scholarly journals An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1628
Author(s):  
Yashuang Deng ◽  
Yuhui Shi
Keyword(s):  
Chaotic System ◽  
Error Compensation ◽  
Chaotic Systems ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Two Dimensional ◽  
High Complexity ◽  
Digital World ◽  
Higher Dimensional ◽  
Generalized Mean

Continuous chaos may collapse in the digital world. This study proposes a method of error compensation for a two-dimensional digital system based on the generalized mean value theorem of differentiation that can restore the fundamental performance of chaotic systems. Different from other methods, the compensation sequence of our method comes from the chaotic system itself and can be applied to higher-dimensional digital chaotic systems. The experimental results show that the improved system is highly consistent with the real chaotic system, and it has excellent chaotic characteristics such as high complexity, randomness, and ergodicity.

scholarly journals Arithmetic of higher-dimensional orbifolds and a mixed Waring problem

2021 ◽  
Author(s):  
Tim Browning ◽  
Shuntaro Yamagishi
Keyword(s):  
Circle Method ◽  
Rational Points ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Waring’S Problem ◽  
Waring Problem ◽  
Waring's Problem ◽  
Main Conjecture ◽  
Higher Dimensional ◽  
Thin Set

AbstractWe study the density of rational points on a higher-dimensional orbifold $$(\mathbb {P}^{n-1},\Delta )$$ ( P n - 1 , Δ ) when $$\Delta $$ Δ is a $$\mathbb {Q}$$ Q -divisor involving hyperplanes. This allows us to address a question of Tanimoto about whether the set of rational points on such an orbifold constitutes a thin set. Our approach relies on the Hardy–Littlewood circle method to first study an asymptotic version of Waring’s problem for mixed powers. In doing so we make crucial use of the recent resolution of the main conjecture in Vinogradov’s mean value theorem, due to Bourgain–Demeter–Guth and Wooley.

Generalizing the Generalized Mean-Value Theorem

1981 ◽  
Vol 88 (7) ◽  
pp. 528-530
Author(s):  
Alexander Abian
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Generalized Mean

scholarly journals Asymptotics for multilinear averages of multiplicative functions

2016 ◽  
Vol 161 (1) ◽  
pp. 87-101 ◽  
Author(s):  
NIKOS FRANTZIKINAKIS ◽  
BERNARD HOST
Keyword(s):  
Unit Disc ◽  
Convergence Result ◽  
Mean Value ◽  
Arithmetic Mean ◽  
Mean Value Theorem ◽  
Two Dimensional ◽  
Multiplicative Functions ◽  
Structural Result ◽  
Convergence Results ◽  
The Mean

AbstractA celebrated result of Halász describes the asymptotic behavior of the arithmetic mean of an arbitrary multiplicative function with values on the unit disc. We extend this result to multilinear averages of multiplicative functions providing similar asymptotics, thus verifying a two dimensional variant of a conjecture of Elliott. As a consequence, we get several convergence results for such multilinear expressions, one of which generalises a well known convergence result of Wirsing. The key ingredients are a recent structural result for multiplicative functions with values on the unit disc proved by the authors and the mean value theorem of Halász.

scholarly journals Extended Generalized Mean Value Theorem for Functions of One Variable

2014 ◽  
Vol 10 (2) ◽  
pp. 39-40
Author(s):  
Phillip Mafuta ◽  
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Generalized Mean

Generalizing the Generalized Mean-Value Theorem

1981 ◽  
Vol 88 (7) ◽  
pp. 528 ◽  
Author(s):  
Alexander Abian
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Generalized Mean

Exploring students’ proof comprehension of the Cauchy Generalized Mean Value Theorem

2019 ◽  
Vol 39 (3) ◽  
pp. 213-235
Author(s):  
Fahimeh Kolahdouz ◽  
Farzad Radmehr ◽  
Hassan Alamolhodaei
Keyword(s):  
Undergraduate Students ◽  
Mean Value ◽  
Mean Value Theorem ◽  
First Year ◽  
Test Design ◽  
Test Results ◽  
Mathematical Proofs ◽  
Proof Comprehension ◽  
Generalized Mean ◽  
First Year University

Abstract Undergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students’ proof comprehension, and Mejia-Ramos et al.’s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The test mainly focused on (a.) investigating students’ understanding of relations between the statements within the CGMVT proof and (b.) the relations between the CGMVT and other theorems. Thirty-five first-year university students voluntarily participated in this study. In addition, 10 of these students were subsequently interviewed to seek their opinion about the test. Test results indicated that most of the students lacked an understanding of the relations between the mathematical statements within the CGMVT proof, and the relations between the CGMVT and other theorems. The results of interviews showed that this type of assessment was new to students and helped them to improve their insights into mathematical proofs. The findings suggested such a test design could be used more frequently in assessments to aid instructors’ understanding of students’ proof comprehension and to teach students how mathematical proofs should be learned.

scholarly journals Analytic Programming – a Novel Tool for Synthesis of Controller for Chaotic Lozi Map

2021 ◽  
Vol 15 ◽  
pp. 50-55
Author(s):  
Roman Senkerik ◽  
Zuzana Kominkova Oplatkova ◽  
Michal Pluhacek
Keyword(s):  
Feedback Control ◽  
Differential Evolution ◽  
Cost Function ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Symbolic Regression ◽  
Control Law ◽  
Two Dimensional ◽  
Function Design ◽  
Analytic Programming

In this paper, it is presented a utilization of a novel tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new feedback control law. This new synthesized chaotic controller secures the fully stabilization of selected discrete chaotic systems, which is the two-dimensional Lozi map. The paper consists of the descriptions of analytic programming as well as selected chaotic system, used heuristic and cost function design. For experimentation, Self-Organizing Migrating Algorithm (SOMA) and Differential evolution (DE) were used. Two selected experiments are detailed described.

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