A modular integer GCD algorithm

This paper describes the first algorithm to compute the greatest common divisor (GCD) of two n-bit integers using a modular representation for intermediate values U, V and also for the result. It is based on a reduction step, similar to one used in the accelerated algorithm [T. Jebelean, A generalization of the binary GCD algorithm, in: ISSAC '93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, 1993, pp. 111–116; K. Weber, The accelerated integer GCD algorithm, ACM Trans. Math. Softw. 21 (1995) 111–122] when U and V are close to the same size, that replaces U by (U−bV)/p, where p is one of the prime moduli and b is the unique integer in the interval (−p/2,p/2) such that . When the algorithm is executed on a bit common CRCW PRAM with O(nlognlogloglogn) processors, it takes O(n) time in the worst case. A heuristic model of the average case yields O(n/logn) time on the same number of processors.     

Modular Total Synthesis of (–)‐Palmyrolide A and (+)‐(5S,7S)‐Palmyrolide A via Ring‐Closing Metathesis and Alkene Isomerization†

A pentamodule assembly approach has been established for total synthesis of the naturally occurring (–)‐palmyrolide A and (+)‐5,7‐epi‐palmyrolide A. By using the racemic tert‐butyl carbinol‐containing alkyl iodide, the two diastereoisomeric macrolides could be obtained from the same sequence of reactions, demonstrating the flexibility of the multimodule assembly strategy for diverted total synthesis.     

自由基聚合的模块化教学及难点剖析

自由基聚合作为高分子化学的重点内容,内容丰富,难点较多。本文拟对作者在教学过程中总结的模块化教学方法进行介绍,并尝试对自由基聚合的动力学链长、聚合度及链转移这一难点内容进行剖析。     

An error-free algorithm to solve a linear system of polynomial equations

The paper presents an error-free algorithm to solve a system of linear equations with polynomial coefficients. Modular arithmetic in residual polynomial class and in residual numeric class is employed. The algorithm is iterative and well suited for implementation for computers with vector operations and fast and error-free convolutors.     

基于ZYNQ平台的阀冷控制保护装置

阀冷设备中的保护和控制装置是整套阀冷设备中非常关键和重要的分项设备,在整套冷却设备系统中起着承上启下的作用,水冷又是最常见的阀冷却形式,针对目前国内水冷设备厂家广泛采用的S7-400系列PLC产品价格高、组态过程复杂、不易维护、体积较大等缺点,设计一套基于ZYNQ的便携式通用型控制保护装置,应用于阀冷系统中,并成功投入稳定运行。     

高压模块的有机硅凝胶灌封工艺设计与改进

介绍了某高压模块产品灌封工艺技术。该高压模块主要由多级倍压整流电路组成,要求具有良好的绝缘、抗振及三防特性,因此采用一体化(即模具作为结构支撑件)的灌封结构设计,以实现小型化、模块化。针对高压模块的灌封要求,选用合适的灌封材料;并针对灌封中出现的问题,通过原因分析找相应问题的解决办法,然后对高压模块灌封工艺进行改进。根据几批次高压模块的试验结果,该灌封工艺技术满足模块的设计要求。     

CM newforms with rational coefficients

We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce tables for weights 3 and 4, where finiteness holds unconditionally. I am indepted to K. Hulek for his continuous interest and encouragement. Partial support by the DFG Schwerpunkt 1094 “Globale Methoden in der komplexen Geometrie” is gratefully acknowledged. My thanks go also to the referee for helpful comments. Part of the revising took place while I enjoyed the hospitality of the Dipartimento di Matematica “Frederico Enriques” of Milano University. Funding from the network Arithmetic Algebraic Geometry, a Marie Curie Research Training Network, is gratefully acknowledged. I particularly thank M. Bertolini and B. van Geemen. The final version was prepared while I was funded by DFG under grant Schu 2266/2-2.     

Modular optimization of enantiopure epoxide-derived P,S-ligands for rhodium-catalyzed hydrogenation of dehydroamino acids

The optimization of P,S-ligands derived from enantiopure (2S,3S)-phenylglycidol for asymmetric rhodium-catalyzed hydrogenation of dehydroamino esters is described. The exceptionally high modular character of the (2S,3S)-phenylglycidol platform is demonstrated by systematic modification of the ether and thioether moieties, the skeletal aryl substituent and the stereo and regiochemistry of the ligands. An experimentally useful method for the monitoring of hydrogenation reactions is also described and used for obtaining relevant data of the catalytic systems studied.     

A generalization of a theorem of Rankin and Swinnerton-Dyer on zeros of modular forms

Rankin and Swinnerton-Dyer (1970) prove that all zeros of the Eisenstein series in the standard fundamental domain for lie on . In this paper we generalize their theorem, providing conditions under which the zeros of other modular forms lie only on the arc . Using this result we prove a speculation of Ono, namely that the zeros of the unique ``gap function" in , the modular form with the maximal number of consecutive zero coefficients in its -expansion following the constant , has zeros only on . In addition, we show that the -invariant maps these zeros to totally real algebraic integers of degree bounded by a simple function of weight .