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  scalar product
     THE SCALAR PRODUCT OF THE WEIGHTS FOR THE ELEMENTARY REPRESENTATION
     初等表示的权的标积
短句来源
     When the set of roots for a semi-simple Lie algehra have beenselected appropriately, the scalar product of the weights of the elementaryrepresentation can be calculated.
     在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积
短句来源
     When the set of roots for a semi-simple Lie algebra have been selected appropriately,the scalar product of the weights of the elementary representation can be calculated.
     在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积.
短句来源
     In this paper by using cartan matrix,a method for calculating the scalar product of the weights of the elementary representation for semi- simple Lie algebra is presented,and from this,the eigen value of the second Casimir operator is worked out.
     本文利用 Cartan 矩阵给出了一种计算半单李代数初等表示的权的标积的方法,并由此算出了二次 Casimir 算符的本征值.
短句来源
  standard product
     In a group of orthogonal vectors,a vector’s standard product is 1 with itself while 0 with others. With this property,watermark information is spread spectrum by vector from orthogonal vectors,then multiple watermark information are linear compounded and embedded as a single information,watermark information can be detected anytime without impacted by other embedded watermark.
     在一组正交向量中,向量与自己的内标积为1,向量之间的内标积为0,利用这一特性,对多个水印信息分别进行扩频调制,将调制后的信息线性组合后嵌入到载体中,使得多个水印在嵌入和提取时互不影响;
短句来源
  “标积”译为未确定词的双语例句
     A Dyadic Calculation of the Vector and Scalar Products of Two Angular Momentum Operators in Quantum Mechanics
     角动量算符的矢积与标积的并矢计算和它的应用
短句来源
     Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation.
     文中利用旋转矩阵的性质,容易得出各坐标轴单位矢量的方向余弦的递推公式,求出这些单位矢量的标积和混合积,并且可以方便地导出第六个约束方程,推导颇为简捷。
短句来源
     In this paper by using cartan matrix, a method for calculating thescalar product of the weights of the elementary representation for semi-simple Lie algebra is presented, and from this, the eigen value of the aecondCasimir operator is worked out.
     本文利用Cartan矩阵给出了一种计算半单李代数初等表示的权的标积的方法,并由此算出了二次Casimir算符的本征值。
短句来源
     A unified electromagnetic field vector is formed in the 3 d space. Its equations,and the relations between square of the field vector and energy,momentum are given. It is found that the dot product of the unified field vector with itself in the 3 d space is a relativistic invariant.
     论述了电场与磁场本质上的统一性质 ,构造了三维空间中电磁场的统一场量 ,给出它的方程、场量的模方与能量和动量的关系 ,发现三维空间中的统一场量自身的标积竟然是相对论变换下的不变量 .
短句来源
  相似匹配句对
     THE SCALAR PRODUCT OF THE WEIGHTS FOR THE ELEMENTARY REPRESENTATION
     初等表示的权的
短句来源
     ON THE σ-PRODUCTS
     σ-
短句来源
     A Dyadic Calculation of the Vector and Scalar Products of Two Angular Momentum Operators in Quantum Mechanics
     角动量算符的矢的并矢计算和它的应用
短句来源
     BLASCHKE PRODUCT OF COEFFI CTENTS
     Blaschke的系数
短句来源
     Sodium benzoate was used as the internal standard .
     苯甲酸钠为内
短句来源
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  scalar product
We introduce a family of linear differential operators ${\cal K}^n =(-i)^nP_n^{\cal M}(i\frac{d}{dt})$, called the chromatic derivatives associated with M, which are orthonormal with respect to a suitably defined scalar product.
      
Define the scalar product in H1 to be (f(x), g(x))1=
      
In this paper we prove an "explicit formula" relating the scalar product of the Hecke series of two fields of algebraic numbers to the zeta-function composites of these fields.
      
Construction of Banach spaces using a generalization of the scalar product
      
For such a space we introduce, as in the case of the usual scalar product, a series of concepts, and prove, as an example a theorem concerning orthogonal expansion.
      
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  inner product
It is shown that there is a similar identity when the inner product is replaced by an indefinite quadratic formq and h is a Л-harmonic distribution, where Л is the differential operator canonically associated toq.
      
We present a method for constructing wavelet bases on the unit sphere S2 of R3, using the radial projection and an inner product associated to a convex polyhedron having the origin inside.
      
A modified Bates and Watts geometric framework is proposed for quasi-likelihood nonlinear models in Euclidean inner product space.
      
We introduce the notion of inner product with sign-sensitive weight and construct systems of nonsymmetrically orthonormalized polynomials.
      
Estimates of polynomials orthogonal with respect to the Legendre-Sobolev inner product
      
更多          
  standard product
The wind fields are taken from the 1998-2004 NCEP/NCAR Reanalysis data with better spatial resolution (1° × 1°) than the standard product, which are publicly available on the Internet.
      
Lack of bioequivalence of a generic mefloquine tablet with the standard product
      
In particular, we show that a simple formula for updating the pricing vector can be used with some advantage in the standard product form simplex algorithm and with very considerable advantage in two recent developments: P.M.J.
      
Certain uses of the analysis of variance with standard product specifications
      
In this paper firms may deviate from standard product specifications by investing in flexible production.
      
更多          


An input-ouptut equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which...

An input-ouptut equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace's Theorem, is given to evaluate the 16X16 determinant according to its characteristic, so that the evaluation is much simplified.

本文利用文[1]的方法,并以旋转矩阵作为主要数学工具,进行一般空间7R机构的位移分析,得出和文[2]相同的结果,而推导和计算显著简化。文中利用旋转矩阵的性质,容易得出各坐标轴单位矢量的方向余弦的递推公式,求出这些单位矢量的标积和混合积,并且可以方便地导出第六个约束方程,推导颇为简捷。此外,文中根据所得16阶行列式的特点,采用先作行变换再按Laplace定理展开的方法进行计算,使计算工作量大为减轻。

The simple roots for any semi-simple Lie algebra can be representedby the weights of appropriate elementary representation. Conversely, theweights for the elementary representation can also be repeesented by simpleroots. When the set of roots for a semi-simple Lie algehra have beenselected appropriately, the scalar product of the weights of the elementaryrepresentation can be calculated. In this paper by using cartan matrix, a method for calculating thescalar product of the weights of the elementary representation...

The simple roots for any semi-simple Lie algebra can be representedby the weights of appropriate elementary representation. Conversely, theweights for the elementary representation can also be repeesented by simpleroots. When the set of roots for a semi-simple Lie algehra have beenselected appropriately, the scalar product of the weights of the elementaryrepresentation can be calculated. In this paper by using cartan matrix, a method for calculating thescalar product of the weights of the elementary representation for semi-simple Lie algebra is presented, and from this, the eigen value of the aecondCasimir operator is worked out.

半单李代数的素根可以用适当的初等表示的权来表示,反过来,初等表示的权也可以用素根来表示。在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积。本文利用Cartan矩阵给出了一种计算半单李代数初等表示的权的标积的方法,并由此算出了二次Casimir算符的本征值。

The simple roots for any semi-simple Lie algebra can be represented by the weights of appropriate elementary representation.Conversely,the weights for the elementary representation can also be represented by simple roots.When the set of roots for a semi-simple Lie algebra have been selected appropriately,the scalar product of the weights of the elementary representation can be calculated. In this paper by using cartan matrix,a method for calculating the scalar product of the weights of the elementary representation...

The simple roots for any semi-simple Lie algebra can be represented by the weights of appropriate elementary representation.Conversely,the weights for the elementary representation can also be represented by simple roots.When the set of roots for a semi-simple Lie algebra have been selected appropriately,the scalar product of the weights of the elementary representation can be calculated. In this paper by using cartan matrix,a method for calculating the scalar product of the weights of the elementary representation for semi- simple Lie algebra is presented,and from this,the eigen value of the second Casimir operator is worked out.

半单李代数的素根可以用适当的初等表示的权来表示,反过来,初等表示的权也可以用素根来表示.在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积.本文利用 Cartan 矩阵给出了一种计算半单李代数初等表示的权的标积的方法,并由此算出了二次 Casimir 算符的本征值.

 
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