Multiple Jacobi Elliptic Function Solutions to Integrable Higher Order Broer-Kaup Equation in (2+1)-Dimensional Spaces

In this paper, we improve the method for deriving Jacobi elliptic function solutions of nonlinear evolution equations given in Ref. [12] and apply it to the integrable higher-order Broer-Kaup system in (2 1)-dimensional spaces.Some new elliptic function solutions are obtained.     

含余割核奇异积分的求积公式

首先讨论了Hermite三角插值的收敛性问题,然后利用Hermite反三角插值公式建立了反周期函数正常积分的求积公式,最后通过分离奇点的方法建立了含余割核奇异积分的求积公式.     

半线性二阶微分方程周期边值问题

本文利用整体反函数理论,研究了半线性二阶微分方程周期边值问题,给出了周期解存在唯一性的充分条件.     

Anticonvulsant Effect of Turmeric and Resveratrol in Lithium/Pilocarpine-Induced Status Epilepticus in Wistar Rats

Epilepsy is a chronic neurological disorder that lacks a cure. The use of plant-derived antioxidant molecules such as those contained in turmeric powder and resveratrol may produce short-term anticonvulsant effects. A total of 42 three-month-old male Wistar rats were divided into six groups (n = 7 in each group): Vehicle (purified water), turmeric (150 and 300 mg/kg, respectively), and resveratrol (30 and 60 mg/kg, respectively), administered per os (p.o.) every 24 h for 35 days. Carbamazepine (300 mg/kg/5 days) was used as a pharmacological control for anticonvulsant activity. At the end of the treatment, status epilepticus was induced using the lithium–pilocarpine model [3 mEq/kg, intraperitoneally (i.p.) and 30 mg/kg subcutaneously (s.c.), respectively]. Seizures were evaluated using the Racine scale. The 300 mg/kg of turmeric and 60 mg/kg of resveratrol groups had an increased latency to the first generalized seizure. The groups treated with 150 and 300 mg/kg of turmeric and 60 mg/kg of resveratrol also had an increased latency to status epilepticus and a decreased number of generalized seizures compared to the vehicle group. The chronic administration of turmeric and resveratrol exerts anticonvulsant effects without producing kidney or liver damage. This suggests that both of these natural products of plant origin could work as adjuvants in the treatment of epilepsy.     

数控加工复合循环功能与子程序编程的特点及其应用

零件的数控加工,为了简化数控加工程序,既可以利用复合循环功能编程,又可以应用子程序技术编程.通过对复合循环功能编程与子程序编程的比较得知,应用子程序编程利大于弊,有利于保证零件的加工质量,提高加工效率,降低生产成本.     

Age Analysis of Status Updating System with Probabilistic Packet Preemption

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.     

双曲数和重复变数的另一种表示法

讨论了用矩阵方法表示双曲数,用矩阵的Kronecker乘积来表示重复变数,并用矩阵表示相应的双曲函数和重复变函数,得到了这两种数局限性的本质,使这两种数及其函数更加直观,易于研究.     

A new adaptive state space construction method for the mobile robot navigation

In order to solve the combinative explosion problems in a continuous and high dimensional state space, a function approximation approach is usually used to represent the state space. The normalized radial basis function （NRBF） was adopted as the local function approximator and a kind of adaptive state space construction strategy based on the NRBF （ASC-NRBF） was proposed, which enables the system to allocate appropriate number and size of the basis functions automatically. Combined with the reinforce- ment learning method, the proposed ASC-NRBF method was applied to the robot navigation problem. Simulation results illustrate the performance of the proposed method.     

Numerical Study on an RBF-FD Tangent Plane Based Method for Convection–Diffusion Equations on Anisotropic Evolving Surfaces

In this paper, we present a fully Lagrangian method based on the radial basis function (RBF) finite difference (FD) method for solving convection–diffusion partial differential equations (PDEs) on evolving surfaces. Surface differential operators are discretized by the tangent plane approach using Gaussian RBFs augmented with two-dimensional (2D) polynomials. The main advantage of our method is the simplicity of calculating differentiation weights. Additionally, we couple the method with anisotropic RBFs (ARBFs) to obtain more accurate numerical solutions for the anisotropic growth of surfaces. In the ARBF interpolation, the Euclidean distance is replaced with a suitable metric that matches the anisotropic surface geometry. Therefore, it will lead to a good result on the aspects of stability and accuracy of the RBF-FD method for this type of problem. The performance of this method is shown for various convection–diffusion equations on evolving surfaces, which include the anisotropic growth of surfaces and growth coupled with the solutions of PDEs.     

一种基于新型小波包阈值的图像去噪方法

提出了一种基于小波包理论去除图像噪声的方法,用小波包把图像分解为高频分量和低频分量,根据高频分量估计噪声的标准差,并利用该标准差以及Birge-Massart惩罚函数计算阈值.鉴于传统软硬阈值的缺陷,采用一种新型阈值量化方法,用三次多项式在硬阈值的基础上插值,使新的阈值函数保持了连续性和可导性.通过这种方法既消除了图像的振铃现象,又保留了细节成分.实验表明：与传统方法相比,新方法使图像视觉效果和峰值信噪比均获得提高.