Good point methods for computing prices and sensitivities of multi-asset European style options

Using number-theoretic methods, we investigate low-discrepancy sequences and weighted-sum estimators which outperform standard low-discrepancy techniques for pricing multi-asset European options on up to 5 underlying factors. The sequences used are simpler to implement than most low-discrepancy sequences, and computation time is considerably faster.     

Cryptographic properties of nonlinear pseudorandom number generators

The cryptographic properties of keystreams generated by stream ciphers based on t-functions are studied. These constructions are of great interest as they allow building highly efficient and secure cryptographic primitives. The randomness of the coordinate sequences generated by such mappings is analyzed in terms of the autocorrelation function. The results derived are valid for all t-functions regardless the type of construction and indicate the existence of nonrandomness. As the problem of the efficient implementation of secure s-boxes is open, the nonlinearity of t-functions is also analyzed. It is shown how some cryptographically undesirable properties, can be solved by application of similarity transformations.      

Batrachion序列的数值求解

Batrachion序列是一类奇特的序列，有着非常的分形图形行为和轨迹，已引起计算机图形领域许多学者的兴趣和重视．本文给出Batrachion序列的完整求解，并且予以严格的证明．在证明过程中，同时显示了它与杨晖三角形密切的关系．     

A NEW FAMILY OF BINARY SEQUENCES WITH OPTIMAL AUTOCORRELATION VALUES AND NICE PSEUDO-RANDOM PROPERTIES

In this paper we present a series of binary sequences which is a generalization of GMW sequences constructed by Scholtz and Welch. Our sequences have optimal autocorrelation values as m -sequences, and nice pseudo-random property. The number of such sequences is counted and the linear span of such sequences is evaluated.     

Lehmer序列中的平方数

设V_n(R,Q)表示参数为R和Q的Lehmer伴随序列,如果R和Q为互素奇数且D=R-4Q>0,我们找出了满足Q_n(R,Q)或nQ_n(R,Q)是平方数的所有奇数n,这里Q_n(R,Q)R~(1/2)=V_n(R,Q)。     

Sets whose sumset avoids a thin sequence

Let {a₁,a₂,a₃,…} be an unbounded sequence of positive integers with an+1/an approaching α as n→∞, and let β>max(α,2). We show that for all sufficiently large x?0, if A⊂[0,x] is a set of nonnegative integers containing 0 and satisfying

     

广义Lucas序列的重复度与相关的不定方程的解数

用ｐ－ａｄｉｃ分析方法讨论了广义Ｌｕｃａｓ序列的重复度,并由此证明了不定方程ａｘ＾２＋Ｄ＝ｃｐ＾ｎ,ｘ〉０,ａＤ〉０,ｃ＝１,２,４,ｐ为素数,除四种例外情形外,最多只有两组解（ｘ,ｎ）。     

最佳跳频序列族的设计与分析

本文提出了基于ｐ元广义ＧＭＷ序列和ｐ元Ｋａｓａｍｉ序列构造跳频序列族的方法,证明了基于广义ＧＭＷ序列所构造的跳频序列族具有最佳Ｈａｍｍｉｎｇ相关特性,而基于Ｋａｓａｍｉ序列所构造的跳频序列族不具有最佳Ｈａｍｍｉｎｇ相关特性。     

On the class of norm limits of nilpotents

It is known that every operator on a Hilbert space whose invariant subspace lattice is possibly is a norm-limit of a sequence of nilpotent operators. In this note we study properties of such approximating sequences.