bluuebunny/crossref_metadata_2025 huggingface dataset:
Hilbert Spaces Formed by Strongly Harmonizable Stable Processes
Authors: Soltani A. R. , Tarami B.
Published: February 2021

A strongly harmonizable continuous time symmetric α-stable process is considered. By using covariations, a Hilbert space is formed from the process elements and used for a purpose of moving average representation and prediction.
Optimal Mean-Variance Robust Hedging under Asset Price Model Misspecification
Authors: Toronjadze T.
Published: February 2021

The problem of constructing robust optimal in the mean-variance sense trading strategies is considered. The approach based on the notion of sensitivity of a risk functional of the problem w.r.t. small perturbation of asset price model parameters is suggested. The optimal mean-variance robust trading strategies are constructed for one-dimensional diffusion models with misspecified volatility.
On Normal Approximation of Large Products of Functions: A Refinement of Blackwell's Result
Authors: Lo Albert Y. , Sazonov V. V.
Published: February 2021

An asymptotic expansion for the approximation of standardized products of large numbers of smooth positive functions by exp(–𝑥2/2) is given. This result is closely related to the Bernstein–von Mises theorem on the normal approximation of posterior distributions.
Asymptotic Behavior of Singular and Entropy Numbers for Some Riemann–Liouville Type Operators
Authors: Meskhi A.
Published: February 2021

The asymptotic behavior of the singular and entropy numbers is established for the Erdelyi–Köber and Hadamard integral operators (see, e.g., [Samko, Kilbas and Marichev, Integrals and derivatives. Theoryand Applications, Gordon and Breach Science Publishers, 1993]) acting in weighted L
2 spaces. In some cases singular value decompositions are obtained as well for these integral transforms.
Weight Inequalities for Singular Integrals Defined on Spaces of Homogeneous and Nonhomogeneous Type
Authors: Edmunds D. E. , Kokilashvili V. , Meskhi A.
Published: February 2021

Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón–Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type.
Perturbation of a Fredholm Complex by Inessential Operators
Authors: Gleason Jim
Published: February 2021

The work of Ambrozie and Vasilescu on perturbations of Fredholm complexes is generalized by discussing the stability theory of Banach space complexes under inessential perturbations.
On the Existence of Singular Solutions
Authors: Bartušek M. , Osička J.
Published: February 2021

Sufficient conditions are given, under which the equation 𝑦(𝑛) = ƒ(𝑡, 𝑦, 𝑦′, . . . , 𝑦(𝑙))𝑔(𝑦(𝑛 – 1)) has a singular solution 𝑦[𝑇, τ) → 𝐑, τ < ∞ satisfying , 𝑖 = 0, 1, . . . , 𝑙 and for 𝑗 = 𝑙 + 1, . . . , 𝑛 – 1 where 𝑙 ∈ {0, 1, . . . , 𝑛 – 2}.
Unilateral Contact of Elastic Bodies (Moment Theory)
Authors: Gachechiladze R.
Published: February 2021

Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.
On the Representation of Numbers by the Direct Sums of Some Quaternary Quadratic Forms
Authors: Kachakhidze N.
Published: February 2021

The systems of bases are constructed for the spaces of cusp forms S
2m
(Γ0(5), χ

m
) and S
2m
(Γ0(13), χ

m
) for an arbitrary integer m ≥ 2. Formulas are obtained for the number of representations of a positive integers by the direct sums of some quaternary quadratic forms.
On Local Invariants of Totally Real Surfaces
Authors: Khimshiashvili G.
Published: February 2021

A class of totally real surface singularities is introduced for which one can define local topological invariants. The main result yields an algebraic estimate for the self-intersection index of a totally real germ. It is derived from an algebraic upper estimate for the index of a quasi-homogeneous vector field which generalizes the previously known estimates in terms of the so-called Petrovsky numbers.
On Some Properties of 𝑟-Maximal Sets and 𝑄1–𝑁-Reducibility
Authors: Omanadze R.
Published: February 2021

It is shown that if 𝑀1, 𝑀2 are 𝑟-maximal sets and 𝑀1 ≡ 𝑄1–𝑁𝑀2, then 𝑀1 ≡ 𝑚𝑀2. In addition, we prove that there exists a simultaneously 𝑄1–𝑁- and 𝑊-complete recursively enumerable set which is not 𝑠𝑄-complete.
On Common Fixed Points
Authors: Liu Zeqing , Khan M. S. , Pathak H. K.
Published: February 2021

Some fixed point theorems based on an asymptotic regularity condition have been obtained, which generalize the previously well-known results.
On Appel-Type Quadrature Rules
Authors: Belingeri C. , Germano B.
Published: February 2021

The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.
On Kan Fibrations for Maltsev Algebras
Authors: Jibladze M. , Pirashvili T.
Published: February 2021

We prove that any surjective homomorphism of Maltsev algebras is a Kan fibration.
Dynamic Programming and Mean-Variance Hedging in Discrete Time
Authors: Gugushvili S.
Published: February 2021

We consider the mean-variance hedging problem in the discrete time setting. Using the dynamic programming approach we obtain recurrent equations for an optimal strategy. Additionally, some technical restrictions of the previous works are removed.
Estimates of Fourier Coefficients
Authors: Tsagareishvili V.
Published: February 2021

Some well-known properties of the trigonometric system as well as of the Haar and Welsh systems are generalized to general orthonormal systems.
On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems
Authors: Agranovich M. S. , Amosov B. A.
Published: February 2021

We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order.

We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given.

These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.
Oscillation and Nonoscillation Criteria for two-Dimensional Systems of Linear Ordinary Differential Equations
Authors: Polák L.
Published: February 2021

Sufficient conditions are established for the oscillation and nonoscillation of the system

𝑢′ = 𝑞(𝑡)𝑣,

𝑣′ = –𝑝(𝑡)𝑢,

where 𝑝, 𝑞 : [0, +∞[→] – ∞, +∞[ are locally summable functions, 𝑞(𝑡) ≥ 0 for 𝑡 ≥ 0, and .
The Predifferential of a Path Fibration
Authors: Berikashvili N. , Mikiashvili M.
Published: February 2021

For a simply connected space 𝐵 the Hirsch model of path fibration is constructed in terms of 𝐵. In particular this means the calculation of loop space cohomology. As an application, the Hirsch model of the fiber of any fibration over 𝐵 is given.
Wintner-Type Oscillation Criteria of Semilinear Elliptic Inequalities
Authors: Xu Zhiting
Published: February 2021

Wintner-type oscillation criteria of semilinear elliptic inequalities are obtained by using partial Riccati technique. The results presented improve the oscillation criteria due to E. S. Noussair and C.A. Swanson [Canad. J. Math. 32: 908–923, 1980].
Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series
Authors: Gát György , Goginava Ushangi
Published: February 2021

We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh–Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.
A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
Authors: Borysenko Sergiy , Matarazzo Giovanni , Pecoraro Massimo
Published: February 2021

This paper presents a generalization of nonlinear integral inequalities of the Gronwall–Bellman–Bihari type for discontinuous functions and its application to the investigation of the practical stability of solutions of systems of integro-differential equations with impulse perturbations at fixed moments of time.
The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
Authors: Castro Luis P. , Natroshvili David
Published: February 2021

This paper is concerned with a screen type boundary value problem arising from the wave diffraction problem with a reactance condition. We consider the problem in a weak formulation within Bessel potential spaces, and where both cases of a complex and a pure real wave number are analyzed. Using the potential method, the boundary value problem is converted into a system of integral equations. The invertibility of the corresponding matrix pseudodifferential operator is shown in appropriate function spaces which allows the conclusion about the existence and uniqueness of a weak solution to the original problem. Higher regularity properties of solutions are also proved to exist in some scale of Bessel potential spaces, upon the corresponding smoothness improvement of given data. In particular, the 𝐶
α
-smoothness of solutions in a neighbourhood of the screen edge is established with arbitrary α < 1 in the two-dimensional case and α < 1/2 in the three-dimensional case.
An Inverse Result in Simultaneous Approximation by Modified Beta Operators
Authors: Maheshwari Prerna
Published: February 2021

In this paper we study the modified Beta operators. We extend the result of [Gupta and Ahmad, İstanbul niv. Fen Fak. Mat. Derg. 54: 11–22 1995] and obtain an inverse result for the linear combination of these modified Beta operators in simultaneous approximation.
Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
Authors: Nadarajah Saralees , Kotz Samuel
Published: February 2021

Exact distributions of |𝑋𝑌| and |𝑋/𝑌| are derived when 𝑋 and 𝑌 are Pearson type VII and Bessel function random variables distributed independently of each other.
An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
Authors: Rogava Jemal , Tsiklauri Mikheil
Published: February 2021

An automatically stable and order three split rational approximation scheme is proposed for solving the Cauchy abstract problem. The third order precision is obtained by introducing the complex parameter and performing a rational approximation of the semigroup. For the considered scheme, an explicit a priori estimate is derived.
Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
Authors: Tsotniashvili Soso , Zarnadze David
Published: February 2021

The paper gives an extension of the fundamental principles of selfadjoint operators in Fréchet–Hilbert spaces, countable-Hilbert and nuclear Fréchet spaces. Generalizations of the well known theorems of von Neumann, Hellinger–Toeplitz, Friedrichs and Ritz are obtained. Definitions of generalized central and generalized spline algorithms are given. The restriction 𝐴∞ of a selfadjoint operator 𝐴 defined on a dense set 𝐷(𝐴) of the Hilbert space 𝐻 to the Frechet space 𝐷(𝐴∞) is substantiated. The extended Ritz method is used for obtaining an approximate solution of the equation 𝐴∞𝑢 = 𝑓 in the Frechet space 𝐷(𝐴∞). It is proved that approximate solutions of this equation constructed by the extended Ritz method do not depend on the number of norms that generate the topology of the space 𝐷(𝐴∞). Hence this approximate method is both a generalized central and generalized spline algorithm.

Examples of selfadjoint and positive definite elliptic differential operators satisfying the above conditions are given. The validity of theoretical results in the case of a harmonic oscillator operator is confirmed by numerical calculations.
Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
Authors: Xu Zhiting , Weng Peixuan
Published: February 2021

By using the general means, we establish some oscillation theorems for the even order delay differential equation

(𝑟(𝑡)|𝑥(𝑛–1)(𝑡)|
α–1𝑥(𝑛–1)(𝑡))′ + 𝐹(𝑡, 𝑥[𝑔(𝑡)]) = 0,

where α > 0 is a constant, , and 𝑔 ∈ 𝐶([𝑡0, ∞), ℝ). The results obtained extend and improve some results known in the literature.
Sums of Squares and Sums of Triangular Numbers
Authors: Cooper Shaun , Hirschhorn Michael
Published: February 2021

Motivated by two results of Ramanujan, we give a family of 15 results and 4 related ones. Several have interesting interpretations in terms of the number of representations of an integer by a quadratic form , where λ1 + . . . + λ𝑚 = 2, 4 or 8. We also give a new and simple combinatorial proof of the modular equation of order seven.
On Oscillation and Nonoscillation for Differential Equations with 𝑝-Laplacian
Authors: Bartušek Miroslav , Cecchi Mariella , Došlá Zuzana , Marini Mauro
Published: February 2021

The existence of at least one oscillatory solution of a second order nonlinear differential equation with 𝑝-Laplacian is considered. The global monotonicity properties and asymptotic estimates for nonoscillatory solutions are investigated as well.
On Doubly Periodic Solutions of Nonlinear Hyperbolic Equations of Higher Order
Authors: Kiguradze Tariel
Published: February 2021

Unimprovable conditions of the existence and uniqueness of doubly periodic solutions are established for nonlinear hyperbolic equations of higher order with two independent variables.
Szegö Asymptotics of Extremal Polynomials on the Segment [–1, +1]: The Case of a Measure with Finite Discrete Part
Authors: Khaldi Rabah
Published: February 2021

The strong asymptotics of monic extremal polynomials with respect to the norm 𝐿𝑝(σ) are studied. The measure σ is concentrated on the segment [–1, 1] plus a finite set of mass points in a region of the complex plane exterior to the segment [–1, 1].
Integrating Over the Inverse Image of Functions in the Besov Space
Authors: Ramos-Fernández Julio C.
Published: February 2021

Let 𝔻 be the open unit disk in the complex plane. For ε > 0 we consider the sector ∑
ε
= {𝑧 : |arg 𝑧| < ε}. We prove that for certain classes of functions 𝑓 in the Besov space (𝔻) such that 𝑓(0) = 0, the norm is obtained by integration over 𝑓–1(∑
ε
).
The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
Authors: Rogava Jemal , Tsiklauri Mikheil
Published: February 2021

Using the rational splitting of a cosine operator-function, the fourth order accuracy decomposition scheme is constructed for hyperbolic equation when the principal operator is self-adjoint positively defined and is represented as a sum of two summands. Stability of the constructed scheme is shown and the error of an approximate solution is estimated.
On the Essential Norm for the Hilbert Transforms in 𝐿𝑝(𝑥) Spaces
Authors: Asif Muhammad , Meskhi Alexander
Published: February 2021

The essential norm of the Hilbert transform acting in weighted Lebesgue spaces with variable exponent is estimated from below.
Essential Spectrum and Exponential Decay Estimates of Solutions of Elliptic Systems of Partial Differential Equations. Applications to Schrödinger and Dirac Operators
Authors: Rabinovich Vladimir S. , Roch Steffen
Published: February 2021

The main aim of the paper is to study relations between the location of the essential spectrum and exponential decay estimates of the eigenfunctions of systems of elliptic partial differential equations. To solve this problem, we apply the limit operators method.

Applications are given to the problem of exponential decay behavior of eigenfunctions of Schrödinger and Dirac operators.
Wavelet Bases in Lorentz and Zygmund Spaces
Authors: Triebel Hans
Published: February 2021

The paper deals with unconditional intrinsic wavelet bases in Lorentz spaces 𝐿𝑝,𝑞(Ω) and Zygmund spaces 𝐿𝑝(log 𝐿)𝑎(Ω) where Ω is an arbitrary domain in (with |Ω| < ∞ in the case of Zygmund spaces).
Principle of Exchange of Stabilities and Dynamic Transitions
Authors: Ma Tian , Wang Shouhong
Published: February 2021

We derive some formulas for the critical crossing, also called the principle of exchange of stability (PES) in physics. These formulas will be crucial for studying dynamic transitions of many problems in science and engineering [Ma and Wang, Bifurcation theory and applications, World Scientific Publishing Co. Pte. Ltd., 2005, Ma and Wang, Stability and bifurcation of nonlinear evolutions equations, Science Press, 2007].
On Iterative Combination of Modified Bernstein-Type Polynomials
Authors: Agrawal P. N. , Gairola Asha Ram , Gupta Vijay
Published: February 2021

The paper deals with some direct results on ordinary and simultaneous approximations for iterative combinations of a new type of Bernstein–Durrmeyer operators. Gupta and Vasishtha [Math. Comput. Modelling 39: 521–527, 2004] have recently claimed that iterative combinations can be applied only for those operators for which 𝑡 maps exactly to 𝑥. Here we disagree with their claim and state that iterative combinations can be applied for other operators which do not reproduce linear functions either.
Periodic Solutions for Nonlinear Differential Equation with Functional Delay
Authors: Deham Hafsia , Djoudi Ahcene
Published: February 2021

We use the modification of Krasnoselskii's fixed point theorem due to T. A. Burton ([Proc. Amer. Math. Soc. 124: 2383–2390, 1996]) to show that the scalar nonlinear differential equation with functional delay

𝑥′(𝑡) = –𝑎(𝑡)𝑥3(𝑡) + 𝐺(𝑡, 𝑥3(𝑡 – 𝑟(𝑡)))

has a periodic solution. It is not required that 𝑟(𝑡) be differentiable, while 𝑎 and 𝐺 are continuous with respect to their arguments.
On the 𝐿1-Convergence of Modified Cosine Sums
Authors: Singh Karanvir , Kaur Kulwinder
Published: February 2021

Concerning the 𝐿1-convergence of modified cosine sums introduced by Kumari and Ram [Indian J. Pure Appl. Math. 19: 1101–1104, 1988], we generalise the results of Kumari, Ram [Indian J. Pure Appl. Math. 19: 1101–1104, 1988] and Bor [Proc. Indian Acad. Sci. Math. Sci. 102: 235–238, 1992]. Also a necessary and sufficient condition for the 𝐿1-convergence of cosine series has been deduced as a corollary for the said class.
Sequential Detection of Drift Change for Brownian Motion with Unknown Sign
Authors: Lerche Hans Rudolf , Maahs Ilse
Published: February 2021

We study tests of power one for the following change-point problem.

Suppose one observes a process 𝑊 which is either a Brownian motion without drift or a Brownian motion that has zero drift up to a random time τ after which with equal probability the drift becomes either θ or –θ, where the value of θ > 0 is known. The distribution of τ is also assumed to be known. We search for a stopping time 𝑇* that minimizes an appropriate Bayes risk and give a solution that is asymptotically optimal, when the cost of observation tends to zero.
Cyclic Gamma Homology and Gamma Homology for Associative Algebras
Authors: Richter Birgit
Published: February 2021

The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes' periodicity sequence becomes almost trivial, because the cyclic version coincides with the ordinary version from homological degree two on. We show that a possible desymmetrized definition of Gamma homology coincides with a shifted version of Hochschild homology and its associated cyclic theory does the same.
Profinite Heyting Algebras and Profinite Completions of Heyting Algebras
Authors: Bezhanishvili Guram , Morandi Patrick J.
Published: February 2021

This paper surveys recent developments in the theory of profinite Heyting algebras (resp. bounded distributive lattices, Boolean algebras) and profinite completions of Heyting algebras (resp. bounded distributive lattices, Boolean algebras). The new contributions include a necessary and sufficient condition for a profinite Heyting algebra (resp. bounded distributive lattice) to be isomorphic to the profinite completion of a Heyting algebra (resp. bounded distributive lattice). This results in simple examples of profinite bounded distributive lattices that are not isomorphic to the profinite completion of any bounded distributive lattice. We also show that each profinite Boolean algebra is isomorphic to the profinite completion of some Boolean algebra. It is still an open question whether each profinite Heyting algebra is isomorphic to the profinite completion of some Heyting algebra.
An Almost Greedy Uniformly Bounded Orthonormal Basis in 𝐿𝑝(·)([0, 1]) Spaces
Authors: Danelia Ana , Kapanadze Ekaterine
Published: February 2021

We construct a uniformly bounded orthonormal almost greedy basis for the variable exponent Lebesgue spaces 𝐿𝑝(·)([0, 1]), 1 < 𝑝– ≤ 𝑝+ ≤ 2 (or 2 ≤ 𝑝– ≤ 𝑝+ < ∞), when the diadic Hardy–Littlewood maximal operator is bounded on these spaces.
Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
Authors: Gachechiladze Avtandil , Gachechiladze Roland , Natroshvili David
Published: February 2021

We study three-dimensional unilateral contact problems with friction for hemitropic elastic solids. We give their mathematical formulation in the form of spatial variational inequalities and show the equivalence to the corresponding minimization problem. Based on our variational inequality approach, we prove existence and uniqueness theorems. We prove also that solutions continuously depend on the data of the original problem and on the friction coefficient. Our investigation includes the special particular case of only traction-contact boundary conditions without prescribing displacement and microrotation vectors along some part of the boundary of a hemitropic elastic body. Then the problems are not unconditionally solvable and we derive the necessary and sufficient conditions of their solvability.
A case study of 𝐴∞-structure
Authors: Alcaraz Ainhoa Berciano , Rubio Julio , Sergeraert Francis
Published: February 2021

The computer program Kenzo is used to study complex 𝐴∞-structures coming from iterated loop spaces. The methods of constructive algebraic topology, due to the authors, do produce chain complexes of finite type and chain equivalences with the Hopf algebras canonically associated to the loop spaces. These chain complexes of finite type are therefore endowed with 𝐴∞-structures. It is then experimentally observed, using the Kenzo program, that 𝐴∞-structures of arbitrarily high orders are nontrivial in these objects. This case study is a good illustration of the computing tools given to the topologists by the Kenzo program.
Cartan's constructions and the twisted Eilenberg–Zilber theorem
Authors: Álvarez Víctor , Armario José Andrés , Frau María Dolores , Real Pedro
Published: February 2021

Let 𝐺 ×
τ
𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 ×
τ
𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 ×
τ
𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.
On a class of bases of the space of cusp forms of level 8
Authors: Kachakhidze Nikoloz
Published: February 2021

A class of bases of the space of cusp forms is constructed for any integer k and character mod 8.
A limit theorem on symmetric matrices
Authors: Hassairi Abdelhamid
Published: February 2021

In this note, we give a limit theorem related to the notion of regular variation for functions defined on symmetric matrices. We consider the problem under the condition of invariance by the orthogonal group, and under the invariance by the subgroup of the orthogonal group corresponding to diagonal matrices.
Necessary and sufficient optimality conditions for set-valued optimization problems
Authors: Benkenza Najia , Gadhi Nazih , Lafhim Lahoussine
Published: February 2021

Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by Ciligot-Travain [Numer. Funct. Anal. Optim. 15: 689–693, 1994], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange–Fritz–John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.
A biregular extension theorem from a fractal surface in
Authors: Abreu Blaya Ricardo , Bory Reyes Juan , Moreno García Tania
Published: February 2021

The aim of this paper is to prove the characterization on a bounded domain of with fractal boundary and a Hölder continuous function on the boundary guaranteeing the biregular extendability of the later function throughout the domain.
Exceptional functions and normal families of holomorphic functions with multiple zeros
Authors: Chen Jun-Fan
Published: February 2021

Let k be a positive integer, and let ℱ be a family of functions holomorphic on a domain D in C, all of whose zeros are of multiplicity at least k + 1. Let h be a function meromorphic on D, h ≢ 0, ∞. Suppose that for each ƒ ∈ ℱ, ƒ(k)(z) ≠ h(z) for z ∈ D. Then ℱ is a normal family on D. The condition that the zeros of functions in ℱ are of multiplicity at least k + 1 cannot be weakened, and the corresponding result for families of meromorphic functions is no longer true.
Variation formulas of solution for a delay differential equation taking into account delay perturbation and the continuous initial condition
Authors: Tadumadze Tamaz
Published: February 2021

Variation formulas of solution are proved for a non-linear differential equation with constant delay. In this paper, the essential novelty is the effect of delay perturbation in the variation formulas. The continuity of the initial condition means that the values of the initial function and the trajectory always coincide at the initial moment.
An admissibility for topological degree of variable Besov and Triebel–Lizorkin spaces
Authors: Xu Jingshi
Published: February 2021

An admissibility for topological degree of variable Lebesgue, Besov and Triebel–Lizorkin spaces is given.
On Gegenbauer transformation on the half-line
Authors: Ibrahimov Elman J.
Published: February 2021

In this paper, the Gegenbauer transformation is constructed and some of its properties similar to the Fourier transformation are proved. An equation of Parseval–Plancherel type is obtained. The inversion theorem for the Gegenbauer transformation is proved.
Boundedness of weighted singular integral operators in grand Lebesgue spaces
Authors: Kokilashvili Vakhtang , Samko Stefan
Published: February 2021

We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set on which the functions are defined is a Carleson curve in the complex plane. Note that weighted boundedness of an operator in grand Lebesgue space is not the same as the boundedness in weighted grand Lebesgue space.
Higher rank Haar wavelet bases in spaces
Authors: Kopaliani Tengiz
Published: February 2021

Using the Bellman function method, we prove that a Haar wavelet system of rank N (N ∈ ℕ, N ≥ 2) is an unconditional basis in , 1 < p < ∞, if and only if .
Trace operators on fractals, entropy and approximation numbers
Authors: Schneider Cornelia
Published: February 2021

First we compute the trace space of Besov spaces – characterized via atomic decompositions – on fractals Γ, for parameters 0 < p < ∞, 0 < q ≤ min(1, p) and s = (n – d)/p. New Besov spaces on fractals are defined via traces for 0 < p, q ≤ ∞, s ≥ (n – d)/p and some embedding assertions are established. We conclude by studying the compactness of the trace operator TrΓ by giving sharp estimates for entropy and approximation numbers of compact embeddings between Besov spaces. Our results on Besov spaces remain valid considering the classical spaces defined via differences. The trace results are used to study traces in Triebel–Lizorkin spaces as well.
The Robin problem for the Helmholtz equation in a starlike planar domain
Authors: Caratelli Diego , Gielis Johan , Natalini Pierpaolo , Ricci Paolo Emilio , Tavkhelidze Ilia
Published: February 2021

The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called “superformula” introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.
The weighted Cauchy problem for linear functional differential equations with strong singularities
Authors: Sokhadze Zaza
Published: February 2021

The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.
Abelian and nilpotent varieties of power groups
Authors: Amaglobeli Mikheil , Bokelavadze Tengiz
Published: February 2021

The present paper continues the series of the papers [Amaglobeli and Bokelavadze, Exponential groups. III. Groups which are exact for tensor complement, Herald of Omsk University, 2009, Myasnikov and Remeslennikov, Sibirsk. Mat. Zh. 35: 1106–1118, 1994, Myasnikov and Remeslennikov, Internat. J. Algebra Comput. 6: 687–711, 1996] and is dedicated to the construction of basic principles of the theory of power group varieties and tensor completions of groups in a variety. We study the relationship between free groups of a given variety for various rings of scalars. Varieties of abelian power groups are described.
DISTRIBUTION AND RACE COMPOSITION OF DOWNY MILDEW (Plasmopara halstedii (Farl.) Berl. and de Toni) IN BULGARIA / EXTENSION Y RAZAS DEL MILDIU (Plasmopara halstedii (Farl.) Berl. y de Toni) EN BULGARIA / ÉTENDUE ET RACES DE LA ROUILLE (Plasmopara halstedii (Farl.) Berl. and de Toni) EN BULGARIE
Authors: Shindrova P.S.
Published: February 2021

Downy mildew caused by the fungus Plasmopara halstedii is the main disease on sunflower in Bulgaria. In recent years a number of authors have reported the occurrence of new more virulent races of the pathogen. According to other authors these races demonstrate resistance to the fungicides used up to now. This fact is rather alarming and imposes the necessity of annual researches with the aim of following the changes in the downy mildew race variability.

In the period 1995-1997 downy mildew isolates were collected from the following locations: Bourgas, Boyanovo, Karnobat, Ognyanovo, Selanovtsi, Kroushari, Lovech, Koubrat, Brashlyan, Sitovo, Tervel, Targovishte, IWS “Dobroudja” and Dobrich. The samples were assessed for virulence on a set of sunflower differential - lines under greenhouse conditions.

The obtained results do not reveal a great race variability of downy mildew population in Bulgaria. In the period of study two races of the pathogen were identified: race 1 which infects the differential lines without genes for resistance to the pathogen. It is distributed in all sunflower production areas of the country. The other one is race 2. It is of limited distribution and has been registered in individual fields of north-east and north-west Bulgaria. It attacks the differential lines carrying the resistance gene Pl-1.
Comparative Studies on Nitrophenol Removal byAdsorption and Simultaneous Adsorption-Biodegradation Processes
Authors: Prateek  , Thakur Chandrakant , Srivastava Vimal Chandra , Mall Indra Deo
Published: February 2021

In this paper, it was aimed to study the removal of 4-nitrophenol (NP) from aqueous solution by adsorption using granular activated carbon (GAC); and in sequencing batch reactor (SBR) without any adsorbent (blank-SBR) and with an SBR loaded with GAC (GAC–SBR). During adsorption study with GAC, effect of pH, adsorbent dose (m) and contact time (t) were studied. Adsorption isotherm, kinetic and thermodynamic parameters were determined. During NP removal in SBR, effect of hydraulic retention time (HRT), initial concentration (C
0) and m were studied. The percent removal in case of GAC–SBR was found to be greater in comparison to blank-SBR. The removal of NP from blank-SBR and GAC–SBR for C
0 of 35, 65 and 100 mg/l was found to be 90.46% and 91.23% (m=2 g/l); 52.33% and 96.05% (m=2.5 g/l); 20.01% and 92.72% (m=2.5 g/l), respectively.
Quantitative analysis of static equilibrium in women after mastectomy
Authors: Rachwał Maciej , Drzał-Grabiec Justyna , Walicka-Cupryś Katarzyna , Truszczyńska Aleksandra
Published: February 2021

Background: The post-mastectomy changes to the locomotor system are related to the scar and adhesion or to the lymphatic edema after amputation which, in turn, lead to local and global distraction of the work of the muscles. These changes lead to body statics disturbance that changes the projection of the center of gravity and worsens motor response due to changing of the muscle sensitivity.

Objective: The aim of the study was to evaluate the static balance of women after undergoing mastectomy.

Methods: The study included 150 women, including 75 who underwent mastectomy (mean age: 60±7.6) years, mean body mass index (BMI): 26 (±3.6) kg/m2) and 75 who were placed in the control group with matched age and BMI. The study was conducted using a tensometric platform.

Results: Statistically significant differences were found for almost all parameters between the post-mastectomy group and group of healthy women, regarding center of foot pressure (COP) path length in the Y and X axes and the mean amplitude of COP.

Conclusions: First, the findings revealed that balance in post-mastectomy women is significantly better than in the control group. Second, physiotherapeutic treatment of post-mastectomy women may have improved their posture stability compared with their peers.
Highly efficient biocide silver-doped soda lime glass for application in water quality optical sensors
Authors: Bajac Branimir , Stanojev Jovana , Birgermajer Slobodan , Radojevic Milena , Matovic Jovan
Published: February 2021

In the last decade, biocidal materials have been extensively researched and applied as a coating for various touchscreen devices, in medicine and civil engineering. This research addresses important practical issues in application of surface- modified biocidal glass in water, and inspects optical properties in the spectral range between 350 nm and 500 nm, the range important for bacteria fluorescence detection. Testing of biocidal efficiency has been conducted in an environment rich with microorganisms and algae. To incorporate silver ions in soda lime glass plates, an ion-exchange process in a molten bath was used. The optical characterization of as-synthesized samples indicates very high transparency, above 90% at 440 nm, specifically important for escherichia coli detection. fter 140 days in the bioreactor, it was found that glass heated for 15 min at 350 0C produced best results, maintaining transparency above 85% in spectral range from 350 nm to 1000 nm.
An Application of the Modified Reductive Perturbation Method to a Generalized Boussinesq Equation
Authors: Demiray Hilmi
Published: February 2021

In this work, we apply “the modified reductive perturbation method” to the generalized Boussinesq equation and obtain various form of generalized KdV equations as the evolution equations. Seeking a localized travelling wave solutions for these evolution equations we determine the scale parameters g
1 and g
2, which corresponds to the correction terms in the wave speed, so as to remove the possible secularities that might occur. Depending on the sign and the values of certain parameters the resulting solutions are shown to be a solitary wave or a periodic solution. The suitability of the method is also shown by comparing the results with the exact travelling wave solution for the generalized Boussinesq equation.
Fabrication and Mechanical Properties of a Micro/Nanoscale Hybrid Composite
Authors: Wang Genwei , Zhao Han , Bai Jinbo , Zhao Ya-Pu
Published: February 2021

Microscale SiC particles with multiwalled carbon nanotubes grow on were filled in epoxy resin to construct multiscale hybrid composite. Static and dynamic compressive responses of composites were investigated. A dynamic experimental technique, split Hopkinson press bar (SHPB), was introduced to study the constitutive laws of materials at high strain rates. SEM observations show good dispersion of carbon nanotubes and SiC particles, but bad link between SiC particles and carbon nanotubes exists. Experimental results of static and dynamic tests verify that increase of strength happens with SiC/CNT as reinforcement Increment of strength under dynamic loading is bigger than under static loading.
Mechanism of High-velocity Projectile Penetration into Concrete
Authors: Wu Hai-Jun
Published: February 2021

The penetration
depth of rigid projectiles is investigated
using the modified spherical cavity expansion
theory and the
Holmquist–Johnson–Cook (HJC)
model for the concrete targets, in which the
model parameters used in the
Mohr–Coulomb Tresca-limit yield
criterion are obtained by the triaxial
compression tests. By comparing the cavity
expansion pressures of the concrete samples
with two different types of aggregate, the
influence of the aggregate hardness on the
penetration processes is discussed. With the
analysis of the tractions acted on the
projectile nose, the influences of the
projectile and target material properties as
well as the projectile structure on the
transition impact velocity are also
discussed. By comparing the theoretical
results with the experimental data, two
penetration mechanisms are demonstrated for
the ogive-nose projectile penetration into
concrete with the striking velocities up to
2.0 km/s.
Prayer and Practical Theology
Authors: van Oudtshoorn Andre
Published: February 2021

The command to pray invites believers to critically engage with their broken reality with a view of transforming it in the light of the new reality in which they participate in Christ. Practical theology, operating in the context of the bi-polar and tense relationship between theory and praxis, should be expanded to accommodate prayer as the inner mode of its operations to embrace the existential dimension of the faith praxis, instead of simply limiting itself to a socio-scientific empirically based descriptive paradigm. This implies that practical theology has to be embedded within the church as the domain of faith. Prayer, understood within the context of practical theology, offers a critique of theological theories that do not adequately address the implications for God, the world and believers inherent in the new anthropological status that the invitation to pray confers on those who pray. Prayer also critiques the existing praxis in three ways: it is, firstly, a transformational act in itself; it, secondly, acknowledges its own inadequacy to accomplish the needed transformation and is thus able to critique its own methodologies and practices; and, thirdly, it continues to hope for the transformation of the existing praxis based on the promise of the presence of God in and through the Spirit of Christ in the church. In looking beyond the existing praxis to God, believers are called to continually work and pray for signs of the coming Kingdom to be realised within their world.
Priming of verb inflections in L1 and L2 French: A comparison of `redundant' versus `non-redundant' training conditions
Authors: Marsden Emma , Altmann Gerry , St Claire Michelle
Published: February 2021

There have been several calls to adopt more implicit techniques for investigating how input is processed by second language (L2) learners. This study tested for aural repetition priming using a lexical decision test to establish whether a French verb inflection (-ons) can be primed amongst beginner classroom learners of L2 French during activities that broadly reflected two types of aural instructional activities. Fifty one school learners of French were randomly assigned either to an exposure activity which directed their attention to the target inflection or to an activity in which they were asked to try to understand sentences which contained the target inflection. The input was designed to simulate learning situations in which learners find aural comprehension effortful. All participants then did a lexical decision test, to measure the activation of representations of the French verb inflection during the exposure conditions. The results from this preliminary study indicated that greater priming effects followed the instructional activity that focused attention on the inflection than the activity that focused attention on sentence meaning. This is compatible with acoustic word priming research that suggests an orientation to meaning inhibits priming for some learners, and also with pedagogical research that suggests that focusing learners' attention to some features of the input is helpful. Our findings in the aural domain seem to run counter to recent research suggesting that regardless of the orientation of attention during training, orthographic representations of suffixes can be primed during visual word recognition. Future applications of this technique for investigating the allocation of attention in L2 input processing are discussed.
Temporal and non-temporal processes in the elderly
Authors: Fostick Leah , Babkoff Harvey
Published: February 2021

Background: The present study examined whether the reported age-related decline in auditory temporal resolution is specific to the temporal domain or rather reflects a general decline in auditory perception, including the stimulus intensity domain.

Methods: The performance of 89 healthy participants aged between 21 and 82 years with normal hearing was tested on a variety of psychophysical tasks, where discrimination was based either on the temporal or on the intensity domains. Stimulus levels for all tasks were 40 dB SL (corrected for threshold). Participants were also tested on two cognitive tasks: Wechsler Adult Intelligence Scale, Third Edition, matrices and digit span.

Results: Findings indicate that age was significantly negatively correlated with performance on three of the temporal resolution tasks, namely, dichotic temporal-order judgment, spectral temporal-order judgment, and gap detection, but not on the intensity discrimination task, thus emphasizing the specificity of the age-related decline to the auditory temporal domain.

Conclusions: The overall results suggest that age-related changes in auditory perception are specific to the temporal domain, even when controlling for hearing sensitivity and cognitive ability, and are not reflected in other aspects of non-temporal perception, such as intensity discrimination.
Facilitating Speech and Discourse: Biblical Interpretation and the Emergence of a Concept of Gender Equality
Authors: Økland Jorunn
Published: February 2021

The article is a case study demonstrating that the Bible at the end of the 19th century could still function as a common rhetorical tool, a frame of reference, and a common court of appeal in important public debates. The case in question is the Anglophone debate over women’s rights, voice, and vote on both sides of the Atlantic Ocean around 1890. The article analyzes three different lay positions represented by Elizabeth Cady Stanton, Christina Rossetti, and Heber Hart. They represent three different directions that reception of the Bible with regard to gender equality and women’s authorial voice could take in this period. The article also argues that a concept of gender equality goes several centuries further back than what is often thought, and that the early development of the concept in a pre-secularized intellectual environment needs much further scholarly attention.
Rib fractures in infancy, case-series and register case-control study from Sweden
Authors: Högberg Ulf , Thiblin Ingemar
Published: February 2021

Objectives

To assess cases with rib fractures in infants under observation for or with an abuse diagnosis, and to compare risk factors with that in infants with fractures but no abuse diagnosis.

Methods

Design was case-series and register case-control of infants (aged <1 year) with rib fractures. Data was clinical records for the case-series (n = 26) and from national health registers for the case-controls (n = 28 and n = 31). Outcome measures were maternal and perinatal characteristics, reasons for appointment, examination, diagnoses, blood tests, and radiologic findings.

Results

The case-series had a median age of 70 days. A majority were detected through a skeletal survey for abuse investigation. Sixteen were boys, three were preterm and six were small-for-gestational age. Three carers had noticed popping sound from the chest; no infants showed signs of pain at physical examination. Mean number of fractures was 4.2, and 24 had callus. Bone mineralisation was scarcely reported. Metabolic panel was not uniformly analysed. The register case-control had a median age of 76 days, sharing risk factors such as maternal overweight/obesity, male sex, prematurity, and being small-for-gestational age. Cases more often had subdural haemorrhage, retinal haemorrhage, or long-bone fractures, controls more often had neonatal morbidity, respiratory infection, or a fall accident. Detection of fracture at time of a major surgery (n = 6) and rickets/vitamin D deficiency (n = 5) appeared in both groups, but was delayed among the cases.

Conclusions

Rib fractures in young infants, diagnosed as abuse, are usually asymptomatic and healing. A substantial proportion had metabolic risk factors, suggesting false positive cases.