检索结果-内蒙古大学图书馆

A Generalized Synthesis Technique for High-Order and Wideband 3-D Frequency-Selective Structures With chebyshev functions

引用

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2021年第7期69卷 3936-3944页

作者： Li, Hanxuan Li, Bo Zhu, Lei Nanjing Univ Posts & Telecommun Sch Elect & Opt Engn Nanjing 210023 Peoples R China Univ Macau Dept Elect & Comp Engn Macau Peoples R China

A generalized synthesis technique for a new class of high-order and wideband 3-D frequency-selective structures (FSSs) is presented in this article. First, a general circuit model with shunt short- ended stubs and an i-section nonuniform transmission line is discussed, whose frequency response can be synthesized with chebyshev functions over a wide frequency range. Following the synthesis procedure, all the circuit parameters can be derived from the specifications of the filtering response, such as filtering order N (>= 4), fractional bandwidth (FBW), and equal-ripple return loss (RL). Then, the general circuit model is applied to design high-order and wideband 3-D bandpass FSS, which is physically realized by using stacked printed circuit board pieces etched with slotlines and microstrip lines. As an example, a fourth-order 3-D FSS with FBW = 80% and equal-ripple RL = 10 dB is designed to show the establishment of good relationship between the circuit model and the physical model. To further improve the frequency selectivity, another two coupling paths independent of the main transmission path are created by simultaneously adjusting the FSS thickness and the separation of slotline sections, thus introducing two transmission zeros at both skirts of the passband. Both design examples are fabricated and measured. Good agreement between measured results and simulated ones indicates that the proposed synthesis method can provide an efficient and accurate solution to design such a class of wideband and high-order 3-D FSSs.

关键词： chebyshev functions frequency-selective structures (FSSs) sharp roll-off skirt synthesis design wide passband

来源：评论

学校读者我要写书评

暂无评论

Universal Graph Filter Design Based on Butterworth, chebyshev, and Elliptic functions

引用

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2023年第1期42卷 564-579页

作者： Ge, Zirui Guo, Haiyan Wang, Tingting Yang, Zhen Nanjing Univ Posts & Telecommun Sch Commun & Informat Engn Nanjing 210023 Peoples R China

Graph filters are crucial tools in processing the spectrum of graph signals. In this paper, we propose to design universal IIR graph filters with low computational complexity by using three kinds of functions, which are Butterworth, chebyshev, and elliptic functions, respectively. Specifically, inspired by the classical analog filter design method, we first derive the zeros and poles of graph frequency responses. With these zeros and poles, we construct the conjugate graph filters to design the Butterworth high-pass graph filter, chebyshev high-pass graph filter, and elliptic high-pass graph filter, respectively. On this basis, we further propose to construct a desired graph filter of low pass, band pass, and band stop by mapping the parameters of the desired graph filter to those of the equivalent high-pass graph filter. Furthermore, we propose to set the graph filter order given the maximum passband attenuation and the minimum stopband attenuation. Our numerical results show that the proposed graph filter design methods realize the desired frequency response more accurately than the autoregressive moving average graph filter design method, the linear least-squares fitting-based graph filter design method, and the chebyshev FIR polynomial graph filter design method.

关键词： Graph filters Butterworth functions chebyshev functions Elliptic functions

来源：评论

学校读者我要写书评

暂无评论

A numerical investigation of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet via rational chebyshev functions

引用

EUROPEAN PHYSICAL JOURNAL PLUS 2017年第7期132卷 325页

作者： Parand, Kourosh Moayeri, Mohammad Mahdi Latifi, Sobhan Delkhosh, Mehdi Shahid Beheshti Univ Dept Comp Sci Gc Tehran *** Iran Shahid Beheshti Univ Inst Cognit & Brain Sci Dept Cognit Modeling Gc Tehran Iran

In this paper, a spectral method based on the four kinds of rational chebyshev functions is proposed to approximate the solution of the boundary layer flow of an Eyring-Powell fluid over a stretching sheet. First, by using the quasilinearization method (QLM), the model which is a nonlinear ordinary differential equation is converted to a sequence of linear ordinary differential equations (ODEs). By applying the proposed method on the ODEs in each iteration, the equations are converted to a system of linear algebraic equations. The results indicate the high accuracy and convergence of our method. Moreover, the effects of the Eyring-Powell fluid material parameters are discussed.

关键词： chebyshev functions Fluid Stretch Ordinary differential equation Rational number boundary layer flow

来源：评论

学校读者我要写书评

暂无评论

chebyshev collocation method for fractional Newell-Whitehead-Segel equation

引用

ALEXANDRIA ENGINEERING JOURNAL 2024年 87卷 39-46页

作者： Gebril, E. El-Azab, M. S. Sameeh, M. Mansoura Univ Fac Engn Math & Engn Phys Dept Mansoura 35516 Egypt

In this paper, a collocation approach for the fractional Newell-Whitehead-Segel equation is described. The finite difference method is used to discretized the time-fractional derivative, and chebyshev functions are used for interpolating the spatial derivatives. An a priori error estimate is derived. The stability of the suggested approach is presented. Several numerical examples are provided to show the viability and effectiveness of the suggested approach.

关键词： Collocation method Newell-Whitehead-Segel equation chebyshev functions Fractional partial differential equations Nonlinear partial differential equations

来源：评论

学校读者我要写书评

暂无评论

Stability analysis and numerical evaluations of a COVID-19 model with vaccination

引用

BMC MEDICAL RESEARCH METHODOLOGY 2024年第1期24卷 1页

作者： Izadi, Mohammad Waezizadeh, Tayebeh Shahid Bahonar Univ Kerman Fac Math & Comp Dept Appl Math Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Pure Math Kerman Iran Shahid Bahonar Univ Kerman Mahani Math Res Ctr Kerman *** Iran

A novel (nonlinear) mathematical model for the transmission of Coronavirus 19 (COVID-19) with eight compartments and considering the impact of vaccination is examined in this manuscript. The qualitative behavior of the system such as the boundedness of solutions, the basic reproduction number, and the stability of the equilibrium points is investigated in detail. Some domestic real data collected from the Kerman University of Medical Science (KUMC) is used to estimate the parameters of the proposed model. We predict the dynamical behavior of the system through numerical simulations based on a combined spectral matrix collocation methodology. In this respect, we first linearize the nonlinear system of equations by the method of quasilinearization (QLM). Hence, the shifted version of chebyshev polynomials of the second kind (SCPSK) is utilized along with the domain-splitting strategy to acquire the solutions of the system over a long time interval. The uniform convergence and upper bound estimation of the SCPSK bases are proved in a rigorous manner. Moreover, the technique of residual error functions is used to testify the accuracy of the QLM-SCPSK method. The presented numerical results justify the robustness and good accuracy of the QLM-SCPSK technique. The achieved numerical orders of convergence indicate that the QLM-SCSK algorithm has exponential rate of convergence. Using the linearization technique in one hand and the domain-splitting strategy on the other hand, enable us to predict the behaviour of similar disease problems with high accuracy and maximum efficiency on an arbitrary domain of interest.

关键词： Collocation points Stability analysis Convergent analysis COVID-19 model chebyshev functions

来源：评论

学校读者我要写书评

暂无评论

A Taylor-chebyshev approximation technique to solve the 1D and 2D nonlinear Burgers equations

引用

MATHEMATICAL SCIENCES 2022年第4期16卷 459-471页

作者： Izadi, Mohammad Yuzbasi, Suayip Baleanu, Dumitru Shahid Bahonar Univ Kerman Fac Math & Comp Dept Appl Math Kerman Iran Akdeniz Univ Fac Sci Dept Math TR-07058 Antalya Turkey Inst Space Sci Magurele Romania Cankaya Univ Dept Math TR-06530 Balgat Turkey

This paper deals with proposing an approximate solution for the well-known Burgers equation as a canonical model of various fields of science and engineering. Our novel combined approximation algorithm is based on the linearized Taylor approach for the time discretization, while the spectral chebyshev collocation method is utilized for the space variables. This implies that in each time step, the proposed combined approach reduces the one- and two-dimensional model problems into a system of linear equations, which consists of polynomial coefficients. The error analysis of the present approach in 1D and 2D is discussed. Through numerical simulations, the utility and efficiency of the combined scheme are examined and comparisons with exact solutions as well as existing available methods have been performed. The comparisons indicate that the combined approach is efficient, practical, and straightforward in implementation. The technique developed can be easily extended to other nonlinear models.

关键词： Burgers equation chebyshev functions Collocation points Error analysis Taylor expansion

来源：评论

学校读者我要写书评

暂无评论

A computational algorithm for simulating fractional order relaxation–oscillation equation

引用

SeMA Journal 2022年第4期79卷 647-661页

作者： Izadi, Mohammad Department of Applied Mathematics Faculty of Mathematics and Computer Shahid Bahonar University of Kerman Kerman Iran

In the present work, a collocation approach is developed to find an approximate solution of fractional relaxation-oscillation differential equation describing the processes of relaxation and oscillation in many physical systems. The method is relied on generalized chebyshev polynomials as basis functions, collocation points, and the matrix operations. The proposed scheme converts the underlying fractional initial value problems into a matrix equation, which corresponds to a set of linear algebraic equations consist of polynomial coefficients. An error estimation based on residual function is performed to show the accuracy of the results. Hence, an improvement of the approximate solutions are obtained based upon this error estimation. To illustrate the utility and applicability of the technique, three numerical examples are given and the comparisons between the numerical results of the proposed method with existing results are carried out. The experiments show the accuracy and efficiency the present work. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.

关键词： Caputo derivative chebyshev functions Collocation scheme Fractional relaxation–oscillation equation

来源：评论

学校读者我要写书评

暂无评论

Collocation method to solve inequality-constrained optimal control problems of arbitrary order

引用

ENGINEERING WITH COMPUTERS 2020年第1期36卷 115-125页

作者： Rabiei, K. Parand, K. Shahid Beheshti Univ Dept Comp Sci GC Tehran Iran Shahid Beheshti Univ Dept Cognit Modelling Cognit & Brain Sci Tehran Iran

In this paper, the generalized fractional order of the chebyshev functions (GFCFs) based on the classical chebyshev polynomials of the first kind is used to obtain the solution of optimal control problems governed by inequality constraints. For this purpose positive slack functions are added to inequality conditions and then the operational matrix for the fractional derivative in the Caputo sense, reduces the problems to those of solving a system of algebraic equations. It is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach one. The applicability and validity of the method are shown by numerical results of some examples, moreover a comparison with the existing results shows the preference of this method.

关键词： Optimal control problems Fractional calculus chebyshev functions Operational matrix Convergence analysis

来源：评论

学校读者我要写书评

暂无评论

LIMIT THEOREMS FOR THE LEAST COMMON MULTIPLE OF A RANDOM SET OF INTEGERS

引用

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 2019年第7期372卷 4585-4603页

作者： Alsmeyer, Gerold Kabluchko, Zakhar Marynych, Alexander Univ Munster Inst Math Stochast Dept Math & Comp Sci Orleans Ring 10 D-48149 Munster Germany Taras Shevchenko Natl Univ kyiv Fac Comp Sci & Cybernet UA-01601 Kiev Ukraine

Let L-n be the least common multiple of a random set of integers obtained from {1,..., n} by retaining each element with probability theta epsilon (0, 1) independently of the others. We prove that the process (log L left perpendiculr nt right perpendiculr)(t) epsilon[0,1], after centering and normalization, converges weakly to a certain Gaussian process that is not Brownian motion. Further results include a strong law of large numbers for log L-n as well as Poisson limit theorems in regimes when theta depends on n in an appropriate way.

关键词： Random set of integers least common multiple law of large numbers central limit theorem functional limit theorem Gaussian process von Mangoldt function chebyshev functions

来源：评论

学校读者我要写书评

暂无评论

Calculation of the detonation state of HN3 with quantum accuracy

引用

JOURNAL OF CHEMICAL PHYSICS 2020年第22期153卷 224102页

作者： Cong Huy Pham Lindsey, Rebecca K. Fried, Laurence E. Goldman, Nir Lawrence Livermore Natl Lab Phys & Life Sci Directorate Livermore CA 94550 USA Univ Calif Davis Dept Chem Engn Davis CA 95616 USA

HN3 is a unique liquid energetic material that exhibits ultrafast detonation chemistry and a transition to metallic states during detonation. We combine the chebyshev interaction model for efficient simulation (ChIMES) many-body reactive force field and the extended-Lagrangian multiscale shock technique molecular dynamics method to calculate the detonation properties of HN3 with the accuracy of Kohn-Sham density-functional theory. ChIMES is based on a chebyshev polynomial expansion and can accurately reproduce density-functional theory molecular dynamics (DFT-MD) simulations for a wide range of unreactive and decomposition conditions of liquid HN3. We show that addition of random displacement configurations and the energies of gas-phase equilibrium products in the training set allows ChIMES to efficiently explore the complex potential energy surface. Schemes for selecting force field parameters and the inclusion of stress tensor and energy data in the training set are examined. Structural and dynamical properties and chemistry predictions for the resulting models are benchmarked against DFT-MD. We demonstrate that the inclusion of explicit four-body energy terms is necessary to capture the potential energy surface across a wide range of conditions. Our results generally retain the accuracy of DFT-MD while yielding a high degree of computational efficiency, allowing simulations to approach orders of magnitude larger time and spatial scales. The techniques and recipes for MD model creation we present allow for direct simulation of nanosecond shock compression experiments and calculation of the detonation properties of materials with the accuracy of Kohn-Sham density-functional theory.

关键词： Reactive force field Molecular dynamics Kohn-Sham density functional theory Shock compression chebyshev functions Energetic materials

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：