Ordinal machines and admissible recursion theory

We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the algorithmic approach to admissible recursion theory by indicating how the proof of the Sacks–Simpson theorem, i.e., the solution of Post’s problem in α-recursion theory, could be based on α-machines, without involving constructibility theory.     

A foundation for real recursive function theory

The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., recursive, primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added.     

基于LMS算法的功率放大器控制系统

高频表面波雷达对发射功率要求很高,通常会采取功率空间合成的办法使数个较小功率的发射机合成一个较大的合成发射功率。首先介绍了子天线输入信号的幅相不一致对阵方向图产生的影响,然后讨论了不同的自适应算法的优缺点,选定了一种合适的算法并给出了硬件框图。选定的自适应控制算法具有较好的收敛性和稳态失调性,计算量小,实现简单,通过单片机及其外围模数、数模转换电路能够很方便的实现功放的幅相校准系统,使功放的输出信号的相位、幅度满足要求。     

A new integrable equation that combines the KdV equation with the negative‐order KdV equation

In this work, we develop a new integrable equation by combining the KdV equation and the negative‐order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painlevé test. As a result, multiple soliton solutions and other soliton and periodic solutions are guaranteed and formally derived.     

钢中晶界区稀土稀土元素与杂质交互作用的电子理论研究

利用位错模型构造纯净的和稀土及杂质偏聚的晶界模型 ,用Recursion方法研究了稀土与杂质的交互作用对Fe 5 .3°小角度晶界的结合性质的影响。环境敏感镶嵌能和键级积分 (BOI)的计算结果表明 :钢中同时存在稀土和杂质时 ,稀土首先偏聚于晶界。稀土偏聚于晶界时 ,起到加强晶界的作用 ;杂质偏聚于晶界时却起到脆化的作用。钢中加入适量的稀土 ,既净化晶界 ,又提高钢的强度。这一结果从电子层次解释了稀土在钢中的作用机制 ,为稀土在钢中的应用提供了理论依据     

10Gb/s 2.2V输出CMOS激光驱动器

采用逆向递推设计法,利用TSMC0．18μm CMOS工艺,设计实现了适用于超高速光纤通信系统的激光驱动器电路。核心电路为两级直接耦合差分放大器。电路设计中采用电感并联峰化技术拓展带宽和降低功耗。后仿真结果表明,在1．8V电源供电时,工作速率10Gb／s,输入单端峰峰值为400mV的差分信号,在50Ω的负载上可提供2．2V的输出电压。电路功耗185mW。版图面积为0．9mm〉40．95mm。     

梵塔问题的两个定理

本文首次证明了梵塔问题的两个定理,建立了一种梵塔问题新算法．     

Recursion Formulas to Find Solutions of Some Nonlinear Evolution Equations

New recursion formulas are obtained for finding solutions of some nonlinear evolution equations.     

Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters

We present a formulation of quantum mechanics based on the theory of orthogonal polynomials.The wavefunction is expanded over a complete set of square integrable basis where the expansion coefficients are orthogonal polynomials in the energy and physical parameters. Information about the corresponding physical systems(both structural and dynamical) are derived from the properties of these polynomials. We demonstrate that an advantage of this formulation is that the class of exactly solvable quantum mechanical problems becomes larger than in the conventional formulation(see, for example, table 3 in the text). We limit our investigation in this work to the Askey classification scheme of hypergeometric orthogonal polynomials and focus on the Wilson polynomial and two of its limiting cases(the Meixner–Pollaczek and continuous dual Hahn polynomials). Nonetheless, the formulation is amenable to other classes of orthogonal polynomials.     

Research of the behaviour of O chemisorption on the (110) surface of Rhx--Pt1－x alloy

An atomic group model of the disordered binary alloy Rhx-Pt1-x has been constructed to investigate surface segregation. According to the model, we have calculated the electronic structure of the Rhx-Pt1-x alloy surface by using the recursion method when O atoms are adsorbed on the Rhx-Pt1-x （110） surface under the condition of coverage 0.5. The calculation results indicate that the chemical adsorption of O changes greatly the density of states near the Fermi level, and the surface segregation exhibits a reversal behaviour. In addition, when x 〈 0.3, the surface on which O is adsorbed displays the property of Pt; whereas when x 〉 0.3 it displays the property of Rh.