Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.     

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.

     

Creep life evaluation of aluminum conductor composite core utilized in high voltage electric transmission

The creep life of aluminum conductor composite core (ACCC) utilized in high voltage electric transmission was investigated using an experimental method based on the equivalence relationship. First, the time-temperature-stress equivalence relationship was developed using the time-temperature and the time-stress equivalence relationships. Then, tensile creep experiments were conducted under different temperatures and different stress levels to obtain the strain-time curves of the ACCC. Finally, the creep strain master curve was obtained using the experimental data based on the time-temperature-stress equivalence relationship, allowing prediction of ACCC creep life. The results will play an important role in evaluation of the long-term characteristics of the ACCC for engineering applications.     

Nonextensive entropies derived from Gauss? principle

Gauss? principle in statistical mechanics is generalized for a q-exponential distribution in nonextensive statistical mechanics. It determines the associated stochastic and statistical nonextensive entropies which satisfy Greene-Callen principle concerning on the equivalence between microcanonical and canonical ensembles.     

Graphs realised by r.e. equivalence relations

We investigate dependence of recursively enumerable graphs on the equality relation given by a specific r.e. equivalence relation on ω. In particular we compare r.e. equivalence relations in terms of graphs they permit to represent. This defines partially ordered sets that depend on classes of graphs under consideration. We investigate some algebraic properties of these partially ordered sets. For instance, we show that some of these partial ordered sets possess atoms, minimal and maximal elements. We also fully describe the isomorphism types of some of these partial orders.     

森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ的表示,确定其几乎分裂序列(也称AR-序列)是非常重要的.通过modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.     

Socle equivalences of weighted surface algebras

We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field K which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in [11]. In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.     

Hopf代数胚上的Smash积的Maschke型定理和Morita关系

本文研究了Hopf代数胚上的Smash积代数.利用Hopf代数胚的积分理论,获得了Hopf代数胚上的Smash的Maschke型定理并构造了一个Morita关系,推广了Cohen和Fishman在文献[1]中的相应结果.作为应用,获得了Hopf代数胚上的余模代数的Maschke型定理.     

A Morita theorem for dual operator algebras

We prove that two dual operator algebras are weak^∗ Morita equivalent in the sense of [D.P. Blecher, U. Kashyap, Morita equivalence of dual operator algebras, J. Pure Appl. Algebra 212 (2008) 2401-2412] if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak^∗-continuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case, we characterize such functors as the module normal Haagerup tensor product with an appropriate weak^∗ Morita equivalence bimodule. We also develop the theory of the W^∗-dilation, which connects the non-selfadjoint dual operator algebra with the W^∗-algebraic framework. In the case of weak^∗ Morita equivalence, this W^∗-dilation is a W^∗-module over a von Neumann algebra generated by the non-selfadjoint dual operator algebra. The theory of the W^∗-dilation is a key part of the proof of our main theorem.