The Rohlin property for shifts of finite type

We show that an automorphism of a unital AF C^*-algebra with a certain approximate Rohlin property has the Rohlin property. This generalizes a result of Kishimoto. Using this we show that the shift automorphism on the bilateral C^*-algebra associated with an aperiodic irreducible shift of finite type has the Rohlin property.     

Quadrics of finite type

We show that the only quadrics of finite type in Euclidean 3-space are the circular cylinder and the sphere.This work was done while the second author was visiting the Michigan State University. He would like to thank MSU, and in particular the staff of the department of mathematics for their hospitality.Research Assistant of the National Fund for Scientific Research (Belgium)     

The hartman-grobman theorem for reversible systems on banach spaces

Summary In this note we give a version of the Hartman-Grobman Theorem for reversible systems defined on a Banach space. We prove that the homeomorphism that reduces the nonlinear system to the linearized one preserves the symmetry. Applications to coupled nonlinear second-order ordinary differential equations and to coupled nonlinear wave equations are discussed.     

A two-dimensional glimm type scheme on cauchy problem of two-dimensional scalar conservation law

In this paper,we construct a new two-dimensional convergent scheme to solve Cauchy problem of following two-dimensional scalar conservation law{?_tu +?_xf(u) + ?_yg(u) = 0,u(x,y,0) = u_0(x,y).In which initial data can be unbounded.Although the existence and uniqueness of the weak entropy solution are obtained,little is known about how to investigate two-dimensional or higher dimensional conservation law by the schemes based on wave interaction of 2D Riemann solutions and their estimation.So we construct such scheme in our paper and get some new results.     

Carleson embedding theorem on convex finite type domains

This paper concerns certain geometric aspects of function theory on smoothly bounded convex domains of finite type in Cn. Specifically, we prove the Carleson-Hörmander inequality for this class of domains and provide examples of Carleson measures improving a known result concerning such measures associated to bounded holomorphic functions.     

Embedded minimal ends of finite type

We prove that the end of a complete embedded minimal surface in with infinite total curvature and finite type has an explicit Weierstrass representation that only depends on a holomorphic function that vanishes at the puncture. Reciprocally, any choice of such an analytic function gives rise to a properly embedded minimal end provided that it solves the corresponding period problem. Furthermore, if the flux along the boundary vanishes, then the end is -asymptotic to a Helicoid. We apply these results to proving that any complete embedded one-ended minimal surface of finite type and infinite total curvature is asymptotic to a Helicoid, and we characterize the Helicoid as the only simply connected complete embedded minimal surface of finite type in .

     

On e-cuspidal pairs of finite groups of exceptional Lie type

Let G be a simple, simply connected algebraic group of exceptional type defined over ${\mathbb{F}}_q$ with Frobenius endomorphism $F:G\to G$. Let $??q$ be a good prime for G. We determine the number of irreducible Brauer characters in the quasi-isolated ?-blocks of $G^F$. This is done by proving that generalized e-Harish-Chandra theory holds for the Lusztig series associated to quasi-isolated elements of $G^{?F}$.     

Weak equivalence for shifts of finite type

We derive a computable set of necessary and sufficient conditions for the existence of a homomorphism from one shift of finite type to another. Also we consider an equivalence relation on subshifts, called weak equivalence, which was introduced and studied by Beal and Perrin. We classify arbitrary shifts of finite type up to weak equivalence.     

Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法

在半离散格式下.研究了Stokes型积分一微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法,在不需要传统Ritz-Volterra投影下,通过辅助空间等新的技巧得到了与传统有限元方法相同的误差估计.     

A maschke type theorem for weak Hopf algebras

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.     

Radon transforms and finite type conditions

We prove regularity of Radon type integral operators in -Sobolev spaces.

     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

Central limit asymptotics for shifts of finite type

We study the rate of convergence and asymptotic expansions in the central limit theorem for the class of Hölder continuous functions on a shift of finite type endowed with a stationary equilibrium state. It is shown that the rate of convergence in the theorem isO(n ^?1/2) and when the function defines a non-lattice distribution an asymptotic expansion to the order ofo(n ^?1/2) is given. Higher-order expansions can be obtained for a subclass of functions. We also make a remark on the central limit theorem for (closed) orbital measures.     

Estimating reachable sets for two-dimensional linear discrete systems

We are concerned with the problem of estimating the reachable set for a two-dimensional linear discrete-time system with bounded controls. Different approaches are adopted depending on whether the system matrix has real or complex eigenvalues. For the complex eigenvalue case, the quasiperiodic nature of minimum time trajectories is exploited in developing a simple, but often accurate, procedure. For the real eigenvalue case, over estimates of reachable sets can be trivially obtained using a decomposition method.The second author was supported by funds supplied by the John M. Bennett Faculty Fellowship, Trinity University, San Antonio, Texas.     

An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions

Following the classical procedure developed by Wiener and Ikehara for the proof of the prime number theorem we find an asymptotic formula for the number of closed orbits of a suspension of a shift of finite type when the suspended flow is topologically weak-mixing and when the suspending function is locally constant.     

Extensions and extremality of recursively generated weighted shifts

Given an -step extension of a recursively generated weight sequence , and if denotes the associated unilateral weighted shift, we prove that

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In particular, the subnormality of an extension of a recursively generated weighted shift is independent of its length if the length is bigger than 1. As a consequence we see that if is a canonical rank-one perturbation of the recursive weight sequence , then subnormality and -hyponormality for eventually coincide. We then examine a converse--an ``extremality" problem: Let be a canonical rank-one perturbation of a weight sequence and assume that -hyponormality and -hyponormality for coincide. We show that is recursively generated, i.e., is recursive subnormal.

     

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the Hausdorff measure of the sets of finite type of the one-sided symbolic space are given. Project partially supported by the Natural Science Foundation of Guangdong Province and the Foundation of Advanced Research of Zhongshan University.