Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau...Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.展开更多
In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma fu...In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].展开更多
A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown.
Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fiel...Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.展开更多
In this paper,the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law(r,q)-distribution functi...In this paper,the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law(r,q)-distribution function.Recent studies have reported the argon-helium plasma and conducted a brief theoretical and experimental survey.To deepen our understanding further,this study aims to analyze the argon-helium plasma comprehensively using the same pattern but with the(r,q)-distribution function.For this purpose,the current balance equations are derived for electron,helium and argon ions,when these charge species attain the quasineutrality condition.We numerically examined the currents of plasma species for a broad range of effective distribution function parameters r and q.It is revealed that the surface potential of dust particles is significantly affected by the parameters r and q,helium ion-to-electron temperature ratio,argon ion-to-electron temperature ratio,and helium ion to argon ion number density ratio.By incorporating the multi-ion(argon-helium)species,the significance of low-temperature nonMaxwellian dusty(complex)plasma is briefly examined.展开更多
A new characterization of Q#p is given, which implies immediately a known result. Also, the authors consider a class Νp of bounded characteristic with order p, 0 < p < ∞, in the unit disk and give some relatio...A new characterization of Q#p is given, which implies immediately a known result. Also, the authors consider a class Νp of bounded characteristic with order p, 0 < p < ∞, in the unit disk and give some relationship between it and other classes of meromorphic functions. This paper answers partly a question mentioned by Aulaskari and Lappan.展开更多
The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several ...The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several special cases have been deducted.展开更多
Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-...Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.展开更多
In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of E...In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.展开更多
The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positi...The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.展开更多
We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators o...We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .展开更多
船舶在自动靠泊过程中会受到风、浪、流和岸壁效应等因素的影响,故需要精确的路径规划方法防止靠泊失败。针对全驱动船舶靠泊过程的基于双深度Q网络(double deep Q network,DDQN)算法,设计了一种船舶自动靠泊路径规划方法。首先建立船...船舶在自动靠泊过程中会受到风、浪、流和岸壁效应等因素的影响,故需要精确的路径规划方法防止靠泊失败。针对全驱动船舶靠泊过程的基于双深度Q网络(double deep Q network,DDQN)算法,设计了一种船舶自动靠泊路径规划方法。首先建立船舶三自由度模型,然后通过将距离、航向、推力、时间和碰撞作为奖励或惩罚,改进奖励函数。随后引入DDQN来学习动作奖励模型,并使用学习结果来操纵船舶运动。通过追求更高的奖励值,船舶可以自行找到最优的靠泊路径。实验结果表明,在不同水流速度下,船舶都可以在完成靠泊的同时减小时间和推力,并且在相同水流速度下,DDQN算法与Q-learning、SARSA(state action reward state action)、深度Q网络(deep Q network,DQN)等算法相比,靠泊过程推力分别减小了241.940、234.614、80.202 N,且时间仅为252.485 s。展开更多
The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown th...The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 40390150 and the International Collaboration Research Team Program of the Chinese Academy of Sciences
文摘Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma （Langmuir） waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized （r, q） distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.
文摘In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].
基金Supported by Beijing Jiaotong University Science Research Foundation (2004SM056)
文摘A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown.
文摘Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.
文摘In this paper,the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law(r,q)-distribution function.Recent studies have reported the argon-helium plasma and conducted a brief theoretical and experimental survey.To deepen our understanding further,this study aims to analyze the argon-helium plasma comprehensively using the same pattern but with the(r,q)-distribution function.For this purpose,the current balance equations are derived for electron,helium and argon ions,when these charge species attain the quasineutrality condition.We numerically examined the currents of plasma species for a broad range of effective distribution function parameters r and q.It is revealed that the surface potential of dust particles is significantly affected by the parameters r and q,helium ion-to-electron temperature ratio,argon ion-to-electron temperature ratio,and helium ion to argon ion number density ratio.By incorporating the multi-ion(argon-helium)species,the significance of low-temperature nonMaxwellian dusty(complex)plasma is briefly examined.
基金This research is supported in part by the National Natural Science Foundation of China (10371069) the NSF of Guangdong Province of China (010446).
文摘A new characterization of Q#p is given, which implies immediately a known result. Also, the authors consider a class Νp of bounded characteristic with order p, 0 < p < ∞, in the unit disk and give some relationship between it and other classes of meromorphic functions. This paper answers partly a question mentioned by Aulaskari and Lappan.
文摘The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several special cases have been deducted.
基金Supported by the National Natural Science Foundation of China(11871191)the Science Foundation of Hebei Province(A2023205006,A2019106037)+2 种基金the Key Development Foundation of Hebei Normal University in2024(L2024ZD08)the Graduate Student Innovation Project Fund of Hebei Province(CXZZBS2022066)the Key Foundation of Hebei Normal University(L2018Z01)。
文摘Firstly,some properties for(p,q)-monogenic functions withα-weight in Clifford analysis are given.Then,the Cauchy-Pompeiu formula is proved.Finally,the Cauchy integral formula and the Cauchy integral theorem for(p,q)-monogenic functions withα-weight are given.
基金Supported by the Program of Fujian Province-HongKong
文摘In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf（x, u, Du）dx, （1） where Ω is an open subset of Euclidean N-space （N ≥ 3）, u：Ω → R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition ｜Du｜^p＊ ｜u｜^p＊-a（x） ≤ f（x,u,Du） ≤ L（｜Du｜^p＋｜u｜^p＊ ＋ a（x））, （2） where L≥1, 1pN,p^＊ = Np/N-p , and a（x） is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of （1）. Our method is to compare the ω-minima of （1） with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal.
文摘The main aim of this paper is to define and study of a new Horn’s matrix function, say, the p and q-Horn’s matrix function of two complex variables. The radius of regularity on this function is given when the positive integers p and q are greater than one, an integral representation of pHq 2 is obtained, recurrence relations are established. Finally, we obtain a higher order partial differential equation satisfied by the p and q-Horn’s matrix function.
文摘We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .
文摘The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).
