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Study Hankel Transforms and Properties of bessel function via Entangled State Representation Transformation in Quantum Mechanics

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Communications in Theoretical Physics 2006年第5期45卷 819-824页

作者： FAN Hong-Yi WANG Yong Department of Material Science and Engineering University of Science and Technology of China Hefei 230026 China Department of Physics Shanghai Jiao Tong University Shanghai 200030 China Department of Special Class for Gifted Young University of Science and Technology of China Hefei 230026 China

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.

关键词： entangled state representation Hankel transform bessel function

Measurement of Optical Fiber Geometry Parameters with bessel function Fitting Method

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Journal of Harbin Institute of Technology(New Series) 2021年第2期28卷 74-81页

作者： Yiming Li Huazhong Xiang Jiankun Tu Gang Zheng Minghui Chen Bin Jiang Shanghai Engineering Research Center of Interventional Medical Device Key Laboratory of Ministry of Education for Applied Optical InstrumentsUniversity of Shanghai for Science and TechnologyShanghai 200093China Shanghai Cable Research Institute Shanghai 200093China

Geometry parameters of optical fiber are crucial in evaluating the quality of the optical ***⁃field light distribution method is recommended in GB15972.20-2008 for the measurement of geometry *** distinguish the boundary between fiber core and cladding,it is necessary to illuminate 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 ***,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 *** of the fiber were fitted by elliptical curves,and the geometry parameters of the fibers could be *** show that the maximum deviations of the diameters and the average differences of the fibers were decreased under normal and abnormal conditions *** proposed method is an efficient way to obtain edge data and can improve the accuracy and stability of geometry parameters of optical fibers.

关键词： geometry parameters of optical fiber bessel function edge detect

A Probabilistic Trust Model and Control Algorithm to Protect 6G Networks against Malicious Data Injection Attacks in Edge Computing Environments

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Computer Modeling in Engineering & Sciences 2024年第10期141卷 631-654页

作者： Borja Bordel Sánchez Ramón Alcarria Tomás Robles Department of Computer Systems Universidad Politécnica de MadridMadrid28031Spain Department of Geospatial Engineering Universidad Politécnica de MadridMadrid28031Spain

Future 6G communications are envisioned to enable a large catalogue of pioneering *** will range from networked Cyber-Physical Systems to edge computing devices,establishing real-time feedback control loops critical for managing Industry 5.0 deployments,digital agriculture systems,and essential *** provision of extensive machine-type communications through 6G will render many of these innovative systems autonomous and *** full automation will enhance industrial efficiency significantly,it concurrently introduces new cyber risks and *** particular,unattended systems are highly susceptible to trust issues:malicious nodes and false information can be easily introduced into control ***,Denialof-Service attacks can be executed by inundating the network with valueless *** anomaly detection schemes require the entire transformation of the control software to integrate new steps and can only mitigate anomalies that conform to predefined mathematical *** based on an exhaustive data collection to detect anomalies are precise but extremely *** models,with their limited understanding of mobile networks,can achieve precision rates no higher than 75%.Therefore,more general and transversal protection mechanisms are needed to detect malicious behaviors *** paper introduces a probabilistic trust model and control algorithm designed to address this *** model determines the probability of any node to be *** channels are pruned for those nodes whose probability is below a given *** trust control algorithmcomprises three primary phases,which feed themodel with three different probabilities,which are weighted and ***,anomalous nodes are identified using Gaussian mixture models and clustering ***,traffic patterns are studied using digital bessel functions and the functional scalar ***,the in

关键词： 6G networks noise injection attacks Gaussian mixture model bessel function traffic filter Volterra filter

ON THE ZEROS OF QUOTIENTS OF bessel functionS

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Chinese Annals of Mathematics,Series B 2000年第3期21卷 285-296页

作者： A.FRIEDMAN B.HU J.J.L.VELAZQUEZ DepartmentofMathematics UniversityofMinnesotaMinneapolisMN55455USA. DepartmentofMathematics UniversityofNotreDameNotreDameIN46556USA. DepartamentodeMatematicaAplicada FacultaddeMatematicasUniversidadComplutense28040MadridSpain.

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

Mechanical model of round window membrane under reverse excitation

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Applied Mathematics and Mechanics(English Edition) 2016年第10期37卷 1341-1348页

作者： Yiqiang CHEN Wenjuan YAO Department of Civil Engineering Shanghai University

According to the vibration characteristics of the round window, a mechani- cal model of a round window membrane is established. The Euler equation of the round window and the complementary boundary conditions are derived by the variational prin- ciple. Combined with the bessel function, an analytical solution of the round window displacement is obtained by MATHEMATICA. Combined with clinical characteristics of round window membrane lesion, the effect of sound transmission due to thickening of the round window membrane caused by the otitis media, shrinkage of the round window membrane area caused by otosclerosis, and hardening of the round window membrane itself is analyzed. The results show that with thickening of the round window membrane, the displacement of the round window membrane is decreased. In the meantime, with hardening of the round window membrane and shrinkage of the membrane area, the max- imum displacement Of the round window membrane is gradually reduced, leading to a decrease in sound transmission. Thus, the analyticM analysis can avoid interference of environment and the technical level of personnel, and it can evaluate transmission per- formance of the round window membrane efficiently, providing a theoretical basis for the reverse excitation of artificial prosthesis.

关键词： round window variational principle Euler equation complementary boundary condition bessel function

Oscillation Modes of Weld Pool in Stationary GTA Welding Using Structure Laser Method

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Chinese Journal of Mechanical Engineering 2021年第5期34卷 243-258页

作者： Xingpei Wu Jiankang Huang Jing He Shien Liu Guangyin Liu Ding Fan School of Materials Science and Engineering Lanzhou University of TechnologyLanzhou 730050China Department of Mechanical Energy Engineering Southern University of Science and TechnologyShenzhen 518055China State Key Laboratory of Advanced Processing and Recycling of Non-Ferrous Metals Lanzhou University of TechnologyLanzhou 730050China

Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision ***,the deficiency of simulation software will result in significant capital *** simulations and experiments are performed in this study,and the bessel equation is used to analyze the oscillation mode of a weld *** laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement *** oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser *** show that the simulated laser dot matrix images are consistent with the experiment *** oscillation mode of the weld pool can be recognized based on the laser dot matrix *** study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.

关键词： Weld pool surface GTA welding bessel function Oscillation mode Geometric optics

On the Existence and Stability of a Global Subsonic Flow in a 3D Infinitely Long Cylindrical Nozzle

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 163-190页

作者： Gang XU Huicheng YIN Faculty of Science Jiangsu University Zhenjiang 212013 Jiangsu China Department of Mathematics ＆ IMS Nanjing University Nanjing 210093 China. Department of Mathematics ＆ IMS Nanjing University Nanjing 210093 China.

This paper is concerned with the problem on the global existence and stability of a subsonic flow in an infinitely long cylindrical nozzle for the 3D steady potential flow equation. Such a problem was indicated by Courant-Friedrichs in [8, p. 377]： A flow through a duct should be considered as a cal symmetry and should be determined steady, isentropic, irrotational flow with cylindriby solving the 3D potential flow equations with appropriate boundary conditions. By introducing some suitably weighted HSlder spaces and establishing a priori estimates, the authors prove the global existence and stability of a subsonic potential flow in a 3D nozzle when the state of subsonic flow at negative infinity is given.

关键词： Subsonic flow Potential flow equation bessel function Weighted HSlder space Global existence

Derivative Estima tes of It era ted Spherical Average and Ext ension

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Acta Mathematica Sinica,English Series 2021年第7期37卷 1109-1130页

作者： Meng WANG Jun Yan ZHAO Department of Mathematics Zhejiang UniversityHangzhou 310027P.R.China Department of Mathematics Zhejiang Normal UniversityJinhua 321004P.R.China

In the paper,we study derivative estimates of the iterated spherical averages(At)^(N)(f).We obtain the optimal range of exponents(α,N,p)to ensure the L^(p)boundedness of P(■/■x)(A1)^(N)(f)for 1≤p≤∞,where P is a homogeneous polynomial of degree *** main theorem extends some known *** an application,we obtain the smallest N such that(A1)^(N):L^(p)(R^(n))→L_(α)^(p)(R^(n)).

关键词： H^(p)space spherical mean bessel function H^(p)multiplier wave operator

Time and Space Fractional Schrdinger Equation with Fractional Factor

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Communications in Theoretical Physics 2019年第1期71卷 16-26页

作者： Pei Xiang Yong-Xin Guo Jing-Li Fu Institute of Mathematical Physics Zhejiang Sci-Tech University Key Laboratory of Optical Field Manipulation of Zhejiang Province School of Physics Liaoning University

In this paper, we introduce a new definition of fractional derivative which contains a fractional factor, and its physical meanings are given. When studying the fractional Schrdinger equation(FSE) with this form of fractional derivative, the result shows that under the description of time FSE with fractional factor, the probability of finding a particle in the whole space is still conserved. By using this new definition to construct space FSE, we achieve a continuous transition from standard Schrdinger equation to the fractional one. When applying this form of Schrdinger equation to a particle in an infinite symmetrical square potential well, we find that the probability density distribution loses spatial symmetry and shows a kind of attenuation property. For the situation of a one-dimensional infinite δ potential well,the first derivative of time-independent wave function Φ to space coordinate x can be continuous everywhere when the particle is at some special discrete energy levels, which is much different from the standard Schrdinger equation.

关键词： fractional derivative fractional factor fractional Schr¨odinger equation bessel function