bluuebunny/crossref_metadata_2025 huggingface dataset:
Postnatal ultrasound follow-up in neonates with prenatal hydronephrosis
Authors: Kebriyaei Elham , Davoodi Ali , Kazemi Seyed Alinaghi , Bazargani Zahra
Published: February 2021

Objectives

Renal anomalies are the most common fetal abnormalities that occur during prenatal development, and are typically detected by observing hydronephrosis on fetal ultrasound imaging. Follow-up with post-natal ultrasound is important to detect clinically-important obstruction, because many of the pre-natal abnormalities resolve spontaneously. This study aimed to evaluate the postnatal hydronephrosis follow-up rate, and reasons for non follow-up in affected neonates.

Methods

In this cross-sectional study all neonates born during a period of one year at Ayatollah Mousavi Hospital with hydronephrosis on fetal ultrasound imaging were recruited. All mothers were also given face-to-face information about fetal hydronephrosis and its postnatal outcomes, and follow-up with at least a postnatal ultrasound was recommended from the fourth day of their neonates’ birth until the end of the fourth week. The neonates were subsequently observed for one month to determine the postnatal ultrasound follow-up rate and to reflect on diagnostic test results, reasons for failure to follow-up, as well as causes of hydronephrosis.

Results

In this study, 71 cases (1.2%) out of 5,952 neonates had fetal hydronephrosis on prenatal ultrasound images. The postnatal ultrasound imaging showed kidney involvement in 18 neonates (25%), particularly in the left kidney (61.1%). Seven neonates had no follow-up at one month (10%). No significant relationship was found between lack of follow-up and the neonates’ place of residence (p=0.42), maternal education (p=0.90), number of siblings (p=0.33), or gender (p=0.64).

Conclusions

Postnatal ultrasound follow-up rate in these neonates with a history of fetal hydronephrosis was incomplete even though parents had been provided with education and advice at their birth time. Accordingly, it is recommended to perform postnatal ultrasound once neonates are discharged from hospitals.
Optimal Design of Cymbal Stack Transducer in a Piezoelectric Linear Actuator by Finite Element Method
Authors: Sheng Wen , Tiemin Zhang , Jiantao Zhang , Xiuli Yang
Published: February 2021

The optimal design of a piezoelectric linear actuator using parametric optimum method-based finite element method (FEM) was presented. First, the FEM model of the cymbal stack transducer was generated with its initial configuration. The structural parameters were chosen as the design variables and the displacement on the top surface of the transducer taken as the objective function. Second, the zero-order optimization method was chosen as the basic tool of the structural updating. The structural optimization scheme of the cymbal stack transducer was carried out based on ANSYS parametric design language (APDL). Finally, an example of dynamic response analysis was performed on the cymbal stack transducer to verify the structural optimization scheme. The results show that the displacement on the top surface is increased by 32.9% compared with the case of initial configuration.
Bosnian, Croatian, Serbian: Inherent Translanguaging in the Linguistic Landscape of Sarajevo
Authors: Tankosić Ana , Litzenberg Jason
Published: February 2021

Language in the Balkan region of Southeastern Europe has a complex and turbulent history, acutely embodied in the tripartite and trilingual state of Bosnia and Herzegovina (BiH) in which Bosniaks, Croats, and Serbs all make claim to their own mutually-intelligible varieties of local “languages”. This study utilizes a linguistic landscape methodology to consider language use in Sarajevo, the capital of BiH, approximately 20 years after a brutal war that led to the establishment of the country. Data originate from three municipalities within the Sarajevo Canton – namely, Old Town, Center, and Ilidža – because of their representation of the region’s diversity and history. Signs were classified according to the three primary language varieties, i.e., Bosnian, Croatian, Serbian; BCS, representing a common core among the three varieties, as well as English, other languages, and mixed languages. The application of BCS uniquely positions the present research in comparison to other studies of language use in the region and allows for a more nuanced, less politically and ethnolinguistically fraught analysis of the communicative tendencies of users. More specifically, data indicate that actors in the linguistic landscape transcend the boundaries of their national, ethnic, and religious identities by tending towards the more neutral BCS, suggesting an orientation towards more translingual dispositions than previous variety-bound approaches have indicated. Thus, instead of the divisiveness of linguistic identity politics, the linguistic landscape of Sarajevo indicates a tendency toward inclusion and linguistic egalitarianism.
Folklore as an evidential category
Authors: Kittilä Seppo
Published: February 2021

Folklore refers to information that we have learnt as a part of the history of our own people and that has passed on from generation to generation for hundreds, or even thousands of years. This paper shows that as an information source folklore has features in common with other information sources, most notably hearsay, but it nevertheless constitutes an information source of its own, characterized as [−personal] [−direct] and [+internalized]. In addition, the paper proposes a formal-functional typology based on the element used for folklore coding. It is also shown that the semantic similarity of the coded element with the proposed definition of folklore corresponds to its frequency. Finally, the paper discusses the central theoretical implications this study has for our understanding of evidentiality.
An Evaluation of the Permittivity of Two Different Rock Types Using Microwave Resonator and Waveguide Cutoff Principles
Authors: Olkkonen Martta-Kaisa , Eskelinen Pekka , Huuskonen-Snicker Eeva , Pellinen Terhi , Olmos Martinez Pablo
Published: February 2021

Methods of measuring the complex permittivity of different rock types are demonstrated in the frequency range from 6 GHz to 17 GHz. The used methods are based on the cylindrical resonator and waveguide cutoff frequency principles. This study is part of a larger research project that aims to characterize the electrical properties of asphalt for road surveying purposes. The studied rock types are metavolcanic rock with intermediate composition and pegmatite. The permittivity values gained with the resonator method are 6.2 for the metavolcanic rock and 4.5 for the pegmatite rock type, whereas the imaginary parts are 0.04 and 0.02. The permittivity values gained with the cutoff frequency method are 6.17 and 4.76 respectively. A reference measurement was made only for the metavolcanic rock in a transmission configuration with two antennas and the permittivity result was 6.21. The three different methods provide consistent permittivity values and are suitable for reliable permittivity evaluation.
Tunable Phase Shifter Based on Inkjet-Printed Ferroelectric MIM Varactors
Authors: Nikfalazar Mohammad , Wiens Alex , Mikolajek Morten , Friederich Andreas , Kohler Christian , Sohrabi Mojtaba , Zheng Yuliang , Kienemund Daniel , Melnyk Sergiy , Binder Joachim R. , Jakoby Rolf
Published: February 2021

This paper presents a new method for the fabrication of tunable multilayer ferroelectric components based on inkjet printing. Inkjet printing is a low-cost technology for selective film fabrication and has high potential for the preparation of tunable dielectric layers for radio frequency and microwave applications.

With this technology, tunable metal-insulator-metal (MIM) capacitor is fabricated, that is composed of inkjet-printed Barium-Strontium-Titanate striplines and photo-lithographically structured gold electrodes. Compared to coplanar capacitors, such MIM varactors require significantly lower DC-voltage for tuning. By applying 20 V across a 1 μm-thick BST film, a tunability of 33% is achieved at 8 GHz and tunability of 60% by applying 50 V. To demonstrate the field of application of this MIM varactor, a tunable phase shifter is designed and fabricated at 8 GHz. A phase shift of 143° and a figure of merit (FoM) of 28°/dB are achieved by applying maximum 50 V tuning voltage.
Second Harmonic Suppression in S-Band Traveling Wave Tube Tapers
Authors: Gehrmann Elke , Birtel Philip , Dürr Wolfgang , André Frédéric , Jacob Arne F.
Published: February 2021

Traveling wave tubes (TWTs) operating at S-band are to be improved by suppressing the second harmonic frequency. Among the different possibilities, two techniques, namely harmonic injection and a filter helix for frequency selective signal suppression, are studied in more detail and applied to S-band tubes in both simulation and measurement. In addition, their suitability to improve tube performance by reducing the second harmonic is discussed. Moreover, filter helix implementation in TWTs with an arbitrary pitch profile along the interaction area is considered. In this context, the dependence of the pitch discontinuity reflection coefficient on several filter helix parameters is investigated. The influence of those parameters on the filter performance is shown by filter helix optimization. Measurement results of the optimized filter helix TWT are presented.
A Self-Adjoint “Simultaneous Crossing of the Axis”
Authors: Kreith Kurt
Published: February 2021

By constructing the corresponding Green's function in a trapezoidal domain, we establish the existence of self-adjoint realizations of incorporating boundary conditions of the form u(s, 0) = u(s, T) = 0. Such operators correspond to the historically important concept of a ”simultaneous crossing of the axis” for vibrating strings.
Stabilization of Functions and its Application
Authors: Kudryavtsev L. D.
Published: February 2021

The concepts of polynomial stabilization, strong polynomial stabilization, and strong stabilization are introduced for a fundamental system of solutions of linear differential equations. Some criteria of such kinds of stabilizations and applications to the theory of existence and uniqueness of solutions of ordinary differential equations are given. An abstract scheme of the obtained results is presented for Banach spaces.
Limit Distribution of the Integrated Squared Error of Trigonometric Series Regression Estimator
Authors: Nadaraya E.
Published: February 2021

Limit distribution is studied for the integrated squared error of the projection regression estimator (2) constructed on the basis of independent observations (1). By means of the obtained limit theorems, a test is given for verifying the hypothesis on the regression, and the power of this test is calculated in the case of Pitman alternatives.
Two-Dimensional Problems of Stationary Flow of A Noncompressible Viscous Fluid in the Case of Ozeen's Linearization
Authors: Buchukuri T. , Chichinadze R.
Published: February 2021

Two-dimensional boundary value problems of flow of a viscous micropolar fluid are investigated in the case of linearization by Ozeen's method.
On Some Two-Point Boundary Value Problems for Two-Dimensional Systems of Ordinary Differential Equations
Authors: Lomtatidze A.
Published: February 2021

Sufficient conditions for the solvability of two-point boundary value problems for the system are given, where f
1 and f
2 : [a
1
, a
2] × R
2 → R are continuous functions.
On the Correctness of Linear Boundary Value Problems for Systems of Generalized Ordinary Differential Equations
Authors: Ashordia M.
Published: February 2021

The sufficient conditions are established for the correctness of the linear boundary value problem

dx(t) = dA(t) · x(t) + df(t); l(x) = c
0,

where and are matrix- and vector-functions of bounded variation, , and l is a linear continuous operator from the space of n-dimentional vector-functions of bounded variation into .
Optimal Transmission of Gaussian Signals Through A Feedback Channel
Authors: Glonti O.
Published: February 2021

Using the methodology and results of the theory of filtering of conditionally Gaussian processes, the optimal schemes of transmission of Gaussian signals through the noisy feedback channel are constructed under the new power conditions.
On the Boundedness of Cauchy Singular Operator from the Space Lp
to Lq
, p > q ≥ 1
Authors: Khuskivadze G. , Paatashvili C.
Published: February 2021

It is proved that for a Cauchy type singular operator, given by equality (Khvedelidze, Current problems of mathematics 7: 5-162, 1975), to be bounded from the Lebesgue space Lp
(Γ) to Lq
(Γ), as , it is necessary and sufficient that either condition (Calderon, Proc. Nat. Acad. Sci. USA 4: 1324-1327, 1977) or (David, L'integrale de Cauchy sur le courbes rectifiables, Prepublications Univ. Paris–Sud; Dept. Math., 1982) be fulfilled.
On Some Generalizations of the Vandermonde Matrix and Their Relations with the Euler Beta-Function
Authors: Lomidze I.
Published: February 2021

A multiple Vandermonde matrix which, besides the powers of variables, also contains their derivatives is introduced and an explicit expression of its determinant is obtained. For the case of arbitrary real powers, when the variables are positive, it is proved that such generalized multiple Vandermonde matrix is positive definite for appropriate enumerations of rows and columns. As an application of these results, some relations are obtained which in the one-dimensional case give the well-known formula for the Euler beta-function.
On the Initial Value Problem for Functional Differential Systems
Authors: Šeda V. , Eliaš J.
Published: February 2021

For a system of functional differential equations of an arbitrary order the conditions are established for the initial value problem to be solvable on an infinite interval, and the structure of the set of solutions to this problem is studied.
Boundary Value Problems of Electroelasticity with Concentrated Singularities
Authors: Buchukuri T. , Yanakidi D.
Published: February 2021

We investigate the solutions of boundary value problems of linear electroelasticity, having growth as a power function in the neighbourhood of infinity or in the neighbourhood of an isolated singular point. The number of linearly independent solutions of this type is established for homogeneous boundary value problems.
Generalized Sierpinski Sets
Authors: Kharazishvili A.
Published: February 2021

The notion of a Sierpinski topological space is introduced and some properties of such spaces connected with Borel measures are considered.
Construction of Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)
Authors: Lomadze G.
Published: February 2021

Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup Γ0(4N). The constructed modular forms as well as the modular forms from [Lomadze, Georgian Math. J. 1: 53-76, 1994] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.
Weighted Reverse Weak Type Inequality for General Maximal Functions
Authors: Genebashvili J.
Published: February 2021

Necessary and sufficient conditions are found to be imposed on a pair of weights, for which a weak type two-weighted reverse inequality holds, in the case of general maximal functions defined in homogeneous type spaces.
Some Negative Results Concerning the Process of Fejér Type Trigonometric Convolution
Authors: Oniani G.
Published: February 2021

The process of Fejér type trigonometric convolution and its discrete analogue have equivalent uniform residues. The situation changes under pointwise comparison. In this direction negative results have been obtained by different authors. One result of such a type is given in the present paper. In particular, a counter-example is constructed for which both comparisons diverge on the set of complete measure. The smoothness of the counter-example as well as some other problems are investigated.
On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
Authors: Kiguradze I. , Chichua D.
Published: February 2021

Sufficient conditions are found for the existence of multiparametrical families of proper oscillatory and vanishing-at-infinity solutions of the differential equation

u(n) (t) = g(t, u(τ
0 (t)); . . ., u(m–1) (τ

m
–1(t))),

where n ≥ 4, m is the integer part of , g : R
+ × R

m
→ R is a function satisfying the local Carathéodory conditions, and τi
: R
+ → R (i = 0, . . . , m – 1) are measurable functions such that τ (t) → +∞ for t → + ∞ (i = 0, . . ., m – 1).
Fixed Points of Semigroups of Lipschitzian Mappings Defined on Nonconvex Domains
Authors: Tan Kok-Keong , Xu Hong-Kun
Published: February 2021

Certain fixed point theorems are established for nonlinear semigroups of Lipschitzian mappings defined on nonconvex domains in Hilbert and Banach spaces. Some known results are thus generalized.
An Algebraic Model of Fibration with the Fiber K(π, n)-Space
Authors: Berikashvili N.
Published: February 2021

For a fibration with the fiber K(π, n)-space, the algebraic model as a twisted tensor product of chains of the base with standard chains of K(π, n)-complex is given which preserves multiplicative structure as well. In terms of this model the action of the n-cohomology of the base with coefficients in π on the homology of fibration is described.
Estimation of the Integral Modulus of Smoothness of an Even Function of Several Variables with Quasiconvex Fourier Coefficients
Authors: Tevzadze T.
Published: February 2021

The estimate of the modulus of smoothness of an even function of several variables with quasiconvex Fourier coefficients obtained in this paper extends one result of S. A. Telyakovski.
On the Two Questions of Lohwater and Piranian
Authors: Gvaradze M.
Published: February 2021

The problem we are dealing with consists in the following: find the necessary and sufficient conditions for the zero measure subset of the circumference at which points the bounded analytic function has no radial limits.
On Projective Methods of Approximate Solution of Singular Integral Equations
Authors: Jishkariani A. , Khvedelidze G.
Published: February 2021

The estimate for the rate of convergence of approximate projective methods with one iteration is established for one class of singular integral equations. The Bubnov–Galerkin and collocation methods are investigated.
On Some Entire Modular Forms of Weights and for the Congruence Group Γ0(4N)
Authors: Lomadze G.
Published: February 2021

Entire modular forms of weights and for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.
On the Uniqueness of Maximal Functions
Authors: Ephremidze L.
Published: February 2021

The uniqueness theorem for the one-sided maximal operator has been proved.
Spatial Problem of Darboux Type for One Model Equation of Third Order
Authors: Jokhadze O.
Published: February 2021

For a hyperbolic type model equation of third order a Darboux type problem is investigated in a dihedral angle. It is shown that there exists a real number ρ0 such that for α > ρ0 the problem under consideration is uniquely solvable in the Frechet space. In the case where the coefficients are constants, Bochner's method is developed in multidimensional domains, and used to prove the uniquely solvability of the problem both in Frechet and in Banach spaces.
Littlewood–Paley Operators on the Generalized Lipschitz Spaces
Authors: Lu Shanzhen , Tan Changmei , Yabuta Kozo
Published: February 2021

Littlewood–Paley operators defined on a new kind of generalized Lipschitz spaces are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in , where –n < α < 1 and 1 < p < ∞.
Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions
Authors: Burchuladze T. , Bezhuashvili Yu.
Published: February 2021

We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [Kupradze, Gegelia, Basheleishvili, and Burchuladze, Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity, North-Holland Publishing Company, 1979, Russian original, 1976–Mikhlin, Multi-dimensional singular integrals and integral equations, 1962], we prove theorems on the existence and uniqueness of the classical solutions of these problems.
On the Number of Representations of Positive Integers by a Direct Sum of Binary Quadratic Forms with Discriminant –23
Authors: Lomadze G.
Published: February 2021

Explicit exact formulas are obtained for the number of representations of positive integers by some direct sums of quadratic forms and .
On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values
Authors: Ephremidze L.
Published: February 2021

It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.
On the Solvability of Nonlinear Boundary Value Problems for Functional Differential Equations
Authors: Kiguradze I. , Půža B.
Published: February 2021

Sufficient conditions are established for the solvability of the boundary value problem

where p : C(I; Rn
) × C(I; Rn
) → L(I; Rn
), q : C(I; Rn
) → L(I; Rn
), l : C(I; Rn
) × C(I; Rn
) → Rn
, and cn
: C(I; Rn
) → Rn
are continuous operators, and p(x, ·) and l(x, ·) are linear operators for any fixed x ∈ C(I; Rn
).
Monotone Solutions of A Higher Order Neutral Difference Equation
Authors: Cheng Sui Sun , Zhang Guang
Published: February 2021

A real sequence {xk
} is said to be (*)-monotone with respect to a sequence {pk
} and a positive integer σ if xk
> 0 and (–1)
n
Δ
n
(xk
– pkxk–σ
) ≥ 0 for n ≥ 0. This paper is concerned with the existence of (*)-monotone solutions of a neutral difference equation. Existence criteria are derived by means of a comparison theorem and by establishing explicit existence criteria for positive and/or bounded solutions of a majorant recurrence relation.
Asymptotic Expansion of Solutions of Parabolic Equations with a Small Parameter
Authors: Gagnidze A.
Published: February 2021

The heat equation with a small parameter,

is considered, where ε ∈ (0, 1), 𝑚 < 1 and χ is a finite function. A complete asymptotic expansion of the solution in powers ε is constructed.
Several Cohomology Algebras Connected with the Poisson Structure
Authors: Giunashvili Z.
Published: February 2021

The structure of a Lie superalgebra is defined on the space of multiderivations of a commutative algebra. This structure is used to define some cohomology algebra of Poisson structure. It is shown that when a commutative algebra is an algebra of 𝐶∞-functions on the 𝐶∞-manifold, the cohomology algebra of Poisson structure is isomorphic to an algebra of vertical cohomologies of the foliation corresponding to the Poisson structure.
Thermoelastic Equilibrium of Bodies in Generalized Cylindrical Coordinates
Authors: Khomasuridze N.
Published: February 2021

Using the method of separation of variables, an exact solution is constructed for some boundary value and boundary-contact problems of thermoelastic equilibrium of one- and multilayer bodies bounded by the coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧. ρ, α are the orthogonal coordinates on the plane and 𝑧 is the linear coordinate. The body, occupying the domain Ω = {ρ
0 < ρ < ρ
1, α
0 < α < α
1, 0 < 𝑧 < 𝑧1}, is subjected to the action of a stationary thermal field and surface disturbances (such as stresses, displacements, or their combinations) for 𝑧 = 0 and 𝑧 = 𝑧1. Special type homogeneous conditions are given on the remainder of the surface. The elastic body is assumed to be transversally isotropic with the plane of isotropy 𝑧 = const and nonhomogeneous along 𝑧. The same assumption is made for the layers of the multilayer body which contact along 𝑧 = const.
On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
Authors: Kachakhidze N.
Published: February 2021

The systems of bases are constructed for the spaces of cusp forms Sk
(Γ0(3), χ) (k≥6), Sk
(Γ0(7), χ) (k≥3) and Sk
(Γ0(11), χ) (k≥3). Formulas are obtained for the number of representation of a positive integer by the sum of k binary quadratic forms of the kind , of the kind and of the kind .
Asymptotic Distribution of Eigenfunctions and Eigenvalues of the Basic Boundary-Contact Oscillation Problems of the Classical Theory of Elasticity
Authors: Burchuladze T. , Rukhadze R.
Published: February 2021

The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman's method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained.
On the Integrability of Strong Maximal Functions Corresponding to Different Frames
Authors: Oniani G.
Published: February 2021

For the frame θ in , let B
2(θ)(𝑥) (𝑥 ∈ ) be a family of all 𝑛-dimensional rectangles containing 𝑥 and having edges parallel to the straight lines of θ, and let MB2(θ)
be a maximal operator corresponding to B
2(θ). The main result of the paper is the following

Theorem.
For any function 𝑓 ∈ 𝐿 (1 + ln+ 𝐿)() (𝑛 ≥ 2) there exists a measure preserving and invertible mapping

such that

1.

{𝑥 : ω(𝑥) ≠ 𝑥} ⊂ supp 𝑓;

2.

This theorem gives a general solution of M. de Guzmán's problem that was previously studied by various authors.
A Radial Derivative with Boundary Values of the Spherical Poisson Integral
Authors: Dzagnidze O.
Published: February 2021

A formula of a radial derivative is obtained with the aid of derivatives with respect to θ and to φ of the functions closely connected with the spherical Poisson integral 𝑢f
(r, θ, φ) and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates , and .
On Some Entire Modular Forms of an Integral Weight for the Congruence Subgroup Γ0(4𝑁)
Authors: Lomadze G.
Published: February 2021

Four types of entire modular forms of weight are constructed for the congruence subgroup Γ0(4𝑁) when 𝑠 is even. One can find these forms helpful in revealing the arithmetical meaning of additional terms in the formulas for the number of representations of positive integers by positive quadratic forms with integral coefficients in an even number of variables.
The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary
Authors: Basheleishvili M.
Published: February 2021

The first three-dimensional boundary value problem is considered for the basic equations of statics of the elastic mixture theory in the finite and infinite domains bounded by the closed surfaces. It is proved that this problem splits into two problems whose investigation is reduced to the first boundary value problem for an elliptic equation which structurally coincides with an equation of statics of an isotropic elastic body. Using the potential method and the theory of Fredholm integral equations of second kind, the existence and uniqueness of the solution of the first boundary value problem is proved for the split equation.
Polymersions of a Disk with Critical Points on the Boundary
Authors: Abdulaev R.
Published: February 2021

The existence of an interior extension with critical points on the boundary is proved for a given closed normal curve and for nonnormal curves of specific kind.
Proper Moving Average Representations and Outer Functions in Two Variables
Authors: Gawarecki L. , Mandrekar V. , Richard P.
Published: February 2021

In this work, we consider the problem of moving average representations for random fields. As in the Kolmogorov–Wiener case, such representations lead to interesting questions in harmonic analysis in the polydisc. In particular, we study outer functions with respect to half-space, semigroup and quarterplane and their interrelations.
Probability Measures with Big Kernels
Authors: Tien Nguyen Duy , Tarieladze V.
Published: February 2021

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [Kernel associated with a cylindrical measure, Springer-Verlag, 1981, p. 69] is solved by proving that the annihilator of the kernel of a measure μ coincides with the annihilator of μ if and only if the topology of μ-convergence in the dual space is essentially dually separated.
On the ξ-Exponentially Asymptotic Stability of Linear Systems of Generalized Ordinary Differential Equations
Authors: Ashordia M. , Kekelia N.
Published: February 2021

Necessary and sufficient conditions and effective sufficient conditions are established for the so-called ξ-exponentially asymptotic stability of the linear system

𝑑𝑥(𝑡) = 𝑑𝘈(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡),

where and are respectively matrix- and vector-functions with bounded variation components, on every closed interval from [0, +∞[ and ξ : [0, +∞[ → [0, +∞[ is a nondecreasing function such that .
Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity
Authors: Bitsadze L.
Published: February 2021

The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary value problems of electroelasticity are proved and the symbolic matrix is calculated. The uniqueness and existence theorem for the basic BVPs of electroelasticity are given.
Existence and Properties of ℎ-Sets
Authors: Bricchi Michele
Published: February 2021

In this note we shall consider the following problem: which conditions should satisfy a function ℎ : (0, 1) → ℝ in order to guarantee the existence of a (regular) measure μ in with compact support and

for some positive constants 𝑐2, and 𝑐2 independent of γ ∈ Γ and 𝑟 ∈ (0,1)? The theory of self-similar fractals provides outstanding examples of sets fulfilling (♡) with ℎ(𝑟) = 𝑟𝑑, 0 ≤ 𝑑 ≤ 𝑛, and a suitable measure μ. Analogously, we shall rely on some recent techniques for the construction of pseudo self-similar fractals in order to deal with our more general task.
Solution of a Linear Integral Equation of Third Kind
Authors: Shulaia D.
Published: February 2021

The aim of this paper is to study, in the class of Hölder functions, a nonhomogeneous linear integral equation with coefficient cos 𝑥. Necessary and sufficient conditions for the solvability of this equation are given under some assumptions on its kernel. The solution is constructed analytically, using the Fredholm theory and the theory of singular integral equations.
Hyperconvex Spaces and Fixed Points
Authors: Agarwal Ravi P. , O'regan Donal
Published: February 2021

New fixed point results for a very general class of maps on hyperconvex spaces are given. Our theory relies on the fact that hyperconvex compact spaces are absolute retracts. Also maps on 𝑘-CAR sets are discussed.
On an Optimal Decomposition in Zygmund Spaces
Authors: Fiorenza Alberto , Krbec Miroslav
Published: February 2021

An optimal decomposition formula for the norm in the Orlicz space 𝐿(log 𝐿)
α
is given. New proofs of some results involving 𝐿(log 𝐿)
α
spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes.
Boundary Integral Equations of Plane Elasticity in Domains with Peaks. Addendum
Authors: Maz'ya V. G. , Soloviev A. A.
Published: February 2021

The missing References section in the authors' recent paper (Georgian Math. J. 8(2001), No. 3, 571–614) is reproduced.
On A Generalization of the Dirichlet Integral
Authors: Chantladze T. , Kandelaki N. , Lomtatidze A. , Ugulava D.
Published: February 2021

Using the theory of spline functions, we investigate the problem of minimization of a generalized Dirichlet integral

where Ω is a bounded domain of an 𝑛-dimensional Euclidean space 𝑅𝑛, λ ≥ 0 is a fixed number, and 𝑢𝑥𝒊
is a generalized according to Sobolev with respect to 𝑥𝒊 derivative of the function 𝑢 defined on Ω. Minimization is realized with respect to the functions 𝑢 whose boundary values on Γ form a preassigned function, and for them 𝐹λ(𝑢) is finite.
On Ideals with Projective Bases
Authors: Cichoń J. , Kharazishvili A.
Published: February 2021

A theorem concerning some descriptive properties of σ-ideals and generalizing the main result of [Brzuchowski, Cichoń, Grzegorek, and Ryll-Nardzewski, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27: 447–448, 1979] is proved. Various applications of this theorem are also presented.
On Intersections of Small Perfect Sets
Authors: Fast H.
Published: February 2021

For a not empty perfect subset of the unit circle C there is a perfect subset of C measure zero which being rotated to every position intersects the first set on a nonempty perfect set. This result may be stated in terms of set of distances between pairs of points from these two sets.

A generalization of this result to a product of tori is suggested.
Cesàro Means of Trigonometric Fourier Series
Authors: Goginava U.
Published: February 2021

L. Zhizhiashvili proved that if for some 𝑝, 1 ≤ 𝑝 ≤ ∞, and α ∈ (0, 1), then the 𝐿𝑝-deviation of 𝑓 from its Cesàro mean is 𝑂(𝑛
α
𝑤(1/𝑛)) where 𝑤(·) is a modulus of continuity. In this paper we show that this estimation is non-amplifiable for 𝑝 = 1.
On the Uniqueness Property for Products of Symmetric Invariant Probability Measures
Authors: Kharazishvili A.
Published: February 2021

Two symmetric invariant probability measures μ
1 and μ
2 are constructed such that each of them possesses the strong uniqueness property but their product μ
1 × μ
2 turns out to be a symmetric invariant probability measure without the uniqueness property.
Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
Authors: Chkadua O.
Published: February 2021

Spatial boundary value problems of statics of couple-stress elasticity for anisotropic homogeneous media (with contact on a part of the boundary) with an open crack are studied supposing that one medium has a smooth boundary and the other one has an open crack.

Using the method of the potential theory and the theory of pseudodifferential equations on manifolds with boundary, the existence and uniqueness theorems are proved in Besov and Bessel-potential spaces. The smoothness and a complete asymptotics of solutions near the contact boundaries and near crack edge are studied.

Properties of exponents of the first terms of the asymptotic expansion of solutions are established. Classes of isotropic, transversally-isotropic and anisotropic bodies are found, where oscillation vanishes.
First Order Partial Functional Differential Equations with Unbounded Delay
Authors: Kamont Z. , Kozieł S.
Published: February 2021

The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.
On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
Authors: Kondrat'ev V. A. , Nikishkin V. A.
Published: February 2021

Two terms of asymptotics near crack are obtained for solutions of the Dirichlet boundary value problem for second-order elliptic equations in divergent form. The front of a crack is from 𝐶1+𝑠 and the coefficients of the equations belong to 𝐶𝑠 (0.5 < 𝑠 < 1).
A Direct Method for Boundary Integral Equations on a Contour with a Peak
Authors: Maz'ya V. , Soloviev A.
Published: February 2021

Boundary integral equations in the logarithmic potential theory are studied by the direct method under the assumption that the contour has a peak.
On Faces of a Convex Polyhedron in 𝐑3 With a Small Number of Sides
Authors: Kharazishvili A.
Published: February 2021

For any convex polyhedron 𝑃 ⊂ 𝐑3 and for any natural number 𝑘, let 𝐹𝑘(𝑃) denote the number of all faces of 𝑃 with exactly 𝑘 sides. It is well known that 𝐹𝑘(𝑃) ≥ 2 for at least one 𝑘. We consider the question whether 𝐹𝑘(𝑃) ≥ 3, for at least one 𝑘, and present a solution to it. Some related questions are also discussed.
Investigation of a Basic Plane Interface Problem of Statics for Elastic Mixtures
Authors: Svanadze K.
Published: February 2021

The two-dimensional interface problem of statics of elastic mixtures is investigated when differences between displacement vectors and stress vectors are given on the contact curve.

For this problem special potentials with complex densities are constructed and by means of them the contact problem is reduced to a system of integral equations of Fredholm type. Analysis of the equations obtained is given.
On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with 𝑝-Orthogonal Summands. Correction
Authors: Rosalsky Andrew , Volodin Andrei I.
Published: February 2021

A result by Móricz, Su, and Taylor from Acta Math. Hungar.
65(1994), 1–16, was misstated in the authors' paper in Georgian Math. J.
8(2001), No. 2, 377–388, where due to this misstatement the invalid formulation and proof of a corollary is given. In this correction note, the needed result is correctly stated and a corrected version of the invalid corollary is proved.
On Homogeneous Coverings of Euclidean Spaces
Authors: Kharazishvili A.
Published: February 2021

The notion of a homogeneous covering of a given set is introduced and examined. Some homogeneous coverings of a Euclidean space, consisting of pairwise congruent geometric figures (spheres, hyperplanes, etc.), are constructed using the method of transfinite induction.
Formulas of Variation for a Solution of Neutral Differential Equations with Continuous Initial Condition
Authors: Ramishvili I. , Tadumadze T.
Published: February 2021

Formulas of variation are proved for a solution of quasi-linear controlled neutral differential equations with variable delays, when at the initial moment of time the value of the initial function always coincides with the value of the trajectory.
Two Sharp Inequalities of Simpson Type and Applications
Authors: Ujević Nenad
Published: February 2021

Two sharp inequalities of Simpson type are established. Applications in numerical integration are also given.
The Structure of 𝐺-Free Nilpotent Groups of Step 3
Authors: Amaglobeli M.
Published: February 2021

The canonical form of elements of a 𝐺-free nilpotent group of step 3 is defined assuming that the group 𝐺 contains no elements of order 2.
Normalization of Interior Boundaries
Authors: Abdulaev R.
Published: February 2021

It is proved that any closed piecewise-continuous curve can be converted by means of a small deformation to a normal curve such that the initial curve and the obtained one may have an interior extension only simultaneously.
Multiplication Operators and Dynamical Systems on Weighted Locally Convex Spaces of Holomorphic Functions
Authors: Manhas J. S.
Published: February 2021

Let 𝐺 be an open subset of ℂ and let 𝑉 be an arbitrary system of weights on 𝐺. Let 𝐻𝑉𝑏(𝐺) and 𝐻𝑉0(𝐺) be the weighted locally convex spaces of holomorphic functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present article, we characterize the analytic functions inducing multiplication operators and invertible multiplication operators on the spaces 𝐻𝑉𝑏(𝐺) and 𝐻𝑉0(𝐺) for different systems of weights 𝑉 on 𝐺. A (linear) dynamical system induced by multiplication operators on these spaces is obtained as an application of the theory of multiplication operators.
Asymptotic Behavior of Generalized Nonexpansive Sequences and Mean Points
Authors: Pathak H. K. , O'Regan D. , Khan M. S. , Agarwal R. P.
Published: February 2021

Let 𝐸 be a real Banach space with norm ‖ · ‖ and let {𝑥𝑛}𝑛≥0 be a generalized nonexpansive sequence in 𝐸 (i.e., ‖ 𝑥𝑖+1 – 𝑥𝑗+1 ‖2 ≤ ‖𝑥𝑖 – 𝑥𝑗‖2 + (ε(𝑖+1, 𝑗+1) – ε(𝑖, 𝑗))2 for all 𝑖, 𝑗 ≥ 0, where the series of nonnegative terms is convergent). Let . We deal with the mean point of concerning a Banach limit μ. If 𝐸 is reflexive and 𝑑 = 𝑑(0, 𝐾), then we show that and there exists a point 𝑧0 with ‖ 𝑧0 ‖= 𝑑 such that . In the sequel, this result is applied to obtain the weak and strong convergence of .
On Nonnegative Solutions of a Certain Nonlocal Boundary Value Problem for Second Order Linear Functional Differential Equations
Authors: Vodstrčil P.
Published: February 2021

On the interval [𝑎, 𝑏], we consider the boundary value problem

where ℓ : 𝐶([𝑎, 𝑏]; ℝ) → 𝐿([𝑎, 𝑏]; ℝ), 𝑞 ∈ 𝐿([𝑎, 𝑏]; ℝ), and 𝑡0 ∈]𝑎, 𝑏[.

The question on the existence and uniqueness of a nonnegative solution of this problem is studied.
Mappings Confluent over Locally Connected Continua
Authors: Charatonik J. J.
Published: February 2021

A mapping is said to be confluent over locally connected continua if for each locally connected subcontinuum 𝑄 of the range each component of its preimage is mapped onto 𝑄. For mappings of compact spaces this class is a very natural generalization of locally confluent mappings. Various properties of these mappings are systematically studied in the paper.
On Hyers–Ulam Stability of Cauchy and Wilson Equations
Authors: Elqorachi Elhoucien , Akkouchi Mohamed
Published: February 2021

We study the Hyers–Ulam stability problem for the Cauchy and Wilson integral equations

where 𝐺 is a topological group, 𝑓, 𝑔 : 𝐺 → ℂ are continuous functions, μ is a complex measure with compact support and σ is a continuous involution of 𝐺. The result obtained in this paper are natural extensions of the previous works concerning the Hyers–Ulam stability of the Cauchy and Wilson functional equations done in the particular case of μ=δe
: The Dirac measure concentrated at the identity element of 𝐺.
Minimal Free Multi-Models for Chain Algebras
Authors: Huebschmann J.
Published: February 2021

Let 𝑅 be a local ring and 𝐴 a connected differential graded algebra over 𝑅 which is free as a graded 𝑅-module. Using homological perturbation theory techniques, we construct a minimal free multi-model for 𝐴 having properties similar to those of an ordinary minimal model over a field; in particular the model is unique up to isomorphism of multialgebras. The attribute ‘multi’ refers to the category of multicomplexes.
Varieties of Universal Algebras with Normal Local Projections
Authors: Janelidze Z.
Published: February 2021

In this paper we characterize varieties of universal algebras in which every fibre Pt(B) of the fibration of points has normal product projections, i.e., (X × Y)/X ≈ Y holds in every fibre Pt(B).
On the Method of Direct Products in the Theory of Quasi-Invariant Measures
Authors: Kirtadze A.
Published: February 2021

For invariant (quasi-invariant) σ-finite measures on an uncountable group (𝐺, ·), the behaviour of small sets with respect to the operation “·” is studied. Some classes of non-commutative groups (𝐺, ·) are discussed especially, by using a representation of the original group in the form of a direct product of its two subgroups, one of which is commutative.
Uniqueness of Non-Linear Differential Polynomials Sharing 1-Points
Authors: Lahiri Indrajit , Sahoo Pulak
Published: February 2021

We prove two theorems on the uniqueness of nonlinear differential polynomials sharing 1-points which improve an earlier result of Fang and Hong.
On Absolutely Negligible Sets in Uncountable Solvable Groups
Authors: Kharazishvili Alexander
Published: February 2021

Absolutely negligible sets in uncountable groups are considered in connection with the measure extension problem (for σ-finite invariant or quasi-invariant measures). In particular, it is proved that, for any uncountable solvable group (𝐺, ·), there exists a countable covering of 𝐺 consisting of 𝐺-absolutely negligible sets.
On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
Authors: Padhi Seshadev
Published: February 2021

Sufficient conditions in terms of coefficient functions have been obtained so that all nonoscillatory solutions along with their first and second derivatives of the third order delay differential equation

𝑦‴(𝑡) + 𝑎(𝑡)𝑦″(𝑡) + 𝑏(𝑡)𝑦′(𝑡) + 𝑐(𝑡)𝑦(𝑔(𝑡)) = 0

tend to zero as 𝑡 → ∞.
Necessary Optimality Conditions for Lipschitz Multiobjective Optimization Problems
Authors: Gadhi N.
Published: February 2021

Optimality conditions are established in terms of Lagrange–Kuhn–Tucker multipliers for multiobjective optimization problems by a scalarization technique. Throughout this note, the data are assumed to be locally Lipschitz.
Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains
Authors: Hussain Nawab , O'Regan Donal , Agarwal Ravi P.
Published: February 2021

We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.
On Mutually Coherent Enumerations of Countable Sets
Authors: Kharazishvili Alexander
Published: February 2021

The notion of compatibility of enumerations of countable (in particular, finite) sets is introduced and investigated. Some purely combinatorial problems connected with this notion are considered and several conditions are presented for the existence of mutually coherent enumerations of all members of a given family of countable sets.
On an Approximation Order of the Optimal Stopping Problem for 𝑛-Dimensional Diffusion Processes
Authors: Lominashvili Giorgi
Published: February 2021

An approximation order of the optimal stopping problem for multidimensional diffusion processes by the corresponding semidiscretization is considered.
Generalized Derivation and Double Operator Integrals
Authors: Mecheri Salah
Published: February 2021

Let 𝐻 be a separable infinite dimensional complex Hilbert space, and let 𝔹(𝐻) denote the algebra of all bounded linear operators on 𝐻. Let 𝐴, 𝐵 be operators in 𝔹(𝐻). We define the generalized derivation δ
𝐴, 𝐵 : 𝔹(𝐻) ↦ 𝔹(𝐻) by δ
𝐴, 𝐵(𝑋) = 𝐴𝑋 – 𝑋𝐵. In this paper we consider the question posed by Turnsek [Publ. Math. Debrecen 63: 293–304, 2003], when ? We prove that this holds in the case where 𝐴 and 𝐵 satisfy the Fuglede–Putnam theorem. Finally, we apply the obtained results to double operator integrals.
Oscillation and Nonoscillation Theorems for Superlinear Emden–Fowler Equations of even Order
Authors: Wong James S. W. , Ou C. H.
Published: February 2021

We study the existence of oscillatory solutions of the even order superlinear ordinary differential equations

where 𝑛 is an even integer ≥ 2, α > 1 and 𝑝(𝑡) ∈ 𝐶[𝑡0, ∞), 𝑡0 > 0 and 𝑝(𝑡) > 0. When 𝑛 = 2, our results reduce to those of Jasny and Kurzweil, and Erbe and Muldowney for (). When 𝑛 = 4, our result becomes that of Kura for equation (). We present here new techniques suitable for the study of oscillation and nonoscillation of solutions of the general equations of even order () and ().