bluuebunny/crossref_metadata_2025 huggingface dataset:
The lifetime risk of revision following total hip arthroplasty
Authors: Nugent Mary , Young Simon W. , Frampton Christopher M. , Hooper Gary J.
Published: February 2021

Aims

Joint registries typically use revision of an implant as an endpoint and report survival rates after a defined number of years. However, reporting lifetime risk of revision may be more meaningful, especially in younger patients. We aimed to assess lifetime risk of revision for patients in defined age groups at the time of primary surgery.

Methods

The New Zealand Joint Registry (NZJR) was used to obtain rates and causes of revision for all primary total hip arthroplasties (THAs) performed between January 1999 and December 2016. The NZJR is linked to the New Zealand Registry of Births, Deaths and Marriages to obtain complete and accurate data. Patients were stratified by age at primary surgery, and lifetime risk of revision calculated according to age, sex, and American Society of Anesthesiologists (ASA) classification. The most common causes for revision were also analyzed for each age group.

Results

The overall, ten-year implant survival rate was 93.6% (95% confidence interval (CI) 93.4% to 93.8%). It was lowest in the youngest age group (46 to 50 years), rising sequentially with increasing age to 97.5% in the oldest group (90 to 95 years). Lifetime risk of revision surgery was 27.6% (95% CI 27.3% to 27.8%) in those aged 46 to 50 years, decreasing with age to 1.1% (95% CI 0.0% to 5.8%) in those aged 90 to 95 years at the time of primary surgery. Higher ASA grades were associated with an increased lifetime risk of revision across all ages. The commonest causes for revision THA were aseptic loosening, infection, periprosthetic fracture, and dislocation.

Conclusion

When counselling patients preoperatively, the lifetime risk of revision may be a more meaningful and useful measure of longer-term outcome than implant survival at defined time periods. This study highlights the considerably increased likelihood of subsequent revision surgery in younger age groups. Cite this article: Bone Joint J 2021;103-B(3):479–485.
O DINAMISMO ECONÔMICO E PRODUTIVO DO ESTADO DE MATO GROSSO DO SUL PÓS-2003: AS TRANSFORMAÇÕES PRODUTIVAS DAS MESORREGIÕES
Authors: Farias Fernando Rodrigo , Espíndola Carlos José , Cunha Roberto César
Published: February 2021

O Estado do Mato Grosso do Sul apresentou, a partir de 2003, um crescimento econômico médio na ordem de 9,5% ao ano. O Produto Interno Bruto, em 2003, somou R$ 21,8 bilhões e, em 2017, saltou para R$ 96,3 bilhões. O setor de exportações, apesar dos períodos de flutuações econômicas, teve crescimento expressivo no período analisado. Em 2003, o volume das receitas das exportações somou R$ 497,9 milhões e, em 2019, atingiu R$ 5,2 bilhões. Diante disso, surge a questão central:  quais os fatores geoeconômicos endógenos e exógenos que contribuíram para a ocorrências dessas transformações? Nesse sentido, o artigo visa demonstrar as recentes alterações na dinâmica produtiva no estado do Mato Grosso do Sul pós-2003 e suas combinações geoeconômicas propulsoras. Metodologicamente, partiu-se de uma revisão bibliográfica acompanhada de coletas de dados nos órgãos oficiais e visando identificar as alterações na dinâmica produtiva no estado. As transformações e o reordenamento regional da matriz produtiva aconteceram de maneira concentrada em número reduzido de municípios em forma de “ilhas de desenvolvimento” nas mesorregiões. Isso ocorreu devido à estreita relação entre os investimentos estatais em setores estratégicos ligados ao movimento da economia nacional e a dinâmica do mercado externo.
HISTÓRIA DA FORMAÇÃO DE PROFESSORES DE GEOGRAFIA NO TRIÂNGULO MINEIRO: IRMÃ LORETO E A FISTA EM UBERABA-MG
Authors: Gonçalves Amanda Regina , Menon Mariana Bernardo
Published: February 2021

Diante da necessidade de compreender melhor aspectos atuais da cultura acadêmica e da cultura escolar em que a disciplina Geografia está imersa, o texto desenvolve-se em torno do objetivo de reconhecer os processos de históricos de institucionalização da Licenciatura em Geografia no Ensino Superior no Triângulo Mineiro. A partir de procedimentos metodológicos de pesquisa da história oral e da pesquisa documental, com uso de entrevistas à Irmã Loreto como uma fonte direta de dados, o texto avalia como a cidade de Uberaba e região fazem parte da história da formação de professores Geografia no Brasil, a partir da criação, em 1949, do Curso de Geografia na Faculdade de Filosofia Ciências e Letras Santo Tomás de Aquino (FISTA), situando-o entre os primeiros do país. Como resultado, traz-se a trajetória de vida e formação da Irmã Loreto, fundadora do Curso de Geografia nesta instituição e que formou professores de Geografia por mais de quarenta e cinco anos, sendo destacados aspectos da história da disciplina e da prática de ensino de Geografia.
Campagnes anti-genre en Europe : des mobilisations contre l’égalité - Roman Kuhar, David Paternotte (dir.), 2018.
Authors: Dolbeau Samuel
Published: February 2021

Recensé : Kuhar R., Paternotte D. (dir.) (2018), Campagnes anti-genre en Europe : des mobilisations contre l’égalité, Lyon, Presses Universitaires de Lyon, 368 p.
The maximal domain of meromorphic continuation of a Dirichlet series
Authors: Bhowmik Gautami , Schlage-Puchta Jan-Christoph
Published: February 2021

Many Dirichlet series are either continuable to the whole complex plane or admit half-planes as their maximal domain of meromorphic continuation. Here we prove that this need not always be true.
The subelliptic ∞-Laplace system on Carnot–Carathéodory spaces
Authors: Katzourakis Nicholas
Published: February 2021

Given a Carnot–Carathéodory space with associated frame of vector fields , we derive the subelliptic ∞-Laplace system for mappings , which reads

in the limit of the subelliptic p-Laplacian as . Here is the horizontal gradient and is the projection on its nullspace. Next, we identify the variational principle characterizing the subelliptic ∞-Laplacian system, which is the “Euler–Lagrange PDE” of the supremal functional

for an appropriately defined notion of horizontally ∞-minimal mappings. We also establish a maximum principle for for solutions to the subelliptic ∞-Laplacian system. These results extend previous work of the author [J. Differential Equations 253 (2012), no. 7, 2123–2139; Proc. Amer. Math. Soc., to appear] on vector-valued calculus of variations in L
∞ from the Euclidean to the subelliptic setting.
Persönlichkeit, Tätigkeitsmerkmale und berufliche Kompetenzen / Personality, job charakteristics and work related competencies
Authors: Bildat Lothar , Schmidt Matthias
Published: February 2021

Zusammenhänge zwischen Persönlichkeitsvariablen und Indikatoren beruflichen Erfolges unterschiedlicher Studien werden überblickshaft dargestellt und kurz erläutert. Berufliche Kompetenzen werden thematisiert und es werden Beispiele moderner Verfahren zur Erfassung berufsrelevanter Aspekte der Persönlichkeit kritisch diskutiert. Die Bedeutung - und partielle Vernachlässigung - von Tätigkeitsanalysen im Zusammenhang mit Kompetenzmodellierung wird ebenso angesprochen wie die notwendige Synthese von persönlichkeits- und tätigkeitsorientierten Verfahren. Implikationen für Forschung und Praxis werden diskutiert und mit einem kurzen Fazit abgeschlossen.
Entwurf und Regelung eines Positioniersystems für robotergestützte Nanomesstechnik
Authors: Thier Markus , Saathof Rudolf , Csencsics Ernst , Hainisch Reinhard , Sinn Andreas , Schitter Georg
Published: February 2021

In einer Produktionsumgebung beeinflussen mechanische Vibrationen den Relativabstand zwischen Inspektionsgerät und Werkstück, was für
Messungen im Nanometerbereich hinderlich ist. Dieser Beitrag stellt eine Metrologieplattform zur Montage eines Inspektionsgerätes vor,
die mittels eines H∞-Reglers den Relativabstand zum Werkstück konstant hält. Ein Laboraufbau mit einem Freiheitsgrad zeigt,
dass in der Produktionsumgebung vorkommende Vibrationen um eine Größenordnung reduziert werden können, was eine
Oberflächencharakterisierung im Nanometerbereich direkt in der Produktion ermöglicht.
Extremum seeking dead-zone pre-compensator for an industrial control system
Authors: Dincmen Erkin
Published: February 2021

PID type industrial controllers such as PI, PD, PID are mature control algorithms and they are intensively used in
industry due to their simplicity and easily implementability. However, they start to fail when there is an unknown or
unpredictable nonlinear behavior in the plant or actuator. In this paper, a novel compensation algorithm is proposed for
PD type industrial control systems, which possess an unknown dead-zone nonlinearity. An extremum-seeking technique is
utilized in the compensation algorithm. The aim is to propose a new, effective and robust compensator which can be added
easily to an existing industrial controller without any need to change/retune the controller settings/parameters. It is
shown that by adding the compensator to an existing PD control system, the sensitivity of the controller to the dead-zone
nonlinearity is removed.
Structural Analysis of the Lactoferrin Iron Binding Pockets
Authors: Marchewka Damian , Roterman Irena , Strus Magdalena , Śpiewak Klaudyna , Majka Grzegorz
Published: February 2021

Lactoferrin (Lf) - member of the transferrin family of proteins responsible for many different functions in the body of mammals participates in regulation of free iron level in the body fluids making the protein bacteriostatic.

The main goal of studies was to test the suitability of molecular dynamic simulation to study structural changes in the tertiary structure of lactoferrin.

According to ConSurf Server analysis one of the most conservative amino acids was found not only in iron- but also in carbohydrates- binding pockets which may suggest a significant impact of carbohydrates on the functions performed by lactoferrin. Pocket-Finder program applied to find iron-binding pockets revealed the potential Fe binding area. The stability of the ligand deprived protein was verified performing the 50 ns dynamic simulation using the Gromacs program. The tertiary structure changes during the simulation were observed in N-lob solely. No structural changes were observed in C-lob iron-binding pocket.
Assessing the impacts of nonindigenous marine macroalgae: an update of current knowledge
Authors: Davidson Alisha D. , Campbell Marnie L. , Hewitt Chad L. , Schaffelke Britta
Published: February 2021

Nonindigenous marine species continue to be one of the foremost threats to marine biodiversity. As an update to a 2007 review of the impacts of introduced macroalgae, we assessed 142 additional publications to describe species’ impacts as well as to appraise information on the mechanisms of impact. Only 10% of the currently known nonindigenous macroalgal species were subjects of ecological impact studies, with changed community composition as the most commonly reported effect. Economic impacts were rarely published. Recent research has focused on the impacts of introduced macroalgal assemblages: red algal introductions to the Hawaiian Islands and turf algae in the Mediterranean. Several general issues were apparent. First, many publications included nonsignificant results of statistical analyses but did not report associated power. As many of the studies also had low effect and sample size, the potential for type II errors is considerable. Second, there was no widely accepted framework to categorize and compare impacts between studies. Information in this updated review was still too sparse to identify general patterns and mechanisms of impact. This is a critical knowledge gap as rates of introductions and hence impacts of nonindigenous macroalgae are expected to accelerate with climate change and increasing global trade connectivity.
The Gezi Resistance and activist citizen reporters
Authors: Çoban Barış , Ataman Bora
Published: February 2021

This study discusses how activist citizen reporters in Turkey, who initiated a brand-new alternative new media practice,
transformed news gathering and writing activities in the process of the Gezi Park Resistance, which erupted in Istanbul in
June 2013. A handful of citizens, outraged by the police violence as well as interested in human rights from a journalistic
perspective chose to create their own make-shift media outlets or to become medium themselves. They gathered and simultaneously
disseminated news and broadcast live on many occasions mostly through social media platforms such as Twitter, Facebook and
livestream, in the absence of traditional mainstream and/or alternative media. They also contributed to the solidarity of the resistance.
In this context, the theoretical framework of this study is based on concepts such as alternative media, citizen media and citizen
journalism. Likewise, concepts like democracy, citizen and journalism are also re-evaluated from a radical perspective. After theorizing
‘Çapulcu Media’, a local variant of the Rodriguez’s ‘citizen media’, constructed in the Gezi Resistance by a few activist citizen reporters,
this ethnographic study concentrates on their activities in the field as well as the process of their identity formation based on data
collected from in-depth interviews and continuous attention given to their social media accounts. Finally, this study aims to develop
a critical understanding of a radical variant of citizen journalism in the context of contemporary Occupy movements.
Extensions of Cantor minimal systems and dimension groups
Authors: Glasner Eli , Host Bernard
Published: February 2021

Given a factor map of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups
in terms of intermediate extensions which are extensions of
(Y,S) by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-abelian
finite group extension can produce a situation where the dimension group of
(Y,S) embeds into a proper subgroup of the dimension group of (X,T),
yet the quotient of the dimension groups is nonetheless torsion free. Next we define higher order cohomology groups
associated to an extension, and study them in various cases (proximal extensions, extensions by,
not necessarily abelian, finite groups, etc.). Our main result here is that all the cohomology groups
are torsion groups. As a consequence we can now identify
as the torsion group of the quotient group .
Tilting modules over tame hereditary algebras
Authors: Angeleri Hügel Lidia , Sánchez Javier
Published: February 2021

We give a complete classification of the infinite dimensional tilting modules over a tame hereditary algebra R.
We start our investigations by considering
tilting modules of the form where is a union of tubes, and denotes the universal localization of R at in the sense of Schofield and Crawley-Boevey. Here is a direct sum of the Prüfer modules corresponding to the tubes in . Over the Kronecker algebra, large tilting modules are of this form in all but one case, the exception being the Lukas tilting module L whose tilting class consists of all modules without indecomposable preprojective summands. Over an arbitrary tame hereditary algebra, T can have finite dimensional summands, but the infinite dimensional part of T is still built up from universal localizations, Prüfer modules and (localizations of) the Lukas tilting module. We also recover the classification of the infinite dimensional cotilting R-modules due to Buan and Krause.
On reduced Beltrami equations and linear families of quasiregular mappings
Authors: Jääskeläinen Jarmo
Published: February 2021

This paper studies linear classes of planar quasiregular mappings. We give a positive answer to a conjecture of K. Astala, T. Iwaniec, and G. Martin (2009) on reduced Beltrami equations. Moreover, we use it to prove a Wronsky-type theorem for general linear Beltrami systems. This is a key to show that the associated Beltrami equation of a linear quasiregular family is unique.
Quantitative stratification of stationary connections
Authors: Wang Yu
Published: February 2021

Let A be a connection of a principal bundle P over a Riemannian manifold M, such that its curvature

F
A

∈

L
loc
2

⁢

(
M
)

{F_{A}\in L_{\mathrm{loc}}^{2}(M)}

satisfies the stationarity equation.
It is a consequence of the stationarity that

θ
A

⁢

(
x
,
r
)

=

e

c
⁢

r
2

⁢

r

4
-
n

⁢

∫

B
r

⁢

(
x
)

|

F
A

|

2

⁢

𝑑

V
g

{\theta_{A}(x,r)=e^{cr^{2}}r^{4-n}\int_{B_{r}(x)}|F_{A}|^{2}\,dV_{g}}

is monotonically increasing in r, for some c depending only on the local geometry of M. We are interested in the singular set defined by

S
⁢

(
A
)

=

{
x
:

lim

r
→
0

⁡

θ
A

⁢

(
x
,
r
)

≠
0

}

{S(A)=\{x:\lim_{r\to 0}\theta_{A}(x,r)\neq 0\}}

, and its stratification

S
k

⁢

(
A
)

=

{
x
:

no tangent measure of 
A
 at 
x
 is 

(

k
+
1

)

-symmetric

}

{S^{k}(A)=\{x:\text{no tangent measure of $A$ at $x$ is $(k+1)$-symmetric}\}}

. We then introduce the quantitative stratification

S
ϵ
k

⁢

(
A
)

{S^{k}_{\epsilon}(A)}

; roughly speaking

S
ϵ
k

⁢

(
A
)

{S^{k}_{\epsilon}(A)}

is the set of points at which no ball

B
r

⁢

(
x
)

{B_{r}(x)}

is ϵ-close to being

(

k
+
1

)

{(k+1)}

-symmetric. In the main theorems, we show that

S
ϵ
k

{S^{k}_{\epsilon}}

is k-rectifiable and satisfies the Minkowski volume estimate

Vol
⁡

(

B
r

⁢

(

S
ϵ
k

)

∩

B
1

)

≤

C
⁢

r

n
-
k

{\operatorname{Vol}(B_{r}(S^{k}_{\epsilon})\cap B_{1})\leq Cr^{n-k}}

. Lastly, we apply the main theorems to the stationary Yang–Mills connections to obtain a rectifiability theorem that extends some previously known results in [G. Tian,
Gauge theory and calibrated geometry. I,
Ann. of Math. (2) 151 2000, 1, 193–268].
Epitaxial Growth and Multiferroic Properties of (001)-Oriented BiFeO3-YMnO3 Films
Authors: Nie Peng-Xiao , Wang Yi-Ping , Yang Ying , Yuan Guo-Liang , Li Wei , Ren Xue-Ting
Published: February 2021

In this paper, high-quality multiferroic (1-x)BiFeO3-xYMnO3 (x=0.05, 0.10, 0.15) thin films were successfully epitaxially grown on (001)SrTiO3 substrates with La0.67Sr0.33MnO3 buffered layers by pulsed laser deposition (PLD). X-ray diffraction shows the thin films are all single-phase perovskite with preferential orientation along the (001) direction. The (002) diffraction angles of thin films (from 0 to 0.15) shift to right, indicating the decrease of lattice parameters. All YMnO3-doped thin films exhibit strong upward self-poling via piezoelectric force microscope (PFM) measurement. Saturated ferroelectric hysteresis loops of thin films cannot be obtained even at the frequency of 50 kHz because of large leakage currents. It is noted that BFO-YMO thin films exhibit ferroelectricity considering the PFM and ferroelectric test. The magnetization measurements show that all BiFeO3-based films exhibit weak ferromagnetic behaviors with saturated magnetization at room temperature. The enhancement of magnetization was observed because of YMO doping, with the maximum saturation magnetization (M
s) of 17.07 emu/cm3 in x=0.10 thin film.
Omkring Johannes V. Jensens himmerlandshistorie ”Wombwell”
Authors: Jørgensen Aage
Published: February 2021

This article discusses one of Johannes V. Jensens ”Himmerland Sto­ries”, ”Wombwell”, which appeared in Nye Himmerlandshistorier in 1904, as well as some related texts. ”Wombwell” may be said to illustrate how the tradition-bound inhabitants of rural Himmerland experienced the hurried, violent modern world passing by in the shape of the well-known, world-famous English menagerie established in 1805 by George Wombwell, whose successors as a matter of fact toured in Northern Jutland in the summer of 1888. A major issue raised in the text is a longing Wombwell’s magnificent appearance inspires in the minds of three local youngsters, now wishing to escape from their familiar milieu. An equivalent longing motivates the hero’s departure from his childhood setting in popular tales in order to take possession of unknown parts of the outer (and inner) world. In Jensen’s story this aspect is represented by Miss Alice, the attractive lion trainer of the menagerie. Aspects like these are also unfolded in three other texts of Jensen to which ”Wombwell” is compared, ”Løverne” (“The Lions”), ”Circus Rieger” and ”Menageriet” (“The Menagerie”).

These texts point to a major generic issue in Jensen’s Himmerland stories, in that he navigates along the borderline between childhood remembrance and fictional creation, or between description and narration. That borderline becomes blurred and even disappears since the process of remembrance turns out to be much more creative than simply reconstructive.
”Jag satt till bords med de bästa”. Interkulturella möten i Vilhelm Ekelunds verk
Authors: Aronsson Mattias
Published: February 2021

The Swedish poet, essayist and aphorist Vilhelm Ekelund wrote extensively on the topic of foreign authors. Some of these writers represent the Greek and Roman cultural heritage; some belong to the modern-day literary canon. This article investigates the nature of these “intercultural encounters” in Ekelund’s body of work. By processing data from Andar i den Ekelundska sfären (1989) and Konkordans till Vilhelm Ekelunds skrifter (2000), we have been able to count all references made to the most important individuals appearing in Ekelund’s texts. At the top end of the table we find such prominent writers as Goethe (1343 references), Nietzsche (985) and Plato (503 references). We show that Ekelund’s oeuvre is largely dominated by male authors and philosophers of Western cultural heritage: the most prominently figured foreign nationalities being German (20,7%), Greek (10,1%), French (9,2%) and Roman (5,4%) writers. The quantitative method applied in our study is a good complement to more textcentered approaches to literature. In this case, it allows us to determine, with a great deal of accuracy, the extent and nature of the intercultural encounters in Vilhelm Ekelund’s body of work.
”Jeg tænker, altså er jeg en del af labyrinten.” – Zum Zusammenhang von System und Sprache in Inger Christensens brev i april
Authors: Schmidt Philipp-Sebastian
Published: February 2021

On the basis of the underlying mathematical permutation, Inger Christensen’s brev i april counts as part of her systemic poetry (’systemdigtning’). The form of the poem, structured by the mathematical permutation, becomes a carrier of significance which is interwoven with the content level of the poem by a pattern of motives. The possible infinity of the permutation as much as the periodical ending of it, refer in its double structure to the cyclic life of mankind. Furthermore, the structure of the poem emphasizes a profound skepticism towards language, which is the central aspect of the poem, and rais­es the question, if language can refer to the world and the things within it. The poem therefore discusses the human (in)ability to name the things in the world. Furthermore, it opens up the picture of a labyrinth between mankind and the world, i.e. the loss of the connection between them. The positive ending, ­however, is, on the basis of the periodical structure, not a guaranty for a positive future.
Litterær eksistensforskning. Eksklusion og marginalisering i Naja Marie Aidts Bavian
Authors: Svendsen Erik
Published: February 2021

Bavian (2006), Danish writer Naja Maria Aidt’s collection of short stories, is not only, as suggested by the title, about the animal in the human being. The stories are also about the ways human beings today are prone to exclude others. The texts are about people on the move and most often Aidt lets descriptions of bodily reactions and affect speak instead of talk and dialogue. However, it is significant for Aidt’s writing that the body never represents an idea about freedom – rather, the opposite of freedom. Moreover, personal freedom is not thought about as a way of escape to Aidt’s characters; it is more an alibi for disregarding others. The article suggests that Bavian maybe read as showing how ‘the naked life’ (Agamben) has been talking about is turning into a common lot.
A simple index of prediction accuracy in multiple regression analysis
Authors: Liu Xiaofeng Steven
Published: February 2021

Objectives

Within the context of multiple regression the coefficient of determination can be converted to a probability of agreement between the actual and predicted outcomes, suitably dichotomized.

Methods

This probability of agreement can be used as a simple index of prediction accuracy to help capture the probability of a correct prediction in multiple regression.

Results

The simple index of prediction accuracy makes the multiple correlation comprehensible to statisticians and laypeople alike. Two examples are provided to demonstrate the application of the simple index.

Conclusions

In short, the paper introduces the simple index, its computation formula, and its theoretical affinity to the confusion matrix, binomial effect size, probit model, and tetrachoric correlation.
Two-party key establishment: From passive to active security without introducing new assumptions
Authors: Neupane Kashi
Published: February 2021

Key establishment protocols based on hardness assumptions, such as the discrete logarithm problem and the integer factorization problem, are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as the conjugacy search problem and the decomposition search problem, can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protocol. Compilers involve some tools such as a signature scheme and a collision-resistant hash function. If there are only passively secure protocols but not a signature scheme based on the same assumption, then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumption.
We offer an approach to derive an actively secure two-party protocol from a passively secure two-party protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebraic method of public key cryptography to the real world applicable cryptographic scheme.
On the Stability of Solutions of Linear Boundary Value Problems for a System of Ordinary Differential Equations
Authors: Ashordia M.
Published: February 2021

Linear boundary value problems for a system of ordinary differential equations are considered. The stability of the solution with respect to small perturbations of coefficients and boundary values is investigated.
On the Correct Formulation of a Multidimensional Problem for Strictly Hyperbolic Equations of Higher Order
Authors: Kharibegashvili S.
Published: February 2021

A theorem of the unique solvability of the first boundary value problem in the Sobolev weighted spaces is proved for higher-order strictly hyperbolic systems in the conic domain with special orientation.
On Cohomotopy-Type Functors
Authors: Khazhomia S.
Published: February 2021

This article deals with Chogoshvili cohomotopy functors which are defined by extending a cohomology functor given on some special auxiliary subcategories of the category of topological spaces. The question of choosing these subcategories is discussed. In particular, it is shown that in the singular case to define absolute groups it is sufficient that auxiliary subcategories should have as objects only spheres Sn
, Moore spaces Pn
(t) = S

n–1 ∪
t

en
, and one-point unions of these spaces.
On Integral Bernstein Operators in Some Classes of Measurable Bivariate Functions
Authors: Taberski Roman
Published: February 2021

The two main theorems are cencerned with the approximation of (complex-valued) functions on the real plane by sums of Bernstein pseudoentire functions. They are formulated and proved in Section 4, after prior determination of the suitable integral operators. Analogous results for pseudopolynomial approximations were obtained by , Gonska, and Jetter ([Izv. Akad. Nauk SSSR, Ser. Mat. 34: 564-583, 1970],[J. Approx. Theory 48: 396-406, 1986]).
Some Open Problems About the Solutions of the Delay Difference Equation
Authors: Arciero M. , Ladas G. , Schultz S. W.
Published: February 2021

We discuss the dynamics of the positive solutions of the delay difference equation in the title for some special values of the parameters A, p and k and we pose a conjecture and two open problems.
On Some Properties of Multiple Conjugate Trigonometric Series
Authors: Leladze D.
Published: February 2021

We have obtained the estimate in the terms of partial and mixed moduli of continuity of deviation of Cesáro (C, ) means of the sequence of rectangular partial sums of n-multiple (n > 1) conjugate trigonometric series from n-multiple truncated conjugate function. This estimate implies the result on the -convergence (⋋ ≥ 1) of (C, ) means , provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown, that the -convergence cannot be replaced by ordinary convergence.
On Optimal Stopping of Inhomogeneous Standard Markov Processes
Authors: Dochviri B.
Published: February 2021

The connection between the optimal stopping problems for inhomogeneous standard Markov process and the corresponding homogeneous Markov process constructed in the extended state space is established. An excessive characterization of the value-function and the limit procedure for its construction in the problem of optimal stopping of an inhomogeneous standard Markov process is given. The form of ε-optimal (optimal) stopping times is also found.
Singular Integral Operators on Manifolds with A Boundary
Authors: Kapanadze R.
Published: February 2021

This paper deals with singular integral operators that are bounded, completely continuous, and Noetherian on manifolds with a boundary in weighted Hölder spaces.
On Some Properties of Solutions of Second Order Linear Functional
Differential Equations
Authors: Kiguradze I.
Published: February 2021

The properties of solutions of the equation
u″(t) =
p
1
(t)u(τ
1(t))
+
p
2(t)u′(
τ

2(t)) are investigated where
pi
: [a,
+∞[→ R (i
= 1, 2) are locally summable functions,
τ
1 : [a,
+∞[→ R is a measurable
function and τ
2 :
[a, +∞[→
R is a nondecreasing locally absolutely continuous one.
Moreover, τ

i
(t) ≥ t (i
= 1, 2), p
1 (t) ≥
0, ,
ε = const > 0 and
. In particular, it is
proved that solutions whose derivatives are square integrable on
[a, +∞ [ form a
one-dimensional linear space and for any such solution to vanish at infinity it
is necessary and sufficient that .
On Some Entire Modular Forms of Weights 5 and 6 for the Congruence Group Γ0(4N)
Authors: Lomadze G.
Published: February 2021

Two entire modular forms of weight 5 and two of weight 6 for the congruence subgroup 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 10 and 12 variables.
Criteria of General Weak Type Inequalities for Integral Transforms with Positive Kernels
Authors: Genebashvili I. , Gogatishvili A. , Kokilashvili V.
Published: February 2021

Necessary and sufficient conditions are derived in order that an inequality of the form

be fulfilled for some positive c independent of λ and a ν-measurable nonnegative function ƒ : X → R
1, where

k : X × X × [0, ∞) → R
1 is a nonnegative measurable kernel, (X, d, μ) is a homogeneous type space, φη and ψ are quasiconvex functions, ψ ∈ Δ2, and t
–α

θ(t) is a decreasing function for some α, 0 < α < 1.

A similar problem was solved in Lorentz spaces with weights.
The Boundary-Contact Problem of Elasticity for Homogeneous Anisotropic Media with a Contact on Some Part of the Boundaries
Authors: Chkadua O.
Published: February 2021

The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied.
Fractional Integrodifferentiation in Hölder Classes of Arbitrary Order
Authors: Karapetyants N. K. , Ginzburg A. I.
Published: February 2021

Hölder classes of variable order μ(x) are introduced and it is shown that the fractional integral has Hölder order μ(x) + α (0 < α, μ
+, α + μ
+ < 1, μ
+ = sup μ(x)).
Kneser-Type Oscillation Criteria for Self-Adjoint Two-Term Differential Equations
Authors: Došlý Ondřej , Osička Jan
Published: February 2021

It is proved that the even-order equation y
(2n)+p(t)y = 0 is (n, n) oscillatory at ∞ if

where .
Geometry of Poisson Structures
Authors: Giunashvili Z.
Published: February 2021

The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields. Further, we shall touch upon the dualism between bivector fields and differential 2-forms.
Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. II
Authors: Gogatishvili A. , Kokilashvili V.
Published: February 2021

This paper continues the investigation of weight problems in Orlicz classes for maximal functions and singular integrals defined on homogeneous type spaces considered in [Gogatishvili and Kokilashvili, Georguian Math. J. 2: 361–384, 1995].
Asymptotic Behavior of Solutions of a Second Order Nonlinear Differential Equation
Authors: Evtukhov V. M. , Drik N. G.
Published: February 2021

Asymptotic properties of proper solutions of a certain class of essentially nonlinear binomial differential equations of the second order are investigated.
Partial Averaging for Impulsive Differential Equations with Supremum
Authors: Bainov D. , Domshlak Yu. , Milusheva S.
Published: February 2021

Partial averaging for impulsive differential equations with supremum is justified. The proposed averaging schemes allow one to simplify considerably the equations considered.
The Skorokhod Oblique Reflection Problem in a Convex Polyhedron
Authors: Shashiashvili M.
Published: February 2021

The Skorokhod oblique reflection problem is studied in the case of n-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to construct in a direct way the reflected (in a convex polyhedral domain) diffusion processes possessing the nice properties.
Oscillatory Criteria for Nonlinear nth-Order Differential Equations with Quasiderivatives
Authors: Bartušek Miroslav
Published: February 2021

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivatives Lny = f(t, L
0
y, . . . , L

n–1
y) under the validity of the sign condition f(t, x
1, . . . , xn
)x
1 ≤ 0, f(t, 0, x
2, . . . , xn
) = 0 on .
Combinatorial Invariance of Stanley–Reisner Rings
Authors: Bruns W. , Gubeladze J.
Published: February 2021

In this short note we show that Stanley–Reisner rings of simplicial complexes, which have had a “dramatic application” in combinatorics [Hibi, Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, 1992, p. 41], possess a rigidity property in the sense that they determine their underlying simplicial complexes.
Solution of Two-Weight Problems for Integral Transforms with Positive Kernels
Authors: Genebashvili I. , Gogatishvili A. , Kokilashvili V.
Published: February 2021

Criteria for weak and strong two-weighted inequalities are obtained for integral transforms with positive kernels.
On the Solvability of a Darboux Type Non-Characteristic Spatial Problem for the Wave Equation
Authors: Kharibegashvili S.
Published: February 2021

The question of the correct formulation of a Darboux type non-characteristic spatial problem for the wave equation is investigated. The correct solvability of the problem is proved in the Sobolev space for surfaces of the temporal type on which Darboux type boundary conditions are given.
On Oscillation of Solutions of Second-Order Systems of Deviated Differential Equations
Authors: Partsvania N.
Published: February 2021

Sufficient conditions are found for the oscillation of proper solutions of the system of differential equations

where fi
: R
+ × R
2m
→ R (i = 1, 2) satisfy the local Carathéodory conditions and σi
, τi
: R
+ → R (i = 1, . . . , m) are continuous functions such that σi
(t) ≤ t for t ∈ R
+, .
On Strong Maximal Operators Corresponding to Different Frames
Authors: Oniani G.
Published: February 2021

The problem is posed and solved whether the conditions and sup
θ∈[0,π/2) ∫{M
2, θ
(ƒ) > 1}
M
2, θ
(ƒ) < ∞ are equivalent for functions (where M
2, θ
denotes the strong maximal operator corresponding to the frame {OXθ, OYθ
}).

The results obtained represent a general solution of M. de Guzmán's problem that was previously studied by various authors.
Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator
Authors: Tetruashvili M.
Published: February 2021

We consider the quantifier-free set theory MLSUn containing the symbols U, \, =, ∈, Un. Un(p) is interpreted as the union of all members of the set p. It is proved that there exists an algorithm which for any formula Q of the MLSUn theory containing at most one occurrence of the symbol Un decides whether Q is true or not using the space cn
3 log2
n (n is the length of Q).
On the Solution of the Dirichlet Problem for an Elliptic Equation Degenerating on the Boundary
Authors: Jvarsheishvili A.
Published: February 2021

The Dirichlet problem for the equation

yΔW + αWy
= –F

is studied in the semi-circle x
2 + y
2 < 1, y > 0. The restrictions on F are established under which the problem is uniquely solvable in the definite generalized sense.
Oscillation and Nonoscillation Criteria for Second-Order Linear Differential Equations
Authors: Lomtatidze A.
Published: February 2021

Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established.
The Hörmander and Maslov Classes and Fomenko's Conjecture
Authors: Tevdoradze Z.
Published: February 2021

Some functorial properties are studied for the Hörmander classes defined for symplectic bundles. The behavior of the Chern first form on a Lagrangian submanifold in an almost Hermitian manifold is also studied, and Fomenko's conjecture about the behavior of a Maslov class on minimal Lagrangian submanifolds is considered.
Analogues of the Kolosov–Muskhelishvili General Representation Formulas and Cauchy–Riemann Conditions in the Theory of Elastic Mixtures
Authors: Basheleishvili M.
Published: February 2021

Analogues of the well-known Kolosov–Muskhelishvili formulas of general representations are obtained for nonhomogeneous equations of statics in the case of the theory of elastic mixtures. It is shown that in this theory the displacement and stress vector components, as well as the stress tensor components, are represented through four arbitrary analytic functions.

The usual Cauchy–Riemann conditions are generalized for homogeneous equations of statics in the theory of elastic mixtures.
On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation
Authors: Kharibegashvili S.
Published: February 2021

A multidimensional version of the first Darboux problem is considered for a model second order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.
Modular Properties of Theta-Functions and Representation of Numbers by Positive Quadratic Forms
Authors: Vepkhvadze T.
Published: February 2021

By means of the theory of modular forms the formulas for a number of representations of positive integers by two positive quaternary quadratic forms of steps 36 and 60 and by all positive diagonal quadratic forms with seven variables of step 8 are obtain.
Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions
Authors: Brykalov S. A.
Published: February 2021

Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.
Bounds for the Characteristic Functions of the System of Monomials in Random Variables and of Its Trigonometric Analogue
Authors: Shervashidze T.
Published: February 2021

Using a multidimensional analogue of Vinogradov's inequality for a trigonometric integral, the upper bounds are constructed for the moduli of the characteristic functions both of the system of monomials in components of a random vector with an absolutely continuous distribution in and of the system

(cos j
1πξ
1 . . . cos j

s
πξ

s
, 0 ≤ j
1, . . . , j

s
≤ k, j
1 + . . . + j

s
≥ 1),

where (ξ
1, . . . , ξ

s
) is uniformly distributed in [0; 1]
s
.
Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
Authors: Ashordia M.
Published: February 2021

Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem

dx
(t) = dA(t) · f(t, x(t)),

xi
(ti
) = ϕi
(x) (i = 1, . . . , n),

where , A : [a, b] → Rn×n
is a matrix-function with bounded variation components, f : [a; b] × Rn
→ Rn
is a vector-function belonging to the Carathéodory class corresponding to A; t
1, . . . , tn
∈ [a, b] and ϕ
1, . . . , ϕn
are the continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.
On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order
Authors: Jokhadze O.
Published: February 2021

Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.
To the Problem of A Strong Differentiability of Integrals Along Different Directions
Authors: Lepsveridze G.
Published: February 2021

It is proved that for any given sequence (σ
n
, n ∈ ℕ) = Γ0 ⊂ Γ, where Γ is the set of all directions in (i.e., pairs of orthogonal straight lines) there exists a locally integrable function f on such that: (1) for almost all directions σ ∈ Γ\Γ0 the integral ∫ f is differentiable with respect to the family B
2σ of open rectangles with sides parallel to the straight lines from σ; (2) for every direction σ
n
∈ Γ0 the upper derivative of ∫ f with respect to B
2σn
equals +∞; (3) for every direction σ ∈ Γ the upper derivative of ∫ |f | with respect to B
2σ equals +∞.
Oscillatory Properties of Solutions of Impulsive Differential Equations with Several Retarded Arguments
Authors: Bainov D. D. , Dimitrova M. B. , Petrov V. A.
Published: February 2021

The impulsive differential equation

with several retarded arguments is considered, where pi
(t) ≥ 0, 1 + bk
> 0 for i = 1, . . . , m, t ≥ 0, k ∈ ℕ. Sufficient conditions for the oscillation of all solutions of this equation are found.
Allied Integrals, Functions, and Series for the Unit Sphere
Authors: Dzagnidze O.
Published: February 2021

Among the functions defined on the two-dimensional unit sphere we distinguish functions generalizing the conjugate integral, the conjugate function, and the conjugate series which depend on one variable. We establish the properties of these functions whose structures essentially differ from those of integrals, functions, and series based on the theory of analytic functions of two complex variables.
Commutativity for a Certain Class of Rings
Authors: Abujabal H. A. S. , Khan M. A.
Published: February 2021

We first establish the commutativity for the semiprime ring satisfying [xn, y]xr
= ±ys
[x, ym
]yt
for all x, y in R, where m, n, r, s and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital.
On Some Boundary Value Problems for an Ultrahyperbolic Equation
Authors: Kharibegashvili S.
Published: February 2021

The correct formulation of a characteristic problem and a Darboux type problem in the special weighted functional spaces for an ultrahyperbolic equation is investigated.
On a Class of Covariance Operators
Authors: Chantladze T. , Kandelaki N.
Published: February 2021

This paper is the continuation of [Vakhania and Kandelaki, Teoriya Veroyatnost. i Primenen 41: 31–52, 1996] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra.
Homotopy Classes of Elliptic Transmission Problems Over C*-Algebras
Authors: Khimshiashvili G.
Published: February 2021

The topological aspects of B.Bojarski's approach to Riemann–Hilbert problems are developed in terms of infinite-dimensional grassmanians and generalized to the case of transmission problems over C*-algebras. In particular, the homotopy groups of certain grassmanians related to elliptic transmission problems are expressed through K-groups of the basic algebra. Also, it is shown that the considered grassmanians are homogeneous spaces of appropriate operator groups. Several specific applications of the obtained results to singular operators are given, and further perspectives of our approach are outlined.
A Note on Weight Enumerators of Linear Self-Dual Codes
Authors: Lomadze N.
Published: February 2021

A partial description of (complete) weight enumerators of linear self-dual codes is given.
Numerical Solutions to the Darboux Problem with the Functional Dependence
Authors: Kamont Z. , Leszczyński H.
Published: February 2021

The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(
x, y
)) where z
(x, y) is a function defined by z(
x, y
)(t, s) = z(x + t, y+ s), (t, s) ∈ [–a
0, 0] × [–b
0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means of a comparison method; moreover we give an error estimate. The convergence of explicit difference schemes is proved under a general assumption that given functions satisfy nonlinear estimates of the Perron type. Our results are illustrated by a numerical example.
On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
Authors: Khosroshvili D.
Published: February 2021

A general formula is derived for the number of representations r(n; f) of a natural number n by diagonal quadratic forms f with five variables of level 16. For f belonging to one-class series, r(n; f) coincides with the sum of a singular series, while in the case of a many-class series an additional term is required, for which the generalized theta-function introduced by T. V. Vepkhvadze [Vepkhvadze, Acta Arithmetica 53: 433–990] is used.