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sum     
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     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的中心极限定理及其在马尔可夫链上的应用
短句来源
     ON THE RANGE OF SUM OF MONOTONE MAPPINGS AND NONLINEAR INTEGRAL EQUATIONS OF URYSOHN TYPE
     单调映射之的值域与Urysohn型非线性积分方程
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的矩的估计的几点结果
短句来源
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  求和
     Computer Method on sum from i=1 to n(i~m)
     sum from i=1 to n(i~m)求和的计算机算法
短句来源
     In this paper, we probe into the method of Summation to the series sum from n=1 to ∞1/[n(n+1)…(n+k)]~m[k≥0 is integar, m = 1, 2, 3; k≠0(m = 1 )].
     本文探讨了级数sum from n=1 to ∞(1/[n(n+1)…(n+k)]~m)(其中k≥0为整数,m=1,2,3且m=1时k≠0)的求和方法.
短句来源
     A Elementary Method Summating the Series sum form n=1 to ∝(1/n~(2m))
     级数sum form n=1 to ∝(1/n~(2m))的一种初等求和
短句来源
     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
     Q~2-Dependence of the Gerasimov-Drell-Hearn Sum Rule
     Gerasimov-Drell-Hearn求和规则的Q~2依赖性质
短句来源
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  总和
     The sum of positive cell area was(7.86±0.49)×102 μm2, and the sum of integral absorbance was (13.66±70.00)×105 in the cmy-c experimental group. Compared with the cmy-c control group, there was significant difference (P < 0.01).
     cmy-c实验组阳性细胞面积总和(7.86±0.49)×102μm2,积分吸光度总和为(13.66±70.00)×105,与cmy-c对照组比较,差异有显著性意义(P<0.01)。
短句来源
     The results showed that the sum of positive cell area was (16.11±3.01)×102 μm2, and the sum of integral absorbance was (19.9±2.42)×105 in the bcl-2 experimental group. Compared with the bcl-2 control group, there was significant difference (P < 0.01).
     实验结果bcl-2实验组阳性细胞面积总和为(16.11±3.01)×102μm2,积分吸光度总和为(19.9±2.42)×105,与bcl-2对照组比较,差异有显著性意义(P<0.01)。
短句来源
     Teachers' quality is the sum of ideological quality,professionalism,competence and mental status,and it is the key to medical education.
     教师素质是教师在教育和管理工作中所具备的思想品质、业务、能力、心理诸多要素的总和,它是医学教育的关键;
短句来源
     Result: Normal blood flow volume of vertebral artery,right side of it stadys at 130.47±56.10ml/min while left side 164.21±63.54ml/min,the sum of both side is 293.70±80.74ml/min.
     结果:正常人椎动脉血流量右侧130.47±56.10ml/min,左侧164.21±63.54ml/min,双侧血流量总和293.70±80.74ml/min;
短句来源
     Cladosporium,Alternaria and Phoma are the dominant species of the two counties and the sum of them account for 81.25 % and 85.94 % in spore-producing fungus,respectively.
     2县青稞籽粒的真菌优势种都是C ladosporium、Alternaria和Phoma,优势种总和分别占尼木、林周2县产孢真菌的81.25%、85.94%。
短句来源
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  总数
     This assembly has definite assembling technological level with size of the assembly 95mm×67mm×1mm , it’s wiring density 12. 5wires/cm2,pore density 7.8pores/cm2 and sum of components and devices 122.
     该组装件尺寸为95mm×67mm×1mm,布线密度为12.5根/cm,介质通孔密度7.8个/cm2,元器件总数为122只,显示了该组装件的组装工艺水平。
短句来源
     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 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 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 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
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      sum
    We show that ${\mathcal M}(G,R)$ is a symmetric tensor category, i.e., the motive of the product of two projective homogeneous G-varieties is a direct sum of twisted motives of projective homogeneous G-varieties.
          
    We also study the problem of uniqueness of a direct sum decomposition of objects in ${\mathcal M}(G,R).$ We prove that the Krull--Schmidt theorem holds in many cases.
          
    For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula.
          
    The new interpretation makes transparent for GLn (and conceivable for other classical groups) a certain invariance of Jantzen's sum formula under "Howe duality" in the sense of Adamovich and Rybnikov.
          
    From elements of the invariant algebra C[V]G we obtain, by polarization, elements of C[kV]G, where k ≥ 1 and kV denotes the direct sum of k copies of V.
          
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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。

    A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron...

    A new approximation method is proposed in this article for the discussion of molecular structures,and this new method includes the two well-known theories,molecular orbital theory and electron-pair bond theory as two special cases.Let a molecule have n bonds and let the ith bond be described by the anti-symmetrical two-electron bond function ψ_i(v_(2i-1),v_(2i)).(If there exist one- electron,three-electron or many-electron bonds,they can be similarly described by the corresponding one-electron,three-electron or many-electron bond func- tions.) Then the stationary state of the molecule is represented by the follow- ing wave function Ψ, where the summation is over all permutations of 1,2,……,2n except those within the interior of the functions,since each ψ_i is already anti-symmetrical.Obviously (2~n/((2n)/!))~(1/2) is the normalization factor. By quantum mechanics the energy of the molecule equals (1) here H_i,T_(ij) and S_(11)' are respectively the following three kinds of operators, (2) (3) (4) The third term of equation (1) is the exchange integral of electrons 1 and 1', while (1,2') is that of electrons 1 and 2'.According to the definition of bond functions,ψ_i may be written as (5) Substituting equation (5) into equation (1) and carrying out the integration over spin coordinates,we obtain (6) It can be easily seen from equation (6) that the combining energy of a mole- cule consists of two parts,one being the binding energy of the bonds represent- ed by the first term of equation (6),and the other being the interaction energy of the bonds denoted by the second term of that equation. If we choose certain functions φ_i~('s) involving several parameters and substi- tute them into equation (6),we may determine the values of those parameters by means of the variation principle. For the discussion of bond interaction energies,we develop a new method for the evaluation of certain types of three-center and four-center integrals.The interaction energy of a unit positive charge and an electron cloud of cylindrical- symmetry distribution may be written as (7) where (8) and R_0~2=a~2+b~2+c~2 The interaction energy of two electron clouds both of cylindrical-symmetry distributions with respect to their own respective axes is evaluated to be (9) (10) where is to sum over j from zero to the lesser value of n-2i and m, is to sum over i from zero to the integral one of n/2 and (n-1)/2,and is to sum over all cases satisfying the relation =m-j,while b_(n,n-2i) represents the coefficient of x~(n-2i) in the n th Legendre polynomial.

    本文在分子结构理论方面,作了下列两点贡献:首先建议了用双电子或多电子键函数作为近似基础,来计算分子的近似能量和近似电子云分布。这样计算得来的结果,一定会比用分子轨道理论或电子配对理论好,因为它更真实的反映了分子的化学性质,同时它也包括了后两者,而以它们为特例。我们得到了分子结合能的表示式,用表示式证明了分子结合能由两部分组成:一部分是键的结合能,另一部分是键与键间的作用能。其次是建议了一种新方法,把在计算化学键相互间的作用能中遇到的一些三中心和四中心积分,还原为容易计算的二中心积分。这方法比以往所用的好,因为它计算比较简单,同时限制性也小。

     
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