一类加随机扰动的Tent-Map数字混沌序列研究

提出了一类加随机扰动的Tent-Map,克服了周期性和不稳定性的缺点.用软件仿真,研究了所加随机扰动的幅度对数字混沌序列特性的影响.结果表明,随机扰动的幅度只有达到合适的值,才能得到性能优良的扩频码.     

Determination of the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of stable atropisomeric PCBs on Chirasil-dex

Pure enantiomers of chiral (atropisomeric) polychlorinated biphenyls (PCBs) obtained by high-performance liquid chromatography were used to establish the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of six PCB atropisomers on Chirasil-Dex. The elution order was found to be (−/+) for PCBs 84, 132, 136, and 176 and (+/−) for PCBs 135 and 174. The retention characteristics of all 19 tri- and tetra-ortho atropisomeric PCBs were also investigated. Nine of the atropisomers could be separated using this chiral selector. PCBs 95, 132, and 149 were completely resovled and PCBs 84, 91, 135, 136, 174, and 176 were partially separated (R = 0.7–0.9). All of the separated congeners are 2,3,6-substituted in at least one ring, and conversely – none of the congeners that lacks 2,3,6-substitution could be separated. Thus, chiral recognition and enantiomer separation seems to be strongly governed by 2,3,6-substitution.     

关于二阶线性递归序列的加权和

设{wn}为二阶线性递归序列,n为整数.给出了关于二阶线性递归序列{wn}的加权和T(m)的定义,研究了二阶线性递归序列{wn}的加权和T(m),得到了关于加权和T(m)的一个公式,本文的主要结果推广了Kiyota Ozeki的一个结果.     

一定条件下PA序列部分和的完全收敛性

根据PA序列的一些基本性质和定理,比照独立随机变量下的结论,对PA序列的完全收敛性作了初步的推导和论证,从而完善了相关结果.     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Conditions for the convergence in distribution of maxima of stationary normal processes

The asymptotic distribution of the maximum M_n=max_1?t?nξ_t in a stationary normal sequence ξ₁,ξ,… depends on the correlation r_t between ξ₀ and ξ_t. It is well known that if r_t log t → 0 as t → ∞ or if Σr²_t<∞, then the limiting distribution is the same as for a sequence of independent normal variables. Here it is shown that this also follows from a weaker condition, which only puts a restriction on the number of t-values for which rt log t islarge. The condition gives some insight into what is essential for this asymptotic behaviour of maxima. Similar results are obtained for a stationary normal process in continuous time.     

An alignment-free measure based on physicochemical properties of amino acids for protein sequence comparison

Sequence comparison is an important topic in bioinformatics. With the exponential increase of biological sequences, the traditional protein sequence comparison methods — the alignment methods become limited, so the alignment-free methods are widely proposed in the past two decades. In this paper, we considered not only the six typical physicochemical properties of amino acids, but also their frequency and positional distribution. A 51-dimensional vector was obtained to describe the protein sequence. We got a pairwise distance matrix by computing the standardized Euclidean distance, and discriminant analysis and phylogenetic analysis can be made. The results on the Influenza A virus and ND5 datasets indicate that our method is accurate and efficient for classifying proteins and inferring the phylogeny of species.     

Extended well-posedness of optimization problems

The well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended well-posedness. It is shown that this new property can be characterized by metric criteria, which parallel to some extent those known about generalized Tikhonov well-posedness.This work was partially supported by MURST, Fondi 40%, Rome, Italy.