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.

MATHEMATICAL ANALYSIS OF THE ACOUSTIC DIFFRACTION BY A MUFFLER CONTAINING PERFORATED DUCTS

2005 ◽  
Vol 15 (07) ◽  
pp. 1059-1090 ◽  
Author(s):  
A. S. BONNET-BEN DHIA ◽  
D. DRISSI ◽  
N. GMATI
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Scalar Problem ◽  
Fredholm Type ◽  
Numerical Examples ◽  
Time Harmonic ◽  
Impedance Condition ◽  
Absorbing Material ◽  
Acoustic Diffraction ◽  
Theoretical Results

We consider the three-dimensional scalar problem of acoustic propagation in a muffler. We develop and analyze a Fredholm-type formulation for a stationary fluid in the time-harmonic setting. We prove a homogenization result for a muffler containing periodically perforated ducts. Essentially, the perforated boundaries become completely transparent when the period of perforations, which is assumed to be of the same order as the size of perforations, tends to zero. We also derive a homogenized impedance condition when the perforated duct is coated by an absorbing material. We present numerical examples in two dimensions, obtained from coupling finite elements in the muffler with modal decompositions in the inlet and outlet ducts, which demonstrate the limiting validity of the theoretical results.

scholarly journals A Semilocal Convergence for a Uniparametric Family of Efficient Secant-Like Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
I. K. Argyros ◽  
D. González ◽  
Á. A. Magreñán
Keyword(s):  
Banach Space ◽  
Computational Cost ◽  
Semilocal Convergence ◽  
Recurrent Functions ◽  
Convergence Conditions ◽  
Precise Information ◽  
Numerical Examples ◽  
Convergence Results ◽  
Special Cases ◽  
Theoretical Results

We present a semilocal convergence analysis for a uniparametric family of efficient secant-like methods (including the secant and Kurchatov method as special cases) in a Banach space setting (Ezquerro et al., 2000–2012). Using our idea of recurrent functions and tighter majorizing sequences, we provide convergence results under the same or less computational cost than the ones of Ezquerro et al., (2013, 2010, and 2012) and Hernández et al., (2000, 2005, and 2002) and with the following advantages: weaker sufficient convergence conditions, tighter error estimates on the distances involved, and at least as precise information on the location of the solution. Numerical examples validating our theoretical results are also provided in this study.

scholarly journals Extended Convergence of a Two-Step-Secant-Type Method Under a Restricted Convergence Domain

2020 ◽  
Vol 45 (01) ◽  
pp. 155-164
Author(s):  
IOANNIS K. ARGYROS ◽  
GEORGE SANTHOSH
Keyword(s):  
Computational Effort ◽  
Convergence Domain ◽  
Type Method ◽  
Precise Information ◽  
Numerical Examples ◽  
Special Cases ◽  
Lipschitz Constants ◽  
Local Convergence Analysis ◽  
Lipschitz Conditions ◽  
Theoretical Results

We present a local as well as a semi-local convergence analysis of a two-step secant-type method for solving nonlinear equations involving Banach space valued operators. By using weakened Lipschitz and center Lipschitz conditions in combination with a more precise domain containing the iterates, we obtain tighter Lipschitz constants than in earlier studies. This technique lead to an extended convergence domain, more precise information on the location of the solution and tighter error bounds on the distances involved. These advantages are obtained under the same computational effort, since the new constants are special cases of the old ones used in earlier studies. The new technique can be used on other iterative methods. The numerical examples further illustrate the theoretical results.

Exergy-Based Ecological Optimization of an Irreversible Quantum Carnot Heat Pump with Spin-1/2 Systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaowei Liu ◽  
Lingen Chen ◽  
Yanlin Ge ◽  
Huijun Feng ◽  
Feng Wu ◽  
...  
Keyword(s):  
Heat Pump ◽  
Performance Comparison ◽  
Ecological Function ◽  
Performance Characteristics ◽  
Numerical Examples ◽  
Ecological Performance ◽  
Special Cases ◽  
Heating Load ◽  
Ecological Optimization

AbstractBased on an irreversible quantum Carnot heat pump model in which spin-1/2 systems are used as working substance, an exergy-based ecological function and some other important parameters of the model heat pump are derived. Numerical examples are provided to investigate its ecological performance characteristics. The influences of various irreversibility factors on the ecological performance are discussed. Performance comparison and discussion among maximum points of ecological function, heating load, and so on, are conducted. At last, three special cases are discussed.

scholarly journals A Convergent Collocation Approach for Generalized Fractional Integro-Differential Equations Using Jacobi Poly-Fractonomials

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 979
Author(s):  
Sandeep Kumar ◽  
Rajesh K. Pandey ◽  
H. M. Srivastava ◽  
G. N. Singh
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Collocation Method ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Special Cases ◽  
Collocation Approach ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Theoretical Results

In this paper, we present a convergent collocation method with which to find the numerical solution of a generalized fractional integro-differential equation (GFIDE). The presented approach is based on the collocation method using Jacobi poly-fractonomials. The GFIDE is defined in terms of the B-operator introduced recently, and it reduces to Caputo fractional derivative and other fractional derivatives in special cases. The convergence and error analysis of the proposed method are also established. Linear and nonlinear cases of the considered GFIDEs are numerically solved and simulation results are presented to validate 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.

scholarly journals A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Renbin Liu ◽  
Yong Wu
Keyword(s):  
Renewal Process ◽  
Decomposition Method ◽  
Process Theory ◽  
Series System ◽  
New Approach ◽  
Numerical Examples ◽  
Special Cases ◽  
The Mean ◽  
Repair Facility

Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in ann-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during(0,t]of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

Convergence of derivative free iterative methods

2019 ◽  
Vol 28 (1) ◽  
pp. 19-26
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
SANTHOSH GEORGE ◽  
Keyword(s):  
Banach Space ◽  
Iterative Methods ◽  
Local Convergence ◽  
Practical Interest ◽  
Systems Of Equations ◽  
Hölder Continuous ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
Derivative Free ◽  
Special Cases

We present the local as well as the semi-local convergence of some iterative methods free of derivatives for Banach space valued operators. These methods contain the secant and the Kurchatov method as special cases. The convergence is based on weak hypotheses specializing to Lipschitz continuous or Holder continuous hypotheses. The results are of theoretical and practical interest. In particular the method is compared favorably ¨ to other methods using concrete numerical examples to solve systems of equations containing a nondifferentiable term.

scholarly journals Generalising Exponential Distributions Using an Extended Marshall–Olkin Procedure

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 464
Author(s):  
Victoriano García ◽  
María Martel-Escobar ◽  
F.J. Vázquez-Polo
Keyword(s):  
Failure Rate ◽  
Real Data ◽  
Rate Function ◽  
Exponential Distributions ◽  
Symmetric Distributions ◽  
Failure Rate Function ◽  
Numerical Examples ◽  
Special Cases ◽  
The Common ◽  
Family Of Distributions

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes.

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.

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