field and the Weingarten Map on Hypersurfaces
Authors: Duduchava Roland , Kapanadze David 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Fixpoint Objects Need Not be Ω-Discrete
Authors: Johnstone Peter 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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.
Some nonlocal problems for second order strictly hyperbolic systems on the plane
Authors: Kharibegashvili Sergo , Midodashvili Bidzina 
Published: February 2021

Abstract
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.
On a problem concerning quaternion valued Gaussian random variables
Authors: Chelidze George , Vakhania Nicholas 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
(σ, τ)-amenability of C*-algebras
Authors: Mirzavaziri Madjid , Moslehian Mohammad Sal 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
A note on Lorentz–Zygmund spaces
Authors: Oba Hiroto , Sato Enji , Sato Yuichi 
Published: February 2021

Abstract
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

SUMMARY
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

SUMMARY
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.