Dynamical Behavior and Expressions of Solutions of a Class of Higher-Order Nonlinear Difference Equations by Ghada AlNemer, Lama Sh. Aljoufi, A. M. Ahmed, Samir Al Mohammady, M. Zakarya, H. M. Rezk

“…The aim of this article is to get the forms of the solutions of the following nonlinear higher-order difference equations χs+1=χs−3k+1/±1±Πl=1kχs−3l+1,s=0,1,2,…, where the initial conditions χ−j,j=0,1,2,…,3k−1 and k∈1,2,… are arbitrary real numbers. Also, we examine stability, boundedness, oscillation, and the periodic nature of these solutions.…”
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Dynamics and Expression of Solution of a Sixth Order Difference Equation by Abdul Khaliq

“…. $$ {\Large \noindent }where the initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers and $\alpha ,\ \beta ,\ \gamma ,\ \delta \ $are positive constants. …”
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On the Global Asymptotic Stability and 4-Period Oscillation of the Third-Order Difference Equation by M. E. Erdogan

“…The main objective of this paper is to study the global behavior and oscillation of the following third-order rational difference equation xn+1=αxnxn−1xn−2/βxn−12+γxn−22, where the initial conditions x−2,x−1,x0 are nonzero real numbers and α,β,γ are positive constants such that α≤β+γ. …”
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A Comparison of Tests for Embeddings by Letellier, C, Moroz, I, Gilmore, R

“…The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. …”

Comparison of tests for embeddings. by Letellier, C, Moroz, I, Gilmore, R

“…The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. …”

Mathematics for elementary school teachers / by Fierro, Ricardo D.

A Real-Valued Modal Logic by Denisa Diaconescu, George Metcalfe, Laura Schnüriger

“…A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is provided and a coNEXPTIME upper bound obtained for checking validity in the logic. …”
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Fractional Integral Inequalities for Some Convex Functions by B.R. Bayraktar, A.Kh. Attaev

“…Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided.…”
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Scattering in Algebraic Approach to Quantum Theory—Associative Algebras by Albert Schwarz

“…An interesting novelty is the consideration of associative algebras over real numbers.…”
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A Note on Gershgorin Disks in the Elliptic Plane by Mehmet Ali Güngör, Hidayet Hüda Kösal, Arzu Sürekçi

“…Elliptic complex numbers are a generalized form of complex and so real numbers. Thus, the obtained results extend, generalize and complement some known Gershgorin discs results from the literature.…”
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A Generalized Version of Polynomial Convex Functions and Some Interesting Inequalities with Applications by Xiaogang Liu, Kiran Naseem Aslam, Muhammad Shoaib Saleem, Shuili Ren

“…At the end, some application to special means of real numbers are also given. It can be observed from the remarks given in this paper that several exiting results of ligature can be obtained immediacy from our results by taking suitable involved parameters.…”
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Fixed point theorem utilizing operators and functionals by Douglas Anderson, Richard Avery, Johnny Henderson, Xueyan Liu

“…The underlying sets in the Leggett-Williams fixed point theorem that were defined using the total order of the real numbers are replaced by sets that are defined using an ordering generated by a border-symmetric set, that is, the sets that were defined using functionals in the original Leggett-Williams fixed point theorem are replaced by sets that are defined using operators.…”
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The Form of the Solutions of System of Rational Difference Equation by E. M. Elsayed, Marwa M. Alzubaidi

“…In this article, we study the form of the solutions of the system of difference equations $x_{n+1}=((y_{n-8})/(1+y_{n-2}x_{n-5}y_{n-8}))$, $y_{n+1}=((x_{n-8})/(\pm1\pm x_{n-2}y_{n-5}x_{n-8}))$, with the initial conditions are real numbers. Also, we give the numerical examples of some of difference equations and got some related graphs and figures using by Matlab.…”
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From positional representation of numbers to positional representation of vectors by Izabella Ingrid Farkas, Edita Pelantová, Milena Svobodová

“…If m = 1, the system coincides with the well known numeration system used to represent real numbers. We study some properties of the vector systems which are transformable from the case m = 1 to higher dimensions. …”
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Fractional Integral Inequalities for Some Convex Functions by B.R. Bayraktar, A.Kh. Attaev

“…Some applications to special means for arbitrary real numbers: arithmetic mean, logarithmic mean, and generalized log-mean, are provided. …”
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Super-exponential Complexity of Presburger Arithmetic by Fischer, Michael J., Rabin, Michael O.

“…Lower bounds are established on the computational complexity of the decision problem and on the inherent lengths of proofs for two classical decidable theories of logic: the first order theory of the real numbers under addition, and Presburger arithmetic -- the first order theory of addition on the natural numbers. …”
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ENTIRE FUNCTIONS SHARING ARGUMENTS OF INTEGRALITY, I by Pila, J

“…Let f be an entire function that is real and strictly increasing for all sufficiently large real arguments, and that satisfies certain additional conditions, and let Xf be the set of non-negative real numbers at which f is integer valued. Suppose g is an entire function that takes integer values on Xf. …”

Bohr sets and multiplicative Diophantine approximation by Chow, S

“…In two dimensions, Gallagher’s theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fiber version of Gallagher’s theorem, sharpening and making unconditional a result recently obtained conditionally by Beresnevich, Haynes, and Velani. …”

Beyond number sense: Contributions of domain-general processes to the development of numeracy in early childhood by Merkley, R

“…In order to explore symbolic representations of real numbers, Chapter 5 focuses on associations between different representational formats of real numbers in young children and how this relates to both domain-specific and domain-general factors. …”

Construction of 4 x 4 symmetric stochastic matrices with given spectra by Jung Jaewon, Kim Donggyun

“…The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. …”
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