bluuebunny/crossref_metadata_2025 huggingface dataset:
Reaching for the Gold Standard: Metaphors and Good University Teachers
Authors: Jin Lixian , Cortazzi Martin
Published: February 2021

This article considers “good” teachers in the context of current developments in universities in China to reach a “gold standard” of considerably higher and more challenging levels of teaching and learning. We outline this context and consider concepts of good teachers in classical Chinese traditions and more recent Western thinking as a possible dialogue within and between cultures of learning. Using cognitive and cultural linguistic perspectives, we analyze metaphorical concepts of “gold” in “the gold standard” as related to teachers. We report our applied metaphor research which analyzes Chinese students’ expectations, values and beliefs about good university language teachers; this presents a rich picture beyond developing knowledge, skills and understanding to include strong social and moral characteristics. Other aspects which recognize the complexity of “good” teachers show a student appreciation of teachers’ tireless effort, devotion and selfless sacrifice: these aspects are absent in many discussions of good teachers. The participant-centered picture from elicited metaphor analysis is part of students’ “cultures of learning,” but this should be developed culturally for the gold standard through further teacher development and student engagement. In line with interaction in cultures of learning, we indicate some classroom ways to extend students’ thinking through scaffolding teacher-student interaction based on textbook activities.
Researching Classroom-Based Assessment for Formative Purposes
Authors: Gu Peter Yongqi , Yu Guoxing
Published: February 2021

This article aims to help teacher-researchers engage in empirical research on classroom-based assessment for formative purposes. We will first introduce the key features of classroom-based formative assessment (CBFA), and analyze the research questions asked in round-one projects funded by the Fund for Assessment Research (FAR) in Foreign Language Education in China. Next, we will illustrate how some research questions can be answered by analyzing a video-taped lesson from a round-one FAR project. We conclude by calling for more teacher-led research and argue that research on CBFA by teachers will not only produce valid interpretations and applicable findings, but also constitute a viable model for teacher professional development.
Why Isnice andAdj So Much More Frequent than Adjand nice?—From the Perspective of Humans’ Social and Limited-Processing-Capacity Attributes
Authors: Peng Jinfang
Published: February 2021

This paper investigates the phenomenon of imbalance between the frequencies of thenice andAdj and Adjand nicepatterns from the perspective of humans’ social and limited-processing-capacity attributes. Humans’ social attribute requires that language users stay informative with minimal effort in communication, resulting in the from-the-least-to-the-most-informative information organization in discourse. Their limited-processing-capacity attribute requires that they resort to the production biases of “easy first” and “plan reuse” in order to achieve communicative efficiency in real-time production. The analysis of the occurrences of thenice andAdj pattern and native speakers’ judgment of the degree of informativeness ofnicein these occurrences suggest thatniceis largely delexicalized. Such delexicalization makesnice andAdj consistent with the information organization and allows language users to stay informative with the use of the pattern, thus in line with the social attribute, but not Adjand nice. In the meantime,niceis not only highly frequent but also conceptually salient when it comes to the positive property (Panther & Thornburg, 2009), makingnice andAdj easier to produce and more likely to be reused than Adjand nice, thus in line with the limited-processing-capacity attribute. The analysis of the unbalanced frequency of the two patterns suggests that human attributes should be considered when studying language form, and this should offer insights into English learning.
Approximate Discontinuous Trajectory Hotspots
Authors: Rudi Ali Gholami
Published: February 2021

A hotspot is an axis-aligned square of fixed side length s, where the amount of time a moving entity spends within it is maximised. An exact hotspot of a polygonal trajectory with n edges can be found with time complexity O(n
2). We define a c-approximate hotspot as an axis-aligned square of side length cs, in which the presence duration of the entity is no less than that of an exact hotspot. In this paper we present an algorithm to find a (1 + ϵ)-approximate hotspot of a polygonal trajectory with time complexity

O

(

n
ϕ

ϵ

log

n
ϕ

ϵ

)

O\left( {{{n\phi } \over \varepsilon }\log {{n\phi } \over \varepsilon }} \right)

, where ϕ is the ratio of average trajectory edge length to s.
Process Emulation System for High-Power Piezoelectric Ultrasonic Actuators
Authors: Ille Igor , Mojrzisch Sebastian , Twiefel Jens
Published: February 2021

Ultrasonic actuators are used for a wide field of applications. The vibration energy can be used to realize many processes like ultrasonic welding or bonding. Furthermore there are many processes which run more efficient and faster combined with ultrasonic vibration like ultrasonic-assisted turning or drilling. Piezoelectric transducers are the main part of those applications. Most of the applications have a time-variant load behavior and need an amplitude feedback control to guarantee a stable process. To ensure correct function tests of the feedback control systems have to be done. In this case the processes have to be executed in association with a high number of cycles. To emulate the behavior of the environment the automotive and aerospace industries use hardware in the loop systems since a long time but there is no such a method for ultrasonic systems. This paper presents a method to realize high dynamic load emulation for different ultrasonic applications. Using a piezoelectric transformer it is possible to reproduce load curves by active damping on the secondary side of the transformer using a current proportional digital feedback circuit. A theoretical and experimental study of hardware in the loop system for ultrasonic applications is given by this paper. The present system allows testing a wide field of feedback control algorithms with high flexibility and a high number of cycles by utilization of low-cost components. This proceeding decreases design periods in association with feedback control.
Temperature-Dependent Properties of a 1–3 Connectivity Piezoelectric Ceramic–Polymer Composite
Authors: Gu Xinyun , Yang Ying , Chen Ji , Wang Yiping
Published: February 2021

In this work, the 1–3 connectivity piezoelectric ceramic–polymer composites have been fabricated by a viscous-polymer processing, where 0.90Pb(Zr0.52Ti0.48)O3–0.05Pb(Mn1/3Sb2/3)O3–0.05Pb(Zn1/3Nb2/3)O3 (PZT–PMS–PZN) fibers with 0.5 volume fraction were aligned in epoxy matrix. The sintered PZT fibers, with average diameter of 300 μm and aspect ratio (height/diameter) higher than 3, all showed a pure perovskite phase structure and highly dense morphology. The dielectric, piezoelectric, ferroelectric properties and the vibration modes of the 1–3 composites were measured and demonstrated in comparison with that of the monolithic piezoelectric ceramics. The results confirmed that the 1–3 composites possessed a low acoustic impedance (Z) of 13 MRayl and a high thickness coupling coefficient (k
t) of 0.59, in addition, only single thickness vibration mode with the resonance frequency over 1.5 MHz was observed. With temperature elevation, the properties including dielectric constant εr
, k
t, the ratio of k
t to k
p (k
t/k
p) and the acoustic impedance (Z) increase, while the planar electromechanical coupling coefficient (k
p) show opposite temperature dependence. Under test temperature of 100°C, the 1–3 composites still present excellent temperature stability with increased k
t/k
p ratio up to 3.6. The researches on temperature-dependent properties of the 1–3 composites are critical for improving its applications in various environments.
Co-firing of PZT–PMS–PZN/Ag Multilayer Actuator Prepared by Tape-Casting Method
Authors: Fan Kang-Kang , Wang Yi-Ping , Yang Ying
Published: February 2021

Multilayer ceramic actuator composed of piezoelectrically active 0.90Pb(Zr0.48Ti0.52)O3–0.05Pb(Mn1/3Sb2/3)O3–0.05Pb(Zn1/3Nb2/3)O3 (PZT–PMS–PZN) layers and electrically conducting silver metal layers were fabricated. Low-temperature sinterable PZT–PMS–PZN ceramics were used as the piezoelectric layers, and silver paste was used as the conductive inner-electrode layers. PZT–PMS–PZN powder, adding 1% CuO as a sintering agent, was prepared by a conventional solid-state reaction process. The green sheet was fabricated by tape-casting method. Silver inner-electrode was printed on the green-tape sheets and the sheets were stacked, warm-pressed, and sintered at 900°C for 4 h after burning out the organic additions. The sintered multilayer ceramics actuator shows distinct layers with few defects in the interfaces. The thicknesses of the piezoelectric and conducting layers are about 40 and 6 μm, respectively. The multilayer PZT–PMS–PZN actuator, composed of 60 active piezoelectric layers, presents a longitudinal displacement of about 2.7 μm at an applied voltage of 80 V, approximately 0.1% of the total thickness of itself.
Love, Guilt, Death and Art in Ibsen’s When We Dead Awaken
Authors: Knápek Pavel
Published: February 2021

This article presents an original interpretation of Henrik Ibsen’s work When We Dead Awaken by advancing a hypothesis which explains Rubek and Irene’s path into death as an act of atonement. The analysis encompasses reflections on the meaning of terms such as love, life, art and guilt in the context of the work. The article emphasises the importance of children’s education, which proves itself to be the only effective way to contribute to mankind’s refinement – something very important in the main character’s view. In its last part the article seeks causes of the altered behaviour of the main characters immediately before their deaths (especially their feeling of attraction to death).
Design and numerical study of turbines operating with MDM as
working fluid
Authors: Klonowicz Piotr , Surwiło Jan , Witanowski Łukasz , Suchocki Tomasz K. , Kozanecki Zbigniew , Lampart Piotr
Published: February 2021

Design processes and numerical simulations
have been presented for a few cases of turbines designated
to work in ORC systems. The chosen working fluid isMDM.
The considered design configurations include single stage
centripetal reaction and centrifugal impulse turbines as
well as multistage axial turbines. The power outputs vary
from about 75 kW to 1 MW. The flow in single stage turbines
is supersonic and requires special design of blades.
The internal efficiencies of these configurations exceed
80% which is considered high for these type of machines.
The efficiency of axial turbines exceed 90%. Possible turbine
optimization directions have been also outlined in the
work.
Numerical investigation of a GTM-140 turbojet
engine
Authors: Suchocki Tomasz , Lampart Piotr , Klonowicz Piotr
Published: February 2021

The paper presents three-dimensional numerical
simulations of combustion in the GTM-140 miniature
turbine engine. The main aim of the work is to understand
the processes occurring in the combustion chamber. The
coupling of chemical kinetics, thermochemistry, transport
of mass, energy and momentum, and fluid mechanics is a
challenge for the engineers. The knowledge of these issues
is essential to achieve a high performance product. The k-
ϵ (RANS) Turbulence Model and Non-Premixed Model for
the combustion was used. The particles of fluid droplets
were described by the Discrete Phase Model.
Predicative possession across Western Iranian languages
Authors: Mohammadirad Masoud
Published: February 2021

This paper offers a first systematic investigation of predicative possessive constructions across Western Iranian languages. The notion of possession is conceived as a prototypical domain. It is shown that investigated languages are classified into two major areally distributed groups with respect to predicative possessive constructions: (i) “be”-verb languages, (ii) “have”-verb languages. “Have”-possessives, which originated from “action schema”, are argued to have superseded the archaic “be”-possessives, which trigger a non-canonical marking of the possessor argument. However, “have”-verb languages have preserved relics of the older “be”-possessive in some neighbouring domains to possession. In addition, two languages exhibit possession split and are in transition from “be”-possession to “have”-possession: these languages demonstrate the effect of alienability/inalienability in such a split.
Nasality in Dagbani prosody
Authors: Hudu Fusheini , Nindow Mohammed Osman
Published: February 2021

This paper presents a detailed analysis of nasality in Dagbani, a Gur language of Ghana, and the role it plays in Dagbani prosody. It demonstrates that the nasal is at the centre of defining the range of what is possible in Dagbani prosodic patterns. Nasals provide the basis for determining the full range of syllable types and the tone bearing unit of Dagbani; nasals are the only coda consonants that licence vowel lengthening; and nasals provide the only cases of phonological non-vocalic geminates. The overall effects of the influence of nasality is the emergence of complex prosodic structures. Contrary to the crosslinguistically acclaimed marked position of the coda, the CVN syllable is the default, unmarked syllable in Dagbani.
Spanish [auto +V+ se] constructions
Authors: Orqueda Verónica , Arriagada Silvana , Toro Francisca
Published: February 2021

In this paper we analyse Spanish verbal constructions that accept both the cliticseand the prefixauto-in order to determine whether these formations are or are not more agentive than the corresponding non-prefixed constructions (autocriticarse vs. criticarse). The proposal arises from the discussion about the different semantic values observed in formations withauto-and explores the distinctive features of such formations in contrast to those withoutauto-. We carried out a twofold analysis: first, we applied a set of tests of agentivity and control to a sample of 130 verbs withauto-extracted from the Modern Spanish Reference Corpus (CREA) and compared the sample with its non-prefixed pronominal pairs (i.e. verbs with cliticse). Second, we carried out a series of surveys using similar tests with Spanish speakers to guarantee the acceptability of the corpus interpretations. We argue that prefixed constructions show a higher degree of agentivity and control by external arguments, which results in the impossibility of bidirectionally replacing these constructions with those that only have the cliticse.
Datives with psych nouns and adjectives in Basque
Authors: Fernández Beatriz , Zúñiga Fernando , Berro Ane
Published: February 2021

This paper explores the formal expression of two Basque dative argument types in combination with psych nouns and adjectives, in intransitive and transitive clauses: (i) those that express the experiencer, and (ii) those that express the stimulus of the psychological state denoted by the psych noun and adjective. In the intransitive structure involving a dative experiencer (DatExpIS), the stimulus is in the absolutive case, and the intransitive copulaizan‘be’ shows both dative and absolutive agreement. This construction basically corresponds to those built upon thepiaceretype of psychological verbs typified in (Belletti, Adriana & Luigi Rizzi. 1988. Psych-verbs andθ-theory.Natural Language and Linguistic Theory6. 291–352) three-way classification of Italian psych verbs. In the intransitive structure involving a dative stimulus (DatStimIS), the experiencer is marked by absolutive case, and the same intransitive copula shows both absolutive and dative agreement (with the latter corresponding to the dative stimulus and not to the experiencer). We show that the behavior of the dative argument in the two constructions is just the opposite of each other regarding a number of morphosyntactic tests, including agreement, constituency, hierarchy and selection. Additionally, we explore two parallel transitive constructions that involve either a dative experiencer and an ergative stimulus (DatExpTS) or a dative stimulus and an ergative experiencer (DatStimTS), which employ the transitive copula *edun‘have’. Considering these configurations, we propose an extended and more fine-grained typology of psych predicates.
Contact Problems for Two Anisotropic Half-Planes with Slits
Authors: Zazashvili SH.
Published: February 2021

The problem of a stressed state in a nonhomogeneous infinite plane consisting of two different anisotropic half-planes and having slits of the finite number on the interface line is investigated. It is assumed that a difference between the displacement and stress vector values is given on interface line segments; on the edges of slits we have the following data: boundary values of the stress vector (problem of stress) or displacement vector values on the one side of slits, and stress vector values on the other side (mixed problem). Solutions are constructed in quadratures.
Two-Weighted Lp
-Inequalities for Singular Integral Operators on Heisenberg Groups
Authors: Guliev V. S.
Published: February 2021

Some sufficient conditions are found for a pair of weight functions, providing the validity of two-weighted inequalities for singular integrals defined on Heisenberg groups.
Two-Weighted Estimates for Some Integral Transforms in the Lebesgue Spaces with Mixed Norm and Imbedding Theorems
Authors: Kokilashvili V.
Published: February 2021

Two-weighted inequalities are proved for anisotropic potentials. These estimates are used to obtain the refinements of the well-known imbedding theorems in the scale of weighted Lebesgue spaces.
Complexity of the Decidability of the Unquantified Set Theory with A Rank Operator
Authors: Tetruashvili M.
Published: February 2021

The unquantified set theory MLSR containing the symbols ∪, \, =, ∈, R (R(x) is interpreted as a rank of x) is considered. It is proved that there exists an algorithm which for any formula Q of the MLSR theory decides whether Q is true or not using the space c|Q|3 (|Q| is the length of Q).
On a Generalization of the Keldysh Theorem
Authors: Jaiani G.
Published: February 2021

The Keldysh theorem for an elliptic equation with characteristic parabolic degeneration is generalized for the case of an elliptic equation of the second-order canonical form with order and type degeneration. The criteria under which the Dirichlet or Keldysh problems are correct are given in a one-sided neighborhood of the degeneration segment, enabling one to write the criteria in a single form. Moreover, some cases are pointed out in which it is even nessesary to give a criterion in the neighborhood because it is impossible to establish it on the segment of degeneracy of the equation.
Global Dimensions of Subidealizer Rings
Authors: Koker John
Published: February 2021

Recently, there have been many results which show that the global dimension of certain rings can be computed using a proper subclass of the cyclic modules, e.g., the simple modules. In this paper we view calculating global dimensions in this fashion as a property of a ring and show that this is a property which transfers to the ring's idealizer and subidealizer ring.
Asymptotic Behavior of Eigenfunctions and Eigenfrequencies of Oscillation Boundary Value Problems of the Linear Theory of Elastic Mixtures
Authors: Svanadze M.
Published: February 2021

The asymptotic behavior of eigenoscillation and eigen-vector-function is studied for the internal boundary value problems of oscillation of the linear theory of a mixture of two isotropic elastic media.
On the Mode-Change Problem for Random Measures
Authors: Hahubia Ts. , Mnatsakanov R.
Published: February 2021

The classical change-point problem in modern terms, i.e., the mode-change problem, is stated for sufficiently general set-indexed random processes, namely for random measures. A method is shown for solving this problem both in the general form and for the intensity of compound Poisson random measures. The results obtained are novel for the change-point problem, too.
Non-Baire Unions in Category Bases
Authors: Hejduk J.
Published: February 2021

We consider a partition of a space X consisting of a meager subset of X and obtain a sufficient condition for the existence of a subfamily of this partition which gives a non-Baire subset of X. The condition is formulated in terms of the theory of J. Morgan [Point Set Theory, Marcel Dekker, 1990].
Hyperplane Singularities of Analytic Functions of Several Complex Variables
Authors: Shubladze M.
Published: February 2021

A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.
Upper Estimate of the Interval of Existence of Solutions of a Nonlinear Timoshenko Equation
Authors: Bainov Drumi , Minchev Emil
Published: February 2021

Solutions to the initial-boundary value problem for a nonlinear Timoshenko equation are considered. Conditions on the initial data and nonlinear term are given so that solutions to the problem under consideration do not exist for all t > 0. An upper estimate of the t-interval of the existence of solutions is obtained. An estimate of the growth rate of the solutions is given.
On the Riemann–Hilbert Problem in the Domain with a Nonsmooth Boundary
Authors: Kokilashvili V. , Paatashvili V.
Published: February 2021

The following Riemann–Hilbert problem is solved: find an analytical function Φ from the Smirnov class Ep
(D), whose angular boundary values satisfy the condition

Re[(a(t) + ib(t))Φ+ (t)] = ƒ(t).

The boundary Γ of the domain D is assumed to be a piecewise smooth curve whose nonintersecting Lyapunov arcs form, with respect to D, the inner angles with values νkπ, 0 < νk
≤ 2.
Non-Abelian Cohomology of Groups
Authors: Inassaridze H.
Published: February 2021

Following Guin's approach to non-abelian cohomology [Guin, Pure Appl. Algebra 50: 109–137, 1988] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2.
On the Bifurcation of Flows of a Heat-Conducting Fluid Between Two Rotating Permeable Cylinders
Authors: Shapakidze L.
Published: February 2021

Sufficient conditions are found for the bifurcation of flow of a viscous heat-conducting fluid between two rotating permeable cylinders.
Asymptotic Solutions for Mixed-Type Equations with A Small Deviation
Authors: Hou Zhanyuan , Cassell J. S.
Published: February 2021

An asymptotic matrix solution is formulated for a class of mixed-type linear vector equations with a single variable deviation which is small at infinity. This matrix solution describes the asymptotic behavior of all exponentially bounded solutions. A sufficient condition is obtained for there to be no other solutions.
Spectral and Boundedness Radii in Locally Convex Algebras
Authors: El Kinani A. , Oubbi L. , Oudadess M.
Published: February 2021

Connections between the spectral radius and the radius of boundedness are studied. Different characterizations of algebras (Q-property, strong saquentiality) are given in terms of these radii. Examples and applications are also provided.
On Some Contact Problems for Bodies with Elastic Inclusions
Authors: Shavlakadze N.
Published: February 2021

The paper deals with the contact problems of the theory of elasticity. The problems are reduced to Prandtl-type integral differential equations with a coefficient at the singular operator which has higher-order zeros at the ends of the integration interval. In some concrete cases the solution is constructed efficiently. Asymptotic representations are obtained.
Multiplicative B-Product and its Properties
Authors: Bhattacharjee D.
Published: February 2021

The author considers a special kind of B-product which is called the multiplicative B-product. The most important property of multiplicative B-product is that it preserves multiplicativity of functions.
Properties of the Salagean Operator
Authors: Lin Li Jian , Owa Shigeyoshi
Published: February 2021

The object of the present paper is to show the properties of the Salagean operator for analytic functions in the open unit disk. The main results obtained here extend and improve the earlier results obtained by several authors.
Boundary Properties of Second-Order Partial Derivatives of the Poisson Integral for a Half-Space
Authors: Topuria S.
Published: February 2021

The boundary properties of second-order partial derivatives of the Poisson integral are studied for a half-space .
On the Buchstaber Subring in MSp∗
Authors: Bakuradze M.
Published: February 2021

A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.
Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients
Authors: Fan Dashan , Lu Shanzhen , Yang Dachun
Published: February 2021

In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.
Iterating the Bar Construction
Authors: Kadeishvili T. , Saneblidze S.
Published: February 2021

For a 1-connected space X Adams's bar construction B(C*(X)) describes H*(ΩX) only as a graded module and gives no information about the multiplicative structure. Thus it is not possible to iterate the bar construction in order to determine the cohomology of iterated loop spaces Ω
iX. In this paper for an n-connected pointed space X a sequence of A(∞)-algebra structures , k = 1, 2, . . . , n, is constructed, such that for each k ≤ n there exists an isomorphism of graded algebras
Crossed Semimodules and Schreier Internal Categories in the Category of Monoids
Authors: Patchkoria A.
Published: February 2021

We introduce the notion of a Schreier internal category in the category of monoids and prove that the category of Schreier internal categories in the category of monoids is equivalent to the category of crossed semimodules. This extends a well-known equivalence of categories between the category of internal categories in the category of groups and the category of crossed modules.
Markov Dilation of Diffusion Type Processes and its Application to the Financial Mathematics
Authors: Tevzadze R.
Published: February 2021

The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.
On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations
Authors: Kiguradze T.
Published: February 2021

In the rectangle 𝐷 = (0, 𝑎) × (0, 𝑏) with the boundary Γ the Dirichlet problem

𝑢(𝑥, 𝑦) = 0 for (𝑥, 𝑦) ∈ Γ

is considered, where 𝑝 and 𝑞 : 𝐷 → ℝ are locally summable functions and may have nonintegrable singularities on Γ. The effective conditions guaranteeing the unique solvability of this problem and the stability of its solution with respect to small perturbations of the coefficients of the equation under consideration are established.
Two-Weighted Inequalities for Integral Operators in Lorentz Spaces Defined on Homogeneous Groups
Authors: Kokilashvili V. , Meskhi A.
Published: February 2021

The optimal sufficient conditions are found for weights, which guarantee the validity of two-weighted inequalities for singular integrals in the Lorentz spaces defined on homogeneous groups. In some particular case the found conditions are necessary for the corresponding inequalities to be valid. Also, the necessary and sufficient conditions are found for pairs of weights, which provide the validity of two-weighted inequalities for the generalized Hardy operator in the Lorentz spaces defined on homogeneous groups.
On the Absolute Summability of Series with Respect to Block-Orthonormal Systems
Authors: Nadibaidze G.
Published: February 2021

Theorems determining Weyl's multipliers for the summability almost everywhere by the |c, 1| method of the series with respect to block-orthonormal systems are proved. In particular, it is stated that if the sequence {ω(n)} is the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all orthogonal series, then there exists a sequence {Nk
} such that {ω(n)} will be the Weyl multiplier for the summability almost everywhere by the |c, 1| method of all series with respect to the Δ
k
-orthonormal systems.
Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization
Authors: Soltani A. R. , Shishebor Z.
Published: February 2021

Let X and Y be two Hilbert spaces, and the space of bounded linear transformations from X into Y. Let {An
} ⊂ be a weakly periodic sequence of period T. Spectral theory of weakly periodic sequences in a Hilbert space is studied by H. L. Hurd and V. Mandrekar (Spectral theory of periodically and quasi-periodically stationary SαS sequences, University of North Carolina, Chapel Hill, 1991). In this work we proceed further to characterize {An
} by a positive measure μ and a number T of -valued functions a
0, . . . , a

T–1; in the spectral form , where and Φ is an -valued Borel set function on [0, 2π) such that

(Φ(Δ)x, Φ(Δ′)x′)
Y
= (x, x′)
X μ(Δ ∩ Δ′).
Topological Spaces with the Strong Skorokhod Property
Authors: Banakh T. O. , Bogachev V. I. , Kolesnikov A. V.
Published: February 2021

We study topological spaces with the strong Skorokhod property, i.e., spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measure on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost everywhere convergent sequences of mappings. We construct nonmetrizable spaces with such a property and investigate the relations between the Skorokhod and Prokhorov properties. It is also shown that a dyadic compact has the strong Skorokhod property precisely when it is metrizable.
On a Characterisation of Inner Product Spaces
Authors: Chelidze G.
Published: February 2021

It is well known that for the Hilbert space H the minimum value of the functional F

μ
(f) = ∫
H
‖f – g‖2
dμ(g), f ∈ H, is achived at the mean of μ for any probability measure μ with strong second moment on H. We show that the validity of this property for measures on a normed space having support at three points with norm 1 and arbitrarily fixed positive weights implies the existence of an inner product that generates the norm.
On the Tail Estimation of the Norm of Rademacher Sums
Authors: Chobanyan S. , Salehi H.
Published: February 2021

The main aim of this paper is to prove a bilateral inequality for , where t > 0, (𝑎𝑘) are elements of a normed space, while (𝑟𝑘) are Rademacher functions. Then this inequality is applied for estimation of . As another corollary we give a maximal inequality for exchangeable random variables that recently has been published in [Pruss, Proc. Amer. Math. Soc. 126: 1811–1819, 1998].
Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces
Authors: Kawabe Jun
Published: February 2021

We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam's criterion for real measures and applies to cases which are not covered by März–Shortt's criterion for Banach space valued vector measures.
Representations of Conditional Means
Authors: Rao M. M.
Published: February 2021

A unified treatment of integral representations of conditional expectations, in terms of Bochner integrals, with specializations to Gaussian conditioning, is given. The integrals in the latter have deterministic kernels. Difficulties in actual calculations of (even regular) conditional probabilities, and the inadequacy of methods related to L'Hospital's procedures, are exemplified. Limitations of the methods used and some new problems for investigation are indicated.
On Accuracy of Improved χ
2-Approximations
Authors: Ulyanov V. V. , Fujikoshi Y.
Published: February 2021

For a statistic S whose distribution can be approximated by χ
2-distributions, there is a considerable interest in constructing improved χ
2-approximations. A typical approach is to consider a transformation T = T(S) based on the Bartlett correction or a Bartlett type correction. In this paper we consider two cases in which S is expressed as a scale mixture of a χ
2-variate or the distribution of S allows an asymptotic expansion in terms of χ
2-distributions. For these statistics, we give sufficient conditions for T to have an improved χ
2-approximation. Furthermore, we present a method for obtaining its error bound.
Tractability of Tensor Product Linear Operators in Weighted Hilbert Spaces
Authors: Woźniakowski Henryk
Published: February 2021

We study tractability in the worst case setting of tensor product linear operators defined over weighted tensor product Hilbert spaces. Tractability means that the minimal number of evaluations needed to reduce the initial error by a factor of ε in the d-dimensional case has a polynomial bound in both ε
–1 and d. By one evaluation we mean the computation of an arbitrary continuous linear functional, and the initial error is the norm of the linear operator S

d
specifying the d-dimensional problem.

We prove that nontrivial problems are tractable iff the dimension of the image under S
1 (the one-dimensional version of S

d
) of the unweighted part of the Hilbert space is one, and the weights of the Hilbert spaces, as well as the singular values of the linear operator S
1, go to zero polynomially fast with their indices.
Weighted Exponential Inequalities
Authors: Heinig H. P. , Kerman R. , Krbec M.
Published: February 2021

Necessary and sufficient conditions on weight pairs are found for the validity of a class of weighted exponential inequalities involving certain classical operators. Among the operators considered are the Hardy averaging operator and its variants in one and two dimensions, as well as the Laplace transform. Discrete analogues yield characterizations of weighted forms of Carleman's inequality.
Global Geometric Aspects of Riemann–Hilbert Problems
Authors: Bojarski B. , Khimshiashvili G.
Published: February 2021

We discuss some global properties of an abstract geometric model for Riemann–Hilbert problems introduced by the first author. In particular, we compute the homotopy groups of elliptic Riemann–Hilbert problems and describe some connections with the theory of Fredholm structures which enable one to introduce more subtle geometrical and topological invariants for families of such problems.
On the Product of Separable Metric Spaces
Authors: Kighuradze D.
Published: February 2021

Some properties of the dimension function dim on the class of separable metric spaces are studied by means of geometric construction which can be realized in Euclidean spaces. In particular, we prove that if dim(𝑋 × 𝙔) = dim 𝑋 + dim 𝙔 for separable metric spaces 𝑋 and 𝙔, then there exists a pair of maps , , 𝑠 = dim 𝑋 + dim 𝙔, with stable intersections.
On Singular Boundary Value Problems for Functional Differential Equations of Higher Order
Authors: Kiguradze I. , Půža B. , Stavroulakis I. P.
Published: February 2021

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

𝑥(𝑛) (𝑡) = 𝑓(𝑥)(𝑡), ℎ𝑖(𝑥) = 0 (𝑖 = 1, . . . , 𝑛),

where 𝑓 is an operator (ℎ𝑖 (𝑖 = 1, . . . , 𝑛) are operators) acting from some subspace of the space of (𝑛 – 1)-times differentiable on the interval ]𝑎, 𝑏[ 𝑚-dimensional vector functions into the space of locally integrable on ]𝑎, 𝑏[ 𝑚-dimensional vector functions (into the space ).
The Bochner Mean Square Deviation and Law of Large Numbers for Squares of Random Elements in Banach Lattices
Authors: Matsak Ivan , Plichko Anatolij
Published: February 2021

A Bochner mean square deviation for random elements of 2-convex Banach lattices is introduced and investigated. Results, analogous to the law of large numbers for squares of random elements are proved in some classes of Köthe function spaces.
A Strong Solution of an Evolution Problem with Integral Conditions
Authors: Mesloub S. , Bouziani A. , Kechkar N.
Published: February 2021

The paper is devoted to proving the existence and uniqueness of a strong solution of a mixed problem with integral boundary conditions for a certain singular parabolic equation. A functional analysis method is used. The proof is based on an energy inequality and on the density of the range of the operator generated by the studied problem.
A Semimartingale Bellman Equation and the Variance-Optimal Martingale Measure. Correction
Authors: Mania M. , Tevzadze R.
Published: February 2021

Corrections are given for [Mania and Tevzadze, Georgian Math. J. 7: 765–792, 2000], most of which consist in replacing “ess sup” by “ess inf” in all the exposed formulas.
A Note on Convexly Independent Subsets of an Infinite Set of Points
Authors: Kharazishvili A.
Published: February 2021

We consider convexly independent subsets of a given infinite set of points in the plane (Euclidean space) and evaluate the cardinality of such subsets. It is demonstrated, in particular, that situations are essentially different for countable and uncountable point sets.
On the Theory of Functional-Differential Inclusion of Neutral Type
Authors: Bulgakov A. I. , Vasilyev V. V.
Published: February 2021

A Cauchy problem for a functional-differential inclusion of neutral type with a nonconvex right-hand side is investigated. Questions of the solvability of such a problem are considered, estimates analogous to the Filippov's estimates are obtained and the density principle is proved.
Strong Innovation and its Applications to Information Diffusion Modelling in Finance
Authors: Toronjadze T.
Published: February 2021

We consider the mean-variance hedging and utility maximization problems under partial information for diffusion models of the stock price process. The special feature of this paper is that we construct a strong innovation process for the stock price process which allows us to reduce the partial information case to the full information one.
Pseudo-Bessel Functions and Applications
Authors: Dattoli G. , Cesarano C. , Sacchetti D.
Published: February 2021

We employ the decomposition theorem with respect to the cyclic group of order 𝑘 to introduce families of pseudo-Bessel functions and to study their properties. We also discuss in brief their applications in probability theory and in electromagnetism.
Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation
Authors: Jangveladze T. , Kiguradze Z.
Published: February 2021

The asymptotic behavior as 𝑡 → ∞ of solutions of a nonlinear integro-differential equation is studied. The equation arises as a model describing the penetration of the electromagnetic field in to a substance.
Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Authors: Zhou Haiyun , Agarwal Ravi P. , Cho Yeol Je , Kim Yong Soo
Published: February 2021

In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors.
Extending Quasi-Invariant Measures by Using Subgroups of a Given Group
Authors: Kharazishvili A.
Published: February 2021

A method of extending σ-finite quasi-invariant measures given on an uncountable group, by using a certain family of its subgroups, is investigated.
Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
Authors: Khomasuridze N.
Published: February 2021

Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ
0 < ρ < ρ
1, α
0 < α < α
1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ
ρ
= ℎ
α
= ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.
A Unified Characterization of 𝑞-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
Authors: Mania M. , Tevzadze R.
Published: February 2021

We give a unified characterization of 𝑞-optimal martingale measures for 𝑞 ∈ [0, ∞) in an incomplete market model, where the dynamics of asset prices are described by a continuous semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases 𝑞 = 2, 𝑞 = 1 and 𝑞 = 0 respectively. Under assumption that the Reverse Hölder condition is satisfied, the continuity (in 𝐿1 and in entropy) of densities of 𝑞-optimal martingale measures with respect to 𝑞 is proved.
Weak Convergence of a Dirichlet-Multinomial Process
Authors: Muliere Pietro , Secchi Piercesare
Published: February 2021

We present a random probability distribution which approximates, in the sense of weak convergence, the Dirichlet process and supports a Bayesian resampling plan called a proper Bayesian bootstrap.
On Approximate Large Deviations for 1D Diffusion
Authors: Veretennikov A. Yu.
Published: February 2021

We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.
Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions
Authors: Dattoli Giuseppe , Ricci Paolo E.
Published: February 2021

Some classes of entire functions which are eigenfunctions of generalizations of the Laguerre derivative operator are considered.

Since this property is an analog of the one characterizing the exponential function, we refer to such functions as Laguerre-type exponentials, or shortly 𝐿-exponentials. The definition of 𝐿-circular and 𝐿-hyperbolic functions easily follows.

Applications in the framework of generalized evolution problems are also mentioned.
The Superstability of the Generalized D'alembert Functional Equation
Authors: Elqorachi Elhoucien , Akkouchi Mohamed
Published: February 2021

We generalize the well-known Baker's superstability result for the d'Alembert functional equation with values in the field of complex numbers to the case of the integral equation

where 𝐺 is a locally compact group, μ is a generalized Gelfand measure and σ is a continuous involution of 𝐺.
On the Solvability of a Nonlocal Problem Arising in Dynamics of Moisture Transfer
Authors: Bouziani Abdelfatah
Published: February 2021

In the recent years, evolution problems with an integral term in the boundary conditions have received a great deal of attention. Such problems, in general, are nonself-adjoint, and this poses the basic source of difficulty, which can considerably complicate the application of standard functional and numerical techniques. To avoid these complications, we have introduced a nonclassical function space to establish a priori estimates without any additional complication as compared to the classical evolution problems. As an example of the applicability of this way of solving problems of this type, we investigate an initial-boundary value problem for a pseudoparabolic equation which combines Neumann and integral conditions.
Oscillation Criteria for Second-Order Nonlinear Differential Equations with Damping Term
Authors: Wang Qi-Ru
Published: February 2021

By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrate the importance of our results are included.
The Bellman Equation Related to the Minimal Entropy Martingale Measure
Authors: Mania M. , Santacroce M. , Tevzadze R.
Published: February 2021

We derive a backward stochastic differential equation and a Bellman equation characterizing the minimal entropy martingale measure for market models, where asset prices are driven by Markov diffusion processes. A relation between these equations is established.
A Recursion Formula for the Coefficients of Entire Functions Satisfying an ODE with Polynomial Coefficients
Authors: Belingeri C.
Published: February 2021

A recursion formula for the coefficients of entire functions which are solutions of linear differential equations with polynomial coefficients is derived. Some explicit examples are developed.

The Newton sum rules for the powers of zeros of a class of entire functions are constructed in terms of Bell polynomials.
On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane
Authors: Kharazishvili A.
Published: February 2021

The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.
Effective Solution of a Class of Boundary Value Problems of Thermoelasticity in Generalized Cylindrical Coordinates
Authors: Khomasuridze N.
Published: February 2021

A class of static boundary value problems of thermoelasticity is effectively solved for bodies bounded by coordinate surfaces of generalized cylindrical coordinates ρ, α, 𝑧 (ρ, α are orthogonal curvilinear coordinates on the plane and 𝑧 is a linear coordinate). Besides in the Cartesian system of coordinates some boundary value thermoelasticity problems are separately considered for a rectangular parallelepiped. An elastic body occupying the domain Ω = {ρ
0 < ρ < ρ
1, α
0 < α < α
1, 0 < 𝑧 < 𝑧1}, is considered to be weakly transversally isotropic (the medium is weakly transversally isotropic if its nine elastic and thermal characteristics are correlated by one or several conditions) and non-homogeneous with respect to 𝑧.
Particular Solutions for a Class of ODE Related to the L-Exponential Functions
Authors: Bretti Gabriella , Natalini Pierpaolo
Published: February 2021

Particular solutions of a class of higher order ordinary differential equations, with non-constant coefficients, are determined by using the properties of the Laguerre exponentials functions introduced by G. Dattoli and P. E. Ricci in [Georgian Math. J. 10: 481–494, 2003]