Additive Kernels and Integral Representation of Potentials

Let P=(P _t ) _t>0 be a submarkovian semigroup of kernels on a measurable space (X,). An additive kernel of P is a kernel K from X into ]0,[ such that P _t K(x,A)=K(x,A+t) for every t>0,xX and every Borel subset A of ]0,[. It is proved in this paper that for every potential f of P, there exits an additive kernel K of P, unique (up to equivalence) such that f=K1=₀ K(,dt). This result is already well known for regular potentials of right processes. If U=(U _p ) _p>0 is a sub-Markovian resolvent of kernels on (X,), we give a notion of additive kernel of U and we prove a similar integral representation of potentials of U.     

A note on triangular derivations of

For a field of characteristic zero, and for each integer , we construct a triangular derivation of whose ring of constants, though finitely generated over , cannot be generated by fewer than elements.

     

Basis Problem for Turbulent Actions II: c0-Equalities

Let (Xⁿ,dⁿ) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c₀-equality.A systematic study is made of c₀-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics d_n, are obtainedfor a c₀-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c₀-equality D either reducesa c₀-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c₀-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c₀-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15.     

Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions

For any stable distribution on the line, recurrence-transience of the selfsimilar additive process {X _t ,t0} with (X ₁)= is determined. Comparison with the stable Lévy process {Y _t ,t0} with (Y ₁)= is made: if is not strictly stable, then {Y _t } is transient but {X _t } is recurrent except the obviously transient case of monotone sample functions.     

基于半导体光放大器的干涉型器件中噪声特性的分析

分析了基于半导体光放大器(SOA)的干涉仪分别处于“开”、“关”两种工作状态时的输出信噪比及噪声指数,发现当干涉仪处于“开”态时输出信噪比有所恶化,并导出了附加噪声因子的表达式。实验结果进一步证明了理论分析的正确性。     

肉牛饲料添加剂中铅含量的测定

利用火焰原子吸收光谱法(FAAS),测定了硫酸铜、硫酸锌、膨润土、米糠、氧化锌、菜渣、盐等7种肉牛饲料添加剂中铅(Pb)元素的含量.各添加剂的加标回收率在98%-108%之间,相对标准偏差(RSD)小于1.3%,具有良好的准确度和精确度.结果表明,试验中所测的硫酸铜、硫酸锌、氧化锌添加剂中铅含量严重超出国家标准.     

Macroporous Morphology of the Titania Films Prepared by a Sol-Gel Dip-Coating Method from the System Containing Poly(Ethylene Glycol). III. Effect of Chemical Additives

The variation of macroporous morphology has been studied for the titania (TIO₂) films prepared by a sol-gel dip-coating method from the system containing poly(ethylene glycol) (PEG) under the addition of various types of organic solvents. The influence of externally-added solvent is interpreted by considering the compatibility between PEG and the solvent mixture, the volatility of the solvent mixture, and the polycondensation rate of titania oligomers. The macroscopic domain formation is remarkable when the compatibility between the solvent mixture and PEG is relatively poor and the boiling point of external solvent is relatively low.     

A characteristic nonoverlapping domain decomposition method for multidimensional convection‐diffusion equations

We develop a quasi‐two‐level, coarse‐mesh‐free characteristic nonoverlapping domain decomposition method for unsteady‐state convection‐diffusion partial differential equations in multidimensional spaces. The development of the domain decomposition method is carried out by utilizing an additive Schwarz domain decomposition preconditioner, by using an Eulerian‐Lagrangian method for convection‐diffusion equations and by delicately choosing appropriate interface conditions that fully respect and utilize the hyperbolic nature of the governing equations. Numerical experiments are presented to illustrate the method. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Mazur-Ulam定理的一个注记

本文的主要结论是给出了一个更广泛形式的Mazur-Ulam定理.讨论的对象是实的赋准范空间,满等距算子被减弱成其像空间构成一个加法子群的算子.最后给出的推论推广了Skof的一个结果.     

广义可加Fuzzy测度

本文首先引入Fuzzy集类上（广义）可加Fuzzy测度的有关概念，然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理，最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。