Non-local conservation laws for the equations of the irrotational isentropic plane-parallel gas motion

By introducing non-local variables, namely, the velocity potential and the stream function, and changing to the hodograph plane, the problem of finding the conservation laws for a non-linear system, describing the plane-parallel steady irrotational isentropic gas motion is reduced to the problem of finding the conservation laws for a linear Chaplygin system. The conservation laws of the zeroth and first orders for the Chaplygin system are obtained. It is established that the set of conservation laws of zeroth order that a Chaplygin system possesses consists of conservation laws that are linear in the velocity potential and the stream function, and a new non-linear conservation law. The linear conservation laws have functional arbitrariness. They produce linearity of this system and are defined by Green's operator formula. It turns out that all the conservation laws in the physical plane, obtained by Rylov, are generated by a linear combination of these linear conservation laws and trivial conservation laws. All the linear conservation laws of the first order for the Chaplygin system, generated by Green's operator formula, that are independent of the stream function, are obtained. It is shown that the Chaplygin system has no more than three first-order conservation laws, independent of the stream function, which are not a linear combination of these linear conservation laws and trivial conservation laws, and their components are quadratic in the velocity potential and its derivatives. All the Chaplygin functions for which the Chaplygin system has three such conservation laws are listed. These conservation laws are obtained.     

Classification of Local Conservation Laws of Maxwell's Equations

A complete and explicit classification of all independent local conservation laws of Maxwell's equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic conservation laws associated to the conserved stress-energy and zilch tensors, there are also chiral quadratic conservation laws which are associated to a new conserved tensor. The chiral conservation laws possess odd parity under the electric–magnetic duality transformation of Maxwell's equations, in contrast to the even parity of the stress-energy and zilch conservation laws. The main result of the classification establishes that every local conservation law of Maxwell's equations is equivalent to a linear combination of the elementary conservation laws, the stress-energy and zilch conservation laws, the chiral conservation laws, and their higher order extensions obtained by replacing the electromagnetic field tensor by its repeated Lie derivatives with respect to the conformal Killing vectors on Minkowski space. The classification is based on spinorial methods and provides a direct, unified characterization of the conservation laws in terms of Killing spinors.     

Mind in a Humean World

The paper defends Humean approaches to autonomous mental causation against recent attacks in the literature. One important criticism launched at Humean approaches says that the truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. This paper argues that special science causal laws and physical causal laws cannot be distinguished in terms of degrees of strictness. It follows that mental-to-physical counterfactuals are supported—or not supported—by laws in just the same way as are physical-to-physical counterfactuals.     

函数S-粗集对偶与F-粗边际规律

函数单向S粗集对偶(dual offunction one direction singular rough sets)是函数S粗集的基本形式之一,函数单向S-粗集对偶具有动态特性与规律(函数)特性.函数S粗集(function singular rough sets)是把函数概念引入到S粗集内(singular rough sets)改进S粗集得到的把导数概念与函数单向S粗集对偶交叉、渗透给出粗边际规律F-粗边际规律概念;给出粗边际规律F-粗边际规律特征;给出F-粗边际规律与粗边际规律的关系;给出F-粗边际规律在经济信息系统中的应用     

重建极性连续统理论的基本定律和原理(Ⅺ)——兼容性问题

对现有连续统场论中存在若干有关兼容性问题进行了简略的评论．根据重建的极性的连续统基本定律阐述三类兼容性问题．第一类是讨论各基本定律间的兼容性问题．第二类是讨论微极连续统基本定律兼容一般连续统基本定律的问题．第三类是讨论微极连续统基本定律兼容刚体动力学基本方程的问题．推导出的结果有助于深刻理解各种连续统理论的基本定律体系的结构和它们之间的联系．明确地指出,在传统的连续统场论的基本均衡定律的框架下,相容性问题是不可能自然地得到解决．     

On the Distinction Between Law Schemata and Causal Laws

The paper argues against the widely accepted assumption that the causal laws of (completed) physics, in contrast to those of the special sciences, are essentially strict. This claim played an important role already in debates about the anomalousness of the mental, and it currently experiences a renaissance in various discussions about mental causation, projectability of special science laws, and the nature of physical laws. By illustrating the distinction with some paradigmatic physical laws, the paper demonstrates that only law schemata are strict whereas causal laws are generally non-strict. Several potential replies to this argument are discussed and rejected as unsound.     

不带微结构的连续统中新的能量守恒定律和C-D不等式

对连续统力学中的基本定律和均衡方程以及C-D不等式进行了认真的再研究.指出了现有的动量矩均衡定律和能量守恒定律以及Clausius-Duhem不等式的不完整性,并且提出了不带微结构的局部和非局部非对称连续统中新的而且更为普遍的能量守恒定律和相应的能量均衡方程以及C-D不等式.     

关于~*-mixing随机变量序列的强大数定律

利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 .     

On generalized stable and related laws

A probabilistic characterization is given for Schneider?s generalized stable laws. They belong to the larger family of laws which are invariant under length-biasing followed by a random beta scaling. Questions of infinite divisibility and self-decomposability are pursued. Moment determinacy of reciprocal generalized stable laws are investigated.     

Hellinger integrals of gaussian processes with independent increments

The aim of this paper is to calculate the Hellinger integral of the distribution laws of Gaussian processes with independent increments. As an application, necessary and sufficient conditions for the equivalence of the distribution laws are derived. Furthermore estimations for the variational distance of the distribution laws are given.     

What do the Engel laws and positive laws have in common?

The work is inspired by a question of R. Burns: What do the Engel laws and positive laws have in common that forces finitely generated, locally graded groups satisfying them to be nilpotent-by-finite? The answer is that these laws have the same so-called Engel construction.     

Multi‐dimensional conservation laws and integrable systems

In this paper, we introduce a new property of two‐dimensional integrable hydrodynamic chains—existence of infinitely many local three‐dimensional conservation laws for pairs of integrable two‐dimensional commuting flows. Infinitely many local three‐dimensional conservation laws for the Benney commuting hydrodynamic chains are constructed. As a by‐product, we established a new method for computation of local conservation laws for three‐dimensional integrable systems. The Mikhalëv equation and the dispersionless limit of the Kadomtsev‐Petviashvili equation are investigated. All known local and infinitely many new quasilocal three‐dimensional conservation laws are presented. Also four‐dimensional conservation laws are considered for couples of three‐dimensional integrable quasilinear systems and for triplets of corresponding hydrodynamic chains.     

带有微结构的连续统中新的能量守恒定律和C-D不等式

对带有微结构的连续统中现有的基本定律、均衡方程和Clausius-Duhem不等式进行了系统的再研究,发现所有的能量均衡方程和相关的C-D不等式都是不完整的.本文对现有的结果进行了评注,并提出新的能量均衡方程和相关的C-D不等式.     

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.     

The joint law of the maximum and terminal value of a martingale

Summary In this paper, we characterise the possible joint laws of the maximum and terminal value of a uniformly-integrable martingale. We also characterise the joint laws of the maximum and terminal value of a convergent continuous local martingale vanishing at zero. A number of earlier results on the possible laws of the maximum can be deduced quite easily.     

Causal Overdetermination for Humeans?

The paper argues against systematic overdetermination being an acceptable solution to the problem of mental causation within a Humean counterfactual theory of causation. The truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical to physical counterfactuals, but no laws in the same sense that support mental to physical counterfactuals.     

Strassen-type Laws of Iterated Logarithm for a Fractional Brownian Sheet

Abstract

We study Strassen-type laws of iterated logarithm for a fractional Brownian sheet including that for small time, which imply most of the former laws of the iterated logarithm and Strassen's laws for one-parameter and two-parameter Wiener processes.     

基于奇异值分解的SGCMG操纵律分析

基于奇异值分解理论,对航天器姿态控制系统中使用的单框架控制力矩陀螺（SGCMG）的操纵律进行了分析和比较研究．借助于奇异值分解方法,分析了各种操纵律逃逸奇异的机理,重点分析了各种操纵律对陀螺构型奇异性、输出力矩误差的影响．通过仿真算例定量地分析与比较了各种操纵律的性能,所得结果可供工程设计人员参考．     

Conservation laws for a modified lubrication equation

In this work we study the conservation laws of a modified lubrication equation, which describes the dynamics of the interfacial motion in phase transition. We show that the equation is nonlinear self-adjoint and has an exact Lagrangian with an auxiliary function. As a result, by a general theorem on conservation laws proved by Nail Ibragimov recently and Noether’s theorem, some new conservation laws for the equation are obtained. Our results show that the non-locally defined conservation laws generated by Noether’s theorem are equivalent to the local ones given by Ibragimov’s theorem.     

Stochastic conservation laws?

We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr–Newman type Black Holes, which are created fluctuationally from a background Zero Point Field as in Prigogine's cosmology also. We conclude that these conservation laws are to be taken in the spirit of thermodynamic laws.