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From the original framer to presentday timefrequency and timescale frames


In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points.


In this paper we analyze solutions of the nscale functional equation Ф(x) = Σk∈?Pk Ф(nxk), where n≥2 is an integer, the coefficients {Pk} are nonnegative and Σpk = 1.


This criterion implies several results concerning the problem of integrable solutions of nscale refinement equations and the problem of absolutely continuity of distribution function of one random series.


TwoScale Homogeneous Functions in Wavelet Analysis

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 Some practical problems arising from the adoption of the absolute scale ol temperature as standard in place of the Celsius scale are discussed. The absolute scale is fixed by assigning a numerical value (say T_3=273.1700) to the triple point of water. The problems 'considered include the correction of gas thermometer readings, the specification of: the platinum resistance thermometer and of the platinum thermocouple. It is pointed out that, when the absolute scale has been chosen as standard,... Some practical problems arising from the adoption of the absolute scale ol temperature as standard in place of the Celsius scale are discussed. The absolute scale is fixed by assigning a numerical value (say T_3=273.1700) to the triple point of water. The problems 'considered include the correction of gas thermometer readings, the specification of: the platinum resistance thermometer and of the platinum thermocouple. It is pointed out that, when the absolute scale has been chosen as standard, the determination of the absolute temperature of the ice point and the correction of gas thermometers become one and the same task. It is further pointed out, that the accuracy in the experimental determination of the absolute temperature will be greatly increased.  本文对在给定水的三相点的绝对温度以一定的数值(例如T_3=273.1700),同时以绝对温标代替摄氏温标以后所引起的一些实际问题作了讨论。这些问题包括气体温度计的改正及电阻温度计和温差电偶温度计的规定。本文指出,在以绝对温标为标准以后,寻求冰点的绝对温度与对气体温度计的改正两种工作统一起来了。又指出,在以绝对温标为标准以后,绝对温度测量的精确度将大大提高。  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... 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?  (1) Cytochrome c containing 0.43% iron has been obtained from beef, pig or horse heart muscles by direct adsorption of the neutralized trichloroacetic acid extracts of heart muscle on the cation exchanger"synthetic zeolite" followed by elution with 3.84 M ammonium sulfate and precipitation with 20% trichloroacetic acid. This provides a simple method for largescale preparation of pure cytochrome c. (2) The ratio of optical densities at 550 mμ(reduced) and 278 mμ of 0.43% iron cytochrome c varies, with... (1) Cytochrome c containing 0.43% iron has been obtained from beef, pig or horse heart muscles by direct adsorption of the neutralized trichloroacetic acid extracts of heart muscle on the cation exchanger"synthetic zeolite" followed by elution with 3.84 M ammonium sulfate and precipitation with 20% trichloroacetic acid. This provides a simple method for largescale preparation of pure cytochrome c. (2) The ratio of optical densities at 550 mμ(reduced) and 278 mμ of 0.43% iron cytochrome c varies, with its degree of reduction, from 1.13 to 1.26. The average ratio of our preparations is 1.23. (3) The absorption spectra(230600 mμ) of oxidized and reduced cytochrome c have been measured. The molecular extinction coefficient at 550 mμ of oxidized, 0.43% iron, cytochrome c is 0.80×10~4. This value differs considerably from that reported in the literature. (4) Some enzymic properties of cytochrome c containing 0.43% iron are compared with those of a preparation containing 0.34% iron and are found to be identical. Both can be converted into''endogenous" cytochrome c. (5) Whether pure cytochrome c contains more than 0.43% iron has been discussed. It seems that no convincing evidence has been presented to show that cytochrome c preparations with iron content higher than 0.43% as obtained by some workers do not contain a small amount of ironrich impurity.  (一)用陽離子交换劑(synthetic zeolite)直接吸附高等動物心肌抽提液一次,並用3.84M硫酸銨作洗脫劑,即可製得含鐵量0.43%的細胞色素c。因此提供了一個大量製備純細胞色素c的簡單方法。 (二)含鐵量0.43%的細胞色素c,它的550mμ和278mμ光密度的比值,視產品的還原程度而定,其範圍從1.13到1.26,我們所製得的產品,其比值在1.23左右。 (三)我們测量了氧化及還原的細胞色素c(含鐵0.43%)從230mμ到600mμ的吸收光譜,並發現和前人所報告的略有不同。氧化細胞色素c在550mμ的消光係數為0.80×10~4,此值與文獻上的數值相差很多。 (四)我們比較了含鐵量0.43%的細胞色素c和含鐵量0.34%的細胞色素c的一些酶性質,證明他們是相同的;並且兩者都可以變成“內源”細胞色素c。 (五)我們認為現有的實驗證據不足以說明純細胞色素c的含鐵量大於0.43%。   << 更多相关文摘 
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