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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)

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Advances in Pure Mathematics 2024年第9期14卷 768-777页

作者： Jorge Olivares Pablo Martín Maria T. Veliz Departamento de Matemticas Universidad de Antofagasta Antofagasta Chile Departamento de Fsica Universidad de Antofagasta Antofagasta Chile

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.

关键词： bessel functions Power Series Asymptotic Expansion MPQA Technique

Some Representations of Unified Voigt functions

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Acta Mathematica Sinica,English Series 2005年第4期21卷 865-868页

作者： M.KAMARUJJAMA DineshSINGH Department of Applied Mathematics Z.H.College of Engg.and Tech.Aligarh Muslim UniversityAligarh-202002India

The authors derive a set of unified representations of the Voigt functions in terms of familiar special functions of Mathematical Physics. Some deductions from these representations are also considered.

关键词： Voigt functions bessel functions Confluent hypergeometric function Laguerre and Hermite polynomials

Scattering of an unpolarized bessel beam by spheres

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Chinese Optics Letters 2010年第12期8卷 1195-1198页

作者：马秀波李恩邦 College of Precision Instrument and Optoelectronics Engineering Tianjin University

The scattering process of an unpolarized bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the bessel beam.

关键词： bessel functions Laser beams Optical waveguides Spheres

Boundedness of Iterated Spherical Average on α-Modulation Spaces

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Chinese Annals of Mathematics,Series B 2021年第5期42卷 721-736页

作者： Qiang HUANG Xiaomei WU Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina College of Data Science Jiaxing UniversityJiaxing 314001ZhejiangChina

For the iteration of spherical average(A_(1))^(N)and the Laplace operator△,we consider the boundedness of the operator△(A_(1))^(N) on theα-modulation spaces M^(s,α)_(p,q).The authors obtain some sufficient and necessary conditions to ensure the boundedness on theα-modulation *** main theorems significantly improve some known results.

关键词： Spherical average α-Modulation spaces bessel functions

Detailing Losses in the M/M/1/1 Transient Loss System

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Acta Mathematicae Applicatae Sinica 2018年第2期34卷 373-385页

作者： Pierpaolo FERRANTE National Workers Compensation Authority (INAIL) Department of Occupational and Environmental Medicine Epidemiology and Hygiene (DiMEILA)

This paper is aimed at investigating the transient losses in the M/M/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval [0, t） and provide two alternative representations： one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.

关键词： transient losses transient loss rate Erlang bessel functions

On the cutoff law of laser induced high harmonic spectra

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Frontiers of physics 2015年第2期10卷 91-96页

作者： Dong-Sheng Guo Chao Yu Jingtao Zhang Ju Gao Zhi-Wei Sun Zhenrong Sun State Key Laboratory of Precision Spectroscopy Department of Physics East China Normal University Shanghai 200062 China School of Physics Peking University Beijing 100871 China State Key Laboratory of High-field Laser Physics Shanghai Institute of Optical and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 China jingpin Opto-Electronic Co. Jiangsu FOHO Science Park Fenhu Town Wujiang 215211 China Key Laboratory of Microgravity Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy Up and the atomic biding energy Ip, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 4√2 ≈ 3.34 and 2√2-1≈1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.

关键词： high harmonic generation cutoff law strong laser physics nonperturbative quantumelectrodynamics bessel functions Einstein photoelectric effect.

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

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Chinese Optics Letters 2006年第10期4卷 559-562页

作者：张逸新王高刚 School of Science Southern Yangtze UniversityWuxi 214036 School of Communication and Control Engineering Southern Yangtze UniversityWuxi 214036

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function, and Gaussian approximation for the product of Gaussian function and bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.

关键词： Atmospheric turbulence bessel functions Coherent light Polynomials Refractive index

Double sinusoidal phase modulating laser diode interferometer for thickness measurements of transparent plates

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Chinese Optics Letters 2004年第6期2卷 328-330页

作者：李代林王向朝刘英明 Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 double sinusoidal phase modulating (SPM) laser diode interferometer for thickness measurements of a transparent plate is presented. A carrier signal is given to the interference signal by using a piezoelectric transducer and the SPM interferometry is applied to measure the thickness of a transparent plate. By combining the double-modulation technique with the Bessel function ratio method the measurement error originating from Sight intensity fluctuations caused by the modulation current can be decreased greatly. The thicknesses of a glass parallel plate and a quartz glass are measured in real time and the corresponding experimental results are also given.

A double sinusoidal phase modulating (SPM) laser diode interferometer for thickness measurements of a transparent plate is presented. A carrier signal is given to the interference signal by using a piezoelectric transducer, and the SPM interferometry is applied to measure the thickness of a transparent plate. By combining the double-modulation technique with the bessel function ratio method, the measurement error originating from Sight intensity fluctuations caused by the modulation current can be decreased greatly. The thicknesses of a glass parallel plate and a quartz glass are measured in real time, and the corresponding experimental results are also given.

关键词： bessel functions Measurement errors Phase modulation Piezoelectric transducers Quartz Semiconductor lasers Thickness measurement

Numerical analysis of non-isothermal viscous jet with peripheral heat transfer

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International Journal of Modeling, Simulation, and Scientific Computing 2016年第3期7卷 50-73页

作者： Sulagna Chatterjee Trisha Sen Anindya Mitra Department of Chemical Engineering Heritage Institute of Technology Kolkata 700107India Department of Chemical Engineering IIT Bombay Mumbai 400076India Department of Chemical Engineering University of Waterloo ON N2L 3G1 Canada

A fluid jet ejected from micron size nozzle is a commonly occurring phenomenon in biomedical engineering,printing technology and micro-fluidic *** of a jet into drops occurs due to disturbances induced by external *** work explores the various sources of perturbation and their effect on jet disintegration through numerical simulation of a two-dimensional non-isothermal *** mathematical approach uses a novel technique to combine analytical solutions for the energy balance equation in the radial direction to solve the complete two dimensional *** two dimensional energy balance equation is simultaneously solved together with the axi-symmetric Navier–Stokes equations using the slender-jet approximation to predict jet *** energy balance takes into account of peripheral heat transfer to the environment through analytical expressions derived from radial *** model helps in understanding the factors in dynamic temperature variations that eventually render the jet *** distinguishing aspect of this work is the analysis of the effect of a periodic thermal perturbation applied at any point in the domain of a progressive jet,a situation typically encountered in thermal inkjet printers and not considered *** presented for non-isothermal jets which are both stationary and moving illustrate the effect of jet velocity in propagation of perturbation and subsequent drop *** major contribution of this numerical study is that it provides an insight on novel ways of controlling droplet formation in bubble jet *** study demonstrates that thermal disturbance propagating from periodic heating can be manipulated to shape the droplets and control their breakage point along the jet.

关键词： Nonlinear viscous microjets bessel functions heat transfer Navier-Stokes slender jet approximation