In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the correspon...This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).展开更多
This paper presents an improved BP algorithm. The approach can reduce the amount of computation by using the logarithmic objective function. The learning rate μ(k) per iteration is determined by dynamic o...This paper presents an improved BP algorithm. The approach can reduce the amount of computation by using the logarithmic objective function. The learning rate μ(k) per iteration is determined by dynamic optimization method to accelerate the convergence rate. Since the determination of the learning rate in the proposed BP algorithm only uses the obtained first order derivatives in standard BP algorithm(SBP), the scale of computational and storage burden is like that of SBP algorithm,and the convergence rate is remarkably accelerated. Computer simulations demonstrate the effectiveness of the proposed algorithm展开更多
It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique...It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is continuous in a domain , where is Hausdorff space and connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is fixed and is stable;for what in this case, the inverse problem turns out to be well-posed.展开更多
We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly de...We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.展开更多
In this paper,based on coupled network generated by chaotic logarithmic map,a novel algorithm for constructing hash functions is proposed,which can transform messages and can establish a mapping from the transformed m...In this paper,based on coupled network generated by chaotic logarithmic map,a novel algorithm for constructing hash functions is proposed,which can transform messages and can establish a mapping from the transformed messages to the coupled matrix of the network.The network model is carefully designed to ensure the network dynamics to be chaotic.Through the chaotic iterations of the network,quantization and exclusive-or (XOR) operations,the algorithm can construct hash value with arbitrary length.It is shown by simulations that the algorithm is extremely sensitive to the initial values and the coupled matrix of the network,and has excellent performance in one-way,confusion and diffusion,and collision resistance.展开更多
Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we est...Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).展开更多
Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + ...Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.展开更多
A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the pote...A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the potential fairness issue that may arise from the maximum sum-rate based objective function and the optical power constraints are set considering the non-negativity of the transmit signal, the requirement of the human eyes safety and all users' quality of service(Qo S). Then, the SSA is utilized to solve this optimization problem. Moreover, to demonstrate the superiority of the proposed strategy, it is compared with the fixed power allocation(FPA) and the gain ratio power allocation(GRPA) schemes. Results show that regardless of the number of users considered, the sum-rate achieved by SSA consistently outperforms that of FPA and GRPA schemes. Specifically, compared to FPA and GRPA schemes, the sum-rate obtained by SSA is increased by 40.45% and 53.44% when the number of users is 7, respectively. The proposed SSA also has better performance in terms of user fairness. This work will benefit the design and development of the NOMA-visible light communication(VLC) systems.展开更多
针对时频谱模型估计语音不准确的问题,文中提出采用模型变换的方式来获得噪声和语音的对数概率密度函数,同时借助带噪语音、干净语音和噪声之间的对数关系并结合最小均方误差(Minimum Mean Square Error,MMSE)估计理论推导出估计语音对...针对时频谱模型估计语音不准确的问题,文中提出采用模型变换的方式来获得噪声和语音的对数概率密度函数,同时借助带噪语音、干净语音和噪声之间的对数关系并结合最小均方误差(Minimum Mean Square Error,MMSE)估计理论推导出估计语音对数谱的时频掩模。基于语音和噪声的对数概率分布推导出了一种软掩模,该软掩模可对带噪语音的对数子带进行加权以降低噪声,提高语音估计的准确性。仿真结果表明,与未处理的含噪语音相比,所提方法在噪声抑制方面具有3 dB以上的提升,基于最小均方误差的时频掩模和软掩模在听觉感知方面的平均提升量分别为27.7%和29.4%,在可懂度方面的平均提升量分别为12.7%和14.3%。展开更多
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
文摘This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).
文摘This paper presents an improved BP algorithm. The approach can reduce the amount of computation by using the logarithmic objective function. The learning rate μ(k) per iteration is determined by dynamic optimization method to accelerate the convergence rate. Since the determination of the learning rate in the proposed BP algorithm only uses the obtained first order derivatives in standard BP algorithm(SBP), the scale of computational and storage burden is like that of SBP algorithm,and the convergence rate is remarkably accelerated. Computer simulations demonstrate the effectiveness of the proposed algorithm
文摘It poses the inverse problem that consists in finding the logarithm of a function. It shows that when the function is holomorphic in a simply connected domain , the solution at the inverse problem exists and is unique if a branch of the logarithm is fixed. In addition, it’s demonstrated that when the function is continuous in a domain , where is Hausdorff space and connected by paths. The solution of the problem exists and is unique if a branch of the logarithm is fixed and is stable;for what in this case, the inverse problem turns out to be well-posed.
基金supported by the Faculty Research Project grant of DTU(DTU/Council/BOM-AC/Notification-/31/2018/5738)Research Fellowship from the Department of Science and Technology,New Delhi(IF170272)。
文摘We introduce a primitive class of analytic functions, by specializing in many wellknown classes, classify Ma-Minda functions based on its conditions and their interesting geometrical aspects. Further, study a newly defined subclass of starlike functions involving a special type of Ma-Minda function introduced here for obtaining inclusion and radius results. We also establish some majorization, Bloch function norms, and other related problems for the same class.
基金supported by the Program for New Century Excellent Talents in University of China(No.NCET-06-0510)National Natural Science Founda-tion of China(No. 60874091)Six Projects Sponsoring Talent Summits of Jiangsu Province(No. SJ209006)
文摘In this paper,based on coupled network generated by chaotic logarithmic map,a novel algorithm for constructing hash functions is proposed,which can transform messages and can establish a mapping from the transformed messages to the coupled matrix of the network.The network model is carefully designed to ensure the network dynamics to be chaotic.Through the chaotic iterations of the network,quantization and exclusive-or (XOR) operations,the algorithm can construct hash value with arbitrary length.It is shown by simulations that the algorithm is extremely sensitive to the initial values and the coupled matrix of the network,and has excellent performance in one-way,confusion and diffusion,and collision resistance.
基金Research supported by National Natural Science Foundation of China.
文摘Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).
文摘Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.
基金supported by the Cooperative Research Project between China Coal Energy Research Institute Co.,Ltd. and Xidian University (No.N-KY-HX-1101-202302-00725)the Key Research and Development Program of Shaanxi Province (No.2017ZDCXL-GY-06-02)。
文摘A non-orthogonal multiple access(NOMA) power allocation scheme on the basis of the sparrow search algorithm(SSA) is proposed in this work. Specifically, the logarithmic utility function is utilized to address the potential fairness issue that may arise from the maximum sum-rate based objective function and the optical power constraints are set considering the non-negativity of the transmit signal, the requirement of the human eyes safety and all users' quality of service(Qo S). Then, the SSA is utilized to solve this optimization problem. Moreover, to demonstrate the superiority of the proposed strategy, it is compared with the fixed power allocation(FPA) and the gain ratio power allocation(GRPA) schemes. Results show that regardless of the number of users considered, the sum-rate achieved by SSA consistently outperforms that of FPA and GRPA schemes. Specifically, compared to FPA and GRPA schemes, the sum-rate obtained by SSA is increased by 40.45% and 53.44% when the number of users is 7, respectively. The proposed SSA also has better performance in terms of user fairness. This work will benefit the design and development of the NOMA-visible light communication(VLC) systems.
文摘针对时频谱模型估计语音不准确的问题,文中提出采用模型变换的方式来获得噪声和语音的对数概率密度函数,同时借助带噪语音、干净语音和噪声之间的对数关系并结合最小均方误差(Minimum Mean Square Error,MMSE)估计理论推导出估计语音对数谱的时频掩模。基于语音和噪声的对数概率分布推导出了一种软掩模,该软掩模可对带噪语音的对数子带进行加权以降低噪声,提高语音估计的准确性。仿真结果表明,与未处理的含噪语音相比,所提方法在噪声抑制方面具有3 dB以上的提升,基于最小均方误差的时频掩模和软掩模在听觉感知方面的平均提升量分别为27.7%和29.4%,在可懂度方面的平均提升量分别为12.7%和14.3%。
