By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conser...By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed展开更多
Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves t...Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.展开更多
The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbe...The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.展开更多
The evaluation of Gaussian functional integrals is essential on the application to statistical physics and the general calculation of path integrals of stochastic processes. In this work, we present an elementary exte...The evaluation of Gaussian functional integrals is essential on the application to statistical physics and the general calculation of path integrals of stochastic processes. In this work, we present an elementary extension of an usual result of the literature as well as an alternative new derivation.展开更多
In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order sol...In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a Gaussian beam. However, because of the difficulty in formulating the couple scattering field, it is almost impossible to find an analytical solution for the second-order scattered field if the shapes of 2D targets are not canonical geometries. In order to overcome this problem, in this paper, the second-order solution is derived by using the technique based on the reciprocity theorem and the equivalence principle. Meanwhile, the relation between the secondary scattered field from target #1 and target #2 is obtained. Specifically, the bi- and mono-static scattering of Gaussian beam by two parallel adjacent inhomogeneous plasma-coated conducting circular cylinders is calculated and the dependence of attenuation of the scattering width on the thickness of the coated layer, electron number density, collision frequency and radar frequency is discussed in detail.展开更多
Suppose that E and F are separable Banach spaces, X and Y are independent symmetric E and F-valued random vectors respectively. This paper is devoted to the study of the central limit theorem for X Y in the injective...Suppose that E and F are separable Banach spaces, X and Y are independent symmetric E and F-valued random vectors respectively. This paper is devoted to the study of the central limit theorem for X Y in the injective and projective tensor product spaces E F and E F. Special attention is paid to l2 l2. In addition, two counter-examples are given.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10572076)
文摘By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed
文摘Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.
基金Supported by the National Natural Science Foundation of China(12171335,12301603)the Science Development Project of Sichuan University(2020SCUNL201)the Scientific Foundation of Nanjing University of Posts and Telecommunications(NY221026)。
文摘The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.
文摘The evaluation of Gaussian functional integrals is essential on the application to statistical physics and the general calculation of path integrals of stochastic processes. In this work, we present an elementary extension of an usual result of the literature as well as an alternative new derivation.
基金Project supported by the National Natural Science Foundation of China （Grant No 60571058）, the National Defense Foundation of China and Graduate Innovation Fund, Xidian University.
文摘In this paper based on the equivalence principle and the reciprocity theorem, the scattered field up to second-order by two parallel 2D targets arbitrarily located in a Gaussian beam is considered. The first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a Gaussian beam. However, because of the difficulty in formulating the couple scattering field, it is almost impossible to find an analytical solution for the second-order scattered field if the shapes of 2D targets are not canonical geometries. In order to overcome this problem, in this paper, the second-order solution is derived by using the technique based on the reciprocity theorem and the equivalence principle. Meanwhile, the relation between the secondary scattered field from target #1 and target #2 is obtained. Specifically, the bi- and mono-static scattering of Gaussian beam by two parallel adjacent inhomogeneous plasma-coated conducting circular cylinders is calculated and the dependence of attenuation of the scattering width on the thickness of the coated layer, electron number density, collision frequency and radar frequency is discussed in detail.
文摘Suppose that E and F are separable Banach spaces, X and Y are independent symmetric E and F-valued random vectors respectively. This paper is devoted to the study of the central limit theorem for X Y in the injective and projective tensor product spaces E F and E F. Special attention is paid to l2 l2. In addition, two counter-examples are given.
