一类逆半群的亚直可约性

本文利用逆半群上的同余扩张，讨论了一类逆半群的亚直可约性，并刻划了这类逆半群的幂等元集的特征。     

Reference priors for exponential families with simple quadratic variance function

Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive reparameterization which allows one, among other things, to construct an enriched conjugate prior. In this paper, under the assumption that the variance function is simple quadratic, the order-invariant group reference prior for the above parameter is found. Furthermore, group reference priors for the mean- and natural parameter of the families are obtained. A brief discussion of the frequentist coverage properties is also presented. The theory is illustrated for the multinomial and negative-multinomial family. Posterior computations are especially straightforward due to the fact that the resulting reference distributions belong to the corresponding enriched conjugate family. A substantive application of the theory relates to the construction of reference priors for the Bayesian analysis of two-way contingency tables with respect to two alternative parameterizations.     

CuO／CeO2和CuO／Al2O3催化剂的催化性能

本文以ＣＯ氧化为模式反应考察了ＣｅＯ２和Ａｌ２Ｏ３负载氧化铜催化剂的氧化活性，运用ＸＲＤ和ＴＰＲ技术研究了催化剂的还原性能和物相结构，结果表明：载体性质对负载ＣｕＯ催化剂的ＣＯ氧化活性有很大影响，ＣｕＯ／ＣｅＯ２催化剂活性明显高于ＣｕＯ／Ａｌ２Ｏ３催化剂．催化剂的还原特性随载体不同而不同．同时发现，热处理对催化剂铜物种的存在形式，晶粒大小、还原特性及其催化活性有明显影响，ＣｕＯ／Ａｌ２Ｏ３催化剂活性下降的主要因素是生成了活性较低的ＣｕＡｌ２Ｏ４相，而ＣｕＯ／ＣｅＯ２催化剂活性下降是由于ＣｕＯ和ＣｅＯ２发生烧结，晶粒变大     

Contravariant forms and extremal projectors

Tensor product of irreducible modules of highest weight over a semi-simple quantum group is completely reducible if and only if a natural contravariant form is non-degenerate when restricted to the span of singular vectors. We express this restriction through the extremal projector of the quantum group providing a computationally feasible criterion for complete reducibility of tensor products.     

Cr－Ag／γ－Al_2O_3催化剂在CO氧化反应中Ag的助催化作用

Ｃｒ－Ａｇ／γ－Ａｌ_２Ｏ_３催化剂在ＣＯ氧化反应中Ａｇ的助催化作用陈平，朱波，钟依均，罗孟飞，李少华，吴红丽（杭州大学催化研究所杭州３１００２８）（杭州大学中心实验室杭州）关键词氧化铬，氧化银，氧化铝，负载催化剂，还原特性，一氧化碳，氧化活性催化燃烧...     

On the (semi)lattices induced by continuous reducibilities

Continuous reducibilities are a proven tool in Computable Analysis, and have applications in other fields such as Constructive Mathematics or Reverse Mathematics. We study the order‐theoretic properties of several variants of the two most important definitions, and especially introduce suprema for them. The suprema are shown to commutate with several characteristic numbers (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reducibility and nonreducibility between equivalence relations

We show that, for , the relation of -equivalence between infinite sequences of real numbers is Borel reducible to the relation of -equivalence (i.e., the Borel cardinality of the quotient is no larger than that of ), but not vice versa. The Borel reduction is constructed using variants of the triadic Koch snowflake curve; the nonreducibility in the other direction is proved by taking a putative Borel reduction, refining it to a reduction map that is not only continuous but `modular,' and using this nicer map to derive a contradiction.

     

On the Relation of Σ-Reducibility Between Admissible Sets

Reducibility on admissible sets is studied which is a stronger version of the usual -presentability of models. One of its informal prototypes is the interpretability of one computational device in the other. We obtain criteria of reducibility for recursively listed and pure sets, introduce the notion of jump, and prove exact boundaries for the ordinals of jumps. We also show that this reducibility is lifted to -superstructures. Several results are proven on the relations of this reducibility to some known reducibilities.     

Linear algebraic groups and countable Borel equivalence relations

If is an equivalence relation on a standard Borel space , then we say that is Borel reducible to if there is a Borel function such that . An equivalence relation on a standard Borel space is Borel if its graph is a Borel subset of . It is countable if each of its equivalence classes is countable. We investigate the complexity of Borel reducibility of countable Borel equivalence relations on standard Borel spaces. We show that it is at least as complex as the relation of inclusion on the collection of Borel subsets of the real line. We also show that Borel reducibility is -complete. The proofs make use of the ergodic theory of linear algebraic groups, and more particularly the superrigidity theory of R. Zimmer.

     

About Segment Complexity of Turing Reductions

We apply complexity concepts to define a new sort of sub-Turing reducibilities ≤ ?? make the degree hierarchy thinner and to obtain some new specifications of the well known jump inversion theorem of Friedberg. We show that this theorem doesn't hold when ≤ T is replaced with ≤ ??, where ?? is any countable subset of the class ?? of all total increasing functions f : ? → ?.