scholarly journals Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor

2012 ◽  
Vol 2012 ◽  
pp. 1-37 ◽  
Author(s):  
Yongdong Huang ◽  
Qiufu Li ◽  
Ming Li
Keyword(s):  
Necessary Conditions ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Spline Functions ◽  
Arbitrary Integer ◽  
B Spline ◽  
Numerical Examples ◽  
Dilation Factor ◽  
Organically Combine

In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B-spline functions.

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

scholarly journals Minimum-Energy Bivariate Wavelet Frame with Arbitrary Dilation Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fengjuan Zhu ◽  
Qiufu Li ◽  
Yongdong Huang
Keyword(s):  
Scaling Function ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Reconstruction Algorithm ◽  
Wavelet Function ◽  
Necessary Condition ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Numerical Examples ◽  
Dilation Matrix

In order to characterize the bivariate signals, minimum-energy bivariate wavelet frames with arbitrary dilation matrix are studied, which are based on superiority of the minimum-energy frame and the significant properties of bivariate wavelet. Firstly, the concept of minimum-energy bivariate wavelet frame is defined, and its equivalent characterizations and a necessary condition are presented. Secondly, based on polyphase form of symbol functions of scaling function and wavelet function, two sufficient conditions and an explicit constructed method are given. Finally, the decomposition algorithm, reconstruction algorithm, and numerical examples are designed.

scholarly journals An Optimization Problem for Quadcopter Reference Flight Trajectory Generation

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Karam Eliker ◽  
Guoqing Zhang ◽  
Said Grouni ◽  
Weidong Zhang
Keyword(s):  
Minimum Energy ◽  
Trajectory Generation ◽  
Optimization Method ◽  
Performance Criteria ◽  
Spline Functions ◽  
Flight Trajectory ◽  
B Spline ◽  
Aerial Vehicle ◽  
And Performance ◽  
Minimum Energy Cost

This paper deals with the reference flight trajectory generation and planning problems for quadcopter Unmanned Aerial Vehicle (UAV). The reference flight trajectory is defined as the composition of path and motion functions. Both of them are generated by using quintic B-spline functions. Based on differential flatness approach, the quadcopter dynamical constraints are satisfied instantaneously by computing the induced aerodynamical moments and lift force. The optimal reference flight trajectory, with respect to the mission requirements and imposed constraints, is reached by manipulating the control points’ vectors of B-spline functions via a nonlinear constrained optimization method. The mission requirements are defined as a set of waypoints with their respective scheduled flight timetable. A minimum-energy cost function is developed to minimize the consumed energy and induced efforts by reference flight trajectory. For the need of the optimal overfly-times schedule, the overfly times with respect to the defined constraints and performance criteria are calculated. Numerical simulation results show the feasibility and effectiveness of the proposed optimization method.

scholarly journals New stability conditions for positive continuous-discrete 2D linear systems

2011 ◽  
Vol 21 (3) ◽  
pp. 521-524 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear Systems ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Conditions ◽  
Stability Tests ◽  
Numerical Examples ◽  
The Stability ◽  
Necessary And Sufficient

New stability conditions for positive continuous-discrete 2D linear systemsNew necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

The Synthesis of Follower Motions of Camoids Using Nonparametric B-Splines

1996 ◽  
Vol 118 (1) ◽  
pp. 138-143 ◽  
Author(s):  
Der Min Tsay ◽  
Guan Shyong Hwang
Keyword(s):  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
B Splines ◽  
Surface Interpolation ◽  
Spline Surface ◽  
Motion Function ◽  
Knot Sequences ◽  
Independent Parameters

This paper proposes a tool to synthesize the motion functions of the camoid-follower mechanisms. The characteristics of these kinds of motion functions are that they possess two independent parameters. To implement the work, this study applies the nonparametric B-spline surface interpolation, whose spline functions are constructed by the closed periodic B-splines and the de Boor’s knot sequences in the two parametric directions of the motion function, respectively. The rules and the restrictions needed to be noticed in the process of synthesis are established. Numerical examples are also given to verify the feasibility of the proposed method.

PB-Spline Finite Element Shell Modeling and Refinement Technique

2009 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Complex Shapes ◽  
Spline Finite Element ◽  
Shell Finite Element ◽  
Element Technique

This paper presents a Point Based (PB) spline degenerate shell finite element model to analyze the behavior of thin and moderately thick-walled structures. Complex shapes are modeled with several B-spline patches assembled as in conventional finite element technique. The refinement of the solution is carried out by superimposing a tensorial set of B-spline functions on a patch and employing the PB-spline generalization. The domains for the numerical integration are defined by making use of the retained tensorial framework. Some numerical examples are presented. Considerations regarding strengths and limits of the approach then follow.

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