The extended symmetry approach for studying the general Korteweg-de Vries-type equation

The extended symmetry approach is used to study the general Korteweg-de Vries-type (KdV-type) equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be constructed by the solutions of original models if their solutions are well known, such as the standard constant coefficient KdV equation and the standard compound KdV--Burgers equation, and so on. Then any one of these variable-coefficient equations can be considered as an original model to obtain new variable-coefficient equations whose solutions can also be known by means of transformation relations between solutions of the resulting new variable-coefficient equations and the original equation.     

Rindler solutions and their physical interpretation

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded. Zh. éksp. Teor. Fiz. 114, 777–785 (September 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

一种解电路網络的方法

本文提出一种解电网的方法,用这种方法来解电网,可以避免解联立方程之麻烦,以节省劳动力。本文分下列两部分:1.一般电网解法——凡是一切直线律电网,不论其中含有若干电动势,都可应用这解法。这解法是首先将电网中的电动势代换以等值的电源电流,其次将电网中的结点逐点化去,使电网化简为一等值支路,以求该支路两端点的电势差,然后再返原为原来的电网,以求其中各结点的电势,如此,最后就很易计算出各支路的电流。2.只含一个电动势电网的特殊解法——凡是一切直线律电网,若其中只含有一个电动势,则用这解法更为简便。这解法与一般电网解法所不同的地方就是可将电网返原的这一步骤省去。为了要省去这一步骤,只须在电网化简前,电网各结点上均虚设一定量的电源电流,如此,当电网化简为一等值支路时,就能直接求得原来电网中各结点的电势。再者,本文所提出的解电网方法对于交流电网及直流电网均能适用,而本文是按解交流电网的方式叙述。     

Proposal for an interpretation of the Hermitian theory of relativity

The equilibrium conditions for charges and currents, apparent in exact solutions of the field equations, lead one to regard the Hermitian theory of relativity as the theory of a field endowed with two sources: electromagnetic and color four-currents.     

用初-边值方法研究具有固定边界的等离子体Kink不稳定性

本文解出了具有固定边界的平衡等离子体磁面方程的解析解和数值解。用简化的Lax-Wendroff方法求出了压力、速度和磁场的扰动值。得到了线性增长率、平均β和平均β_p以及安全因子。我们发现:1.具有凹向电流剖面的等离子体比具有均匀电流剖面的等离子体更稳定,而具有凸向电流剖面的等离子体是最不稳定的;2.具有逆磁电流的等离子体比具有顺磁电流的等离子体更稳定。 关键词：     

Signature Change and Clifford Algebras

Given the real Clifford algebra of a quadratic space with a given signature, we define a new product in this structure such that it simulates the Clifford product of a quadratic space with another signature different from the original one. Among the possible applications of this new product, we use it in order to write the Minkowskian Dirac equation over the Euclidean spacetime and to define a new duality operation in terms of which one can find self-dual and anti-self-dual solutions of gauge fields over Minkowski spacetime analogous to the ones over Euclidean spacetime and without needing to complexify the original real algebra.     

Spin currents in non-inertial frames

The covariant Dirac equation and its solutions show that rotation and acceleration can be used to generate and control spin currents.     

Optically injected spin currents in semiconductors

We show that quantum interference of one and two photon absorption from a two color field allows one to optically inject ballistic spin currents in unbiased semiconductors. The spin currents can be generated with or without an accompanying electrical current and can be controlled using the relative phase of the two colors. We characterize the injected spin currents using symmetry arguments and an eight-band Kane model.     

An extension of the plane-symmetric electrovac general solution to Einstein equations

We present the general solution to Einstein-Maxwell equations representing plane-symmetric metrics associated with electromagnetic fields that are not fully plane-symmetric. There are two classes in the general solution, the first approaches Taub's static metric or Kasner's spatially homogeneous one as the electromagnetic field goes to zero, while the second approaches the fiat metric.     

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.     

Continuous symmetries of three-dimensional diffusion equations

Lie transformation groups are given which leave the three-dimensional linear diffusion equation invariant, with and without chemical reactions. We show how similarity solutions and conserved currents can be obtained with the help of these groups. We apply these methods to nonlinear three-dimensional diffusion equations which can be exactly linearized by nonlinear transformations.     

Algebraically explicit analytical solutions for the unsteady non-Newtonian swirling flow in an annular pipe

This paper presents two algebraically explicit analytical solutions for the incompressible unsteady rotational flow of Oldroyd-B type in an annular pipe. The first solution is derived with the common method of separation of variables. The second one is deduced with the method of separation of variables with addition developed in recent years. The first analytical solution is of clear physical meaning and both of them are fairly simple and valuable for the newly developing computational fluid dynamics. They can be used as the benchmark solutions to verify the applicability of the existing numerical computational methods and to inspire new differencing schemes, grid generation ways, etc. Moreover, a steady solution for the generalized second grade rheologic fluid flow is also presented. The correctness of these solutions can be easily proven by substituting them into the original governing equation.     

Multifluxon dynamics in driven Josephson junctions

The dynamics of fluxons in a long Josephson junction driven by time-varying nonuniform bias currents are described by a generalization of the sine-Gordon equation. This equation has solitary wave solutions which correspond to current vortices or quantized packets of magnetic flux in the junction. As with the sine-Gordon equation, multifluxon solutions may be demonstrated for the long Josephson junction. Our numerical calculations show that several fluxons may be launched or annihilated at the end of a junction. We also show multiple steady state conditions which correspond to one or more flux quanta trapped in the junction.     

基于压缩感知的一维海面与二维舰船复合后向电磁散射快速算法研究

矩量法作为数值方法中积分方程方法的代表, 具有计算精度高、所用格林函数自动满足辐射条件、无须额外设置边界条件等优点. 但是在舰船目标与海面复合后向电磁散射仿真中, 传统矩量法需针对每个入射角反复求解矩阵方程组, 导致其在处理后向散射问题时计算量大, 耗时长, 仿真效率低下. 为解决上述问题, 本文提出了一种基于压缩感知技术的矩量法的改进算法. 该算法在求解复合后向散射问题时, 首先利用观测矩阵与传统矩量法中的电压矩阵相乘, 得到一组新的低维度的电压矩阵; 其次通过求解新电压矩阵下的矩阵方程组, 获得电流矩阵的观测值; 最后利用恢复算法(本文采用正交匹配追踪算法)重构出所需的原始入射源照射下的电流系数. 通过与传统矩量法的计算结果对比, 表明本文所提算法能够在保证计算精度的前提下, 明显减少计算时间, 提高计算效率.     

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

In this paper, the short-wave model equations are investigated, which are associated with the Camassa- Holm （CH） and Degasperis Procesi （DP） shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformatioas back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems.     

Improvement of Security of Three-Party Quantum Secure Direct Communication Based on GHZ States

A protocol for three-party quantum secure direct communication based on Greenberger-Horne-Zeilinger （GHZ） states was recently proposed by 3in et al. [Phys. Lett. A 354 （2006） 67] By analysing the protocol we find some security loopholes, e.g. one bit of secret messages of a party （Alice in the original paper） can always be leaked straight to the public without any eavesdropping. These problems suggested previously are discussed and possible solutions are presented to improve the security of the original protocol.     

Similarity solution and lie symmetry for a coupled nonlinear system

The Lie point symmetries of a set of coupled nonlinear partial differential equations are considered. The system is an extended version of the usual nonlinear Schrödinger equation. In the similarity variable deduced from the symmetry analysis, the system is equivalent to the Painlevé III in Ince's classification. By starting from a solution of the Painlevé equation, one can reproduce various classes of solutions of the original PDEs. Such solutions include both rational and progressive types or a combination of the two.     

Three-body scattering at positive energies: Solving the problem of moving logarithmic singularities

For three-body scattering at positive total energies, integral equations are obtained whose kernels have no logarithmic singularities on the contour of integration. The corresponding singularities that are present in original integral equations can be circumvented by shifting a part of the contour of integration from the real axis to the complex plane. This is done only for a special auxiliary solution appearing to be an analytic function in this region. The physical amplitude proper is found as one of the solutions to the resulting set of equations. In contrast to conventional techniques, an additional analysis is therefore not required here, so that numerical solutions can be obtained within standard computational schemes.     

Differential Replication for Credit Scoring in Regulated Environments

Differential replication is a method to adapt existing machine learning solutions to the demands of highly regulated environments by reusing knowledge from one generation to the next. Copying is a technique that allows differential replication by projecting a given classifier onto a new hypothesis space, in circumstances where access to both the original solution and its training data is limited. The resulting model replicates the original decision behavior while displaying new features and characteristics. In this paper, we apply this approach to a use case in the context of credit scoring. We use a private residential mortgage default dataset. We show that differential replication through copying can be exploited to adapt a given solution to the changing demands of a constrained environment such as that of the financial market. In particular, we show how copying can be used to replicate the decision behavior not only of a model, but also of a full pipeline. As a result, we can ensure the decomposability of the attributes used to provide explanations for credit scoring models and reduce the time-to-market delivery of these solutions.     

General symmetries in optimal control

In this paper we study general symmetries for optimal control problems making use of the geometric formulation proposed in [7]. This framework allows us to reduce the number of equations associated with optimal control problems with symmetry and compare the solutions of the original system with the solutions of the reduced one. The reconstruction of the optimal controls starting from the reduced problem is also explored.