On the structure of digital explicit nonlinear and inversive pseudorandom number generators

We analyze the lattice structure and distribution of the digital explicit inversive pseudorandom number generator introduced by Niederreiter and Winterhof as well as of a general digital explicit nonlinear generator. In particular, we extend a lattice test designed for this class of pseudorandom number generators to parts of the period and arbitrary lags and prove that these generators pass this test up to very high dimensions. We also analyze the behavior of digital explicit inversive and nonlinear generators under another very strong lattice test which in its easiest form can be traced back to Marsaglia and provides a complexity measure essentially equivalent to linear complexity.     

Dynamic modelling of once-through subcritical steam generator for solar applications

This brief paper outlines a nonlinear dynamic model of a once-through subcritical steam generator for solar thermal plants. The purpose of the model is to describe the overall system performance and component interaction with sufficient accuracy for controller design, rather than to describe the microscopic details occuring within the steam generator. The model equations are arranged in state-space form to facilitate digital simulation and control system design. The modelling methodology is an extension of the earlier work of Ray and Bowman.     

Synchronized hybrid chaotic generators: Application to real-time wireless speech encryption

In this paper, a new stream key generator Hybrid Discrete Continuous Chaotic System (HDCCS) based on continuous and discrete chaotic systems is proposed. Our solution provides an easy and robust chaos synchronization while decrease the degradation due to finite precision during a digital implementation. Real-time application to wireless speech encryption effectively hides the original signal. Statistical security analysis for the proposed cryptosystem against cryptanalysis attacks, from a strict cryptographic viewpoint, are presented. These results verify and prove that the proposed speech cryptosystem is highly secure and has a very powerful diffusion and confusion mechanisms widely used in conventional cryptography.     

Combined random number generator via the generalized Chinese remainder theorem

The combined random number (RN) generator has been considered by many scholars as a good RN generator. One promising type of combined RN generator, recommended by L'Ecuyer (Oper. Res. 44 (1996) 816; 47 (1999) 159), is the combined multiple recursive generator (MRG). This paper analyzes the combined MRG via the Chinese remainder theorem. A new combined generator based on the generalized Chinese remainder theorem and on the Ore algorithm (Amer. Math. Monthly 59 (1952) 365) is presented. The proposed combined generator improves the combined MRG in terms of both the suitability for various types of RN generators and the restriction on the moduli of the individual generators. Therefore, the proposed combined generator is an ideal RN generator and is most recommended.     

Probability model of Gunther generator

This paper constructs the probability model of Gunther generator at first,and the finite dimension union distribution of the output sequence is presented.The result shows that the output sequence is an independent and uniformly distributed 0,1 random variable sequence. It gives the theoretical foundation about why Gunther generator can avoid the statistic weakness of the output sequence of stop-and-go generator,and analyzes the coincidence between output sequence and input sequences of Gunther generator.The conclusions of this paper would offer theoretical references for designers and analyzers of clock-controlled generators.     

倒向随机微分方程中生成元g的经济含义

将倒向随机微分方程看作金融市场中的一个定价机制,而该机制具体体现就是生成元g.本文通过经典的Black-Scholes模型探讨了生成元g的经济含义,首次提出了生成元g的表达式中含有折现的概念,同时详细分析并说明了不同的生成元g可以反应同一未定权益价格过程的不同形态.最后结合上面的讨论给出了关于一定形式的生成元g的类Jensen不等式性质.     

Design of Practical and Provably Good Random Number Generators

We present a construction for a family of pseudo-random generators that are very fast in practice, yet possess provable statistical and cryptographic unpredictability properties. Such generators are useful for simulations, randomized algorithms, and cryptography.Our starting point is a slow but high quality generator whose use can be mostly confined to a preprocessing step. We give a method of stretching its outputs that yields a faster generator. The fast generator offers smooth memory–time–security trade-offs and also has many desired properties that are provable. The slow generator can be based on strong one-way permutations or block ciphers. Our implementation based on the block cipher DES is faster than popular generators.     

关于非线性Lipschitz算子半群生成元的存在性

基于作者先前提出的Lipschitz对偶思想,对非线性Lipschitz算子半群引入了若干Lipschitz对偶概念,得到了一类非线性Lipschitz算子半群存在生成元的特征刻画.这一结果直接将关于C0-半群如下结论推广到了非线性情形:C0-半群具有有界生成元当且仅当它一致连续.     

The computation of the adjoint generator for a singular neutral equation

We compute the adjoint generator for the infinitesimal generator A of a C₀-semigroup. The operator A is associated with a particular scalar nonatomic neutral equation.     

Cohomology of the rational “electric” tetrahedron relation

A tetrahedral cochain complex is generalized to the case of the functional “electric” solution of the tetrahedron equation, which is expressed in terms of rational functions. The nontrivial part of the 3-cohomology group for this solution is calculated. It turns out to be the free Abelian group with one generator; the generator is explicitly specified.     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

A dynamic data structure suitable for adaptive mesh refinement in finite element method

This paper describes a dynamic data structure and its implementation, used for an optimum mesh generator. The implementation of this mesh generator was a part of a software package implemented to solve electromagnetic field problems using the finite element method. This mesh generator takes advantage of the Delaunay algorithm, which maximizes the summation of the smallest angles in all triangles and thus creates a mesh that is proved to be an optimum mesh for use in the finite element method. The dynamic data structure is explained and the source code is reviewed. The programs have been written in Pascal programming language.     

More efficient DDH pseudorandom generators

In this paper, we first show a DDH Lemma, which states that a multi-variable version of the decisional Diffie–Hellman problem is hard under the standard DDH assumption, where the group size is not necessarily known. Our proof, based on a self-reducibility technique, has a small reduction complexity. Using DDH Lemma, we extend the FSS pseudorandom generator of Farashahi et al. to a new one. The new generator is almost twice faster than FSS while still provably secure under the DDH assumption. Using the similar technique for the RSA modulus, we improve the Goldreich–Rosen generator. The new generator is provably secure under the factoring assumption and DDH assumption over \mathbbZ_N^*{\mathbb{Z}_N^*}. Evidently, to achieve the same security level, different generators may have different security parameters (e.g., distinct length of modulus). We compare our generators with other generators under the same security level. For simplicity, we make comparisons without any pre-computation. As a result, our first generator is the most efficient among all generators that are provably secure under standard assumptions. It has the similar efficiency as Gennaro generator, where the latter is proven secure under a non-standard assumption. Our second generator is more efficient than Goldreich–Rosen generator.     

K[X]~m中模的生成基及其应用

本文研究了多项式环上的素模中的生成基理论和方法．通过建立新的约化准则,得到了模中生成基的结构和机械化计算方法．对于低维情形给出了素模中生成基的充分必要条件．文中的方法本质地简化了传统的模中Ｇｒｏｂｎｅｒ基方法．文中同时介绍了该方法在样条理论研究中的应用,并给出了一些计算例子．     

K[X]^m中模的生成基及其应用

本文研究了多项式环上的素模中的生成基理论和方法。通过建立新的约化准则,得到了模中生成基的结构和机械计算方法。对于低维情形给出了素右生成基的充分必要条件。文中的方法本质地简化了传统的模中Grobner基方法。文中同时介绍了该方法在样条理论研究中的应用,并给出了一些计算例子。     

Design and implementation of an optimization-based decision support system generator

Decision makers today need to be able to rapidly find good solutions to increasingly complex problems. Optimization-based decision support systems (OBDSSs) can help decision makers to meet this challenge. Building such systems, however, is expensive and time consuming.In this paper we present the design of an OBDSS generator that greatly automates the development process by integrating a model specification with a database, a solver, and a graphical user interface (GUI). The generator automatically creates the database for storing the instantiating data, the GUI, and the solver interface. With this generator, an OR/MS analyst can build an OBDSS faster and more efficiently than using traditional tools. The resulting OBDSSs can be used by decision makers with little knowledge of the underlying OR/MS technology. We also discuss our experience using the generator to develop production planning and truck dispatching OBDSSs for several firms in the context of a three-year R&D project.     

Hidden symmetries and nonlocal group generators for ordinary differential equations

Hidden symmetries of ordinary differential equations (ODEs)are studied with nonlocal group generators. General forms aregiven for an exponential nonlocal group generator of an ODEthat is reduced from a higher-order ODE, which is expressedin canonical variables and which is invariant under a two-parameterLie group. The nonlocal group generator identifies a type Ihidden symmetry. Type II hidden symmetries are found in somereduction pathways of an ODE invariant under a solvable, nonabelian,three-parameter Lie group. The algorithm for the appearanceof the type II hidden symmetry is stated. General forms forthe reduced nonlocal group generator, which identifies the typeII hidden symmetry, are presented when the other two commutingoriginal group generators are in normal form.     

A Random-number Generator for Microcomputers

A very efficient and statistically sound random-number generator of the prime modulus multiplicative congruential method is devised for 16-bit microcomputers (8-bit machines have to be double-precisioned). This generator combines several generators, and cycles every (2¹⁵-20)² numbers with 2¹⁵-20 different numbers in one cycle. When precision is relatively unimportant, this generator is demonstrated to be a good random-number generator.     

Improvements on Delaunay-based three-dimensional automatic mesh generator

This paper describes an automatic mesh generator providing tetrahedral meshes suitable in general for finite element simulations. The mesh generator is of the Delaunay type and the paper focuses on recent improvements relative to this a priori well-known method.