Killing-Yano Tensors and Superintegrable Systems

Killing-Yano (KY) and Killing tensors of the four types of metrics, that represent the two-dimensional spaces given in Darbouxs classification, are obtained. It is proved that all spaces admit dual manifolds and their KY tensors are calculated.     

含有五度旋转轴点群的超拉曼张量的计算

超拉曼散射涉及晶格振动, 因此它需要由动态张量来描述。根据坐标积与张量元在对称操作下的变换形式相同的原理, 通过C语言编程, 计算了属于不同不可约表示的动态张量, 并列出了含有五度旋转轴点群的三阶超拉曼张量。     

A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables

We propose a geometrical approach to the problem of integrability of Hamiltonian systems of low dimensions using the Hamilton–Jacobi method of separation of variables, based on the method of moving frames. As an illustration we present a complete classification of all separable Hamiltonian systems defined in two-dimensional Riemannian manifolds of arbitrary curvature and a criterion for separability. Connections to bi-Hamiltonian theory are also found.     

The Tensors of the Averaged Relative Energy–Momentum and Angular Momentum in General Relativity and Some of Their Applications

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper.      

A General Approach to the Construction of Conservation Laws for Birkhoffian Systems in Event Space

For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.     

Integration in the GHP Formalism IV: A New Lie Derivative Operator Leading to an Efficient Treatment of Killing Vectors

In order to achieve efficient calculations and easy interpretations of symmetries, a strategy for investigations in tetrad formalisms is outlined: work in an intrinsic tetrad using intrinsic coordinates. The key result is that a vector field is a Killing vector field if and only if there exists a tetrad which is Lie derived with respect to ; this result is translated into the GHP formalism using a new generalised Lie derivative operator with respect to a vector field . We identify a class of it intrinsic GHP tetrads, which belongs to the class of GHP tetrads which is generalised Lie derived by this new generalised Lie derivative operator in the presence of a Killing vector field . This new operator also has the important property that, with respect to an intrinsic GHP tetrad, it commutes with the usual GHP operators if and only if is a Killing vector field. Practically, this means, for any spacetime obtained by integration in the GHP formalism using an intrinsic GHP tetrad, that the Killing vector properties can be deduced from the tetrad or metric using the Lie-GHP commutator equations, without a detailed additional analysis. Killing vectors are found in this manner for a number of special spaces.     

A Phase Space Approach to Gravitational Entropy

We examine the definition S=ln as a candidate function for gravitational entropy. We calculate its behavior for gravitational and density perturbations in closed, open and flat cosmological models and find that in all cases it increases monotonically. We are also able to calculate the entropy density of gravitational radiation produced by inflation. We compare the results with the behavior of the Weyl-tensor squared. Applying the formalism to black holes has proved more problematical.     

On the space-times admitting two shear-free geodesic null congruences

We analyze the space-times admitting two shear-free geodesic null congruences. The integrability conditions are presented in a plain tensorial way as equations on the volume element U of the time-like 2-plane that these directions define. From these we easily deduce significant consequences. We obtain explicit expressions for the Ricci and Weyl tensors in terms of U and its first and second order covariant derivatives. We study the different compatible Petrov-Bel types and give the necessary and sufficient conditions that characterize every type in terms of U. The type D case is analyzed in detail and we show that every type D space-time admitting a 2 + 2 conformal Killing tensor also admits a conformal Killing-Yano tensor.     

A note on the p-elastica in a constant sectional curvature manifold

In this paper, we study the p-elastica, the critical point of the total polynomial curvature functional on those immersed curves satisfying suitable boundary conditions in a Riemannian manifold with constant sectional curvature. We express the torsion of the p-elastica in terms of its curvature in a closed form and completely solve the Euler–Lagrange equation by quadratures. We study the Frenet equation of the p-elastica by using the Killing field.     

氩原子和类氩离子相对论修正

以相对论修正哈密顿(包括质量修正、单体和双体达尔文修正、自旋-自旋接触相互作用)的球张量形式为基础, 借助不可约张量理论导出了类氩体系基态能量的相对论修正的解析表达式. 在斯莱特表象中完成了所有的角向积分和自旋求和计算, 能量的相对论修正式用径向矩阵元的线性组合来表示.对类氩体系基态能量的相对论修正值进行了具体计算,相对误差均小于0.0459%     

LETTER: A Note on the Algebraic Symmetries of the Riemann and Lanczos Tensors

The usual algebraic symmetries of the Riemanntensor involve four convenient relations. It is shownthat these can be encompassed in three, two or just onerelation. Similar results are shown for the Lanczos tensor.     

A Hybrid Analysis-Based Approach to Android Malware Family Classification

With the popularity of Android, malware detection and family classification have also become a research focus. Many excellent methods have been proposed by previous authors, but static and dynamic analyses inevitably require complex processes. A hybrid analysis method for detecting Android malware and classifying malware families is presented in this paper, and is partially optimized for multiple-feature data. For static analysis, we use permissions and intent as static features and use three feature selection methods to form a subset of three candidate features. Compared with various models, including k-nearest neighbors and random forest, random forest is the best, with a detection rate of 95.04%, while the chi-square test is the best feature selection method. After using feature selection to explore the critical static features contained in this dataset, we analyzed a subset of important features to gain more insight into the malware. In a dynamic analysis based on network traffic, unlike those that focus on a one-way flow of traffic and work on HTTP protocols and transport layer protocols, we focused on sessions and retained protocol layers. The Res7LSTM model is then used to further classify the malicious and partially benign samples detected in the static detection. The experimental results show that our approach can not only work with fewer static features and guarantee sufficient accuracy, but also improve the detection rate of Android malware family classification from 71.48% in previous work to 99% when cutting the traffic in terms of the sessions and protocols of all layers.     

A Logical Approach to Entanglement

In this paper we innovate a logical approach to develop an intuition regarding the phenomenon of quantum entanglement. In the vein of the logic introduced we substantiate that particles that were entangled in the past will be entangled in perpetuity and thereby abide a rule that restricts them to act otherwise. We also introduce a game and by virtue of the concept of Nash equilibrium we have been able to show that entangled particles will mutually correspond to an experiment that is performed on any one of the particle.     

A Second Quantized Approach to the Rabi Problem

In the present work, the Rabi Problem, involving the response of a spin 1/2 particle subjected to a magnetic field, is considered in a second quantized approach. In this concrete physical scenario, we show that the second quantization procedure can be applied directly in a non-covariant theory. The proposed development explicits not only the relation between the full quantum treatment of the problem and the semiclassical Rabi model, but also the connection of these approaches with the Jaynes-Cummings model. The consistency of the method is checked in the semiclassical limit. The treatment is then extended to the matter component of the Rabi problem so that the Schrödinger equation is directly quantized. Considering the spinorial field, the appearance of a negative energy sector implies a specific identification between Schrödinger’s and Maxwell’s theories. The generalized theory is consistent, strictly quantum and non-relativistic.