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.

Conformal invariance and integration of first-order differential equations

This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.

J_2 invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

ON THE LOCAL SOLVABILITY OF DIFFERENTIAL EQUATIONS ASSOCIATED TO UNSOLVABLE INHOMOGENEOUS LEFT INVARIANT DIFFERENTIAL OPERATORS ON THE HEISENBERG GROUP

This paper studies the local solvability of the differental equations associated to unsolvable inhomogeneous left invariant differential operators on the Heisenberg group.It is provedthat for a class of inhomogeneous left invariant differental operators on the Heisenberg group,the local solvability of the corresponding equations is equivalent to the local sovability of the equations associated to their highest order terms.Then,under certain conditions on the highest order term,we obtain the necessary and sufficient conditions for the functon f to satisfy ill order for the differential equation Lu=f to be locally solvable

Application of Differential Invariant Method for Solving the Electromagnetic Fields

We study the first integral and the solution of electromagnetic field by Lie symmetry technique and the differential invariant method.The definition and properties of differential invariants are introduced and the infinitesimal generators of Lie symmetries and the differential invariants of electromagnetic field are obtained.The first integral and the solution of electromagnetic field are given by the Lie symmetry technique and the differential invariants method.A typical example is presented to illustrate the application of our theoretical results.

ASYMPTOTIC PROPERTIES OF FUNCTIONAL DIFFERENTIAL EQUATIONS IN BANACH SPACES

The paper is devoted to the asymptotic properties of functional differential equations in Banach spaces.The criteria of the invariant and attracting sets are obtained.Particularly, the sufficient condition of asymptotic stability of the equilibrium point is given as the system has an equilibrium point.Several examples are also worked out to demonstrate the validity of the results.

INVARIANT FORM AND INTEGRAL INVARIANTS ON KAHLER MANIFOLD

The important notions and results of the integral invariants of Poincard and Cartan-Poincard and the relationship between integral invariant and invariant form established first by E. Cartan in the classical mechanics are generalized to Hamilton mechanics on Kiihler manifold, by the theory of modern geometry and advanced calculus, to get the corresponding wider arid deeper results. differential

A new type of adiabatic invariants for disturbed non-conservative nonholonomic system

According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

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.

一类特殊Riccati微分方程通解理论的分析及其统一

Riccati微分方程在实际工程中有着广泛的应用,但由于不可积的特性,使其解法具有挑战性。针对相关文献中有关Riccati微分方程通解的问题,利用Riccati微分方程的不变量关系式进行分析讨论,揭示该微分方程解的内在本质,并且将相关文献中的Riccati微分方程解法统一起来,达到求解的简单美。

基于FPDE-SIFT的声呐干涉图像配准方法

图像配准是声呐进行高精度干涉测量的保障,该文针对水下目标的声呐图像配准,提出了一种基于4阶偏微分方程尺度不变特征变换的声呐干涉图像配准方法。该方法聚焦声呐图像配准的难点,首先基于4阶偏微分方程构建尺度空间,在保持图像细节的前提下滤除噪声,提高特征提取的准确度;对于残余噪声造成的特征点误检,借助特征点的相位一致性信息加以筛选,精简特征点样本集;最后对特征点匹配策略进行优化,提出改进的快速样本一致性匹配策略剔除特征点的误匹配。算法增加了匹配点对的数量,提高了匹配点对的准确度,实现了声呐干涉图像的精确配准。水池实验和外场试验表明,该文所提出的算法相较现有算法对声呐图像有着更好的适用性,配准后的均方根误差与留一法均方根均小于1像素,达到了亚像素配准精度。

广义的WBKL方程和HS-KdV方程的微分不变量、微分不变方程

以数学物理等领域中两个重要的非线性发展方程为研究对象,即广义的Whitham-Broer-Kaup-Like(WBKL)方程组和广义的HS-KdV方程组.WBKL方程描述了长波在浅水中的双向传播,此方程也可约化为变形的Boussinesq方程、色散长波方程、Whitham-Broer-Kaup方程等.由于WBKL方程和广义的Hirota-Satsuma耦合KdV方程的非线性和经典活动标架法的局限性,运用最新的等变活动标架理论,通过选择合适的群轨道横截面进行规范化,进而得到活动标架,同时借助符号计算系统Maple避免了复杂的高阶微分计算,切实有效地求得了WBKL方程组和广义的HS-KdV方程组的微分不变量、微分不变量代数以及微分不变方程.所得到的结果可用于深入研究WBKL方程和广义的HS-KdV方程解的不变性、等价性和对称性,以及海洋、大气、水波等非线性运动的趋势和规律.

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

Mucosal-associated invariant T cells from induced pluripotent stem cells:A novel approach for modeling human diseases

Mice have frequently been used to model human diseases involving immune dysregulation such as autoimmune and inflammatory diseases.These models help elucidatethe mechanisms underlying the disease and in the development of novel therapies.However,if mice are deficient in certain cells and/or effectors associated with human diseases,how can their functions be investigated in this species?Mucosal-associated invariant T(MAIT)cells,a novel innate-like T cell family member,are a good example.MAIT cells are abundant in humans but scarce in laboratory mice.MAIT cells harbor an invariant T cell receptor and recognize nonpeptidic antigens vitamin B2metabolites from bacteria and yeasts.Recent studies have shown that MAIT cells play a pivotal role in human diseases such as bacterial infections and autoimmune and inflammatory diseases.MAIT cells possess granulysin,a human-specific effector molecule,but granulysin and its homologue are absent in mice.Furthermore,MAIT cells show poor proliferation in vitro.To overcome these problems and further our knowledge of MAIT cells,we have established a method to expand MAIT cells via induced pluripotent stem cells(iP SCs).In this review,we describe recent advances in the field of MAIT cell research and our approach for human disease modeling with iP SCderived MAIT cells.

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.

Recent advances of cluster of differentiation 74 in cancer

Cluster of differentiation 74 （CD74） performs multiple roles in B cells, T cells, and antigen-presenting cells within the immune system; it also participates in ma-jor histocompatibility complex class Ⅱ-restricted an-tigen presentation and inflammation. Recently, a role for CD74 in carcinogenesis has been described. CD74 promotes cell proliferation and motility and prevents cell death in a macrophage migration inhibitory factor-dependent manner. Its roles as an accessory signal receptor on the cell surface and the ability to interact with other signaling molecules make CD74 an attrac-tive therapeutic target for the treatment of cancer. This review focuses on the original role of CD74 in the immune system and its emerging tumor-related func-tions. First, the structure of CD74 will be summarized. Second, the current understandings about the expres-sion, cellular localization, molecular mechanisms and signaling pathways of CD74 in immunity and cancer will be reviewed. Third, the examples that suggest CD74 is a promising molecular therapeutic target are reviewed and discussed. Although the safety and ef-fcacy of CD74-targeted strategies are under develop-ment, deeply understanding of the regulation of CD74 will hold promise for the use of CD74 as a therapeutic target and may develop the CD74-targeted therapeutic agents such as neutralized antibody and compounds.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

职业英语技能测量的不变性研究

本研究采用MG-CFA和Rasch模型,基于实用英语交际职业技能等级证书(VETS)初级首考数据,从性别、学校类型和专业类型三个维度对VETS的测量不变性进行了检验。MG-CFA用于检验考试整体层面的测量不变性,包括结构不变性、弱不变性、强不变性和严格不变性检验;Rasch用于检验考试题目层面是否存在DIF以及DIF的效应量。MG-CFA分析结果发现VETS对于不同性别和类型的考生均呈现严格不变性,不存在测量偏差;对于财经商贸类和教育与体育类考生的测量呈现弱不变性,这可能和该维度个别任务出现DIF有关。虽然基于Rasch的分析结果显示三个维度的任务呈现显著DIF,但都属于轻度DIF,可以忽略不计。