Irregular vectors of Hilbert space operators

A vector x in a Hilbert space H is called irregular for an operator provided that supn‖Tnx‖=∞ and infn‖Tnx‖=0. We establish some basic properties of operators having irregular vectors and present examples that highlight the relationship, or lack thereof, between irregularity and hypercyclicity.     

Electron Gun for Powerful Large Orbit Gyrotron

In the article, results of numerical simulation of the gun with the cusp of magnetic field are presented. Short pulse version of the gun with explosion emission is investigated. Some preliminary analytical estimation of the beam and gun parameters are performed. Then, numerical optimization of the electrodes shape as well as magnetic field distribution is carried out. For preliminary separation of electrons and formation of the rectilinear beam, anode diaphragm is installed. After then, additional selection of electrons for decreasing the ripple is performed. For this purpose, channel walls are used for interception of some part of the electron beam. Reverse of the magnetic field in the diode part of the gun is formed. So, the formation of the rectilinear beam is combined with the region, where electrons obtain initial gyration energy. To prevent the disperse action of the own beam space charge forces, the system with big gradient of magnetic field (about 0.5-1 kGs/mm) is needed. According to results of the simulation, helical electron beam can be performed even at total compression ratio about 1000 and current density more than 50 kA/cm². The designed electron gun provides acceptable performance for the large orbit gyrotron, such as operating current close to 300 A, the pitch-factor value about 1.5-1.7, deviation of the guiding centers from the axis (the ripple) /10 and /6 for operation on 3-rd and 5-th cyclotron harmonic correspondingly (wavelength =0.5 and 0.3 mm) and velocity spread within the range 10-15%.     

On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense–Thirring effect

The possibility of analyzing the node of the GP-B satellite in order to measure also the Lense–Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1%. of better. The aliasing effect of the solid Earth and ocean components of the solar K₁ tidal perturbations would make the measurement of the Lense–Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense–Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10³ years and amplitudes of the order of 10⁵ mas.     

Minimal invariant Markov basis for sampling contingency tables with fixed marginals

In this paper we define an invariant Markov basis for a connected Markov chain over the set of contingency tables with fixed marginals and derive some characterizations of minimality of the invariant basis. We also give a necessary and sufficient condition for uniqueness of minimal invariant Markov bases. By considering the invariance, Markov bases can be presented very concisely. As an example, we present minimal invariant Markov bases for all 2 × 2 × 2 × 2 hierarchical models. The invariance here refers to permutation of indices of each axis of the contingency tables. If the categories of each axis do not have any order relations among them, it is natural to consider the action of the symmetric group on each axis of the contingency table. A general algebraic algorithm for obtaining a Markov basis was given by Diaconis and Sturmfels (The Annals of Statistics, 26, 363–397, 1998). Their algorithm is based on computing Gröbner basis of a well-specified polynomial ideal. However, the reduced Gröbner basis depends on the particular term order and is not symmetric. Therefore, it is of interest to consider the properties of invariant Markov basis.     

A Theory of Orbit Braids*

In this paper, the authors systematically discuss orbit braids in M × I with regards to orbit configuration space FG(M, n), where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G. These orbit braids form a group, named orbit braid group, which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M, n), F(M/G, n) and F(M, n). They also co...     

比较发散量积分法的改进

本文从多方面改进了比较发散量积分法,利用这新方法给出了Ｌｉｅｎａｒｄ系统 极限环唯二性与唯一性的一些比以前更有效的判定条件．     

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same plane with uniform angular velocity, lying at the vertices of an equilateral triangle. The insertion of the radiation factor in the restricted four-body problem, let us model the dynamics of a test particle orbiting an astrophysical system with an active star. The dynamical mechanisms responsible for the smoothening on the basin structures of the configuration space is related to the decrease in the total number of fixed points with increasing values of the radiation parameter. In our model of the Sun-Jupiter-Trojan Asteroid system, it is found that despite the solar radiation pressure, there exist two stable libration points.     

合肥光源储存环聚焦模型标定

 描述了利用轨道响应矩阵拟合技术标定合肥光源储存环聚焦模型的过程及实验结果。通过响应矩阵分析,得到了合肥光源储存环弯铁边缘聚焦强度约为0.1 mrad/A,场积分为0.62~0.63,考虑了四极铁聚焦强度的修正系数的影响,发现了原四极铁磁测数据中较大的系统偏差,分析结果和备用磁铁的磁场测量数据吻合良好。在此基础上建立的合肥光源储存环理论模型可以准确地描述实际储存环线性光学特性。     

On sheaves in finite group representations

Given a general finite group G, we consider several categories built on it, their Grothendieck topologies and resulting sheaf categories. For a certain class of transporter categories and their quotients, equipped with atomic topology, we explicitly compute their sheaf categories via sheafification. This enables us to identify G-representations with various fixed-point sheaves. As a consequence, it provides an intrinsic new proof to the equivalence of M. Artin between the category of sheaves on the orbit category and that of group representations.