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polynomial
相关语句
  多项式
     Biquadratic Polynomial Dynamics
     双二次多项式动力学
短句来源
     Polynomial Algebra and Its Applications
     多项式代数及其应用
短句来源
     The Ringel-Hall Algebra and Hall Polynomial of Tubular Category
     管范畴上的Ringel-Hall代数及Hall多项式
短句来源
     Research on Polynomial Functions and Permutation Polynomials
     关于多项式函数与置换多项式的研究
短句来源
     Qualitative Analysis of Polynomial Poincaré Equation and Existence of Periodic Solutions of a Class of Ecology Equations
     多项式Poincaré方程的定性分析和一类生态方程周期解的存在性
短句来源
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  多项式的
     Research on Polynomial Functions and Permutation Polynomials
     关于多项式函数与置换多项式的研究
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     FINITE STRIP METHOD OF SINE SERIES AND POLYNOMIAL
     正弦级数与多项式的有限条法
短句来源
     CONVERGENCE OF TWO POINTS HERMITE INTERPOLAT ION POLYNOMIAL
     两点Hermite插值多项式的收敛性
短句来源
     AN ASYMPTOTIC ESTIMATE FORMULA ON HERMITE-FEJER INTERPOLATION POLYNOMIAL
     关于Hermite—Fejèr插值多项式的一个渐近估计式
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     The L_p-norm of a Polynomial with Perturbed Coefficients
     具有摄动系数的多项式的L_p范数
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  “polynomial”译为未确定词的双语例句
     FM Space Depend on Operator T and the Normal Solvability of Operator Polynomial P(T)
     FM Space Depend on Operator T and the Normal Solvability of Operator Polynomial P(T)
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     COMPLEMENT AND COMMENTARY OF"ALGEBRAIC CLASSIFICATION OF POLYNOMIAL SYSTEM IN THE PLANE
     COMPLEMENT AND COMMENTARY OF"ALGEBRAIC CLASSIFICATION OF POLYNOMIAL SYSTEM IN THE PLANE
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     POLYNOMIAL SYSTEMS POSSESSING FOUR FINITE ELEMENTARY CRITICAL POINTS AND AT MOST THREE CRITICAL POINTS AT INFINITY
     POLYNOMIAL SYSTEMS POSSESSING FOUR FINITE ELEMENTARY CRITICAL POINTS AND AT MOST THREE CRITICAL POINTS AT INFINITY
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     EFFICIENCY OF ESTIMATION OF FIXED POLYNOMIAL EFFECTS IN MIXED MODELS BASED ON PBIB DESIGN
     EFFICIENCY OF ESTIMATION OF FIXED POLYNOMIAL EFFECTS IN MIXED MODELS BASED ON PBIB DESIGN
短句来源
     ON DETERMINING THE SOLVABLE DOMAIN OF A SYSTEM OF EQUATIONS WITH PARAMETERS──Part 1: Algebraic Polynomial Equations
     ON DETERMINING THE SOLVABLE DOMAIN OF A SYSTEM OF EQUATIONS WITH PARAMETERS──Part1: Algebraic Polynomial Equations
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  polynomial
The finite irreducible linear groups with polynomial ring of invariants
      
Then the ring of invariants ofG is a polynomial ring if and only ifG is generated by pseudoreflections and the pointwise stabilizer inG of any nontrivial subspace has a polynomial ring of invariants.
      
This allows us to obtain a complete list of all irreducible linear groups with a polynomial ring of invariants.
      
If the variety is a complex affine space and the ring of invariants is isomorphic to a polynomial ring, then the action is conjugate to a translation (Theorem 3).
      
The kernel of a certain derivation of the polynomial ringk[6] is shown to be nonfinitely generated overk (a field of charactersitic zero), thus giving a new counterexample to Hilbert's Fourteenth Problem.
      
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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 first writer suggests a distribution function for the roots of the complex polynomial corresponding to the nulls of the radiation pattern of a nonuniform array on the unit circle in a complex plane for the purpose of suppression of the side-lobes near the main beam of radiation.

为了减小线形天线阵辐射图形中的旁瓣,本文前一作者提出了与辐射图形中零点相对应的复量多项式的根在复数面中单位圆上的一个分布函数。这个分布函数是 φ_k=2βl/(1-n){1+ξk~(1-lnε/ln(n-2))},它包含了谢昆诺夫的均匀分布(ξ=1);因此,谢昆诺夫的分布可以看成是我们的分布的一个特例。 计算结果证明,应用我们的分布函数,对于不均匀线形天线阵的辐射图形将有较好的控制,尤其对于减小主瓣附近的旁瓣有利。这样作会使远离主瓣的旁瓣变大一些,但后一清况可以用本文前一作者所提出的移动最末一个零点的位置加以改善。

The present author suggests a new distribution function for the roots of the complex polynomial corresponding to the nulls of the radiation pattern of a linear antenna array on the unit circle in a complex plane which is more general than the one suggested by the same author in a previous paper[2]. The new distribution function is of the form

在本文中,作者提出了与线形天线阵辐射图形中零点相对应的复量多项式的根在复数面中单位圆上的一个分布函数,它比作者在前一篇论文中所提出的分布函数有更普遍的意义。这个普遍函数是: 当ψ_0和ξ被适当地选择时,这个普遍函数所代表的天线阵将包括以下各式天线阵作为特例:(1)均匀横射式天线阵;(2)均匀端射式天线阵;(3)谢昆诺夫天线阵;(4)道尔夫-捷比谢夫天线阵当阵中单元数不超过7时。但是,应用所提出的分布函数并当合理地选择ψ_0和ξ时,却可以改善以上各式天线阵,尤其在压小主瓣附近的旁瓣方面。这一情况是具有重大实用意义的。此外,因为天线阵中各单元的场强或其方向图中的旁瓣一般都随着离开主瓣的角距的增加而下降的,所以为了使天线阵的总方向图有均等或接近均等的小的旁瓣(这是具有实用意义的),就必须设计一个由均匀辐射器所组成的天线阵,它有随着离开主瓣的角距的增加而上升的小的旁瓣。利用谢昆诺夫的分布或道尔夫-捷比谢夫的分布都不能达到此目的,但是应用所提出的分布函数却可以办到。计算结果证实了上述各点。 在本文中,作者还将代表各式天线阵的多项式的乘积形式加以展开,从而将其中的系数化为显式以便于阵中各单元上相对电流的计算。

 
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