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There are natural concepts of the action of annvalued group on a space and of a representation in an algebra of operators.


This is a survey of recent work involving concepts of selfsimilarity that relate to


The characterization of low pass filters and some basic properties of wavelets, scaling functions and related concepts


In this article, a comprehensive examination of the interrelations among these localization and approximation concepts is made, with most implications shown to be sharp.


The method converts the frame problem into a set of ordinary differential equations using concepts from classical mechanics and orthogonal group techniques.

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 A general theory on the realistic stress space of solids was formulated in a previous paper. In this paper, the bell stress spaces of several metals are compared, the concept of "efficiency of plastic deformation" is introduced and formulated, and the locus of deformation is discussed in connection with the theory of bell stress space. The main concepts of this paper are:  前文[1]综合四理论[2],[3],[4],[5]构成固体现实应力空间之一初步理论,大体反映固态静力学性质,对金属较对非金属固体反映得当,后者受范形变曲面有异于弥氏圆柱。总起来看,前文仅涉及原则概念,未触及具体问题。为使此理论对金属压力加工及材料试验研究有所帮助,本文进一步研究几个问题: 1)由应力空间图形比较不同金属的静力学性质; 2)受范形变效率及其计算; 3)形变过程之轨迹;并得到一定数量或质量上的结论。 同时,附带对前文[1]中一个实验记录图的错误作修正,包括在附录内。  Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in... Fineness modulus (F. M.) has served as an index of fineness of aggregates since it was first introduced by Prof. Duff A. Abrams in 1918. In the concrete mix design, the F. M. of sand governs the sand content and hence the proportions of other ingredients. But there are undesirable features in F. M.: it does not represent the grading of sand and manifests no significant physical concept.Prof. suggested an "average diameter" (d_(cp)) in 1943 as a measure of fineness of sand. In 1944, d_(cp) was adopted in 278144 as national standard to specify the fine aggregate for concrete in USSR. It was introduced to China in 1952 and soon becomes popular in all technical literatures concerning concrete aggregates and materials of construction.After careful and thorough investigation from ordinary and special gradings of sand, the equation of d_(cp) appears to be not so sound in principle and the value of d_(cp) computed from this equation is not applicable to engineering practice. The assumption that the initial average diameter (ν) of sand grains between consecutive seives is the arithmetical mean of the openings is not in best logic. The value of an average diameter computed from the total number of grains irrespective of their sizes will depend solely on the fines, because the fines are much more in number than the coarses. Grains in the two coarser grades (larger than 1.2 mm or retained on No. 16 seive) comprising about 2/5 of the whole lot are not duly represented and become null and void in d_(cp) equation. This is why the initiator neglected the last two terms of the equation in his own computation. Furthermore, the value of d_(cp) varies irregularly and even inversely while the sands are progressing from fine to coarse (see Fig. 4).As F. M. is still the only practical and yet the simplest index in controlling fineness of sand, this paper attempts to interpret it with a sound physical concept. By analyzing the F. M. equation (2a) in the form of Table 9, it is discovered that the coefficients (1, 2…6) of the separate fractions (the percentages retained between consecutive seives, a1, a2…a6) are not "size factors" as called by Prof. H. T. Gilkey (see p. 93, reference 4), but are "coarseness coefficients" which indicate the number of seives that each separate fraction can retain on them. The more seives the fraction can retain, the coarser is the fraction. So, it is logical to call it a "coarseness coefficient". The product of separate fraction by its corresponding coarseness coefficient will be the "separate coarseness modulus". The sum of all the separate coarseness moduli is the total "coarseness modulus" (M_c).Similarly, if we compute the total modulus from the coefficients based on number of seives that any fraction can pass instead of retain, we shall arrive at the true "fineness modulus" (M_f).By assuming the initial mean diameter (ν') of sand grains between consecutive seives to be the geometrical mean of the openings instead of the arithmetical mean, a "modular diameter" (d_m), measured in mm (or in micron) is derived as a function of M_c (or F. M.) and can be expressed by a rational formula in a very generalized form (see equation 12). This equation is very instructive and can be stated as a definition of mqdular diameter as following:"The modular diameter (d_m) is the product of the geometrical mean ((d_0×d_(1))~(1/2) next below the finest seive of the series and the seive ratio (R_s) in power of modulus (M_c)." If we convert the exponential equation into a logarithmic equation with inch as unit, we get equation (11) which coincides with the equation for F. M. suggested by Prof. Abrams in 1918.Modular diameter can be solved graphically in the following way: (1) Draw an "equivalent modular curve" of two grades based on M_c (or F. M.) (see Fig. 6). (2) Along the ordinate between the two grades, find its intersecting point with the modular curve. (3) Read the log scale on the ordinate, thus get the value of the required d_m corresponding to M_c (see Fig. 5).As the modular diameter has a linear dimension with a defin  細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是... 細度模數用為砂的粗細程度的指標,已有三十餘年的歷史;尤其是在混凝土的配合上,砂的細度模數如有變化,含砂率和加水量也要加以相應的調整,才能維持混凝土的稠度(以陷度代表)不變。但是細度模數有兩大缺點,一個是模數的物理意義不明,另一個是模數不能表示出砂的級配來。蘇聯斯克拉姆塔耶夫教授於1943年提出砂的平均粒徑(d_(cp))來,以為砂的細度指標;雖然平均粒徑仍不包含級配的意義,但是有了比較明確的物理意義,並且可以用毫米來度量,這是一種新的發展。不過砂的細度問題還不能由平均粒徑而得到解决,且平均粒徑計算式中的五項,僅首三項有效,1.2和2.5毫米以上的兩級粗砂在計算式中不生作用,以致影響了它的實用效果。本文對於平均粒徑計算式的創立方法加以追尋和推演,發現其基本假設及物理意義,又設例演算,以考察其變化的規律性;認為細度模數還有其一定的實用價值,不能為平均粒徑所代替。至於補救細度模數缺點的方法,本文試由模數本身中去尋找;將模數的計算式加以理論上的補充後,不但能分析出模數的物理意義,並且還發現模數有細度和粗度之別。根據累計篩餘計算出來的F.M.應稱為“粗度模數”,根據通過量計算出來的才是“細度模數”。假定兩隣篩间的顆粒是兩篩篩孔的幾何平均值,以代替數學平均值(即斯氏平均?  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。   << 更多相关文摘 
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