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Stable computations of the spherically layered media theory with high lossy media by using scaled Bessel functions 认领 引用
1
作者 Jia-Hui Wang Bo O.Zhu 《Journal of Electronic Science and Technology》 EI CAS CSCD 2025年第1期22-34,共13页
The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer fro... The spherically layered media theory has wide applications for electromagnetic wave scattering analysis.Due to the involved Bessel functions,the conventional formulations of spherically layered media theory suffer from numerical overflow or underflow when the Bessel function’s order is large,the argument is small or the argument has a large imaginary part.The first two issues have been solved recently by employing small-argument asymptotic formulas of Bessel functions,while the third issue remains unsolved.In this paper,the Bessel functions in the conventional formulation of the theory are replaced by scaled Bessel functions which have good numerical properties for high loss media,and stable formulas are derived.Numerical tests show that this approach can work properly with very high lossy media.Also,this approach can be seamlessly combined with the stable computation method for cases of small argument and large order of Bessel functions. 展开更多
关键词 Lossy media Numerical stability Scaled Bessel function Spherically layered media theory
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THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS 认领 引用 被引量：4
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作者 汤获 Erhan DENIZ 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1707-1719,共13页
In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel function... In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out. 展开更多
关键词 differential subordination univalent functions Hadamard product admissible functions generalized Bessel functions
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Study Hankel Transforms and Properties of Bessel Function via Entangled State Representation Transformation in Quantum Mechanics 认领 引用 被引量：1
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作者 FAN Hong-Yi WANG Yong 《Communications in Theoretical Physics》 SCIE CAS 2006年第5期819-824,共6页
In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum varia... In Phys. Lett. A 313 （2003） 343 we have found that the self-recipràcal Hankel transformation （HT） is embodied in quantum mechanics by a transform between two entangled state representations of continuum variables. In this work we study Hankel transforms and properties of Bessel function via entangled state representations＇ transformation in quantum mechanics. 展开更多
关键词 entangled state representation Hankel transform Bessel function
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SIMPLIFICATION OF FREQUENCY EQUATION OF MULTILAYERED CYLINDERS AND SOME RECURSION FORMULAE OF BESSEL FUNCTIONS 认领 引用
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作者 尹晓春 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期332-337,共6页
In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of... In this paper the axially symmetric, radial vibration frequency equation of multilayered cylinders made of the same materials in plain strain state is studied. It is proved in this paper that the frequency equation of:several contact hallow cylinders can be replaced by the frequency equation of a single hollow cylinder, so that the solving process is greatly simplified. Some recursion formulae of Bessel functions are derived from such practical problems as well. 展开更多
关键词 frequency vibration Bessel functions
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Measurement of Optical Fiber Geometry Parameters with Bessel Function Fitting Method 认领 引用 被引量：1
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作者 Yiming Li Huazhong Xiang +3 位作者 Jiankun Tu Gang Zheng Minghui Chen Bin Jiang 《Journal of Harbin Institute of Technology(New Series)》 CAS 2021年第2期74-81,共8页
Geometry parameters of optical fiber are crucial in evaluating the quality of the optical fiber.Near⁃field light distribution method is recommended in GB15972.20-2008 for the measurement of geometry parameters.To dist... Geometry parameters of optical fiber are crucial in evaluating the quality of the optical fiber.Near⁃field light distribution method is recommended in GB15972.20-2008 for the measurement of geometry parameters.To distinguish the boundary between fiber core and cladding,it is necessary to illuminate the fiber.The end face of the core is a bright spot with unclear edge,so the true edge of the core and the cladding cannot be accurately judged.A method is proposed in this paper to measure the geometry parameters of optical fiber by Bessel function fitting.Theoretically,the solution to the electromagnetic vector of mode field satisfies Bessel function,and the boundary between the core and the cladding can be precisely extracted by Bessel function fitting.Edges of the fiber were fitted by elliptical curves,and the geometry parameters of the fibers could be calculated.Results show that the maximum deviations of the diameters and the average differences of the fibers were decreased under normal and abnormal conditions respectively.The proposed method is an efficient way to obtain edge data and can improve the accuracy and stability of geometry parameters of optical fibers. 展开更多
关键词 geometry parameters of optical fiber Bessel function edge detect
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Determinantal Expressions and Recursive Relations for the Bessel Zeta Function and for a Sequence Originating from a Series Expansion of the Power of Modified Bessel Function of the First Kind 认领 引用
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作者 Yan Hong Bai-Ni Guo Feng Qi 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第10期409-423,共15页
In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expre... In the paper,by virtue of a general formula for any derivative of the ratio of two differentiable functions,with the aid of a recursive property of the Hessenberg determinants,the authors establish determinantal expressions and recursive relations for the Bessel zeta function and for a sequence originating from a series expansion of the power of modified Bessel function of the first kind. 展开更多
关键词 Determinantal representation recursive relation series expansion first kind modified Bessel function Bessel zeta function Pochhammer symbol gamma function Hessenberg determinant
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CHEBYSHEV APPROXIMATION OF THE SECOND KIND OF MODIFIED BESSEL FUNCTION OF ORDER ZERO 认领 引用
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作者 张璟 周哲玮 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第5期483-487,共5页
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational... The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis. 展开更多
关键词 second kind of modified Bessel function of order zero exponential transformation rational Chebyshev basis
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Duality between Bessel Functions and Chebyshev Polynomials in Expansions of Functions 认领 引用
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2023年第8期504-536,共33页
In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo... In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found. 展开更多
关键词 Spherical Bessel Functions Chebyshev Polynomials Legendre Polynomials Hermite Polynomials Derivatives of Delta Functions Normally and Anti-Normally Ordered Operators
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A General Analytic Approximation Technique for the Modified Bessel Functions with Fractional Order Iv (x), Applied to I1/6(x) and I1/7(x) 认领 引用
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作者 Jorge Olivares Pablo Martín Maria T. Veliz 《Advances in Pure Mathematics》 2024年第9期768-777,共10页
A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to th... A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones. 展开更多
关键词 Bessel Functions Power Series Asymptotic Expansion MPQA Technique
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An integral estimate of Bessel function and its application 认领 引用 被引量：3
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作者 DING Yong LI Ran 《Science China Mathematics》 2008年第5期897-906,共10页
In this paper the authors give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz ... In this paper the authors give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz integral μ Ω ρ with variable kernels is of type (2, 2), where the kernel function Θ does not have any smoothness on the unit sphere in ? n . 展开更多
关键词 Bessel function Marcinkiewicz integral variable kernel 42B30 42B99
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Error Bounds for Uniform Asymptotic Expansions-Modified Bessel Function of Purely Imaginary Order 认领 引用
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作者 Wei SHI Roderick WONG 《Chinese Annals of Mathematics,Series B》 SCIE 2010年第5期759-780,共22页
The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms... The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived. 展开更多
关键词 Modified Bessel function of purely imaginary order Airy function Uniform asymptotic expansion Error bound
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ON THE ZEROS OF QUOTIENTS OF BESSEL FUNCTIONS 认领 引用
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作者 A.FRIEDMAN B.HU J.J.L.VELAZQUEZ 《Chinese Annals of Mathematics,Series B》 SCIE 2000年第3期285-296,共12页
The paper studies the zeros of 2mIm/Im-1- (m+1)I1 /I0, where Im are the Bessel functions.
关键词 Zeros Quotient Bessel function
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Elastodynamic Infinite Elements with Modified Bessel Shape Functions for Dynamic Soil-Structure Interaction 认领 引用
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作者 Konstantin Savkov Kazakov 《Journal of Mechanics Engineering and Automation》 2011年第1期38-43,共6页
The paper is devoted to formulations of decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions. These elements are appropriate for Soil-Structure Interaction （SSI） problems, solve... The paper is devoted to formulations of decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions. These elements are appropriate for Soil-Structure Interaction （SSI） problems, solved in time or frequency domain and can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions （EIEUSF） infinite elements. The formulation of 2D Horizontal type Infinite Elements （HIE） is demonstrated here, but by similar techniques 2D Vertical （VIE） and 2D Comer （CIE） Infinite Elements can also be formulated. Using elastodynamic infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary （the line between finite and infinite elements） is discussed as well and the application of the proposed elastodynamic infinite elements in the Finite Element Method （FEM） is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements. 展开更多
关键词 Soil-structure interaction （SSI） wave propagation infinite elements finite element method （FEM） bessel functions.
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Some Generalized q-Bessel Type Wavelets and Associated Transforms 认领 引用
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作者 Imen Rezgui Anouar Ben Mabrouk 《Analysis in Theory and Applications》 CSCD 2018年第1期57-76,共20页
In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = ... In this paper wavelet functions are introduced in the context of q-theory. We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets. Starting from the （q,v）-extension （v = （α,β）） of the q-case, associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context. Reconstruction and Placherel type formulas are proved. 展开更多
关键词 Wavelets Besel function q-Bessel function modified Bessel functions generalizedq-Bessel functions q-Bessel wavelets.
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OAM-radar imaging:A review 认领 引用
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作者 Rui Li Liulin Li +1 位作者 Hongping Zhou Zhongyi Guo 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2026年第7期75-92,共18页
Due to the spiral phase wavefront of vortex electromagnetic waves(VEMW),there will exist the orbital angular momentum(OAM)in the VEMW,which supplies additional spatial dimensional for the information process.In radar ... Due to the spiral phase wavefront of vortex electromagnetic waves(VEMW),there will exist the orbital angular momentum(OAM)in the VEMW,which supplies additional spatial dimensional for the information process.In radar imaging,when the VEMW is used to illuminate targets,it can be regarded as the superposition of multiple plane waves incident on targets from various angles simultaneously.The target within the beam is radiated by electromagnetic(EM)fields with different phase information.These differences make the scattered echoes contain more target information.Providing a feasible technical path to improve the traditional radar imaging technology.This paper introduces the challenges faced by traditional radar imaging and the advantages of EM vortex wave imaging.It briefly derives the principles of vortex radar imaging and azimuthal resolution based on circular array antennas.Then,it reviews the development history and research status of vortex radar imaging technology,which divides into six research directions:vortex radar imaging model,Bessel function modulation,vortex radar gazing algorithm,EM vortex synthetic aperture radar(SAR)/inverse synthetic aperture radar(ISAR)imaging,vortex radar 3D imaging,and vortex radar forward imaging.Finally,the future development trends of vortex radar imaging technology are outlined and discussed. 展开更多
关键词 Vortex electromagnetic waves (VEMW) Orbital angular momentum (OAM) Vortex radar imaging Bessel function modulation
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The Jackson Inequality for the Best L^2-Approximation of Functions on[0,1]with the Weight x 认领 引用 被引量：2
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作者 Jian Li Yongping Liu 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE EI 2008年第3期340-356,共17页
Let L^2([0,1],x)be the space of the real valued,measurable,square summable functions on[0,1]with weight x,and let n be the subspace of L2([0,1],x)defined by a linear combination of Jo(μkX),where Jo is the Bessel func... Let L^2([0,1],x)be the space of the real valued,measurable,square summable functions on[0,1]with weight x,and let n be the subspace of L2([0,1],x)defined by a linear combination of Jo(μkX),where Jo is the Bessel function of order 0 and{μk}is the strictly increasing sequence of all positive zeros of Jo.For f∈L^2([0,1],x),let E(f,n)be the error of the best L2([0,1],x),i.e.,approximation of f by elements of n.The shift operator off at point x∈[0,1]with step t∈[0,1]is defined by T(t)f(x)=1/π∫0^πf(√x^2+t^2-2xtcosO)dθThe differences(I-T(t))^r/2f=∑j=0^∞(-1)^j(j^r/2)T^j(t)f of order r∈(0,∞)and the L^2([0,1],x)-modulus of continuityωr(f,τ)=sup{||(I-T(t))^r/2f||:0≤t≤τ]of order r are defined in the standard way,where T^0(t)=I is the identity operator.In this paper,we establish the sharp Jackson inequality between E(f,n)andωr(f,τ)for some cases of r andτ.More precisely,we will find the smallest constant n(τ,r)which depends only on n,r,and%such that the inequality E(f,n)≤n(τ,r)ωr(f,τ)is valid. 展开更多
关键词 Jackson inequality modulus of continuity best approximation Bessel function.
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浸没型点吸收式波浪能发电装置的辐射波特征研究 认领 引用
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作者 吴金明 李恒瑞 +3 位作者 王军 倪玺杰 杨浩杰 Peter D.Lund 《太阳能学报》 EI CAS CSCD 北大核心 2026年第4期495-503,共9页
为揭示浸没型点吸收式波浪能发电装置在自由表面所产生波浪的特征,以作规则垂荡运动的浸没圆柱浮体的辐射波特征为研究对象,采用特征函数展开法求解垂荡圆柱的辐射波速度势,研究浮体的形状、位置、运动参数及水深对辐射波特征的影响规... 为揭示浸没型点吸收式波浪能发电装置在自由表面所产生波浪的特征,以作规则垂荡运动的浸没圆柱浮体的辐射波特征为研究对象,采用特征函数展开法求解垂荡圆柱的辐射波速度势,研究浮体的形状、位置、运动参数及水深对辐射波特征的影响规律。结果表明:作垂荡运动的浸没圆柱浮体在自由表面形成沿浮体中心轴对称的环状辐射波;其波幅在浮体正上方达到最大,并沿远离浮体的方向逐渐衰减;随着浮体上表面与自由表面距离的减小,辐射波波幅的最大值提高,但沿远离浮体方向衰减的速率亦增大;相比于增大浮体半径可使辐射波波幅显著提高,增大浮体高度和水深并未明显提高辐射波波幅;随着浮体垂荡周期的增大,辐射波波幅下降;辐射波相对于浮体位移的相位差主要取决于与浮体的无量纲距离,而不受浮体形状、位置及运动参数和水深的显著影响。 展开更多
关键词 波浪能发电 波浪能 波浪交互 特征函数展开法 势流 贝塞尔函数
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柱坐标系下二维非稳态对流扩散方程的求解及验证 认领 引用
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作者 张同旺 刘马林 李炳达 《广州化工》 CAS 2026年第14期39-41,67,共3页
基于轴对称假设,将柱坐标系中的三维对流扩散方程简化为二维对流扩散方程,无因次化后、关于时间项进行Laplace变换,应用分离变量法,示踪剂浓度函数可化为径向函数和轴向函数的乘积。径向函数可表示为以贝塞尔函数为基函数的广义傅里叶... 基于轴对称假设,将柱坐标系中的三维对流扩散方程简化为二维对流扩散方程,无因次化后、关于时间项进行Laplace变换,应用分离变量法,示踪剂浓度函数可化为径向函数和轴向函数的乘积。径向函数可表示为以贝塞尔函数为基函数的广义傅里叶展开式。逆Laplace变换后,轴向函数可表示为入口函数与传递函数的卷积,得到了二维对流扩散方程的解析解。将时间脉冲函数应用于前述解析解,得到了时间脉冲时空间的示踪剂浓度分布,计算了示踪剂在系统内的累积量、轴向截面流出量,表明解满足质量守恒。 展开更多
关键词 柱坐标 对流扩散方程 解析解 贝塞尔函数 质量守恒
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Bessel函数测距模型的RSSI测距方法 认领 引用 被引量：5
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作者 姜媛媛 余泳 +1 位作者 时美乐 刘延彬 《传感技术学报》 CAS CSCD 北大核心 2020年第2期279-285,共7页
针对现有RSSI测距方法中,影响测距精度的RSSI测量值难以准确估计和RSSI值与距离对应衰减关系不明确的问题,给出一种基于Bessel函数测距模型的RSSI测距方法。首先对RSSI原始测量数据进行异常值剔除,滤波和凸优化提取趋势项的预处理,然后... 针对现有RSSI测距方法中,影响测距精度的RSSI测量值难以准确估计和RSSI值与距离对应衰减关系不明确的问题,给出一种基于Bessel函数测距模型的RSSI测距方法。首先对RSSI原始测量数据进行异常值剔除,滤波和凸优化提取趋势项的预处理,然后建立基于Bessel函数的测距模型,基于预处理所得光滑数据,利用最小二乘法辨识测距模型中未知参数,从而得到具体测距模型表达式。基于实测数据对所提方法进行实验验证,与Shadowing模型、分段函数测距模型对比,结果表明,Bessel函数测距模型的RSSI误差均值在1.8dBm范围以内,能更有效反映RSSI值衰减关系,提高了测距精度且计算开销不大。 展开更多
关键词 RSSI测距 Bessel函数测距模型 凸优化 曲线拟合
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基于Bessel函数的两电平逆变器TCPWM输出频谱特性分析 认领 引用 被引量：5
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作者 洪欣雨 朱长青 +2 位作者 安树 廖梓柔 赵友诚 《智慧电力》 北大核心 2021年第9期95-102,共8页
提出了基于第一类整数型线性相关Bessel函数解的三角复合函数单边无穷级数表示方法。首先阐述了传统谐波理论分析原理与局限性;随后基于广义二项式定理给出高次初等三角函数Maclaurin展开式,利用Bessel等效幂函数特点对复合函数进行等... 提出了基于第一类整数型线性相关Bessel函数解的三角复合函数单边无穷级数表示方法。首先阐述了传统谐波理论分析原理与局限性;随后基于广义二项式定理给出高次初等三角函数Maclaurin展开式,利用Bessel等效幂函数特点对复合函数进行等价变化,得出输出谐波的简化表达式;最后分析比较了单相半桥与三相两电平逆变器在TCPWM方式下的输出频谱特性,并使用Matlab进行仿真,在验证了理论正确性的同时,填补了PWM逆变电路输出特性分析领域理论支撑的空白。 展开更多
关键词 Bessel函数 二项式定量 TCPWM 两电平逆变器 谐波 频谱特性
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