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Reductive group actions on affine quadrics with 1dimensional quotient: Linearization when a linear model exists


Such an action is called linearizable if it is equivalent to the restriction of a linear orthogonal action in the ambient affine space of the quadric.


A linear model for a given action is a linear orthogonal action with the same orbit types and equivalent slice representations.


We prove that if a reductive group action on an affine quadric with a 1dimensional quotient has a linear model, then the action is linearizable.


We find presentations for the irreducible crystallographic complex reflection groupsW whose linear part is not the complexification of a real reflection group.

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 With the rapid progress of the electronic art, there has been a steadily increasing demand for still widerbandwidth amplifiers. The recent introduction of distributed amplification concept has provided a new technique and powerful means for designing amplifiers with top cutoff frequencies far in excess of those previously obtainable with,ordinary amplifier circuits. A distributed amplifier of the lowpass type can easily be constructed to have a uniform frequency response from audio frequencies to frequencies... With the rapid progress of the electronic art, there has been a steadily increasing demand for still widerbandwidth amplifiers. The recent introduction of distributed amplification concept has provided a new technique and powerful means for designing amplifiers with top cutoff frequencies far in excess of those previously obtainable with,ordinary amplifier circuits. A distributed amplifier of the lowpass type can easily be constructed to have a uniform frequency response from audio frequencies to frequencies as high as several hundred me using conventional vacuum tubes. Unlike conventional circuits, distributed amplifiers have an attainable gainbandwidth product which is not limited by shunt capacitance associated with the vacuum tubes and circuit wiring; the highfrequency limit being determined entirely by highfrequency effects within the tube proper.The purpose of this paper is to describe the basic principle of distributed amplification and to show how such an amplifier employing various types of transmission lines may be designed. Practical methods hi design and design details are given for a threestage distributed amplifier, using fourteen 6AK5 pentodes with a frequency response of 0.1 mo to 140 mo and a gain of 33±1 db.Both the negative mutualinductance mderived and constant K artificial delay lines hare been used. The former offers the advantage of a more linear phase characteristic and a more uniform response both in amplitude and delay time.The experimental results corroborate the predictions based on the firstorder theory described in this paper.  分布式放大是最近宽频带放大的最大成就,过去多年来电子学所应用的各种宽频带放大方法,其高频部分因受电子管电容和线路的分布电容所限制,不能获得理想的结果,而利用分布式放大的理论,所制成的宽频带放大器,远较一般普通的宽频带放大器,有更为宽阔的频带;从它的设计和构造上来看,也较负反馈的宽频带放大器为简单。制造一架自数千周至数百兆周的分布式放大器,在技术上并没有很大困难。本文拟对分布式放大的原理作扼要的分析;并提出了采用各类型仿真线所构成的分布式放大器的设计方法,并利用该设计方法,试作了一只三级十四管的分布式放大器,其增益为33±<1分贝,频宽自100千周至140兆周。由实验结果证明,采用m导出式低通滤波器所构成的仿真线的分布式放大器,实较用常K式者,具有更佳的相移特性和频率特性,这与理论上的分析是一致的。  Some supplementations, unifications, and simplifications of the problem of optimum bandwidth of a filter approximately matched to highfrequency pulsed signal were made in this paper.For a filter approximately matched to a single rectangular highfrequency pulse, the case for a linear system with rectangular freguency characteristic detuned with respect to the rectangular highfrequency signal was discussed and the formula for calculating the optimum bandwidth of the system was obtained.For the case... Some supplementations, unifications, and simplifications of the problem of optimum bandwidth of a filter approximately matched to highfrequency pulsed signal were made in this paper.For a filter approximately matched to a single rectangular highfrequency pulse, the case for a linear system with rectangular freguency characteristic detuned with respect to the rectangular highfrequency signal was discussed and the formula for calculating the optimum bandwidth of the system was obtained.For the case of pulse trains with uniform amplitudes, simplification and unification of some results of the other authors were made, it was pointed out that there exists a simple relation between the optimum value of attenuation of the delayed feedback system with unlimited bandwidth and the optimum teethwidth of a comb filter with singletuned characteristic of the teeth. The comparison between these two systems was made by the use of the data of the other authors.For the case of rectangular pulse trains with nonuniform amplitudes, the accumulation of the rectangular pulse trains with trapezoidal envelope by the delayed feedback system with finite bandwidth was discussed, and formula of the signal to noise ratio at the output terminals was obtained. For finding the optimum bandwidth of the delayed feedback system, some numerical calculations were made, and curves of the signal to noise ratio with respect to the bandwidth were plotted. From these curves we found that in this case there exists an optimum bandwidth of the system, the value of which is wider then the optimum bandwidth of the system in the case of accumulation of rectangular pulse trains with uniform amplitudes.  本文对高频脉冲讯号近似匹配滤波器的最佳通频带问题,作了一些补充、统一和简化。 对单个矩形高频脉冲的近似匹配滤波器,本文讨论了矩形高频脉冲在失谐的情况下通过矩形频率特性系统时的最佳通频带,得出了计算公式。 对于等幅矩形脉冲串的情形,本文将前人的一些结果在计算方面作了简化和统一。明确指出了有衰减但频带不受限制的延时反馈系统的最佳衰减值和具有单谐振回路特性梳齿的梳形滤波器的最佳梳齿通频带间的对应关系,并用文献上的数据作了比较。 对于非等幅矩形脉冲串的情形,本文讨论了频带有限的延时反馈系统对包迹为梯形的矩形脉冲串进行积累的情形,得出了输出端讯噪比的表示式。为了求得最佳通频带,进行了一些数字计算,作出曲线。从曲线中得到这一系统对包迹为梯形的矩形脉冲串积累时,存在有最佳通频带,它的宽度比对等幅矩形脉冲串积累时的最佳通频带为宽。  At the present paper the available properties of the linear FM signal are summed up. And the transfer function of the compression network analogous to a matched filter is discussed. It is suggested that the program for the active pulse compression system can be accomplished by using a wiretype dispersive ultrasonic delay line. The experimental results of the active system are also given. Following the discussion of the principle for the passive pulse compression system, the practical program of the passive... At the present paper the available properties of the linear FM signal are summed up. And the transfer function of the compression network analogous to a matched filter is discussed. It is suggested that the program for the active pulse compression system can be accomplished by using a wiretype dispersive ultrasonic delay line. The experimental results of the active system are also given. Following the discussion of the principle for the passive pulse compression system, the practical program of the passive system used in the laboratory is introduced. The experimental results of the passive system are given. The research work on the active pulse compression system with the compression ratio of 100 and the passive one with that of 140 has succeeded. The compressedpulse width of the former is 5μs, and that of the latter, 3μs. The experimental results, agree with the theoretical estimations.  本文总结了线性调频信号的许多有用特性,讨论了近似于匹配滤波器的压缩网络传递函数。提出了用金属丝色散型超声延迟线完成有源脉冲压缩方案,报道了有源系统的实验结果。在讨论了无源压缩的工作原理之后,报道了实验室采用的无源脉冲压缩的实现方案,给出了无源系统的实验结果。有源压缩100倍和无源压缩140倍的工作系统已经研究成功,前者压缩脉冲宽度为5微秒,后者压缩脉冲宽度为3微秒,实验结果和理论预计非常吻合。   << 更多相关文摘 
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