High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

Weak Noether symmetry and conserved laws of Birkhoffian systems

A new kind of weak Noether symmetry is obtained that arises in the study of Birkhoffian systems. The conserved quantities, which includes Noether conserved quantity, Hojman type conserved quantity and new type conserved quantity, are also calculated from this symmetry. Finally, two examples are presented to illustrated the application of these new results.

Characterization of Type p Banach Spaces by the Weak Law of Large Numbers

For weighted sums of the form ?j = 1kn anj Xnj\sum {_{j = 1}^{k_n } } a_{nj} X_{nj} where {a nj , 1 ?j?k n ↑∞,n?1} is a real constant array and {X aj , 1≤j≤k n, n≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.

Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space

This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space R+= {x |x > 0} where a>0 , u(x,t) is an unknown function of x ∈ R+ and t>0 , u ± , um are three given constants satisfying um=u+≠u- or um=u-≠u+ , and the flux function f is a given continuous function with a weak discontinuous point ud. The main purpose of our present manuscript is devoted to studying the structure of the global weak entropy solution for the above initial-boundary value problem under the condition of f '-(ud) > f '+(ud). By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial-boundary value problem, and investigate the interaction of elementary waves with the boundary and the boundary behavior of the weak entropy solution.

A NOTE ON THE RIEMANN PROBLEM TO HYPERBOLIC CONSERVATION LAWS

This paper is a extension of [1], [3]. By the method in [1], the authors prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws.

Discovering exact,gauge-invariant,local energy–momentum conservation laws for the electromagnetic gyrokinetic system by high-order field theory on heterogeneous manifolds

Gyrokinetic theory is arguably the most important tool for numerical studies of transport physics in magnetized plasmas.However,exact local energy–momentum conservation laws for the electromagnetic gyrokinetic system have not been found despite continuous effort.Without such local conservation laws,energy and momentum can be instantaneously transported across spacetime,which is unphysical and casts doubt on the validity of numerical simulations based on the gyrokinetic theory.The standard Noether procedure for deriving conservation laws from corresponding symmetries does not apply to gyrokinetic systems because the gyrocenters and electromagnetic field reside on different manifolds.To overcome this difficulty,we develop a high-order field theory on heterogeneous manifolds for classical particle-field systems and apply it to derive exact,local conservation laws,in particular the energy–momentum conservation laws,for the electromagnetic gyrokinetic system.A weak Euler–Lagrange(EL)equation is established to replace the standard EL equation for the particles.It is discovered that an induced weak EL current enters the local conservation laws,and it is the new physics captured by the high-order field theory on heterogeneous manifolds.A recently developed gauge-symmetrization method for high-order electromagnetic field theories using the electromagnetic displacement-potential tensor is applied to render the derived energy–momentum conservation laws electromagnetic gauge-invariant.

Gnedenko-Raikov’s Theorem Fails for Exchangeable Sequences

We study the connection between the central limit theorem and law of large numbers for exchangeable sequences, and provide a counterexample to the Gnedenko-Raikov theorem for such sequences.

A New Application of the Flux Approximation Method on Hyperbolic Conservation Systems

In this paper, we first summarize several applications of the flux approximation method on hyperbolic conservation systems. Then, we introduce two hyperbolic conservation systems (2.1) and (2.2) of Temple’s type, and prove that the global weak solutions of each system could be obtained by the limit of the linear combination of two systems.

On the Functional Empirical Process and Its Application to the Mutual Influence of the Theil-Like Inequality Measure and the Growth

We set in this paper a coherent theory based on functional empirical processes that allows to consider both the poverty and the inequality indices in one Gaussian field in which the study of the influence of the one over the other is done. We use the General Poverty Index (GPI), that is a class of poverty indices gathering the most common ones and a functional class of inequality measures including the Entropy Measure, the Mean Logarithmic Deviation, the different inequality measures of Atkinson, Champernowne, Kolm and Theil called Theil-Like Inequality Measures (TLIM). Our results are given in a unified approach with respect to the two classes instead of their particular elements. We provide the asymptotic laws of the variations of each class over two given periods and the ratio of the variation and derive confidence intervals for them. Although the variances may seem somehow complicated, we provide R codes for their computations and apply the results for the pseudo-panel data for Senegalwith a simple analysis.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

Global existence of weak solutions to the drift-flux system for general pressure laws

The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.

地震作用下含弱层顺向坡响应规律分析

以抚顺西露天矿南帮含弱层顺向坡作为参考原型,利用FLAC3D软件模拟实际地震动及地震动输入、斜坡模型的边界条件、岩体参数以及网格模型划分,对含弱层顺向坡进行数值模拟计算,通过监测点的加速度和速度探讨含弱层顺向坡在地震作用下的响应规律。研究结果表明:(1)地震作用下对于含单一弱层斜坡响应特征起到决定性的影响因素是弱层的厚度,在地震荷载作用下影响斜坡的稳定程度要大于单一弱层倾角的影响。(2)通过弱层与斜坡坡面的相交部位监测点2#在水平方向速度可以得出,厚度对于X方向的速度大小影响程度较大。(3)对于地震作用下双弱层特性斜坡的响应规律分析时,弱层与斜坡相交部位的破坏响应规律会随着坡高的增大而有所变化,双弱层监测点3#的加速度幅值变化及速度变化程度均比双弱层监测点2#明显。地震作用下顺向坡的响应规律与含有弱层的倾角、厚度和弱层的数量位置有关,在对斜坡的治理与防护的过程中应当充分考虑地震与弱层特性的耦合作用对斜坡稳定性的影响。

软弱地层盾构穿越老旧民居变形规律分析

老旧浅基础民居安全性较低,盾构穿越会对其造成不利影响。本文以杭州某出入线段盾构穿越老旧民居为背景,分析盾构穿越民居变形规律,探讨盾构穿越民居掘进参数最优区间。结果表明,出入线段无论先下穿后侧穿或先侧穿后下穿,民居竖向位移曲线较一致,且第一次穿越前后变形较小,第二次穿越时变形迅速增大,主要表现为沉降;盾构埋深、注浆参数等对老旧民居变形、倾斜影响较大;地表沉降曲线大致呈漏斗形,出线段施工对地表变形影响较小,入线段施工对出线段地表变形影响较大,对自身上部土体变形影响较小。

Strong Law of Large Numbers under an Upper Probability

Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.

THE WEAK LAW OF LARGE NUMBERS WHEN EXTREME TERMS ARE EXCLUDED FROM SUMS

ＴＨＥＷＥＡＫＬＡＷＯＦＬＡＲＧＥＮＵＭＢＥＲＳＷＨＥＮＥＸＴＲＥＭＥＴＥＲＭＳＡＲＥＥＸＣＬＵＤＥＤＦＲＯＭＳＵＭＳ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ...

弱电网条件下并网逆变器控制环路稳定判据及交互作用规律分析

为分析新能源并网发电系统中弱电网与逆变器交互作用对稳定性的影响,该文从控制器带宽交叠角度出发,将表征系统闭环稳定性能的电流环开环传递函数G0表示为电网阻抗、锁相环和电流控制器3个环节相乘,进而把锁相环和电网阻抗环节组合并与电流控制器环节相比得到等效的环路比表达式,据此提出弱电网下基于奈奎斯特定理的并网逆变器控制环路稳定判据,当G0分子和分母幅值相等时,幅频曲线产生交点,易使系统闭环增益无穷大而失稳。接着,为分析3个环节间交互作用规律,该文推导得到满足控制环路稳定判据的锁相环与电流控制器带宽比n的表达式,研究发现:在不同弱电网条件下,带宽比大于n的临界值时,各环节间会产生交互作用,在波德图中主要表现为G0分子和分母幅频曲线的交叠,且电网越弱或锁相环与电流控制器带宽越接近,幅频曲线交叠面积越大,越易导致闭环增益无穷大,即系统愈易失稳;此外,当电流控制器带宽固定时,n的临界值随电网减弱在小于1和大于1之间的区间范围变化,即锁相环与电流控制器的带宽比大于或小于1都可以使得系统保持稳定。最后,通过Matlab仿真和半实物实验平台验证了该文理论分析的准确性。

《民法典(婚姻家庭编)》的伦理、自治与强制

受个人主义和自由主义思潮的影响,近年来家庭秩序与传统家国观念频受挑战。《民法典(婚姻家庭编)》规定的婚姻自由、男女平等、一夫一妻、弱者保护等原则,反映了立法者对婚姻家庭关系中的传统伦理与现代法理、家庭本位与个体自由、国家管制与家庭自治等理念的贯彻与平衡。家庭伦理与现代法理的共治旨在追求家庭共同体的完整和睦、家庭成员在情感与利益上的互利互助,以及个人尊严、自由与幸福的自我实现之间的平衡。《民法典(婚姻家庭编)》的“婚姻家庭受国家保护”原则(第1041条第1款)以及强调家风建设等伦理道德理念,表明婚姻家庭编兼顾维护家庭团体属性与保障成员个人自由的立法思路;婚姻家庭编基本原则所包含的实质正义理念,为法官对有关身份关系协议进行形式控制与法律审查提供了价值指引,有利于妥当平衡家庭法领域个人的自治权与弱者获得实质公平保护之间的冲突。

高精密红外探硫传感器的研究与设计

根据气体的红外吸收特性,SO2的特征吸收峰所在的波长与人体红外波长范围正好重叠。因此,红外硫探测器成为了敏感元件,国内生产的红外硫探测系统测量精度不够,进口红外硫探测系统很大程度对国内进行了技术封锁。基于此,该文采用非分光红外技术,针对当前高精密红外低硫传感器最重要信噪比影响源进行了研究,优化了光源驱动、红外气室恒温控制、信号采样与微弱信号处理电路设计等,完成了一套低硫探测装置的设计,经过测试,信号的噪声波动从原来的140 uV减小到50 uV左右,检出限达到0.01 ppm,实现了低硫检测领域的技术创新,该项目成果已经成功实现量产。