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the sum
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  求和
     A Formula for Calculating the Sum of sum from n=1 to ∞(f(n)x~(n-1))
     幂级数sum from n=1 to ∞(f(n)x~(n-1))的一个求和公式
短句来源
     Theorem of the General Term Coefficient D_(k,j) Andthe Equation of the Sum sum from i=1 to n(i~K)(K∈N)
     通项系数D_(K,j)定理与sum from i-1 to Ni~K(K∈N)的求和公式
短句来源
     The Application of the Sum Formula of Infinite Geometric Series ∑from n=0 to ∞(ax~n)=a/(1-x) in Power Series
     无穷等比级数求和公式∑from n=0 to ∞(ax~n)=a/(1-x)在级数中的应用
短句来源
     We find that mp_ 0π =1.00±0.17GeV and mp_ 0K =1.46± 0.23GeV after including α_S corrections to the perturbative part of the sum rules.
     与运动方程的要求不同,计算结果表明(把求和规则微扰部分的αs修正考虑之后),mp0π=1.00±0.17GeV,mp0K=1.46±0.23GeV.应该指出的是,它们与运动方程给出的结果相比要小不少.
短句来源
     This article Shows a simple method with which we can obtain the sum formula of S_(x+1)(n) from the sum formula of S_K(n)=1~K+2~k+…+n~k where K=1,2,…. Using this method, we can obtain the next Bernowlli's number B_(k+1) in passing.
     本文给出由S_K(n)=1~K+2~K+…+n~K,K=1,2,…的求和公式,得出S_K+1(n)的求和公式的简单方法,此法可顺便得出下一个伯努利数B_K+1。
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  总数
     The sum of heterotrophic bacteria was( 2.37±1.83)×10~7 cfu/L and Vibrio were (11.77±13.86)×10~5 cfu/L in cultural water, but in sediment surface the heterotrophic bacteria were (7.90±29.08)×10~8 cfu/L, the Vibrio (1.18±3.27)×10~7 cfu/L.
     健康虾池水体异养菌群数量(2 37±1 83)×107cfu/L,弧菌数量(11 77±13 86)×105cfu/L,底泥异养细菌总数(7 90±29 08)×108cfu/L,弧菌总数(1 18±3 27)×107cfu/L。
短句来源
     the sum of ischemia ST segments was 60 at baseline,51 after ISDN was infused.
     缺血ST段片段总数,基线为60段,ISDN静脉滴注后51段。
短句来源
     the sum of ischemia ST segments was 58 at baseline,(47 after) ISDN was infused.
     缺血ST段片段总数,基线为58段,ISDN静脉滴注后47段。
短句来源
     the sum of ischemia ST segments was 64 at baseline,41 after ISDN was infused.
     缺血ST段片段总数,基线为64段,ISDN静脉滴注后41段。
短句来源
     The energy response function of the array has been given,i, e. lg(E_0)=lg(0.4×∑N_i)±0.226,where E_0(TeV) is the primary energy of the incident particle,∑N_i is the sum of detected particle number on FT detectors.
     原初粒子能量按lgE_0=lg(0.45∑N_i)±0.226确定,其中E_0(TeV)为初级入射粒子能量,∑N_i为FT探测器上探测到的粒子总数.
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  “the sum”译为未确定词的双语例句
     THE CENTRAL LIMIT THEOREM FOR THE SUM OF A RANDOM NUMBER OF INDEPENDENT RANDOM VARIABLES AND ITS APPLICATIONS IN MARKOV CHAINS
     随机个数独立随机变量之和的中心极限定理及其在马尔可夫链上的应用
短句来源
     Certain problems on local dimension and The Sum theorem in dimension theory
     关于局部维数及维数论中加法定理的某些问题
短句来源
     The Expectation of the Sum of Consecutive AL Variables and the Double“Zero-One”Linear Estimates for the Standard Deviation of Normal Population
     相邻AL变数和的期望值与正态总体标准差的双“零—壹”线性估计量
短句来源
     ON THE CENTRAL LIMIT THEOREM FOR THE SUM OF THE RANDOM NUMBERS OF INDEPENDENT RANDOM VARIABLES
     关于随机个数独立随机变量之和的中心极限定理
短句来源
     Some results on the estimaticn of moments of the sum of independent random variables with symmetric distributions
     关于对称型分布的随机变量独立和的矩的估计的几点结果
短句来源
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  the sum
We suggest that the relative abundances be normalized so that the sum of the abundances for all spots considered is the same for all maps.
      
LetJ={1,2,...}d and let {Xj, j∈J} be an α-mixing sequence which is not necessarily stationary and letS(nA) be the sum of allXj for whichj/n∈A.
      
Let G be a graph and denote by Q(G)=D(G)+A(G), L(G)=D(G)-A(G) the sum and the difference between the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively.
      
In particular, if d?3 and the sum of degrees of any s (s=2 or 3) nonadjacent vertices is at least n+(s-1)k+1-d, then dk(G)?d.
      
The results indicate that the original number of OSL traps that have captured electroncs is linearly related with the sum of TL decay during the OSL process.
      
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This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the...

This paper is a supplement to the author's previous paper "The Constants and Analysis of Rigid Frames", published in the first issue of the Journal. Its purpose is to amplify as well as to improve the method of propagating joint rotations developed, separately and independently, by Dr. Klouěek and Prof. Meng, so that the formulas are applicable to rigid frames with non-prismatic bars and of closed type. The method employs joint propagation factor between two adjacent joints as the basic frame constant and the sum of modified stiffness of all the bar-ends at a joint as the auxiliary frame constant. The basic frame constants at the left of right ends of all the bars are computed by the consecutive applications of a single formula in a chain manner. The auxiliary frame constant at any joint where it is needed is computed from the basic frame constants at the two ends of any bar connected to the joint, so that its value may be easily checked by computing it from two or more bars connected to the same joint.Although the principle of this method was developed by Dr. Klouěek and Prof. Meng, the formulas presented in this paper for computing the basic and auxiliary frame constants, besides being believed to be original and by no means the mere amplification of those presented by the two predecessors, are of much improved form and more convenient to apply.By the author's formula, the basic frame constants in closed frames of comparatively simple form may be computed in a straight-forward manner without much difficulties, and this is not the case with any other similar methods except Dr. Klouěek's.The case of sidesway is treated as usual by balancing the shears at the tops of all the columns, but special formulas are deduced for comput- ing those column shears directly from joint rotations and sidesway angle without pre-computing the moments at the two ends of all the columns.In the method of propagating unbalanced moments proposed by Mr. Koo I-Ying and improved by the author, the unbalanced moments at all the bar-ends of each joint are first propagated to the bar-ends of all the other joints to obtain the total unbalanced moments at all the bar-ends, and then are distributed at each joint only once to arrive at the balanced moments at all the bar-ends of that joint. Thus the principle of propagating joint rotations with indirect computation of the bar-end moments is ingeneously applied to propagate unbalanced moments with direct computation of the bar-end moments, and, at the same time, without the inconvenient use of two different moment distribution factors as necessary in all the onecycle methods of moment distribution. The basic frame constant employed in this method is the same as that in the method of propagating joint rotations, so that its nearest approximate value at any bar end may be computed at once by the formula deduced by the author. Evidently, this method combines all the main advantages of the methods proposed by Profs.T. Y. Lin and Meng Chao-Li and Dr. Klouěek, and is undoubtedly the most superior one-cycle method of moment distribution yet proposed as far as the author knows.Typical numerical examples are worked out in details to illustrate the applications of the two methods.

本文為著者前文“剛構常數與剛構分析”之補充,其目的在將角變傳播法及不均衡力矩傳播法加以改善,以便實用。此二法均只需一個公式以計算剛構中所有各桿端之基本剛構常數(即任何二相鄰結點间之角變傳播係數),將此項公式與柯勞塞克之公式相比較,藉以指出前者較後者為便於應用,並亦可用之以直接分析較簡單之閉合式剛構,此外補充說明此法中之剛構常數與定點法之關係,剛構有側移時計算各結點角變所需之各項公式亦行求出。不均衡力矩傳播法係顧翼鹰同志最近研究所得者,既係直接以桿端力矩為計算之對象,而且只須採用不均衡力矩分配比將各結點作用於各桿端不均衡力矩之總和,一次分配,即得所求各桿端分配力矩之總值,實係力矩一次分配法之一大改進,著者將顧氏之法加以推廣与改善,使其原則簡明而計算便捷,著者認為此法係將林、柯、孟三氏法之所有優點熔冶於一爐,實可稱為现下最優之力矩一次分配法。最後列舉算例,以說明此二法在實際工作中之應用。

(1) Sodium salt of reduced codehydrogenase I has been obtained in good yield as a dry powder from codehydrogenase I by reduction with alcohol and alcohol dehydrogenase. This preparation was stable for at least 5 months when kept dry at -15℃. (2) The properties of the particle-bound codehydrogenase I cytochrome reductase system in heart muscle preparation were found to differ considerably from those of the soluble enzyme as obtained by Mahler et al. Among other things, the affinity for cytochrome c of the particle-bound...

(1) Sodium salt of reduced codehydrogenase I has been obtained in good yield as a dry powder from codehydrogenase I by reduction with alcohol and alcohol dehydrogenase. This preparation was stable for at least 5 months when kept dry at -15℃. (2) The properties of the particle-bound codehydrogenase I cytochrome reductase system in heart muscle preparation were found to differ considerably from those of the soluble enzyme as obtained by Mahler et al. Among other things, the affinity for cytochrome c of the particle-bound enzyme is much greater than the soluble enzyme. The Michaelis constant for cytochrome c of the former is only one twelfth of that of the latter.(Fig. 2A). (3) With either oxygen or excess cytochrome c as electron acceptor, it was found that the overall activity, in terms of rate of oxygen consumption or cytochrome c reduction, when both succinate and reduced codehydrogenase I were oxidized simultanously, did not represent the sum of the rates of oxidation when these two substrates were separately oxidized but equalled only the faster of the two separate oxidation rates(Fig. 5, Tables 1, 2). If 2,6-dichlorophenol indophenol was used as the electron acceptor, the overall rate of simultaneous oxidation of these two substrates was found to equal exactly the sum of the rates of separate oxidation(Table 3). (4) When either oxygen or excess cytochrome c was used as the electron acceptor, reduced codehydrogenase I and succinate each inhibited the rate of oxidation of the other(Figs 4, 6 & 7). Evidence has been presented to show that the inhibition of succinate oxidation by reduced codehydrogenase I is not due to the accumulation of oxaloacetate. (5) When malonate was also added to the reaction mixture, succinate no longer produced any inhibition of the oxidation of reduced codehydrogenase I(Fig. 8). (6) It is therefore concluded that in heart muscle preparation both succinate and reduced codehydrogenase I are oxidized by cytochrome c through a common, velocity limiting factor. This is in accordance with the view previously reached by some workers from studies on the action of certain inhibitors. However, it should be noted that in our experiments no agents which might produce any conceivable change in the colloidal structure of the enzyme system has been employed. (7) It should be emphasized that our results clearly show that great caution must be exercised in drawing conslusion on the role an enzyme might play in a complex enzyme system from studies of the properties of a solubilized enzyme. (8) It is believed that the competition of two enzyme systems for a common linking factor as demonstrated in this report has provided a new method for studies on the mutual relations of two or more enzyme systems.

(一)本報告提供了一個從輔酶Ⅰ,用酶還原法製備還原輔酶Ⅰ的方法。我們所製得的還原輔酶Ⅰ鈉鹽乾粉,可以在低温保存數月而不被氧化。 (二)與心肌製劑中顆粒相結合的輔酶Ⅰ細胞色素還原酶系,和用乙醇抽出的水溶性的輔酶Ⅰ細胞色素還原酶的性質頗不相同。其中比較重要的不同點是對於細胞色素c的親力,前者遠大於後者,其米氏常數僅約為後者的十二分之一。 (三)用一心肌顆粒製劑作為材料,無論用氧或過量之細胞色素c作為氫受體,還原輔酶Ⅰ與琥珀酸同時氧化時的總速度,不等於二者分別氧化時速度之和,而僅等於其中氧化較快者單獨氧化時之速度。但如用[2,6]二氯靛酚作為氫受體時,二者共同氧化時之總速度完全等於二者分別氧化時速度的和。 (四)當用氧或過量之細胞色素c作為氫受體時,琥珀酸與還原輔酶Ⅰ能彼此互相抑制對方氧化的速度。有足夠的實驗材料說明,還原輔酶Ⅰ對於琥珀酸氧化的抑制,不是由於草醯乙酸聚集的緣故。 (五)如果在反應混合物中同時含有琥珀酸脫氫酶的專一抑制劑,丙二酸,則琥珀酸對於還原輔酶Ⅰ氧化作用的抑制即被解除。 (六)根據以上的實驗結果,可以認為,還原輔酶Ⅰ及琥珀酸先通過一個共同的因子與細胞色素c作用。這個共同的因子在一般情形之下,也是...

(一)本報告提供了一個從輔酶Ⅰ,用酶還原法製備還原輔酶Ⅰ的方法。我們所製得的還原輔酶Ⅰ鈉鹽乾粉,可以在低温保存數月而不被氧化。 (二)與心肌製劑中顆粒相結合的輔酶Ⅰ細胞色素還原酶系,和用乙醇抽出的水溶性的輔酶Ⅰ細胞色素還原酶的性質頗不相同。其中比較重要的不同點是對於細胞色素c的親力,前者遠大於後者,其米氏常數僅約為後者的十二分之一。 (三)用一心肌顆粒製劑作為材料,無論用氧或過量之細胞色素c作為氫受體,還原輔酶Ⅰ與琥珀酸同時氧化時的總速度,不等於二者分別氧化時速度之和,而僅等於其中氧化較快者單獨氧化時之速度。但如用[2,6]二氯靛酚作為氫受體時,二者共同氧化時之總速度完全等於二者分別氧化時速度的和。 (四)當用氧或過量之細胞色素c作為氫受體時,琥珀酸與還原輔酶Ⅰ能彼此互相抑制對方氧化的速度。有足夠的實驗材料說明,還原輔酶Ⅰ對於琥珀酸氧化的抑制,不是由於草醯乙酸聚集的緣故。 (五)如果在反應混合物中同時含有琥珀酸脫氫酶的專一抑制劑,丙二酸,則琥珀酸對於還原輔酶Ⅰ氧化作用的抑制即被解除。 (六)根據以上的實驗結果,可以認為,還原輔酶Ⅰ及琥珀酸先通過一個共同的因子與細胞色素c作用。這個共同的因子在一般情形之下,也是這兩個酶系統的速度限制因子。應該指出在我們的實驗中,並未使用任何可能影響酶系統結構的條件,因此我們的結果是在一個比較接近於生理狀態的情形之下獲得的。 (七)應該着重指出,從本報告的結果可以看到,一個用人為的方法從複雜酶系上溶解下來的酶的性質,有時並不能代表這個酶在有組織的酶系統中的真實情况。 (八)我們相信,本報告所說明的兩酶系競爭一個共同因子的一些現象,將为研究複雜酶系之間的相互關係,提供一個新的方法。

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 2781-44...

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 2781-44 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?

 
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