scholarly journals Output Reachable Set Analysis for Periodic Positive Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ilyas Sitli ◽  
Fouad Lahmidi ◽  
Abdelwahed Namir ◽  
Mouhcine Naim
Keyword(s):  
Optimization Algorithms ◽  
Reachable Set ◽  
Positive Systems ◽  
Numerical Examples ◽  
Exogenous Disturbances ◽  
Theoretical Results

In this study, we use the union of the bounding hyperpyramids to estimate the output reachable set for periodic positive systems under two classes of exogenous disturbances. Optimization algorithms are used to obtain the smallest bounding hyperpyramids possible. Finally, numerical examples are given to verify the theoretical results.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

scholarly journals More Low Differential Uniformity Permutations over F22k with k Odd

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yue Leng ◽  
Jinyang Chen ◽  
Tao Xie
Keyword(s):  
Block Ciphers ◽  
Algebraic Degree ◽  
Differential Uniformity ◽  
Numerical Examples ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Theoretical Results

Permutations with low differential uniformity, high algebraic degree, and high nonlinearity over F22k can be used as the substitution boxes for many block ciphers. In this paper, several classes of low differential uniformity permutations are constructed based on the method of choosing two permutations over F22k to get the desired permutations. The resulted low differential uniformity permutations have high algebraic degrees and nonlinearities simultaneously, which provide more choices for the substitution boxes. Moreover, some numerical examples are provided to show the efficacy of the theoretical results.

Compact splitting symplectic scheme for the fourth-order dispersive Schrödinger equation with Cubic-Quintic nonlinear term

2019 ◽  
Vol 10 (02) ◽  
pp. 1950007 ◽  
Author(s):  
Lang-Yang Huang ◽  
Zhi-Feng Weng ◽  
Chao-Ying Lin
Keyword(s):  
Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Nonlinear Term ◽  
Order Accuracy ◽  
Numerical Examples ◽  
Splitting Technique ◽  
Symplectic Scheme ◽  
Theoretical Results ◽  
Discrete Charge

Combining symplectic algorithm, splitting technique and compact method, a compact splitting symplectic scheme is proposed to solve the fourth-order dispersive Schrödinger equation with cubic-quintic nonlinear term. The scheme has fourth-order accuracy in space and second-order accuracy in time. The discrete charge conservation law and stability of the scheme are analyzed. Numerical examples are given to confirm the theoretical results.

scholarly journals Reachable Set Bounding for Homogeneous Nonlinear Systems with Delay and Disturbance

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Xingao Zhu ◽  
Yuangong Sun
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Nonlinear Systems ◽  
Reachable Set ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

Reachable set bounding for homogeneous nonlinear systems with delay and disturbance is studied. By the usage of a new method for stability analysis of positive systems, an explicit necessary and sufficient condition is first derived to guarantee that all the states of positive homogeneous time-delay systems with degree p>1 converge asymptotically within a specific ball. Furthermore, the main result is extended to a class of nonlinear time variant systems. A numerical example is given to demonstrate the effectiveness of the obtained results.

scholarly journals Competitive Analysis for Online Leasing Problem with Compound Interest Rate

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Xingyu Yang ◽  
Weiguo Zhang ◽  
Weijun Xu ◽  
Yong Zhang
Keyword(s):  
Interest Rate ◽  
Competitive Analysis ◽  
The Other ◽  
Continuous Version ◽  
Numerical Examples ◽  
The Interest Rate ◽  
The One ◽  
Compound Interest ◽  
Theoretical Results ◽  
Deterministic Strategy

We introduce the compound interest rate into the continuous version of the online leasing problem and discuss the generalized model by competitive analysis. On the one hand, the optimal deterministic strategy and its competitive ratio are obtained; on the other hand, a nearly optimal randomized strategy is constructed and a lower bound for the randomized competitive ratios is proved by Yao's principle. With the help of numerical examples, the theoretical results show that the interest rate puts off the purchase date and diminishes the uncertainty involved in the decision making.

scholarly journals Turbulence generation from a stochastic wavelet model

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180093
Author(s):  
Y. Du ◽  
G. Lin
Keyword(s):  
Input Data ◽  
Computation Cost ◽  
Fourier Methods ◽  
Numerical Examples ◽  
Scale Reduction ◽  
Inhomogeneous Turbulence ◽  
Comparable Accuracy ◽  
Turbulence Generation ◽  
Theoretical Results ◽  
Good Agreement

This research presents a new turbulence generation method based on stochastic wavelets and tests various properties of the generated turbulence field in both the homogeneous and inhomogeneous cases. Numerical results indicate that turbulence fields can be generated with much smaller bases in comparison to synthetic Fourier methods while maintaining comparable accuracy. Adaptive generation of inhomogeneous turbulence is achieved by a scale reduction algorithm, which greatly reduces the computation cost and practically introduces no error. The generating formula issued in this research could be adjusted to generate fully inhomogeneous and anisotropic turbulence with given RANS data under divergence-free constraint, which was not achieved previously in similar research. Numerical examples shows that the generated homogeneous and inhomogeneous turbulence are in good agreement with the input data and theoretical results.

Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System

2017 ◽  
Vol 27 (13) ◽  
pp. 1750205 ◽  
Author(s):  
Tonghua Zhang ◽  
Jibin Li
Keyword(s):  
Vector Field ◽  
Periodic Orbits ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Homoclinic Orbits ◽  
Numerical Examples ◽  
Torus Knot ◽  
Cubic System ◽  
Theoretical Results

This paper considers a class of three-dimensional systems constructed by a rotating planar symmetric cubic vector field. To study its periodic orbits including homoclinic orbits, which may be knotted in space, we classify the types of periodic orbits and then calculate their exact parametric representations. Our study shows that this class of systems has infinitely many distinct types of knotted periodic orbits, which lie on three families of invariant tori. Numerical examples of [Formula: see text]-torus knot periodic orbits have also been provided to illustrate our theoretical results.

ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS OF DIFFERENCE EQUATION SYSTEM OF EXPONENTIAL FORM

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050118
Author(s):  
ABDUL KHALIQ ◽  
MUHAMMAD ZUBAIR ◽  
A. Q. KHAN
Keyword(s):  
Initial Conditions ◽  
Equation System ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Form ◽  
Numerical Examples ◽  
Rational Difference Equations ◽  
Boundedness Character ◽  
Theoretical Results

In this paper, we study the boundedness character and persistence, local and global behavior, and rate of convergence of positive solutions of following system of rational difference equations [Formula: see text] wherein the parameters [Formula: see text] for [Formula: see text] and the initial conditions [Formula: see text] are positive real numbers. Some numerical examples are given to verify our theoretical results.

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