In the present paper, three kinds of forms for Noether’s conservation laws of hol-onomic nonconservative dynamical systems in generalized mechanics are given.
If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the...If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.展开更多
In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called Planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to...In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called Planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to Einstein’s mass-energy equation, we have studied Planck’s law and De Bloy’s wavelength, and generalized it to the De Bloy’s wavelength formula from low speed to light speed. Then, on this basis, the smallest particle is defined as mass quantum. The new wavelength formula is obtained from the mass quantum and converted into the frequency formula. The generalized Planck’s law is obtained.展开更多
By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-inter...By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.展开更多
给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function rou...给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。展开更多
In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we i...In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.展开更多
Developing host materials with high specific surface area, good electron conductivity, and fast ion transportation channel is critical for high performance lithium-selenium(Li-Se) batteries. Herein, a series of three ...Developing host materials with high specific surface area, good electron conductivity, and fast ion transportation channel is critical for high performance lithium-selenium(Li-Se) batteries. Herein, a series of three dimensional ordered hierarchically porous carbon(3D OHPC) materials with micro/meso/macropores are designed and synthesized for Li-Se battery. The porous structure is tuned by following the concept of the generalized Murray’s law to facilitate the mass diffusion and reduce ion transport resistance.The optimized 3D Se/OHPC cathode exhibits a very high 2 nd discharge capacity of 651 m Ah/g and retains 361 m Ah/g after 200 cycles at 0.2 C. Even at a high current rate of 5 C, the battery still shows a discharge capacity as high as 155 m Ah/g. The improved electrochemical performance is attributed to the synergy effect of the interconnected and well-designed micro, meso and macroporosity while shortened ions diffusion pathways of such Murray materials accelerate its ionic and electronic conductivities leading to the enhanced electrochemical reaction. The diffusivity coefficient in Se/OHPC can reach a very high value of 1.3 × 10^(-11)cm^(2)/s, much higher than those in single pore size carbon hosts. Their effective volume expansion accommodation capability and reduced dissolution of polyselenides ensure the high stability of the battery. This work, for the first time, established the clear relationship between textural properties of cathode materials and their performance and demonstrates that the concept of the generalized Murray’s law can be used as efficient guidance for the rational design and synthesis of advanced hierarchically porous materials and the great potential of 3D OHPC materials as a practical high performance cathode material for Li-Se batteries.展开更多
To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However,...To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However, no systematic algorithm yet exists to evaluate the consistency of the current distribution of short-circuit tests. A methodology is proposed in this paper to address this problem. Based on Kirchhoff’s current law and the generalized method of symmetrical components, the current deviations of the AT feeding systems are analysed and then normalized with the short-circuit current as they vary greatly with systems and short-circuit sites. It is also found that the short-circuit current varies with the calculation methods, and its unbiased standard deviation also reflects the consistency of the short-circuit test. The mean and maximum of the current deviations, as well as the unbiased standard deviation of the short-circuit current, show the consistency of the short-circuit test from different aspects,although the last two items are highly relevant. Therefore, a unified evaluation index is defined as the sum of the three items, and then applied in two case studies to test its performance. The results show that, the proposed index canclearly distinguish the consistency of the short-circuit tests and may be used to sort the short-circuit tests for fault location systems. Besides, some short-circuit tests may have very poor consistency indices, and thus are not applicable to the tuning of fault location systems. In the authors’ opinion, the determination of the threshold of the proposed index needs further investigation.展开更多
It is well-established that waves are inhomogeneous in a lossy isotropic medium, and the validation of the classical Snell's law is still questionable for light refraction at the dissipative and dispersive interfa...It is well-established that waves are inhomogeneous in a lossy isotropic medium, and the validation of the classical Snell's law is still questionable for light refraction at the dissipative and dispersive interface. With high absorption, direct experimental investigation is rather difficult due to the extremely short penetration depth; i.e., the skin depth. In this paper, a simple and unified description of this issue is proposed, which can be applied to both materials with anomalous dispersion and in the Drude region. The gradient ▽_k~ω is found to be incident angle θ_i-dependent, and the direction of the group velocity may deviate significantly from the phase velocity due to the loss induced permittivity structure. The physics behind the negative refraction effect is explained, and a novel loss induced super-prism effect is also predicted.展开更多
文摘In the present paper, three kinds of forms for Noether’s conservation laws of hol-onomic nonconservative dynamical systems in generalized mechanics are given.
基金This project was supported by the Ministry of Education of China (206089)Shangdong Provincial Natural Science Foundation of China (Y2004A04)Fujian Provincial Natural Science Foundation of China (Z051049).
文摘If a system is not disturbed （or invaded） by some law, there is no doubt that each system will move according to the expected law and keep stable. Although such a fact often appears, some unknown law breaks into the system and leads it into turbulence. Using function one direction S-rough sets, this article gives the concept of the F-generation law in the system, the generation model of the F-generation law and the recognition method of the system law. Function one direction singular rough sets is a new theory and method in recognizing the disturbance law existing in the system and recognizing the system law.
文摘In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called Planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to Einstein’s mass-energy equation, we have studied Planck’s law and De Bloy’s wavelength, and generalized it to the De Bloy’s wavelength formula from low speed to light speed. Then, on this basis, the smallest particle is defined as mass quantum. The new wavelength formula is obtained from the mass quantum and converted into the frequency formula. The generalized Planck’s law is obtained.
基金Science and Technology Foundations of the Education Committee of Fujian Province of China (No.JA09232, No.JA08236)Science and Technology Projects of Sanming University, China (No. HX201007/Z)
文摘By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.
文摘给出函数单向S-粗集(function one direction singular rough sets)、函数单向S-粗集对偶(dual of function one direction singular rough sets)、函数双向S-粗集(function two direction singular rough sets)与函数粗集(function roughsets)。它们都是把函数概念引入到S-粗集中,改进S-粗集得到的。函数粗集是把函数概念引入到Z.Pawlak粗集中,改进Z.Pawlak粗集得到的。函数单向S-粗集、函数单向S-粗集对偶、函数双向S-粗集是函数S-粗集的三类形式。给出函数S-粗集与S-粗集的关系;给出函数粗集与Z.Pawlak粗集的关系;给出函数S-粗集与函数粗集的关系。利用这些结果,给出函数的区间离散与有限元素集的生成、函数离散-元素集合生成原理;给出函数S-粗集生成的信息规律、函数等价类动态特性-属性补充与删除原理;给出数据拆分-合成原理、信息规律动态拆分-合成的属性特征;给出信息规律动态拆分-合成不变性原理;利用这些概念与结果,给出信息规律拆分-合成与信息图像嵌入-分离的应用,给出嵌入信息图像的分离-辨识。函数S-粗集、函数粗集是粗集理论与应用研究中的一个新的研究方向。
基金supported by National Science Foundation of China(11071162)Shanghai Municipal Natural Science Foundation (09ZR1413500)
文摘In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.
基金financial support from the China Scholarship Council (CSC) and a scholarship from the Laboratory of Inorganic Materials Chemistry,Universitéde Namur,Belgiumfinancially supported by the National Postdoctoral Program (Grant No. 2020M672782)+2 种基金the National Natural Science Foundation of China (Grant No. U1663225)the the Program of Introducing Talents of Discipline to Universities-National 111 Project from the Ministry of Science and Technology and the Ministry of Education of China (Grant No. B20002)the National Key R&D Program of China (Grant No. 2016YFA0202602)。
文摘Developing host materials with high specific surface area, good electron conductivity, and fast ion transportation channel is critical for high performance lithium-selenium(Li-Se) batteries. Herein, a series of three dimensional ordered hierarchically porous carbon(3D OHPC) materials with micro/meso/macropores are designed and synthesized for Li-Se battery. The porous structure is tuned by following the concept of the generalized Murray’s law to facilitate the mass diffusion and reduce ion transport resistance.The optimized 3D Se/OHPC cathode exhibits a very high 2 nd discharge capacity of 651 m Ah/g and retains 361 m Ah/g after 200 cycles at 0.2 C. Even at a high current rate of 5 C, the battery still shows a discharge capacity as high as 155 m Ah/g. The improved electrochemical performance is attributed to the synergy effect of the interconnected and well-designed micro, meso and macroporosity while shortened ions diffusion pathways of such Murray materials accelerate its ionic and electronic conductivities leading to the enhanced electrochemical reaction. The diffusivity coefficient in Se/OHPC can reach a very high value of 1.3 × 10^(-11)cm^(2)/s, much higher than those in single pore size carbon hosts. Their effective volume expansion accommodation capability and reduced dissolution of polyselenides ensure the high stability of the battery. This work, for the first time, established the clear relationship between textural properties of cathode materials and their performance and demonstrates that the concept of the generalized Murray’s law can be used as efficient guidance for the rational design and synthesis of advanced hierarchically porous materials and the great potential of 3D OHPC materials as a practical high performance cathode material for Li-Se batteries.
文摘To improve the accuracy of fault location system, several short-circuit tests need to be conducted before being brought into service in autotransformer （AT） feeding systems for high-speed railways in China. However, no systematic algorithm yet exists to evaluate the consistency of the current distribution of short-circuit tests. A methodology is proposed in this paper to address this problem. Based on Kirchhoff’s current law and the generalized method of symmetrical components, the current deviations of the AT feeding systems are analysed and then normalized with the short-circuit current as they vary greatly with systems and short-circuit sites. It is also found that the short-circuit current varies with the calculation methods, and its unbiased standard deviation also reflects the consistency of the short-circuit test. The mean and maximum of the current deviations, as well as the unbiased standard deviation of the short-circuit current, show the consistency of the short-circuit test from different aspects,although the last two items are highly relevant. Therefore, a unified evaluation index is defined as the sum of the three items, and then applied in two case studies to test its performance. The results show that, the proposed index canclearly distinguish the consistency of the short-circuit tests and may be used to sort the short-circuit tests for fault location systems. Besides, some short-circuit tests may have very poor consistency indices, and thus are not applicable to the tuning of fault location systems. In the authors’ opinion, the determination of the threshold of the proposed index needs further investigation.
基金Project supported by the China Postdoctoral Science Foundation(Grant No.2016M601586)the National Natural Science Foundation of China(Grant No.11404092)the Opening Funding of Hunan Provincial Key Laboratory of High Energy Laser Technology,China(Grant No.GNJGJS07)
文摘It is well-established that waves are inhomogeneous in a lossy isotropic medium, and the validation of the classical Snell's law is still questionable for light refraction at the dissipative and dispersive interface. With high absorption, direct experimental investigation is rather difficult due to the extremely short penetration depth; i.e., the skin depth. In this paper, a simple and unified description of this issue is proposed, which can be applied to both materials with anomalous dispersion and in the Drude region. The gradient ▽_k~ω is found to be incident angle θ_i-dependent, and the direction of the group velocity may deviate significantly from the phase velocity due to the loss induced permittivity structure. The physics behind the negative refraction effect is explained, and a novel loss induced super-prism effect is also predicted.
