基于S12X系列双核单片机的CAN网关设计

集成XGATE协处理器内核的S12XE系列双核单片机具有处理速度快、反应时间短、功耗低等优点,在嵌入式应用中具有独特优势和很好的应用前景。本文采用16位双核单片机MC9S12XEQ512作为主控制器,以集成信号和电源隔离功能的CAN收发器芯片ADM3053来实现CAN接口电路,设计并实现了一个可以连接3个CAN通信子网的CAN网关,有效实现了系统的小型化、低功耗、低成本。采用双核处理技术来优化CAN网关的处理流程,由协处理器XGATE来处理各种中断,S12X主CPU则专注于协议处理和消息转发。实际应用表明,系统运行稳定可靠,与传统的采用单处理器实现的CAN网关相比,系统的数据吞吐能力和实时性得到了明显改善。     

<Emphasis Type="Italic">P</Emphasis>-adic sets of range uniqueness

We study sets of range uniqueness (SRU’s) in a complete, ultrametric, algebraically closed fieldK for analytic elements. We find monotonic distances sequences which appear to be SRU’s completely different from those known in ©. On the other hand, most of open closed sets cannot be SRU’s.     

The global Cauchy problem for the NLS and NLKG with small rough data

By using the unit-cube decomposition to the frequency spaces, we study the Cauchy problem for the nonlinear Schrödinger equation and the nonlinear Klein-Gordon equation. Some global well posedness results are obtained for the small Cauchy data in some modulation spaces .     

On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds

In this paper we extend some results of the paper [M. Gromov, G. Henkin, M. Shubin, Holomorphic L²-functions on coverings of pseudoconvex manifolds, Geom. Funct. Anal. 8 (1998) 552-585].     

Spectrum and analytical indices of the C-algebra of Wiener-Hopf operators

We study multivariate generalisations of the classical Wiener-Hopf algebra, which is the C^∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C^∗-algebra is known to be isomorphic to the reduced C^∗-algebra of a certain restricted action groupoid, given by the action of Euclidean space on a certain compactification. Using groupoid methods, we construct composition series for the Wiener-Hopf C^∗-algebra by a detailed study of this compactification. We compute the spectrum, and express homomorphisms in K-theory induced by the symbol maps which arise by the subquotients of the composition series in analytical terms. Namely, these symbols maps turn out to be given by an analytical family index of a continuous family of Fredholm operators. In a subsequent paper, we also obtain a topological expression of these indices.     

A unique decomposition result for HT factors with torsion free core

We prove that II₁ factors M have a unique (up to unitary conjugacy) cross-product type decomposition around “core subfactors” N⊂M satisfying the property HT of [S. Popa, On a class of type II₁ factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809-899] and a certain “torsion freeness” condition. In particular, this shows that isomorphism of factors of the form Lαi(Z²)?Fni, i=1,2, for Fni⊂SL(2,Z) free groups of rank ni and αj=e2πitj, tj∉Q, implies n₁=n₂.     

Direct limits of infinite-dimensional Lie groups compared to direct limits in related categories

Let G be a Lie group which is the union of an ascending sequence G₁⊆G₂⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C^∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups.     

Functional spectrum of contractions

In this paper, we introduce a new kind of spectrum for the C⋅0-class contractions. Since elements in this spectrum are functions, rather than numbers, we shall call it functional spectrum. Functional spectrum is a “large” closed subset of the Hardy space over the unit disk, and in many cases there is a canonical embedding of classical spectrum into functional spectrum. The study is carried out in the setting of the Hardy space over the bidisk H²(D²), on which every C⋅0-class contraction has a representation. A key tool is reduction operator. The reduction operator also gives rise to an equivalent statement of the Invariant Subspace Problem.