Some remarks on general commutators theorems

The paper proves some general facts on commutators that refer to Fuglede-Putnam classical theorem in the spectral theory of not necessarily selfadjoint operators.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Cyclic cohomology and algebra extensions

We construct a spectral sequence to study cyclic cohomology for an extension A = R/I of algebras. When R is a free algebra we describe the cyclic cohomology of A in terms of traces defined on R or powers of I. Explicit cyclic cocycles representing the cyclic cohomology class belonging to the trace are constructed as analogues of Chern character and Chern-Simons forms.Dedicated to Alexander Grothendieck     

两个非线性方程的准确解

借助于计算机代数系统Ｍａｔｈｅｍａｔｉｃａ利用直接代数方法获得了两个有数学物理意义的非线性耗散－色散方程的准确解，这种方法也适用于高维非线性方程。     

Some Oscillatory Singular Integrals on Herz-type Spaces (Ⅱ)

In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).     

Symmetry of the Barochronous Motions of a Gas

We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.     

A continuous function space with a Faber basis

Let be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (P_n)_n=0^∞ with deg P_n=n such that every fC(S) has a unique representation f=∑_i=0^∞ α_iP_i and call such a basis Faber basis. In the special case of , 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(S_q)≠U(S_q)=C(S_q), where A(S_q) is the so-called Wiener algebra and U(S_q) is the set of all fC(S_q) which are uniquely represented by its Fourier series.