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Articles de revues sur le sujet « Bernoulli systems »

Auteur : Grafiati

Publié le 14 décembre 2024

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1

GERBER, MARLIES, and PHILIPP KUNDE. "Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli." Ergodic Theory and Dynamical Systems 42, no. 3 (2021): 917–73. http://dx.doi.org/10.1017/etds.2021.73.

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AbstractForeman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing e

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2

Chernov, N. I., and C. Haskell. "Nonuniformly hyperbolic K-systems are Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 1 (1996): 19–44. http://dx.doi.org/10.1017/s0143385700008695.

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AbstractWe prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.

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3

Filipovic, Mirjana. "New form of the Euler-Bernoulli rod equation applied to robotic systems." Theoretical and Applied Mechanics 35, no. 4 (2008): 381–406. http://dx.doi.org/10.2298/tam0804381f.

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This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation

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4

ORNSTEIN, DONALD, and BENJAMIN WEISS. "On the Bernoulli nature of systems with some hyperbolic structure." Ergodic Theory and Dynamical Systems 18, no. 2 (1998): 441–56. http://dx.doi.org/10.1017/s0143385798100354.

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It is shown that systems with hyperbolic structure have the Bernoulli property. Some new results on smooth cross-sections of hyperbolic Bernoulli flows are also derived. The proofs involve an abstract version of our original methods for showing that the geodesic flow on surfaces of negative curvature are Bernoulli.

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LIAO, GANG, WENXIANG SUN, EDSON VARGAS, and SHIROU WANG. "Approximation of Bernoulli measures for non-uniformly hyperbolic systems." Ergodic Theory and Dynamical Systems 40, no. 1 (2018): 233–47. http://dx.doi.org/10.1017/etds.2018.33.

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An invariant measure is called a Bernoulli measure if the corresponding dynamics is isomorphic to a Bernoulli shift. We prove that for$C^{1+\unicode[STIX]{x1D6FC}}$diffeomorphisms any weak mixing hyperbolic measure could be approximated by Bernoulli measures. This also holds true for$C^{1}$diffeomorphisms preserving a weak mixing hyperbolic measure with respect to which the Oseledets decomposition is dominated.

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DOOLEY, A. H., V. YA GOLODETS, D. J. RUDOLPH, and S. D. SINEL’SHCHIKOV. "Non-Bernoulli systems with completely positive entropy." Ergodic Theory and Dynamical Systems 28, no. 1 (2008): 87–124. http://dx.doi.org/10.1017/s014338570700034x.

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AbstractA new approach to actions of countable amenable groups with completely positive entropy (cpe), allowing one to answer some basic questions in this field, was recently developed. The question of the existence of cpe actions which are not Bernoulli was raised. In this paper, we prove that every countable amenable groupG, which contains an element of infinite order, has non-Bernoulli cpe actions. In fact we can produce, for any$h \in (0, \infty ]$, an uncountable family of cpe actions of entropyh, which are pairwise automorphically non-isomorphic. These actions are given by a construction

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Barbieri, Giuseppina, and Giacomo Lenzi. "Entropy of MV-algebraic dynamical systems: An example." Mathematica Slovaca 69, no. 2 (2019): 267–74. http://dx.doi.org/10.1515/ms-2017-0221.

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Abstract We give examples showing that the Kolmogorov-Sinai entropy generator theorem is false for both upper and lower Riesz entropy of MV-algebraic dynamical systems, both two sided (i.e., analogous to two sided Bernoulli shifts) and one sided (i.e., analogous to one sided Bernoulli shifts).

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8

Nicol, Matthew. "Induced maps of hyperbolic Bernoulli systems." Discrete & Continuous Dynamical Systems - A 7, no. 1 (2001): 147–54. http://dx.doi.org/10.3934/dcds.2001.7.147.

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Beebee, John. "Bernoulli Numbers and Exact Covering Systems." American Mathematical Monthly 99, no. 10 (1992): 946. http://dx.doi.org/10.2307/2324488.

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10

Akaishi, A., M. Hirata, K. Yamamoto, and A. Shudo. "Meeting time distributions in Bernoulli systems." Journal of Physics A: Mathematical and Theoretical 44, no. 37 (2011): 375101. http://dx.doi.org/10.1088/1751-8113/44/37/375101.

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11

Beebee, John. "Bernoulli Numbers and Exact Covering Systems." American Mathematical Monthly 99, no. 10 (1992): 946–48. http://dx.doi.org/10.1080/00029890.1992.11995959.

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12

Kanamori, Takafumi, and Naoya Osugi. "Model Description of Similarity-Based Recommendation Systems." Entropy 21, no. 7 (2019): 702. http://dx.doi.org/10.3390/e21070702.

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The quality of online services highly depends on the accuracy of the recommendations they can provide to users. Researchers have proposed various similarity measures based on the assumption that similar people like or dislike similar items or people, in order to improve the accuracy of their services. Additionally, statistical models, such as the stochastic block models, have been used to understand network structures. In this paper, we discuss the relationship between similarity-based methods and statistical models using the Bernoulli mixture models and the expectation-maximization (EM) algor

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13

Sahu, P. K., and S. Saha Ray. "A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations." International Journal of Computational Methods 14, no. 03 (2017): 1750022. http://dx.doi.org/10.1142/s0219876217500220.

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In this paper, Bernoulli wavelet method has been developed to solve nonlinear weakly singular Volterra integro-differential equations. Bernoulli wavelets are generated by dilation and translation of Bernoulli polynomials. The properties of Bernoulli wavelets and Bernoulli polynomials are first presented. The present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this paper. Some illustrative examples ha

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14

Arbieto, Alexander, Carlos Matheus, and Maria José Pacifico. "The Bernoulli Property for Weakly Hyperbolic Systems." Journal of Statistical Physics 117, no. 1/2 (2004): 243–60. http://dx.doi.org/10.1023/b:joss.0000044058.99450.c9.

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15

Qu, Changzheng, and Liu Chao. "Heterotic Liouville systems from the Bernoulli equation." Physics Letters A 199, no. 5-6 (1995): 349–52. http://dx.doi.org/10.1016/0375-9601(95)00147-u.

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16

Blanc, J. P. C., and R. D. van der Mei. "Optimization of polling systems with Bernoulli schedules." Performance Evaluation 22, no. 2 (1995): 139–58. http://dx.doi.org/10.1016/0166-5316(93)e0045-7.

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17

Ju, Feng, and Jingshan Li. "A Bernoulli Model of Selective Assembly Systems." IFAC Proceedings Volumes 47, no. 3 (2014): 1692–97. http://dx.doi.org/10.3182/20140824-6-za-1003.00525.

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18

Bershadskii, A. "Multifractal Bernoulli fluctuations in disordered mesoscopic systems." Journal of Physics A: Mathematical and General 31, no. 41 (1998): L707—L711. http://dx.doi.org/10.1088/0305-4470/31/41/001.

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19

Elishakoff, Isaac, Menahem Baruch, Liping Zhu, and Raoul Caimi. "Random Vibration of Space Shuttle Weather Protection Systems." Shock and Vibration 2, no. 2 (1995): 111–18. http://dx.doi.org/10.1155/1995/562346.

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The article deals with random vibrations of the space shuttle weather protection systems. The excitation model represents a fit to the measured experimental data. The cross-spectral density is given as a convex combination of three exponential functions. It is shown that for the type of loading considered, the Bernoulli-Euler theory cannot be used as a simplified approach, and the structure will be more properly modeled as a Timoshenko beam. Use of the simple Bernoulli-Euler theory may result in an error of about 50% in determining the mean-square value of the bending moment in the weather pro

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20

Katok, Anatole, and Keith Burns. "Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems." Ergodic Theory and Dynamical Systems 14, no. 4 (1994): 757–85. http://dx.doi.org/10.1017/s0143385700008142.

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AbstractWe establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.

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21

Hicks, J. W., and H. S. Badeer. "Gravity and the circulation: "open" vs. "closed" systems." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 262, no. 5 (1992): R725—R732. http://dx.doi.org/10.1152/ajpregu.1992.262.5.r725.

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The elementary principles of liquid dynamics are described by the equations of Bernoulli and Poiseuille. Bernoulli's equation deals with nonviscous liquids under steady streamline flow. Pressures in such flows are related to gravity and/or acceleration. Changes in elevation affect the gravitational potential energy of the liquid and the velocity of flow determines the kinetic energy. The sum of these three factors represented in the Bernoulli equation remains constant, but the variables are interconvertible. In contrast, the Poiseuille equation describes the pressures related to viscous resist

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22

Wang, Guoliang. "Control of Multiagent Systems: A Stochastic Pinning Viewpoint." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/985356.

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A stochastic pinning approach for multiagent systems is developed, which guarantees such systems being almost surely stable. It is seen that the pinning is closely related to being a Bernoulli variable. It has been proved for the first time that a series of systems can be stabilized by a Brownian noise perturbation in terms of a pinning scheme. A new terminology named “stochastic pinning control” is introduced to describe the given pinning algorithm. Additionally, two general cases that the expectation of the Bernoulli variable with bounded uncertainty or being unknown are studied. Finally, tw

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23

Pei, Yangjun, Qi Han, Chao Liu, Dedong Tang, and Junjian Huang. "Chaotic Behaviors of Symbolic Dynamics about Rule 58 in Cellular Automata." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/834268.

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The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulliστ-shift rule, which is members of Wolfram’s class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected gra

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24

Zhao, Cong, and Jingshan Li. "A Bernoulli Model of Multi-Product Manufacturing Systems." IFAC Proceedings Volumes 46, no. 9 (2013): 1268–73. http://dx.doi.org/10.3182/20130619-3-ru-3018.00235.

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25

Bershadskii, A. "Quasi Bernoulli fluctuations in random and disordered systems." European Physical Journal B 3, no. 2 (1998): 141–42. http://dx.doi.org/10.1007/s100510050293.

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26

Athorne, Chris. "Projective Lifts and Generalised Ermakov and Bernoulli Systems." Journal of Mathematical Analysis and Applications 233, no. 2 (1999): 552–63. http://dx.doi.org/10.1006/jmaa.1999.6305.

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27

Llibre, Jaume, Weber F. Pereira, and Claudio Pessoa. "Phase portraits of Bernoulli quadratic polynomial differential systems." Electronic Journal of Differential Equations 2020, no. 01-132 (2020): 48. http://dx.doi.org/10.58997/ejde.2020.48.

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In this article we study a new class of quadratic polynomial differential systems. We classify all global phase portraits in the Poincare disk of Bernoulli quadratic polynomial differential systems in R^2. For more information see https://ejde.math.txstate.edu/Volumes/2020/48/abstr.html

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MUNTEANU, RADU B. "Entropy of systems." Ergodic Theory and Dynamical Systems 38, no. 3 (2016): 1118–26. http://dx.doi.org/10.1017/etds.2016.52.

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In this paper we show that any ergodic measure preserving transformation of a standard probability space which is $\text{AT}(n)$ for some positive integer $n$ has zero entropy. We show that for every positive integer $n$ any Bernoulli shift is not $\text{AT}(n)$. We also give an example of a transformation which has zero entropy but does not have property $\text{AT}(n)$ for any integer $n\geq 1$.

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KÜMMERER, B., and H. MAASSEN. "A SCATTERING THEORY FOR MARKOV CHAINS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 01 (2000): 161–76. http://dx.doi.org/10.1142/s0219025700000091.

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In the operator algebraic formulation of probability theory Markov processes typically appear as perturbations of Bernoulli processes. We develop a scattering theory for this situation. This theory applies to the isomorphism problem between Markov processes and Bernoulli shifts as well as to the description of open quantum systems.

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Micheal, Mathavavisakan, and Kandaiyan Indhira. "A literature review on retrial queueing system with Bernoulli vacation." Yugoslav Journal of Operations Research, no. 00 (2023): 20. http://dx.doi.org/10.2298/yjor230415020m.

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The retrial phenomenon occurs inherently in a wide range of queueing systems. The majority of retrial queueing models do not account for vacation. However, in practice, retrial queueing systems undergo vacations for maintenance or other reasons. In this study, we provide an in-depth analysis of the many possible retrial queueing systems when Bernoulli vacations are in effect. Moreover, this study outlines the key principles and reviews the relevant literature. The framework of a retrial queue with Bernoulli vacation has numerous applications in computer networking systems, manufacturing and pr

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Dingle, Kamal, Mohammad Alaskandarani, Boumediene Hamzi, and Ard A. Louis. "Exploring Simplicity Bias in 1D Dynamical Systems." Entropy 26, no. 5 (2024): 426. http://dx.doi.org/10.3390/e26050426.

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Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input–output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and te

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De La Rue, Thierry. "Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 2 (1996): 379–404. http://dx.doi.org/10.1017/s0143385700008865.

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AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.

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Петров, Антон Олександрович. "Improvement test of critical systems survivability the Bernoulli scheme." Technology audit and production reserves 6, no. 3(8) (2012): 35–36. http://dx.doi.org/10.15587/2312-8372.2012.5525.

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Ortega, Fernando, Raúl Lara-Cabrera, Ángel González-Prieto, and Jesús Bobadilla. "Providing reliability in recommender systems through Bernoulli Matrix Factorization." Information Sciences 553 (April 2021): 110–28. http://dx.doi.org/10.1016/j.ins.2020.12.001.

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35

Jia, Zhiyang, Liang Zhang, Jorge Arinez, and Guoxian Xiao. "Transient Performance Evaluation of Assembly Systems with Bernoulli MachinesÕ." IFAC-PapersOnLine 48, no. 3 (2015): 88–93. http://dx.doi.org/10.1016/j.ifacol.2015.06.063.

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Madine, K. H., and D. J. Colquitt. "Dynamic Green’s functions in discrete flexural systems." Quarterly Journal of Mechanics and Applied Mathematics 74, no. 3 (2021): 323–50. http://dx.doi.org/10.1093/qjmam/hbab006.

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Summary The article presents an analysis of the dynamic behaviour of discrete flexural systems composed of Euler–Bernoulli beams. The canonical object of study is the discrete Green’s function, from which information regarding the dynamic response of the lattice under point loading by forces and moments can be obtained. Special attention is devoted to the interaction between flexural and torsional waves in a square lattice of Euler–Bernoulli beams, which is shown to yield a range of novel effects, including extreme dynamic anisotropy, asymmetric wave propagation, wave-guiding, filtering and th

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Ban, Jung-Chao, Chih-Hung Chang, Ting-Ju Chen, and Mei-Shao Lin. "Dimension Spectrum for Sofic Systems." Advances in Mathematical Physics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/624523.

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We study the dimension spectrum of sofic system with the potential functions being matrix valued. For finite-coordinate dependent positive matrix potential, we set up the entropy spectrum by constructing the quasi-Bernoulli measure and the cut-off method is applied to deal with the infinite-coordinate dependent case. We extend this method to nonnegative matrix and give a series of examples of the sofic-affine set on which we can compute the spectrum concretely.

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Tohidi, Emran, M. M. Ezadkhah, and S. Shateyi. "Numerical Solution of Nonlinear Fractional Volterra Integro-Differential Equations via Bernoulli Polynomials." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/162896.

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This paper presents a computational approach for solving a class of nonlinear Volterra integro-differential equations of fractional order which is based on the Bernoulli polynomials approximation. Our method consists of reducing the main problems to the solution of algebraic equations systems by expanding the required approximate solutions as the linear combination of the Bernoulli polynomials. Several examples are given and the numerical results are shown to demonstrate the efficiency of the proposed method.

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RODRIGUEZ HERTZ, F., M. A. RODRIGUEZ HERTZ, A. TAHZIBI, and R. URES. "Maximizing measures for partially hyperbolic systems with compact center leaves." Ergodic Theory and Dynamical Systems 32, no. 2 (2011): 825–39. http://dx.doi.org/10.1017/s0143385711000757.

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AbstractWe obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topological

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ZHENG, YONGAI, GUANRONG CHEN, and ZENGRONG LIU. "ON CHAOTIFICATION OF DISCRETE SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 11 (2003): 3443–47. http://dx.doi.org/10.1142/s0218127403008661.

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In this paper, the problem of making a nonlinear system chaotic by using state-feedback control is studied. The feedback controller uses a simple sine function of the system state, but only one component in each dimension. It is proved, by using the anti-integrable limit method, that the designed control system generates chaos in the sense of Devaney. In fact, the controlled system so designed is a perturbation of the original system, which turns out to be a simple Bernoulli shift.

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Takine, T., H. Takagi, and T. Hasegawa. "Sojourn times in vacation and polling systems with Bernoulli feedback." Journal of Applied Probability 28, no. 2 (1991): 422–32. http://dx.doi.org/10.2307/3214877.

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We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture

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Takine, T., H. Takagi, and T. Hasegawa. "Sojourn times in vacation and polling systems with Bernoulli feedback." Journal of Applied Probability 28, no. 02 (1991): 422–32. http://dx.doi.org/10.1017/s0021900200039796.

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We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture

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Suresh Babu, Sumith Babu, and R. Kumar. "Multigroup Synchronization in 1D-Bernoulli Chaotic Collaborative CDMA." Wireless Communications and Mobile Computing 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/7561757.

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Code-division multiple access (CDMA) has played a remarkable role in the field of wireless communication systems, and its capacity and security requirements are still being addressed. Collaborative multiuser transmission and detection are a contemporary technique used in CDMA systems. The performance of these systems is governed by the proper accommodation of the users and by proper synchronization schemes. The major research concerns in the existing multiuser overloaded CDMA schemes are (i) statistically uncorrelated PN sequences that cause multiple-access interference (MAI) and (ii) the secu

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Komori, Yasushi, Kohji Matsumoto, and Hirofumi Tsumura. "Zeta and $L$-functions and Bernoulli polynomials of root systems." Proceedings of the Japan Academy, Series A, Mathematical Sciences 84, no. 5 (2008): 57–62. http://dx.doi.org/10.3792/pjaa.84.57.

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Zimmels, Y. "The Bernoulli equation for fluids in electromagnetic and interfacial systems." Journal of Colloid and Interface Science 125, no. 2 (1988): 399–419. http://dx.doi.org/10.1016/0021-9797(88)90004-5.

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Fioravanti, A. R., A. P. C. Gonçalves, and J. C. Geromel. "Optimal and mode-independent filters for generalised Bernoulli jump systems." International Journal of Systems Science 46, no. 3 (2013): 405–17. http://dx.doi.org/10.1080/00207721.2013.784373.

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Toivanen, J. I., J. Haslinger, and R. A. E. Mäkinen. "Shape optimization of systems governed by Bernoulli free boundary problems." Computer Methods in Applied Mechanics and Engineering 197, no. 45-48 (2008): 3803–15. http://dx.doi.org/10.1016/j.cma.2008.03.002.

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Kosloff, Zemer, and Terry Soo. "Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows." Journal of Modern Dynamics 20 (2024): 597–634. http://dx.doi.org/10.3934/jmd.2024016.

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Hadžić, Neven, Viktor Ložar, Tihomir Opetuk, and Robert Keser. "Transient Response of Homogenous and Nonhomogenous Bernoulli Production Lines." Mathematics 11, no. 24 (2023): 4945. http://dx.doi.org/10.3390/math11244945.

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The transient response of production systems is of significant importance especially if present advancements in Digital Twinning technology are taken into account. While the steady-state response enables long-term strategic decision making, the transient response enables more detailed simulation concerning aspects like production losses and preventive maintenance. This is especially relevant if nonhomogenous aspects of production systems are taken into account. An analytical and approximative solution to the problem of the transient response of homogenous and nonhomogenous Bernoulli production

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Liu, Xikui, Xinye Guo, Wencheng Liu, and Yan Li. "Finite-Time H∞ Control for Time-Delay Markovian Jump Systems with Partially Unknown Transition Rate via General Controllers." Entropy 25, no. 3 (2023): 402. http://dx.doi.org/10.3390/e25030402.

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This paper deals with the problems of finite-time boundedness (FTB) and H∞ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and H∞ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given H∞ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related t

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