Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers by Jerzy Gorecki

“…As an example, I consider a simple network of interacting chemical oscillators that operates as a comparator of two real numbers. The information on which of the two numbers is larger is coded in the number of excitations observed on oscillators forming the network. …”
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ELECTRICAL CIRCUIT MODELLING WITH PETRI NET BY USING OF CONTROL ARCS by abbas Dideban, meghdad Sabouri Rad

“…The continuous Petri net is a model in which the number of marks in the places are real numbers instead of integers. This kind of Petri Nets is useful for modeling of systems that have one flux variable. …”
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ElGamal-type encryption for optimal dynamic quantizer in encrypted control systems by Kaoru Teranishi, Kiminao Kogiso

“…It is difficult to design an optimal dynamic quantizer that converts real numbers to plaintexts for encrypted control systems with ElGamal encryption because the plaintext space of ElGamal encryption is intermittent and does not include zero and negative numbers. …”
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Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications by Hari M. Srivastava, Sana Mehrez, Sergei M. Sitnik

“…As applications, some new inequalities for the digamma function in terms of the trigamma function and some inequalities involving special means of real numbers are given. The results also include estimates via arithmetic, geometric and logarithmic means. …”
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Coordination of Classical and Dynamic Inequalities Complying on Time Scales by Muhammad Jibril Shahab Sahir

“…A time scale is an arbitrary nonempty closed subset of the real numbers. The theory of time scales is applied to combine results in one comprehensive form. …”
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A Further Generalization of limn→∞n!/nn=1/e{\lim _{n \to \infty }}\root n \of {n!/n} = 1/e by Farhadian Reza, Jakimczuk Rafael

“…The aim of this work is to establish a new generalization that is in fact an improvement of Schaumberger’s formula for a general sequence An of positive real numbers. All of the results are applied to some well-known sequences in mathematics, for example, for the prime numbers sequence and the sequence of perfect powers.…”
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On a certain characterisation of the semigroup of positive natural numbers with multiplication by Edward Tutaj

“…This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in R. …”
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Further research on complete moment convergence for moving average process of a class of random variables by Yong Zhang, Xue Ding

“…Abstract In this article, the complete moment convergence for the partial sum of moving average processes { X n = ∑ i = − ∞ ∞ a i Y i + n , n ≥ 1 } $\{X_{n}=\sum_{i=-\infty}^{\infty}a_{i}Y_{i+n},n\geq 1\}$ is established under some mild conditions, where { Y i , − ∞ < i < ∞ } $\{Y_{i},-\infty < i<\infty\}$ is a doubly infinite sequence of random variables satisfying the Rosenthal type maximal inequality and { a i , − ∞ < i < ∞ } $\{a_{i},-\infty< i<\infty\}$ is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results given by Ko (J. …”
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Complete convergence of moving average processes produced by negatively dependent random variables under sub-linear expectations by Mingzhou Xu

“…Suppose that $ \{a_i, -\infty &lt; i &lt; \infty\} $ is an absolutely summable set of real numbers, $ \{Y_i, -\infty &lt; i &lt; \infty\} $ is a subset of identically distributed, negatively dependent random variables under sub-linear expectations. …”
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Analysis and Applications of Some New Fractional Integral Inequalities by Sofia Ramzan, Muhammad Uzair Awan, Silvestru Sever Dragomir, Bandar Bin-Mohsin, Muhammad Aslam Noor

“…Additionally, some applications of our main outcomes to special means of real numbers have been explored. Moreover, we have derived a new generic numerical scheme for solving non-linear equations, demonstrating an application of our main results in numerical analysis.…”
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Some New Parameterized Quantum Fractional Integral Inequalities Involving <i>s</i>-Convex Functions and Applications by Artion Kashuri, Muhammad Samraiz, Gauhar Rahman, Kamsing Nonlaopon

“…To validate our theoretical findings, an example and application to special means of positive real numbers are presented. Numerical analysis investigation shows that the mixed fractional calculus with quantum calculus give better estimates compared with fractional calculus or quantum calculus separately.…”
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Affine Nash groups over real closed fields by Hrushovski, E, Pillay, A

“…In the case when R is the field of real numbers this result was claimed in the paper "Groups definable in local fields and pseudofinite fields", Israel J. …”

Backward Induction for Repeated Games by Jules Hedges

“…This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of 'topologically compact' nondeterminism, and a simple model of computable real numbers. This is the first application of Escardó and Oliva's theory of higher-order sequential games to games of imperfect information, in which (as well as its mathematical elegance) lazy evaluation does nontrivial work for us compared with a traditional game-theoretic analysis. …”
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Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function by Sahel Ashhab

“…We present a protocol for encoding N real numbers stored in N memory registers into the amplitudes of the quantum superposition that describes the state of log_{2}N qubits. …”
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Holderian functional central limit theorem for linear processes by Mindaugas Juodis

“… Let (Xt)t ≥ 1 be a linear process defined by Xt =  ∑i=0∞ψi εt-1 where (ψi, i ≥ 0) is a sequence of  real numbers and (εi , i ∈ Z) is a sequence of random variables with null expectation and variance 1. …”
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An Algorithm for Solution of an Interval Valued EOQ Model by Susovan CHAKRABORTTY, Madhumangal PAL, Prasun Kumar NAYAK

“…A purchasing inventory model with shortages and lead time, whose carryingcost, shortage cost, setup cost, demand quantity and lead time are considered as interval numbers,instead of real numbers. First, a brief survey of the existing works on comparing and ranking anytwo interval numbers on the real line is presented. …”
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Linear programming approach to matrix games with intuitionistic fuzzy goals by Jiang-Xia Nan, Deng-Feng Li

“…The aim of this paper is to develop the concept and methodology of matrix games with IF-set goals in which goals of players are expressed with IF-sets and payoffs are expressed with real numbers rather than IF-sets. In this methodology, the concepts of IF-set goals and the solutions of matrix games with IF-set goals are proposed. …”
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Asymptotic Behavior of Equilibrium Point for a Class of Nonlinear Difference Equation by Gong Fei, Wang Shu, Li Lin-rui, Shi Qi-hong, Wang Chang-you

“…<p/> <p>We study the asymptotic behavior of the solutions for the following nonlinear difference equation <inline-formula><graphic file="1687-1847-2009-214309-i1.gif"/></inline-formula> where the initial conditions <inline-formula><graphic file="1687-1847-2009-214309-i2.gif"/></inline-formula> are arbitrary nonnegative real numbers, <inline-formula><graphic file="1687-1847-2009-214309-i3.gif"/></inline-formula> are nonnegative integers, <inline-formula><graphic file="1687-1847-2009-214309-i4.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2009-214309-i5.gif"/></inline-formula> are positive constants. …”
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The expressions and behavior of solutions for nonlinear systems of rational difference equations by Kholoud N. Alharbi, E. M. Elsayed

“… In this paper, we investigate the form of the solutions of the following systems of difference equations of second order xn+1xn+1==xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xnyn−1xn−yn,yn+1=xn−1ynxn−yn,   n=0,1,...,xn+1=xnyn−1xn+yn,yn+1=xn−1ynxn+yn,xn+1=xnyn−1xn−yn,yn+1=xn−1ynxn−yn,   n=0,1,..., where the initial conditions x−1, x0, y−1 x−1, x0, y−1  and  y0 y0 are arbitrary nonzero real numbers. …”
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Backward Induction for Repeated Games by Hedges, J

“…This uses the selection monad transformer, combined with the searchable set monad viewed as a notion of ‘topologically compact’ nondeterminism, and a simple model of computable real numbers. This is the first application of Escard ´o and Oliva’s theory of higher-order sequential games to games of imperfect information, in which (as well as its mathematical elegance) lazy evaluation does nontrivial work for us compared with a traditional game-theoretic analysis. …”