An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

关于拟Einstein场方程

In this paper some properties of a symmetric tensor field T(X, Y) = g(A(X), Y) on a Riemannian manifold (M,g) without boundary which satisfies the quasi-Einstein equation Rij-S/2gij=Tij+bξiξj are given. The necessary and sufficient conditions for this tensor to satisfy the quasi-Einstein equation are also obtained.     

Second-Order Covariant Tensor Decomposition in Curved Spacetime

Local four-dimensional tensor decomposition formulae for generic vectors and 2-tensors in spacetime, in terms of scalar and antisymmetric covariant tensor potentials, are studied within the framework of tensor distributions. Earlier first-order decompositions are extended to include the case of four-dimensional symmetric 2-tensors and new second-order decompositions are introduced.     

Universal Extension and Excision for Topological Algebras

We construct a topology on the tensor algebra that makes the multiplication jointly continuous and is universal for algebras with jointly continuous multiplication. This result, together with the methods developed by Cuntz for m-algebras are used to prove the excision theorem of Cuntz and Quillen in the more general case of c-algebras.     

The wall theorem for elastic moduli

New expressions for the elastic moduli of a classical system are derived. They involve only the two-point correlation function and the derivative of the onepoint correlation function, both only on the boundary of the system. These expressions, valid for any interaction derivable from a potential, are proved from a mechanical point of view by generalizing the virial theorem of Clausius, and from a statistical point of view by a direct method that constitutes an alternative to Green's dilatation method.     

The structure of some classes of <Emphasis Type="Italic">K</Emphasis>-contact manifolds

We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi projectively flat and φ-projectively flat are obtained. We also prove that for a (2n + 1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, φ-projectively flat and locally isometric to the unit sphere S ²ⁿ⁺¹ (1) are equivalent. Finally, we prove that a compact φ-projectively flat K-contact manifold with regular contact vector field is a principal S ¹-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.     

Nucleon-nucleon interaction with tensor forces in the quark compound bag model

A model forN-N interaction proposed earlier by two of us (VSB and VKG), has been extended to incorporate the tensor component of the nuclear force. Based on the quark compound bag model (QCB), the nucleon-nucleon potential has a short range repulsive core which is non-local and has a characteristic energy dependence and is expressed in terms of the parameters relating to the six-quark compound bag. To account for the low energy properties, this repulsive core interaction is supplemented by a phenomenological non-local potential containing both central (S-wave) and tensor components and operates only outside the QCB. Using this model, we analyse and compare the results with the experimental data for the electromagnetic form factors of the deuteron, theD-state observables, such as the quadrupole moment, theD-state probability, and theD/S ratio along with then-p scattering phase shifts up to about 400 MeV.     

Banach空间的张量积及其共轭空间

张量积函子是同调代数中研究模范畴的重要工具。在[1]的基础上,本文对B-空间的张量积做了讨论,得出一些新的结论。设E是B-空间,{E_i,j∈J}是B-空间族,作为赋范空间,则E(?)∪_(i∈J)E_i与∪_(i∈J)(E(?)E_i)等距同构。作为B-空间,E(?)_(?)∪_(i=1)~(?)E_i与∪_(i=1)~(?)(E(?)_(β_(?))E_i)的子空间等距同构。其次本文推广了著名的伴随同构定理([2]Th2.11).设E_1,E_2与F是B-空间,则(?)(E_1(?)_(?)E_2,F)分别与(?)(E_2,(?)(E_1,F)),(?)(E_1,(?)(E_2,F))等距同构.特别(E_1(?)_(?)E_2)分别与(?)(E_2,E_1),(?)(E_1,E_2)等距同构.最后,设E_i,F_i是B-空间,f∈(?)(E_1,F_1),g∈(?)(E_2,F_2),则存在唯一的φ∈(?)(E_1(?)_(β_1)E_2,F_1(?)_(β_2)F_2),记φ=f(?)g.令P={sum from i to f_i(?)g_i},则P与(?)(E_1,F_1)(?)_(?)(?)(E_2,F_2)的稠密子空间(?)(E_1,F_1)(?)(E_2,F_2)等距同构。特别E_1(?)E_2是(E_1(?)_(β_1)E_2)的子空间。本文中的记号同于[1]。文中涉及到张量积的范数都是Cross-范数。     

Poisson流形上微缩算子η的应用

本文根据Poisson流形P的1-形式空间∧1(P)上的微缩算子η及其性质,给出了η-代数胚的定义,进一步得到了微缩算子在η-代数胚及Poisson流形中的一些应用.     

紧支撑三元正交小波滤波器的参数化

高维小波分析是分析和处理多维数字信号的有力工具．非张量积多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域．本文给出方体域上三元正交滤波器的一种参数化构造算法,三元小波滤波器的这种构造方法使我们能更方便地研究非张量积的三元正交小波．最后给出数值算例．