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sum over
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  求和
     On the basis of AM1 and ZINDO, according to the sum over state expression, we devised the program for calculating the nonlinear second order optical susceptibilities β ijk and β μ . The structure, electron spectra and β(-2ω, ω, ω), β (0, 0, 0) of a series of novel pull push polycyclic conjugated molecules have been studied.
     在 AM1和 ZINDO方法基础上 ,按完全态求和 ( SOS)公式编制了计算分子二阶非线性光学系数βijk和βμ 的程序 ,研究了一系列新推拉型多环共轭分子的结构、光谱和二阶非线性光学系数β( -2ω,ω,ω)和β( 0 ,0 ,0 ) .
短句来源
     On the basis of ZINDO, according to the sum over state expression, we designed the program for calculating the first hyperpolarizability β . The structures, electron spectra and β (-2ω,ω,ω), β (0,0,0) of a series of babituric acid derivative molecules have been studied.
     在 ZINDO方法基础上 ,按完全态求和 ( SOS)公式编制程序并计算了第一超极化率 β,研究了巴比妥酸系列衍生物分子的结构、光谱和第一超极化率β( -2ω,ω,ω) ,β( 0 ,0 ,0 ) .
短句来源
     The first hyperpolarizabilities β(-2ω;ω,ω) and β(-ω;ω,0) of hemicyanine derivatives chromophore, 4-N,N-dimethylamino-4'-N'-methyl stilbazolium (DAS), are calculated by using time-dependent Hartree-Fock (TDHF) and sum over states (SOS) method at infrared wavelength, respectively.
     采用含时耦合微扰(TDHF)和多态求和(SOS)方法计算了半花菁衍生物分子生色团4-N,N-dimethylami-no-4′-N′-methylstilbazolium(DAS)的第一超极化率频率色散效应。
短句来源
     On the basis of ZINDO methods, according to the Sum Over States (SOS) formula, the program for the calculation of second order optical susceptibility β has been devised. The MO interaction in (dithiophene 3,2 b:3,2 d cyclopentan 4 ylidene)fullerene 60 has been studied, moreover, the electronic spectrum and second order optical susceptibility of this molecule have been calculated. The former is in good accordence with the experimental result, and the latter is a theoretical prediction.
     在ZINDO方法基础上,按完全态求和(SOS)公式编制了计算分子二阶非线性光学系数β的程序.研究了(二噻吩[3,2-b:3,2-d]环戊烷-4-亚基)C60中的分子轨道相互作用,计算了该分子的电子光谱和二阶非线性光学系数β,前者与实验结果吻合较好,后者属于理论预测性质.
短句来源
     On the basis of ZINDO, the program for calculating the third order NLO susceptibility γ ijkl was devised according to the sum over state expression.
     在 ZINDO方法基础上 ,按完全态求和 (SOS)公式编制了计算三阶非线性光学系数γijkl的程序 ,研究了多取代巴比妥酸系列衍生物分子的结构 ,光谱和三阶非线性光学系数 γ(- ω;- ω,ω,ω) ,γ(0 ;0 ,0 ,0 ) .
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  “sum over”译为未确定词的双语例句
     The proofs are based on the estimate of certain character sum over F_q. If t is the period of the sequences, then the bound of the discrepancy is O(t~(-1/4)q~(1/8+ε) log q) for any ε> 0 when t≥q~(1/2+2ε). It shows that the sequences are asymptotically uniformly distributed.
     设t为序列的周期,则对任意给定的ε>0,当t≥q~(1/2+2ε)时,均有偏差的上界为O(t~(-1/4)q~(1/8+ε)logq),从而说明了输出序列是渐进均匀分布的。
短句来源
     On certain divisor sum over square-full integers
     全平方数集中的除数问题
短句来源
     We also show that with the system decohering to itspointer states, the geometric phase factor tends to a sum over the phase factors pertainingto the pointer states.
     研究结果也表明,随着体系向它的指示态(pointer states)的退相干,它的几何相因子在数值上也趋于其指示态相因子的加权平均。
短句来源
     The result of the QCD calculation is then matched, via dispersionrelation, to a sum over hadronic states.
     然后,把QCD计算的结果通过色散关系与强子态之和相匹配。
短句来源
     The partition function, also called the sum over states, It plays an important role in the evaluation of thermodynamic functions and in the derivation of distribution functions.
     配分函数,也称状态和函数。 对于热力学函数的获得及在分布函数的导出中拌演着重要角色。
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  相似匹配句对
     Sum Graphs Over the Integral Set
     关于整数集上的和图的几个新结果
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     Parallel Sum of Matrices over Division Ring
     除环上矩阵的平行和
短句来源
     Over the Rainbow
     飞越彩虹——Mariatorget广场及Rival旅馆室内照明设计
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     Over the Hedge
     篱笆墙外
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     To the Sum of Series
     级数求和
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  sum over
An asymptotic formula with power lowering in the remainder of the trigonometric sum over primes from the set E is obtained.
      
The contribution to the sum over topologies in three-dimensional quantum gravity is briefly discussed.
      
An expression for the nanotube conductivity is obtained in the form of a sum over magnetic-quantization states.
      
The first term is a sum over the roots of the dispersion relation; the second, an improper integral.
      
The proofs are based on the estimate of certain character sum over Fq.
      
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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。

The quantum theory of two-level atom single-mode laser system of Sargent, Scully and Lamb is extended to two-mode laser in a three-level atomic system with common lower level, and master equation is obtained for the system with all the three levels being pumped. There appear four terms in the master equation that are absent in the single-mode case and those interpreted as 2-photon processes play an especial role in the present case. The master equation is represented by a probability flow diagram in two-dimensions...

The quantum theory of two-level atom single-mode laser system of Sargent, Scully and Lamb is extended to two-mode laser in a three-level atomic system with common lower level, and master equation is obtained for the system with all the three levels being pumped. There appear four terms in the master equation that are absent in the single-mode case and those interpreted as 2-photon processes play an especial role in the present case. The master equation is represented by a probability flow diagram in two-dimensions with the photon numbers n1 and n2 of the two-mode as variables. The probability flow diagram can be extended to infinity, and each arrow of it represents a term of the right hand side of master equation. By taking sum over one of the variables n1 or n2, the master equation is reduced to two equations, each of them can be represented by an one-dimensional probability flow diagram. The equation of motion under steady state is obtained by considering the correspondence between the macroscopic balance and the microscopic balance.A parameter H is introduced to reduce the equation of motion and to facilitate the mathematical procedure and a formal solution is thus obtained. Using the equation of motion and its formal solution various operation characteristics are discussed. Among them are: the threshold condition for each mode; the condition of only one mode operation; the variation of photon statistics between single-mode operation and two-mode operation and the variation of photon statistics with lower level being pumped and not pumped.

本文将Sargent,Scully和Lamb的二能级单模激光全量子理论推广到共下能级三能级双模激光系统中,获得了三个能级都有泵浦情况下的共下能级三能级原子系统双模激光运转的主方程。考虑到细致平衡与宏观平衡之间的对应性,合理地应用细致平衡原理得到定态运动方程。通过引入一个参数H,从而获得了形式解。利用运动方程和形式解,讨论了不同条件下的一些运转特性和光子统计分布的变化.

A general foimula for angular integrations in many—dimensional spaces (derived in a previous paper) is applied fo several problems conectes with solution of the Schrodinger eqation for many-particle systems.Matrix elements of the Hamiltonian are derived for cases where the potential can be expressed in terms of functims of the generaliyed radius multiplied by polynonials in the m coordinntes. The theory of hyperspherical harmonics is reviewed, and a sum rule is derived relating the sum over all the harmonics...

A general foimula for angular integrations in many—dimensional spaces (derived in a previous paper) is applied fo several problems conectes with solution of the Schrodinger eqation for many-particle systems.Matrix elements of the Hamiltonian are derived for cases where the potential can be expressed in terms of functims of the generaliyed radius multiplied by polynonials in the m coordinntes. The theory of hyperspherical harmonics is reviewed, and a sum rule is derived relating the sum over all the harmonics belong to a Particular eigenvalue of angular momen turn to the Gegenbauer polynomial corresponding to that eigenvalue.A formula is derived for projecting out the component of an arbitrary funcfion corresponding fo a particular eigenvalue of generaliyed angular momentum, and the formula is applied fo polynomials in the m coordinafes An expansion is derived for expressing a many-dimensional plane wave in terms.of hyperspherical harmonics and functions which might be called "hyperspherical Bessel functions" .It is shown how this expansion may be used fo calculate many-dimensional Fourier transforms. A fonmula is is derived expressing the effect of a group - theoretical projection operator acting on a many—dimensional plane wave. Finally the techniques mentioned above are used to expand the Coulomb potential of a many-particle system in terms of Gegenbauer Polynomials.

本文利用过去得到的多维空间角积分的一般公式讨论多电子体系Schrodinger方程解的某些问题。给出了哈密顿算子的矩阵元,其中的势能写成超球半径与m个坐标的多项式的乘积·重新评述了超球谐并推出了求和规则,找到了一个投影公式,这个公式可以投影出广义角动量指定本征值的分量,并应用到m个坐标的多项式,得到了多维平面波以超球谐展开的公式。展开式的径向部分称为“超球Bessel函数”,讨论了这个展开式怎样用于计算多维Foarier变换。此外,推导出了一个群论投影算子作用于多维平面波的公式。最后,上面讨论的方法用来展开Coalomb势成为Gegenbauer多项式。

 
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