Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

定轴转动带电体的远区磁场分布

类比定轴转动刚体转动惯量以及电偶极子电场的计算方法，得出定轴转动带电体的磁矩及其远区磁场分布。     

含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

A field-sensitivity analysis of the relativistic motion of a single electron submitted to a perpendicular magnetic field

Sensitivity of the velocity of a single electron, in the relativistic case, to a perpendicular magnetic field is evaluated by defining a parameter which becomes useful in a number of cases related to dynamical systems. In particular, the ultrarelativistic case is examined.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

The fifth dimension: Theodor Kaluza's ground‐breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.     

On the trajectory of a single electron under the action of a linearly polarized laser field

The dynamics of a single electron submitted to a linearly polarized laser field is examined in the non-relativistic case by calculating an upper bound of the position of the electron in the time domain.     

Cosmological Particle Creation and Dynamical Casimir Effect

We compute particle creation for a real massive scalar field conformally coupled to a spatially closed Robertson–Walker space-time background, with time-dependent scale factor. This is a dynamical Casimir effect with moving boundaries.     

Monotone Mappings and Flows of Viscous Media

We establish solvability of the boundary-value problems describing stationary and periodic flows of viscoplastic media. In the case of stationary flows we study the question of convergence of the Galerkin method. For the problem of periodic flows we prove a version of the second Bogolyubov theorem.     

Problem of the free oscillations of a capillary bridge

The free oscillations of a capillary bridge whose equilibrium shape is determined by the surface tension forces and the static gravity field are investigated. The values of 25 “lower” levels of the spectrum of natural oscillations of the capillary bridge are found for various control parameters in accordance with the experimental conditions.