On the Eventually Periodic Continued <i>β</i>-Fractions and Their Lévy Constants by Qian Xiao, Chao Ma, Shuailing Wang

“…We show that if the continued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-fraction expansion of a non-negative real number is eventually periodic, then it is the root of a quadratic irreducible polynomial with the coefficients in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="double-struck">Z</mi><mo>[</mo><mi>β</mi><mo>]</mo></mrow></semantics></math></inline-formula> and we conjecture the converse is false, which is different from Lagrange’s theorem for the regular continued fractions. …”
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Tails of the Moments for Sums with Dominatedly Varying Random Summands by Mantas Dirma, Saulius Paukštys, Jonas Šiaulys

“…</mn><mrow><mo>{</mo><msubsup><mi>S</mi><mi>n</mi><mi>ξ</mi></msubsup><mo>></mo><mi>x</mi><mo>}</mo></mrow></msub></mfenced></mrow></semantics></math></inline-formula> is investigated, where exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is a nonnegative real number and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mi>n</mi><mi>ξ</mi></msubsup><mo>=</mo><msub><mi>ξ</mi><mn>1</mn></msub><mo>+</mo><mo>…</mo><mo>+</mo><msub><mi>ξ</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula> is a sum of dominatedly varying and not necessarily identically distributed random summands, following a specific dependence structure. …”
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Multiple Capture in a Group Pursuit Problem with Fractional Derivatives and Phase Restrictions by Nikolay Nikandrovich Petrov

“…The set of admissible controls <i>V</i> is a strictly convex compact and <i>a</i> is a real number. The goal of the group of pursuers is to capture of the evader by no less than <i>m</i> different pursuers (the instants of capture may or may not coincide). …”
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Comportamento reprodutivo de fêmeas de Stomoxys calcitrans (L.) (Diptera: Muscidae) criadas isoladamente em laboratório Reproductive behavior of isolated Stomoscys calcitrans (L.)... by Rubens Pinto de Mello, Maria Luzia Maués Garcia

“…Neitz, Universidade Federal Rural do Rio de Janeiro", under temperature of 27°C and 70-80% of relative humidity, one female and two males were isolated in individual cages to the observations of some biological parameters formely determined as number of ovipositant female, real number o eggs by female, oviposition periodicity and female longevity. …”
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Rupture of the Pleomorphic Adenoma of the Parotid Gland: What to Know before, during and after Surgery by Michele Grasso, Massimo Fusconi, Fabrizio Cialente, Giulia de Soccio, Massimo Ralli, Antonio Minni, Griselda Agolli, Marco de Vincentiis, Marc Remacle, Paolo Petrone, Domenico Di Maria, Vito D’Andrea, Antonio Greco

“…Conclusion: We believe that the real number of the events of spillage is underestimated and underreported by surgeons. …”
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General Practitioner Transfer in Xinjiang Uygur Autonomous Region from 2012 to 2020 by CHEN Hong, SHAMA· Mulati, LI Qifeng, XU Peilan

“…Methods During December 2021 to March 2022, this study reviewed China Health Statistical Yearbook from 2013 to 2021 to obtain the data about GPs in Xinjiang from 2012 to 2020, reviewed trainees&apos; lists of GPs job transfer training program from 2010 to 2022 organized by the Health Commission of Xinjiang Uygur Autonomous Region to obtain the real number of GPs transferred to training, and obtained the data about GPs distribution from the Science and Technology Education Department of the Health Commission of Xinjiang Uygur Autonomous Region. …”
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Embeddings of Schatten norms with applications to data streams by Li, Yi, Woodruff, David P.

“…Specifically, given a set of matrices A_1, ... , A_poly(nd) in R^{n x d}, suppose we want to construct a linear map L such that L(A_i) in R^{n' x d'} for each i, where n' < n and d' < d, and further, |A_i|p <= |L(A_i)|_q <= D_{p,q}|A_i|_p for a given approximation factor D_{p,q} and real number q >= 1. Then how large do n' and d' need to be as a function of D_{p,q}? …”
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Prospects for the digital transformation of the “Affordable medicines” program and cooperation with the European union market of medical products by Hanna Smirnova

“…Thus, it is worth assuming that the real number of Uktainians living abroad in one way or another is at least twice or even three times higher. …”
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On Second Order <i>q</i>-Difference Equations Satisfied by Al-Salam–Carlitz I-Sobolev Type Polynomials of Higher Order by Carlos Hermoso, Edmundo J. Huertas, Alberto Lastra, Anier Soria-Lorente

“…This contribution deals with the sequence <inline-formula><math display="inline"><semantics><msub><mrow><mo>{</mo><msubsup><mi mathvariant="double-struck">U</mi><mrow><mi>n</mi></mrow><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>}</mo></mrow><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></msub></semantics></math></inline-formula> of monic polynomials in <i>x</i>, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam–Carlitz I orthogonal polynomials, and involving an arbitrary number <i>j</i> of <i>q</i>-derivatives on the two boundaries of the corresponding orthogonality interval, for some fixed real number <inline-formula><math display="inline"><semantics><mrow><mi>q</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Patient Representation From Structured Electronic Medical Records Based on Embedding Technique: Development and Validation Study by Yanqun Huang, Ni Wang, Zhiqiang Zhang, Honglei Liu, Xiaolu Fei, Lan Wei, Hui Chen

“…Each medical concept was embedded into a 200-dimensional real number vector using the Skip-gram algorithm with some adaptive changes from shuffling the medical concepts in a record 20 times. …”
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Improving Drug Safety in Pediatric and Young Adult Patients with Hemato-Oncological Diseases: A Prospective Study of Active Pharmacovigilance by Anna Parzianello, Giulia Fornasier, Valentina Kiren, Federico Pigato, Sabrina Orzetti, Giulia Zamagni, Anna Arbo, Paolo Baldo, Paola Rossi, Marco Rabusin, Maurizio Mascarin, Marta Paulina Trojniak

“…The acquisition of relevant pediatric clinical safety data is essential to ensure tolerable drug therapies. Comparing the real number of Adverse Drug Reaction (ADR) reports in clinical practice with the literature, the idea of ADR underreporting emerges. …”
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Rapid, Cheap, and Effective COVID-19 Diagnostics for Africa by Lukman Yusuf, Mark Appeaning, Taiwo Gboluwaga Amole, Baba Maiyaki Musa, Hadiza Shehu Galadanci, Peter Kojo Quashie, Isah Abubakar Aliyu

“…Despite the fact that the COVID-19 pandemic has been downgraded to epidemic status in many countries, the real number of infections is unknown, particularly in low-income countries. …”
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Model-Based Optimization of Design Parameters of Subsurface Drain in Cotton Field under Mulch Drip Irrigation by Yibin Xu, Hongguang Liu, Ping Gong, Pengfei Li, Ling Li, Qiang Xu, Bao Xue, Yaru Guo, Yao Zhang, Rumeng Tian

“…The projection pursuit classification model has been combined with the accelerated genetic algorithm based on real-number coding. The comprehensive benefits of the subsurface pipe layout were evaluated using the construction cost, average desalination rate, and relative yield of cotton as the evaluation indices. …”
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Computing the Atom Graph of a Graph and the Union Join Graph of a Hypergraph by Anne Berry, Geneviève Simonet

“…We provide two efficient algorithms for computing this atom graph, with a complexity in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>m</mi><mi>i</mi><mi>n</mi><mrow><mo>(</mo><msup><mi>n</mi><mi>ω</mi></msup><mo form="prefix">log</mo><mi>n</mi><mo>,</mo><mi>n</mi><mi>m</mi><mo>,</mo><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mover><mi>m</mi><mo>¯</mo></mover><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> time, where <i>n</i> is the number of vertices of <i>G</i>, <i>m</i> is the number of its edges, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>m</mi><mo>¯</mo></mover></semantics></math></inline-formula> is the number of edges of the complement of <i>G</i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ω</mi></semantics></math></inline-formula>, also denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> in the literature, is a real number, such that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mi>ω</mi></msup><mo>)</mo></mrow></semantics></math></inline-formula> is the best known time complexity for matrix multiplication, whose current value is 2,3728596. …”
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A Non-Local Problem for the Fractional-Order Rayleigh–Stokes Equation by Ravshan Ashurov, Oqila Mukhiddinova, Sabir Umarov

“…Namely, the condition <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>T</mi><mo>)</mo><mo>=</mo><mi>β</mi><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo><mo>+</mo><mi>φ</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is an arbitrary real number, is proposed instead of the initial condition. …”
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β-Barrels and Amyloids: Structural Transitions, Biological Functions, and Pathogenesis by Anna I. Sulatskaya, Anastasiia O. Kosolapova, Alexander G. Bobylev, Mikhail V. Belousov, Kirill S. Antonets, Maksim I. Sulatsky, Irina M. Kuznetsova, Konstantin K. Turoverov, Olesya V. Stepanenko, Anton A. Nizhnikov

“…Considering rapidly growing discoveries of the amyloid-forming β-barrels, we may suggest that their real number and diversity of functions are significantly higher than identified to date, and represent only “the tip of the iceberg”. …”
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A Family of Higher Order Scheme for Multiple Roots by Tajinder Singh, Himani Arora, Lorentz Jäntschi

“…The weight function named as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>(</mo><msub><mi>υ</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> is used, which is a function of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>υ</mi><mi>t</mi></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>υ</mi><mi>t</mi></msub></semantics></math></inline-formula> is a function of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mi>t</mi></msub></semantics></math></inline-formula>, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>υ</mi><mi>t</mi></msub><mo>=</mo><mfrac><msub><mi>ω</mi><mi>t</mi></msub><mrow><mn>1</mn><mo>+</mo><mi>a</mi><msub><mi>ω</mi><mi>t</mi></msub></mrow></mfrac><mo>,</mo></mrow></semantics></math></inline-formula> where <i>a</i> is a real number and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>t</mi></msub><mo>=</mo><msup><mfenced separators="" open="(" close=")"><mfrac><mrow><mi>g</mi><mo>(</mo><msub><mi mathvariant="monospace">y</mi><mi>t</mi></msub><mo>)</mo></mrow><mrow><mi>g</mi><mo>(</mo><msub><mi mathvariant="monospace">x</mi><mi>t</mi></msub><mo>)</mo></mrow></mfrac></mfenced><mfrac><mn>1</mn><mover accent="true"><mi>m</mi><mo stretchy="false">˜</mo></mover></mfrac></msup></mrow></semantics></math></inline-formula> is a multi-valued function. …”
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Resolution of the First Ukrainian endometriosis forum “Drug treatment for endometriosis-associated pelvic pain. The quality of a woman’s life” by A.V. Boichuk, D.G. Herman, Y.O. Dubossarska, N.F. Zakharenko, L.V. Kalugina, N.V. Kosei, S.I. Reheda, N.M. Rozhkovska, T.F. Tatarchuk, O.V. Trokhymovich, O.G. Yashina, N.V. Yarotska

“…Ukraine currently does not gather statistics on the incidence of endometriosis, but, at a rough estimate, this number is approximately 280 thousand women and the real number may be higher. Endometriosis has known significant social, medical and economic impact. …”
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Multi-Additivity in Kaniadakis Entropy by Antonio M. Scarfone, Tatsuaki Wada

“…In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>ℵ</mo><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> that makes Kaniadakis entropy multi-additive, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mi>κ</mi></msub><mrow><mo>[</mo><msup><mi>p</mi><mrow><mi mathvariant="normal">A</mi><mo>∪</mo><mi mathvariant="normal">B</mi></mrow></msup><mo>]</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mo>ℵ</mo><mo>)</mo></mrow><mspace width="0.166667em"></mspace><mfenced separators="" open="(" close=")"><msub><mi>S</mi><mi>κ</mi></msub><mrow><mo>[</mo><msup><mi>p</mi><mi mathvariant="normal">A</mi></msup><mo>]</mo></mrow><mo>+</mo><msub><mi>S</mi><mi>κ</mi></msub><mrow><mo>[</mo><msup><mi>p</mi><mi mathvariant="normal">B</mi></msup><mo>]</mo></mrow></mfenced></mrow></semantics></math></inline-formula>, under the composition of two statistically independent and identically distributed distributions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>p</mi><mrow><mi mathvariant="normal">A</mi><mo>∪</mo><mi mathvariant="normal">B</mi></mrow></msup><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>p</mi><mi mathvariant="normal">A</mi></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mspace width="0.166667em"></mspace><msup><mi>p</mi><mi mathvariant="normal">B</mi></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, with reduced distributions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>p</mi><mi mathvariant="normal">A</mi></msup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>p</mi><mi mathvariant="normal">B</mi></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> belonging to the same class.…”
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Crossover and mutation operators of real coded genetic algorithms for global optimization problems by Lim, Siew Mooi

“…In relation to this, Real Coded GA (RCGA) refers to GAs which incorporate real number vector representations of chromosomes. …”
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