A Generalization of the Collatz Problem. Building Cycles and a Stochastic Approach

The (3x+1)/2 problem is generalized into the n-furcation problem (l _i x+m _i )/n where i[0, 1, ..., n–1]. It is shown that, under some constraints on l _i and m _i , the main bijection property between the k less significant digits of the seed, written in base n, and the sequence of generalized parities of the k first iterates is preserved. This property is used to investigate a stochastic treatment of ensemble of large value seeds. The bijection property predicts stochasticity for a number of iterations equals to the number of significant digits of the seed. In fact, the stochastic approach is valid for much larger numbers, a property which is more easily shown by using increasing sequences than decreasing ones. Finally, we extend the stochastic approach to cases where the bijection theorem does not hold, introducing the matrix giving the probability that a j number (where j is the last significant digit of this number written in base n) gives a i number iterate.     

Stable conformations of 12-crown-O3N and its Li+ complex in aqueous solution

Stable conformations of 12-crown-O3N and its Li complexes in aqueous solution were investigated. To calculate the free energy differences of conformers of 12-crown-O3N and its Li+ complex, our procedure was to make use of two programs, CONFLEX and BOSS. The former generates conformers, and the latter calculates the differences in free energy of solvation between two conformers in aqueous solution. It was confirmed that the present procedure is applicable in solving the question of what is the most stable conformation of 12-crown-O3N in aqueous solution. Results of the calculations suggest that the order of stability for conformers in a vacuum is different from that in aqueous solution. It was also confirmed that the coordination geometry of solvent waters to Li+ changes depending on the distance between the cation and the crown ring.     

Design and synthesis of artificial ribonucleases based on 1,4-diazabicyclo[2.2.2]octane and imidazole

The review surveys the results of our studies devoted to the design of highly efficient catalysts of hydrolysis of the phosphodiester bonds in RNA. These catalysts contain the imidazole residue in the catalytic domain, one or several bis-quaternized rings of 1,4-diazabicyclo[2.2.2]octane as a polycationic RNA-binding domain, and a lipophilic radical. A versatile approach to artificial ribonucleases of this type was proposed, which allows one to vary not only the number of positive charges in the RNA-binding domain, the structure of the catalytic site, and their mutual arrangement but also the domain structure of the molecule as a whole. Analysis of the catalytic properties of the synthesized constructs makes it possible to optimize the domain structure and the geometry of the molecule ensuring its maximum ribonuclease activity.     

Scaling concepts for polymer brushes and their test with computer simulation

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of “dimples”. Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given. Dedicated to Prof. H.E. Stanley on the occasion of his 60th birthday Received 11 March 2002 and Received in final form 3 June 2002     

NCl(a~1Δ)自猝灭对NCl(a~1Δ)/I激光能量提取的影响

利用连续流平面型光腔动力学模型对NCl(a1Δ)/I 激光体系进行了模拟计算,探讨了温度在300 K 时NCl(a1Δ)自猝灭对NCl(a1Δ)/I激光能量提取的影响。计算结果表明,NCl(a1Δ)自猝灭反应对光腔位置的选取、功率密度沿流动方向的分布和总输出功率都有较大的影响。其中,光腔位置的可选范围大大缩短,在较小的初始HI粒子数密度和适当的输出镜反射率下总输出功率大幅度降低,而随着HI粒子数密度的增加,NCl(a1Δ)自猝灭对总输出功率的影响逐渐减小。     

Design metal-dot based QCA circuits using SPICE model

This paper proposes a SPICE model development methodology for quantum-dot cellular automata (QCA) cells and presents a SPICE model for QCA cells. The model is validated by simulating the basic logic gates such as inverter and majority voter. The proposed model makes it possible to design and simulate QCA combinational circuits and hybrid circuits of QCA and other NANO devices using SPICE. In the second half part of the paper, SET and QCA co-design methodology is proposed and SET is used as a readout interface of the QCA cell array. The SET and QCA hybrid circuit is a promising nano-scale solution.     

使用遗传算法进行微波非线性电路包络仿真

介绍用于分析任意调制信号激励的微波非线性电路包络仿真技术,相应给出了线性器件的伴随模型,并将该方法发展为分析多载波调制信号激励的强非线性电路。此外,本文给出了一种求解非线性谐波平衡方程组或交调波平衡方程组的非数值方法———基于十进制编码的混沌遗传算法(DCGA),融合设计了相应的交叉和变异操作,并将混沌过程引入其中以避免陷入早熟状态,可有效地产生更优解,并加速种群的收敛。最后,给出了运用这种方法的两个计算实例。     

分布式仿真中通用态势可视化系统的开发研究

文章在分析了分布式仿真中传统态势可视化系统的基础上，提出了一种通用态势可视化系统的设计。它是基于面向对象的态势对象模型，使用基于消息的松散耦合方式实现态势对象与仿真通信模块相关联．通过态势模型配置解决了态势可视化的可组织性，态势对象定制解决了态势可视化的可扩充性。从而实现了通用的态势可视化系统。最后通过实践给出了通用态势可视化系统的特性和优点。     

海面杂波模拟

首先推导了特定海情下海杂波的平均雷达截面积,然后讨论了海杂波的幅度起伏模型,并给出了一种产生服从对数正态分布随机序列的算法。海杂波的功率谱模拟通常采用的是高斯模型,这与实际情况有所出入,所以采用频域取样法对模拟序列进一步处理,产生即具有特定概率分布,又具有所要求的功率谱的海杂波模拟序列。     

ISAR目标中频回波模拟器设计

介绍了一种ISAR目标中频回波模拟器的设计实现方法：首先以固定点目标为例，分析了ISAR目标的中频回波信号特点；然后根据信号特点，介绍了基于AD9857正交数字上变频器的中频回波信号产生技术；最后给出了信号模拟中相参性问题的解决方法。经过实践证明，该模拟器产生的信号相位稳定，频谱纯度高，并具有复杂波形生成的能力。该模拟器已经成功地在某型高分辨率空间目标跟踪探测雷达的研制过程中得到应用。