NEW PROOFS AND A GENERALIZATION OF INEQUALITIES OF FAN, TAUSSKY, AND TODD by Lunter, G

“…Using the same techniques, the inequality [formula] is proved for all real numbers 0=b0, b1, ..., bn, bn+1=0, which answers a question raised by Alzer [J. …”

Models for intuitionistic logic by Cuckle, H, Cuckle, Howard

“…</p> <p>The expressive power of M-L is used to formalize certain theories. The Theory of Real Numbers, an Intuitionistic Set Theory and Category Theory are all formalizable. …”

On complex bipolar fuzzy weighted aggregation operators by Ali, Mabruka, Kilicman, Adem

“…The unpredictability in the data was controlled using membership degrees that are subset of real numbers, which can reduce some useful information and therefore impact decision-making results. …”

Arithmetic operations of intuitionistic Z numbers using horizontal membership functions by Nik Muhammad Farhan Hakim, Nik Badrul Alam, Ku Muhammad Naim, Ku Khalif, Nor Izzati, Jaini

“…The proposed operations preserve the arithmetic operations over real numbers and the original IZN-based information, avoiding any significant loss of information. …”
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New Equivalents of Kurepa’s Hypothesis for Left Factorial by Aleksandar Petojević, Snežana Gordić, Milinko Mandić, Marijana Gorjanac Ranitović

“…The new equivalent based on the properties of the integer part of real numbers is proven. Moreover, a new equivalent based on the properties of two well-known sequences is given. …”
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Quantum Kolmogorov complexity and quantum correlations in deterministic-control quantum Turing machines by Mariano Lemus, Ricardo Faleiro, Paulo Mateus, Nikola Paunković, André Souto

“…Moreover, we introduce (conditional) Kolmogorov complexity of quantum states and use it to study three particular aspects of the algorithmic information contained in a quantum state: a comparison of the information in a quantum state with that of its classical representation as an array of real numbers, an exploration of the limits of quantum state copying in the context of algorithmic complexity, and study of the complexity of correlations in quantum systems, resulting in a correlation-aware definition for algorithmic mutual information that satisfies symmetry of information property.…”
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Solutions of a System of Two Higher-Order Difference Equations in Terms of Lucas Sequence by Amira Khelifa, Yacine Halim, Massaoud Berkal

“…In this paper we give some theoretical explanations related to the representation for the general solution of the   system of the  higher-order rational difference equations $$ x_{n+1} = \frac{5 y_{n-k}-5}{y_{n-k}}, \qquad y_{n+1} = \frac{5 x_{n-k}-5}{x_{n-k}} ,\qquad n, k\in \mathbb{N}_0, $$ where  $\mathbb{N}_{0}=\mathbb{N}\cup \left\{0\right\}$,  and the initial conditions $x_{-k}$, $x_{-k+1},\ldots$, $x_{0}$, $y_{-k}$, $y_{-k+1},\ldots$, $y_{0}$ are non zero real numbers such that their solutions are associated to Lucas numbers. …”
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On the estimation of functions belonging to Lipschitz class by block pulse functions and hybrid Legendre polynomials by S. Lal, V.K. Sharma

“…The estimators of a function $f$ having first and second derivative belonging to $Lip_\alpha[a,b]$ class, $0 < \alpha \leq 1$, and $a$, $b$ are finite real numbers, by block pulse functions and hybrid Legendre polynomials have been calculated. …”
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Some 0/1 polytopes need exponential size extended formulations by Rothvoss, Thomas

“…Conditioning on NP⊈P[subscript /poly], our result rules out the existence of a compact formulation for any NP -hard optimization problem even if the formulation may contain arbitrary real numbers.…”
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On positivity and minimality for second-order holonomic sequences by Kenison, G, Klurman, O, Lefaucheux, E, Luca, F, Moree, P, Ouaknine, J, Whiteland, MA, Worrell, J

“…An infinite sequence ⟨u_n⟩_n of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with polynomial coefficients. …”

Satu kaedah alternatif bagi menyelesaikan masalah transformasi dan aplikasinya dalam bidang biostatistik [QC1]. by W Ahmad, Wan Muhamad Amir

“…The aim of this research is to expose the issue of the data problems from various studies which do not fulfill the assumptions for analysis of variance (ANOVA), regression analysis, and other such procedures in detail together with the steps to overcome this problem with modifying the original of Box-Cox formula until it can be used for all the real numbers. …”
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Finite choice, convex choice and finding roots by Stéphane Le Roux, Arno Pauly

“…We provide an algorithm producing 3n real numbers containing all zeros of a continuous function with up to n local minima. …”
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Fixed-Point Arithmetic Unit with a Scaling Mechanism for FPGA-Based Embedded Systems by Andrzej Przybył

“…As a result, the real-time processing of real numbers is simplified and, therefore, faster. The described method provides a better ratio of the processing efficiency to the complexity of the digital system than other methods. …”
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Higher-order system of p-nonlinear difference equations solvable in closed-form with variable coefficients by Ahmed Ghezal

“… In this paper, we investigate the solutions of the following system of p-nonlinear difference equations x_{n+1}^{(i)}=((a_{n}x_{n-m}^{(i+1)mod(p)})/(b_{n}+c_{n}x_{n-m}^{(i+1)mod(p)})),n,m∈N₀,p∈N,i∈{1,...,p}, where N₀=N∪{0}, the sequences (a_{n}), (b_{n}),(c_{n}), are non-zero real numbers and initial values x_{-j}^{(i)}, j∈{0,...,m}, i∈{1,...,p}, do not equal -b_{n}c_{n}⁻¹, for all n∈ N₀. …”
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Using.Liouville’s function for Creating a weird numbers from Reals by Nagham A. Hameed, Faez Al-Maamori

“…The challenging of this work is the dealing with an algorithm for generating a weird numbers (or maybe a primitive weird numbers) from a large enough real numbers x. The idea of this work can be used for an application of modeling, data simulation and security subjects. …”
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On Gaussian Leonardo Hybrid Polynomials by Tülay Yaǧmur

“…After that, we introduce the Gaussian Leonardo hybrid polynomials, using the Gaussian Leonardo polynomials as coefficients instead of real numbers in hybrid numbers. Moreover, we obtain the recurrence relations, generating functions, Binet-like formulas, Vajda-like identities, Catalan-like identities, Cassini-like identities, and d’Ocagne-like identities for the Gaussian Leonardo polynomials and hybrid polynomials, respectively.…”
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Fučík spectra for vector equations by Christian Fabry

“…The aim of this paper is to study the Fu\v c\'\i k spectrum for vector problems of the form $Lu=\alpha Au^+ -\beta Au^-$, where $A$ is an $N\times N$ matrix, $\alpha, \beta$ are real numbers, $u^+$ a vector defined componentwise by $(u^+)_i=\max\{u_i,0\}$, $u^-$ being defined similarly. …”
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Some New Estimates of Hermite–Hadamard Inequality with Application by Tao Zhang, Alatancang Chen

“…As application, some error estimates on special means of real numbers are given.…”
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Robust Image Watermarking in the Wavelet Domain by Dr. Hameed A. Younis

“…A chaotic sequence of real numbers, depends on a secret key, is embedded as a watermark in the DCT coefficients of the selected blocks. …”
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Exploring the use of topological data analysis to automatically detect data quality faults by M. Eduard Tudoreanu

“…A distance function is used to transform each record of a dataset into an n-dimensional vector of real numbers, which effectively transforms the original data into a high-dimensional point cloud. …”
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