Erratum to: Static Limit and Penrose Effect in Rotating Reference Frames

Theoretical and Mathematical Physics - Reference [3] on page 1125, 3. A. A. Grib and Yu. V. Pavlov, “Comparison of particle properties in Kerr metric and in rotating coordinates,” Gen....     

Generalized Frames in the Space of Strong Limit Power Functions

By using the existence of a larger orthonormal basis, the space of strong limit power functions is extended. We use the windowed Fourier transform and wavelet transform to analyze strong limit power signals and we construct generalized frame decompositions using the discretized versions of these transforms.     

非完整非有势系统相对于非惯性系的广义Noether定理

本文构造了力学系统相对运动的Lagrange函数,建立了非线性非完整非有势系统相对于非惯性系的Jourdain型变分原理,提出并证明了这类力学系统相对于非惯性系的广义Noether定理,研究了其守恒量.     

Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames

Mathematical Notes - Tangent-valued forms, tangent and cotangent vectors of the first and the second order are considered. For an affine connection, second-order tangent-valued (vertical and...     

变质量非完整系统相对于非惯性系的第一积分与积分不变量

本文给出了变质量非完整系统相对于非惯性系的第一积分存在的条件，建立了这类系统的正则方程和变分方程，证明了由第一积分可直接构造系统的积分不变量，并给出一系列推论和一个例子．     

非线性非完整系统相对于非惯性系动力学的积分理论*

本文建立非线性非完整系统相对于非惯性系动力学的积分理论.首先,由这种相对运动的Routh方程给出系统的第一积分;其次,分别利用系统的循环积分、能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程;再次,建立这类系统运动的正则方程和变分方程,并由第一积分构造系统的积分不变量;然后,给出系统的Poincare-Cartan型积分变量关系和积分不变量.最后,给出一系列推论.     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.Supported partly by the Wittgenstein 2000 Award of Peter Markowich, funded by the Austrian Science Foundation (FWF), research grants of DFG (436 RUS 113/615/0-1(R)) and RFBR (01-01-04002).On leave Department of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia. Supported partly by Max Planck Institute for the Mathematics in Sciences (Leipzig) and the Austrian Science Foundation (FWF) START Project (Y-137-TEC) of Norbert Mauser.     

Irregular Wavelet Frames and Gabor Frames

Given g∈L²(R ⁿ ), we consider irregular wavelet for the form\(\left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j \) > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L²(R ⁿ ) are given. For a class of functions g∈L²²(R ⁿ ) we prove that certain growth conditions on {λ _j } will frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system\(\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} \)to be a frame.     

Irregular Wavelet Frames and Gabor Frames

Given g { l^\fracn2 g( l_j x - kb ) }_jezjezⁿ ,where  l_j \left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L ²(R ⁿ ) are given. For a class of functions g{ e^{zrib( j,x )} g( x - l_k ) }_{jezⁿ ,kez}\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} to be a frame.     

变质量非完整非保守系统相对于非惯性系的最小作用量原理*

本文求得变质量非完整非保守系统相对于非惯性系的广义最小作用量原理,推证其H?lder形式与Суслов形式的等价性.最后,用求得的相应系统的最小作用量原理建立其运动微分方程.     

The Penrose transform in quaternionic geometry

We study the Penrose transform for the ‘quaternionic objects’ whose twistor spaces are complex manifolds endowed with locally complete families of embedded Riemann spheres with positive normal bundles.     

Hopf Algebras and the Penrose Polynomial

Let λ be a positive integer and let G be a plane graph. LetP (G, λ) be the Penrose polynomial of G. We will present an interpretation ofP (G, − λ) in terms of colourings of G. In order to prove our main theorem we construct a Hopf algebra A of graphs and a homomorphism of Hopf algebras Ψ fromA onto a Hopf algebra of polynomials in one indeterminate. If G is a plane graph, thenΨ (G) coincides with the Penrose polynomial of G.     

Penrose transformation and complex integral geometry

A survey is given of results on the representation of solutions of systems of massless equations in terms of solutions of the Cauchy-Riemann equations on the space of Penrose twisters. A detailed introduction to the theory of twistors is given. The basic integral transform — the Penrose transformation — is investigated by means of complex integral geometry. Other approaches to the theory of twistors are discussed and compared. In addition, the Yang-Mills equation is considered from the point of view of nonlinear Cauchy-Riemann equations.     

广义Frame与广义Frame的商

本文将frame、frame同态、商frame与核的概念在范畴意义下作推广,并且证明Frame范畴是广义Frame范畴的反射子范畴.进而讨论了一个广义frame A的商与A上核函子之间的关系.特别地,我们证明了A上全部核函子所构成的范畴N(A)是一个广义frame.     

A Numerical Method for the Dynamical Correction of Celestial Reference Frames from Non-Regular Samples

The aim of this paper is to analyze the orientation errors of a celestial reference system. These errors can be obtained by analyzing the differences between the observed and calculated positions for a set of selected minor planets. The classical methods do not work well if the sample is non-homogeneous on the region covered by the observations. In this paper a new algorithm based on a new class of spatial estimators and an appropriate reconstruction operator is proposed.     

Some Penrose transforms in complex differential geometry

In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The other concerns obstructions to the embedding of CR structures on the three-sphere. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

框架的强分离性与紧框架的构造

Hilbert空间上框架的分离性概念是由Han与Larson首先提出的.分离框架有很多有用的性质.本文利用强分离紧框架来构造出新的紧框架.特别地,我们将给出一些充分或充要条件使得正规紧框架的算子系数的线性组合是某些特殊的紧框架.并给出一个框架存在界满足一定条件的紧对偶框架的充要条件.最后还讨论了实Hilbert空间中的一些相关问题.