A comprehensive review of the characterization of real numbers by Víctor Arturo Martínez León, Rodrigo Bloot, Ana Letícia de Oliveira

“…The real number system is a fundamental tool for rigorous demonstrations of the differential and integral calculus results. …”
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Some lacunarity properties of partial quotients of real numbers by Zhao, Xuan, Zhang, Zhenliang

“…We consider lacunarity properties of sequence of partial quotients for real numbers in their continued fraction expansions. …”
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Comparing Implementations of a Calculator for Exact Real Number Computation by José Raymundo Marcial-Romero, José Antonio Hernández Servín, Héctor Alejandro Montes-Venegas

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Some Double Sequence Spaces of Fuzzy Real Numbers of Paranormed Type by Bipul Sarma

“…We study different properties of convergent, null, and bounded double sequence spaces of fuzzy real numbers like completeness, solidness, sequence algebra, symmetricity, convergence-free, and so forth. …”
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Some Classes of Difference Sequence Spaces of Fuzzy Real Numbers Defined by Orlicz Function by Binod Chandra Tripathy, Stuti Borgohain

“…We introduce the classes of generalized difference bounded, convergent, and null sequences of fuzzy real numbers defined by an Orlicz function. Some properties of these sequence spaces like solidness, symmetricity, and convergence-free are studied. …”
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Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers by Yi-Wu Chang, Shan-Pang Liu

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Fuzzy Similar Priority Method for Mixed Attributes by Jinshan Ma, Changsheng Ji, Jing Sun

“…However, this method considering only the index values of real number has its disadvantages of inaccuracy in result and complexity in calculation. …”
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Multitask Oriented Virtual Resource Integration and Optimal Scheduling in Cloud Manufacturing by Zhen Cheng, Dechen Zhan, Xibin Zhao, Hai Wan

“…The genetic algorithm based on the real number matrix encoding is proposed. And crossover and mutation operation rules are designed for the real number matrix. …”
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On a Diophantine Inequality with s Primes by Xiaofei Yan, Lu Zhang

“…In this study, for prime numbers p1,…,ps and a sufficiently large real number N, we prove the Diophantine inequality p1c+⋯+psc−N<N−9/10cδ−c, where δ=294−210s/123−97s and s≥5. …”
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Hilbert Space Representations of Generalized Canonical Commutation Relations by Asao Arai

“…We consider Hilbert space representations of a generalization of canonical commutation relations , where 's are the elements of an algebra with identity , is the imaginary unit, and is a real number with antisymmetry . Some basic aspects on Hilbert space representations of the generalized CCR (GCCR) are discussed. …”
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Watermarking text document based on statistic property of part of speech string by DAI Zu-xu1, HONG Fan1, CUI Guo-hua1, FU Min2

“…An algorithm resolving nonlinear entropy equation with multivariable was described and proved firstly,then a new scheme where a text document is marked by accommodating probability distribution of certain part of speech strings to entropy constitutes the watermark was designed.Watermark function in the scheme values in a real number set domi-nated by computing precision,it is helpful to advances watermark capacity significantly.…”
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Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation by Wen-Xiu Ma

“…Let k be a nonnegative integer and c a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c),  n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.…”
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Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation by Moustafa El-Shahed

“…We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D0+αu(t)+λa(t) f(u(t))=0, 0<t<1,  u(0)=u′(0)=u′(1)=0, where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. …”
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A Numerical Method for Delayed Fractional-Order Differential Equations by Zhen Wang

“…The order here is an arbitrary positive real number, and the differential operator is with the Caputo definition. …”
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Trapezoidal Type Fejér Inequalities Related to Harmonically Convex Functions and Application by Sercan Turhan

“…Taking advantage of these, applications were given for some real number averages.…”
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The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations by Yanli Chen, Yongxiang Li

“…We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem -D0+αu(t)=f(t,u(t)),   0<t<1,  u(0)=u'(0)=u'(1)=0, where 2<α≤3 is a real number, D0+α is the Riemann-Liouville fractional derivative of order α, and f is a given continuous function. …”
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On Minimum Generalized Degree Distance Index of Cyclic Graphs by Nadia Khan, M. Javaid, M. K. Aslam, Mamo Abebe Ashebo

“…Topological index (TI) is a mapping that associates a real number to the under study (molecular) graph which predicts its various physical and chemical properties. …”
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A note on uniformly dominated sets of summing operators by J. M. Delgado, C. Piñeiro

“…Let Y be a Banach space that has no finite cotype and p a real number satisfying 1≤p<∞. We prove that a set ℳ⊂Πp(X,Y) is uniformly dominated if and only if there exists a constant C>0 such that, for every finite set {(xi,Ti):i=1,…,n}⊂X×ℳ, there is an operator T∈Πp(X,Y) satisfying πp(T)≤C and ‖Tixi‖≤‖Txi‖ for i=1,…,n.…”
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Engel Series and Cohen-Egyptian Fraction Expansions by Vichian Laohakosol, Tuangrat Chaichana, Jittinart Rattanamoong, Narakorn Rompurk Kanasri

“…Two kinds of series representations, referred to as the Engel series and the Cohen-Egyptian fraction expansions, of elements in two different fields, namely, the real number and the discrete-valued non-archimedean fields are constructed. …”
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Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations by Wen-Xue Zhou, Ji-Gen Peng, Yan-Dong Chu

“…We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problem D0+αu(t)=p(t)f(t,u(t))-q(t),0<t<1,u(0)=u(1)=u'(1)=0, where 2<α≤3 is a real number and D0+α is the standard Riemann-Liouville differentiation. …”
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