Joint Invariants and Joint Differential Invariants of Some Transformation Groups

The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.

GL（n, R）-Equivalence of a Pair of Curves in Terms of Invariants

In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl（n,R）. The conditions of G = Gl（n, R） -equivalence of a pair of curves are found in terms of G = Gl（n, R）-invariants. And the independence of GL（n, R） -invariants is shown.

Extension of covariant derivative(Ⅱ): From flat space to curved space

This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

The HeatKernel ofthe Sym m etric Space P_n

In this paper the heat kernel of the symmetric space P n is obtained.

Existence Theorem of the Multipliers on Riemannian Symmetric Space SL(3,H)/SP(3)

Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.

Equivalence of Paths under the Action of the Real Representation of Sp(n)

In this article, we will consider questions of G-equivalence of paths for the case when G was the group of the real representation of a symplectic transformation in an n-dimensional quaternion vector space. In determining the solution of this problem, we give an explicit description of differential generators of a differential field of differential rational functions that are invariant under the action of this group. Necessary and sufficient conditions for the G-equivalence of paths in a 4n-dimensional real space are obtained with the help of differential generators.

Introduction to an Invariant Quantity Method

It is impossible,mathematically, to use a time series which is regarded as a set of observational facts of a dynamicsystem to reconstruct the particular system.Physically, however, with a few assumptions put, a dynamic system canbe rebuilt approximately by means of observational facts.This is the goal of the so called invariant quantity method(IQM),whose research and experiment are of potential significance to atmospheric sciences.

The J_2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement

A 3-craft formation configuration is proposed to perform the digital elevation model （DEM） for the distributed spacebome interferometric synthetic aperture radar （InSAR）, and it is optimized by the modified ant colony algorithm to have the best compatibility with J2 invariant orbits created by differential correction algorithm. The configuration has succeeded in assigning the across-track baseline to vary periodically and with its mean value equal to the optimal baseline determined by the relative height measurement accuracy. The required relationship between crafts＇ magnitudes and phases is formulated for the general case of interferometry measure from non-orthographic and non-lateral view. The J2 invariant configurations created by differential correction algorithm are employed to investigate their compatibility with the required configuration. The colony algorithm is applied to search the optimal configuration holding the near-constant across-track baseline under the J2 perturbation, and the absolute height measurement accuracy is preferable as expected.

THE GENERATING SET OF THE DIFFERENTIAL INVARIANT ALGEBRA AND MAURER-CARTAN EQUATIONS OF A(2+1)-DIMENSIONAL BURGERS EQUATION

The authors construct Maurer-Cartan equation, the generating set of the differential invariant algebra and their syzygies for the symmetry groups of a （2＋1）-dimensional Burgers equation, based on the theory of equivariant moving frames of infinite-dimensional Lie pseudo-groups.