Transition-metal-free nucleophilic allylic substitutions of Morita–Baylis–Hillman bromides with aliphatic and aromatic amines

A simple protocol for the preparation of functionalized allylic amines under mild, transition-metal-free conditions from the reaction of Morita–Baylis–Hillman (MBH) bromides with amines is described herein. The treatment of the MBH bromides with various amines in the presence of NaI and Et₃N in aqueous acetone solution and at room temperature affords the corresponding functionalized allyl amines in moderate to good yields (45–87%). The reaction is rapid and carried out at room temperature.     

Summands of Stable Equivalences of Morita Type

A stable equivalence of Morita type between two finite dimensional algebras with no separable summand will be shown to restrict to stable equivalences of Morita type between their summands. We will apply this to prove that stable equivalence of Morita type preserves self-injectivity of algebras and the property of being symmetric.     

Rings of the Morita Contexts and Semihereditary Maximal V-Orders

Some necessary and sufficient conditions are given for rings of the Morita contexts to be semihereditary maximal V-orders, Prüfer rings and Dubrovin valuation rings.     

Study of Morita contexts

Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in n variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic polynomials. Canonical forms under standard-form congruence for three-by-three matrices are derived. This is then used to give a classification of algebras defined by two generators and one degree two relation. We also apply standard-form congruence to classify homogenizations of these algebras.     

Existence of Gradings on Associative Algebras

In this article, we study the existence of gradings on finite dimensional associative algebras. We prove that a connected algebra A does not have a nontrivial grading if and only if A is basic, its quiver has one vertex, and its group of outer automorphisms is unipotent. We apply this result to prove that up to graded Morita equivalence there do not exist nontrivial gradings on the blocks of group algebras with quaternion defect groups and one isomorphism class of simple modules.     

Initiating a state of the art system for real-time supply chain coordination

Intelligent Wireless Web (IWW) employs the capabilities of high speed wireless networks and exploits the parallel advancements in Internet-based technologies such as the Semantic Web, Web Services, Agent-based Technologies, and context awareness. Considering its great potentials to be applied in business systems, we have devised an innovative model, based on the IWW services, for a typical mobile real-time supply chain coordination system which has been developed and tested in a real operational environment. Our article investigates the proposed system in this way: at the start, the building blocks of the IWW are discussed in detail. Then, we fully explain the basic concepts of mobile real-time supply chain coordination and concentrate on the motivations to implement such a modern system. The vision of intelligent wireless web services, as discussed in this paper, centers on the need to provide mobile supply chain members highly specific data and services in real-time on an as-needed basis, with the flexibility of use for the user. In this regard, we investigate nine enabling technologies of the IWW for our system and discuss how, by exploiting the convergence and synergy between different technologies, it has become possible to deliver intelligent wireless web support to mobile real-time supply chain coordination. Afterwards, a practical framework is clearly established in four phases. This initiative system has been implemented in the laboratory and has passed the evaluation processes successfully. Further details will be announced in near future in another research article.     

The maximal C*-algebra of quotients as an operator bimodule

In this article we extend the work on strongly p-embedded subgroups in Parker and Stroth (Strongly p-embedded subgroups, arxiv:0901.0805) to include the Lie type groups of rank 2.     

模糊形式背景下的类近似算子

分别在形式背景和模糊形式背景下定义类下近似算子和类模糊下近似算子,并研究它们的性质.证明这两种算子分剐等价于形式背景和模糊形式背景下的*算子和模糊*算子.进一步给出类下近似算子与类模糊下近似算子的公理刺画.最后,对偶地讨论类上近似算子和类模糊上近似算子的定义和性质.     

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C ^*-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E ^*(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E ^*) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math. Soc. 49(1984), 289–306].