bluuebunny/crossref_metadata_2025_split huggingface dataset:
Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
Authors: Xu Zhiting , Weng Peixuan 
Published: February 2021

Abstract
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

Abstract
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

Abstract
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.
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

Abstract
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

Abstract
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

Abstract
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.
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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′.
Necessary and sufficient optimality conditions for set-valued optimization problems
Authors: Benkenza Najia , Gadhi Nazih , Lafhim Lahoussine 
Published: February 2021

Abstract
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.
Exceptional functions and normal families of holomorphic functions with multiple zeros
Authors: Chen Jun-Fan 
Published: February 2021

Abstract
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

Abstract
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.
Boundedness of weighted singular integral operators in grand Lebesgue spaces
Authors: Kokilashvili Vakhtang , Samko Stefan 
Published: February 2021

Abstract
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.
Trace operators on fractals, entropy and approximation numbers
Authors: Schneider Cornelia 
Published: February 2021

Abstract
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

Abstract
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.
Abelian and nilpotent varieties of power groups
Authors: Amaglobeli Mikheil , Bokelavadze Tengiz 
Published: February 2021

Abstract
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

SUMMARY
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

Abstract
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

Abstract

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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.