Large Zero Autocorrelation Zone of Golay Sequences and 4q4^q-QAM Golay Complementary Sequences

Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single $H$-ary Golay sequence and $4^q$-QAM Golay complementary sequence with a large zero autocorrelation zone, where $H\ge 2$ is an arbitrary even integer and $q\ge 2$ is an arbitrary integer. Those new results on Golay sequences and QAM Golay complementary sequences can be explored during synchronization and detection at the receiver end and thus improve the performance of the communication system

Directed Transmission Method, A Fully Asynchronous approach to Solve Sparse Linear Systems in Parallel

In this paper, we propose a new distributed algorithm, called Directed Transmission Method (DTM). DTM is a fully asynchronous and continuous-time iterative algorithm to solve SPD sparse linear system. As an architecture-aware algorithm, DTM could be freely running on all kinds of heterogeneous parallel computer. We proved that DTM is convergent by making use of the final-value theorem of Laplacian Transformation. Numerical experiments show that DTM is stable and efficient.Comment: v1: poster presented in SPAA'08; v2: full paper; v3: rename EVS to GNBT; v4: reuse EVS. More info, see my web page at http://weifei00.googlepages.co

On the dynamics of a family of renormalization transformations

We study the family of renormalization transformations of the generalized $d$--dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where $d\geq 2$. In particular, we prove that their Julia sets can never be a Sierpi\'{n}ski carpet if the parameter is real. We show that the Julia set is a quasicircle if and only if the parameter lies in the unbounded capture domain of these models. Moreover, the asymptotic formula of the Hausdorff dimension of the Julia set is calculated as the parameter tends to infinity.Comment: 21 pages, 5 figures, to appear in J. Math. Anal. App