scholarly journals Shape Preserving Piecewise KNR Fractional Order Biquadratic C 2 Spline

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Syed Khawar Nadeem Kirmani ◽  
Muhammad Bilal Riaz ◽  
Fahd Jarad ◽  
Hayder Natiq Jasim ◽  
Aytekin Enver
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Shape Control ◽  
Recent Article ◽  
Spline Function ◽  
Control Parameters ◽  
Shape Preserving ◽  
Data Points

In a recent article, a piecewise cubic fractional spline function is developed which produces C 1 continuity to given data points. In the present paper, an interpolant continuity class C 2 is preserved which gives visually pleasing piecewise curves. The behavior of the resulting representations is analyzed intrinsically with respect to variation of the shape control parameters t and s. The data points are restricted to be strictly monotonic along real line.

scholarly journals Modified Bézier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammad Asif Zaman ◽  
Shuvro Chowdhury
Keyword(s):  
Differential Evolution ◽  
Optimization Algorithm ◽  
Shape Control ◽  
Parametric Equation ◽  
Shape Preserving ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Data Points ◽  
Cost Parameters ◽  
Differential Evolution Optimization Algorithm

A parametric equation for a modified Bézier curve is proposed for curve fitting applications. The proposed equation contains shaping parameters to adjust the shape of the fitted curve. This flexibility of shape control is expected to produce a curve which is capable of following any sets of discrete data points. A Differential Evolution (DE) optimization based technique is proposed to find the optimum value of these shaping parameters. The optimality of the fitted curve is defined in terms of some proposed cost parameters. These parameters are defined based on sum of squares errors. Numerical results are presented highlighting the effectiveness of the proposed curves compared with conventional Bézier curves. From the obtained results, it is observed that the proposed method produces a curve that fits the data points more accurately.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

The Relationship between the Letters of Al-Iḫlāṣ (Q 112:1-4) and Their Iterations Using B-Spline Function

2019 ◽  
Vol 17 (1) ◽  
pp. 60-86
Author(s):  
Faoziya S.M. Musbah
Keyword(s):  
Spline Function ◽  
Piecewise Linear ◽  
Two Dimensional ◽  
B Spline ◽  
Holy Quran ◽  
Data Points ◽  
The Holy Quran ◽  
The Absolute ◽  
Unity Of God ◽  
The Relationship

Abstract Al-Iḫlāṣ is an important chapter within the Holy Quran (words of God) because it is a brief declaration of the absolute unity of God (Allah). This paper analyzes al-Iḫlāṣ mathematically in order to gain an understanding of the relationship between the letters of this chapter and their iterations. The analyzed two-dimensional data points (xi,yi) define a piecewise linear curve that is shaped like Allah’s name as it is written in Arabic. The B-spline function is used to analyze this data so as to obtain a second degree curve.

scholarly journals An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 355 ◽  
Author(s):  
Jens Jauch ◽  
Felix Bleimund ◽  
Michael Frey ◽  
Frank Gauterin
Keyword(s):  
Trajectory Optimization ◽  
Spline Function ◽  
Nonlinear Approximation ◽  
Computational Effort ◽  
Optimization Approach ◽  
Data Approximation ◽  
B Spline ◽  
Marquardt Algorithm ◽  
Trajectory Length ◽  
Data Points

The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for NWLS approximation are restricted to a bounded definition range. We present an algorithm termed NRBA for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a MPF, in which a KF solves the linear subproblem optimally while a PF deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. We demonstrate how NRBA can be applied for a multiobjective trajectory optimization for a BEV in order to determine an energy-efficient velocity trajectory. With NRBA, the effort increases only linearly with the processed data points and the trajectory length.

scholarly journals Calibration of Radiocarbon Ages by Computer

Radiocarbon ◽  
1989 ◽  
Vol 31 (03) ◽  
pp. 805-816 ◽  
Author(s):  
Johannes Van Der Plicht ◽  
W G Mook
Keyword(s):  
Computer Program ◽  
Calibration Curve ◽  
Spline Function ◽  
Moving Average ◽  
Age Distribution ◽  
Automatic Calibration ◽  
Calibration Data ◽  
Average Procedure ◽  
Data Points ◽  
Radiocarbon Calibration

A PC-based computer program for automatic calibration of 14C dates has been developed in Turbo-Pascal (version 4.0). It transforms the Gaussian 14C dating result on the 3σ level into a real calendar age distribution. It uses as a calibration curve a spline function, generated along the calibration data points as published in the Radiocarbon Calibration Issue. Special versions of the code can average several 14C dates into one calibrated result, generate smoothed curves by a moving average procedure and perform wiggle matching.

scholarly journals Data Visualization Using Rational Trigonometric Spline

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Uzma Bashir ◽  
Jamaludin Md. Ali
Keyword(s):  
Data Visualization ◽  
The Other ◽  
Shape Features ◽  
Shape Parameters ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Data Points ◽  
Trigonometric Spline ◽  
The Given

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

scholarly journals Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yan-Ping Wu ◽  
Guo-Dong Wang
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Chaotic System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Integer Order ◽  
Response Systems ◽  
Hyperchaotic Systems

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

scholarly journals Synchronization of Coupled Nonidentical Fractional-Order Hyperchaotic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Zhouchao Wei
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Control Parameters ◽  
Chen System ◽  
Mode Method ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show the effectiveness of the proposed controller.

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