Evolutionary Random Sequence Generators Based on LFSR

Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.

SOME SMALL DEVIATION THEOREMS FOR ARBITRARY CONTINUOUS RANDOM SEQUENCE

Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.

On Strong Law of Large Numbers for Random Sequence

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.

Limiting Distribution of Extreme Values for FGM Random Sequences

This paper mainly study extreme values of FGM random sequences.We prove a technique theorem by the dependence structure of FGM sequences,and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.

An Invariance Principle for ρ^--Mixing Random Sequences

In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.

Some Strong Deviation Theorems for Dependent Continuous Random Sequence

Let {Xn,n ≥ 1} be a sequence of arbitrary continuous random variables,we introduce the notion of limit asymptotic logarithm likelihood ratio r（ω）,as a measure of dissimilarity between probability measure P and reference measure Q.We get some strong deviation theorems for the partial sums of arbitrary continuous random variables under Chung-Teicher＇s type conditions[6-7].

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

A STRONG LIMIT THEOREM FOR GENERALIZED CANTOR-LIKE RANDOM SEQUENCES

Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.

SOME LIMIT THEOREMS FOR SEQUENCES OF PAIRWISE NQD RANDOM VARIABLES

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

THE GROWTH AND BOREL POINTS OF RANDOM ALGEBROID FUNCTIONS IN THE UNIT DISC

In this paper,we construct k-valued random analytic algebroid functions for the first time.By combining the properties of random series,we study the growth and Bor el points of random analytic algebroid functions in the unit disc and obtain some interesting theorems.

A recoverable stress testing algorithm for compression and encryption cards

This study proposes a recoverable stress testing algorithm （RSTA） for such special devices as compression/decompression card and encryption/deeryption card. It uses a chaos function to generate a random sequence, and then, according to the random sequence, generates an effective command sequence. The dispatch of command obeys a special schedule strategy we designed for such devices, i.e., the commands are sent according to the command sequence, and the complete commands are put in a buffer for further result check. RSTA is used to test the HIFN compression acceleration card SAICHI-1000. Test results show that RSTA can make the card work continuously and adequately.

SeeDNA: A Visualization Tool for K-string Content of Long DNA Sequences and Their Randomized Counterparts

Fudan University, Shanghai 200433, China; Department of Physics, National Central University, Chungli, 3 Taiwan 320, China; Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, China. 4 An interactive tool to visualize the K-string composition of long DNA sequences including bacterial complete genomes is described. It is especially useful for ex- ploring short palindromic structures in the sequences. The SeeDNA program runs on Red Hat Linux with GTK+ support. It displays two-dimensional (2D) or one-dimensional (1D) histograms of the K-string distribution of a given sequence and/or its randomized counterpart. It is also capable of showing the di?erence of K-string distributions between two sequences. The C source code using the GTK+ package is freely available.

Some Remarks for Sequences of Pairwise NQD Random Variables

We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.

On a Conjecture of an Invariance Principle for Sequences of Associated Random Variables

A finite collection of random variables, X1} —, Xm, is said to be associated if any two coordinatewise nondecreasing functions /i and /a on Rm such that Jt = fj(Xi} , Xm~) has finite variance for j = l, 2, Oov(/i,fa)>0; an infinite collection is said to be associated if every finite subcollection is. associated. Thus the concept of "association" is introduced as dependence in probability (Esary, Proschan and Walkup (1967)). It is relative to a lot of practical models, such as the percolation models, the Ising models of statistical mechanics. Therefore, some people are

Propagation of quasi-periodic random sound pulse sequence signals in shallow-water waveguides

It is an efficient method to model ship radiated noise as quasi-periodic random sound pulse sequences. Based on the model, this paper discusses the characteristics change of ship noise after through shallow-water waveguides. Theoretical analysis and numerical simulation show that random waveguides and multi-path effects can bring much additional transmission loss for the noise line spectra, demonstrating the instability of ship radiated noise line spectra to a certain extent, and providing some theoretical support for advanced studies of ship radiated noise.