查询词典 degree of a representation

Since any n x n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n - 1 in the shift operator wn, the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix.

由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式，从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程。

Since any n×n doubly stochastic circulant matrix has a unique representation as a polynomial of degree n-1 in the shift operatorω_n,the classification problem of primes in the doubly stochastic circulant matrices can be reduced to the solution of an equation over a doubly stochastic circulant matrix.

由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式，从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程。

In this paper, the computation of original likelihood function is transformed into the optimal problem of its low bound through the conjugate representation of the convex function, and a additional parameter is introduced to control the smoothing degree of low bound, and so the performance of local optimal solution can be improved.

我们利用凸泛函的对偶性，将原似然函数的复杂计算问题转化为对其下界函数的优化问题，从而降低学习算法的复杂性；并通过引入一个参数来控制下界函数的光滑程度来改善局部最优解的性能；指出了传统的期望最大化算法(Expectation Maximization Algorithm)是变分学习算法的特殊情况。

Timid, commonly known as胆儿small, is a common psychological reactions, in the only-child in a certain degree of representation, even in adults is also very common, but adults are better at nothing to conceal.

胆怯俗称胆儿小，是很常见的一种心理反应，在独生子女中有一定的代表性，即使在成人中也很常见，只是成人更善于掩饰罢了。

Mentioned South Korea's food, people immediately think of the absolute is "kimchi", Koreans love kimchi right level has reached a degree of cultural representation, the majority of South Korean households have two refrigerators and an ice-general food, and the other is the storage refrigerator pickles, pickled vegetables because of different temperatures show a different flavor.

讲到韩国的食物，让人马上联想到的絶对是"泡菜"，韩国人对泡菜喜爱程度，己经到了一个文化代表的程度，大部份韩国家庭还有二个冰箱，一个冰一般的食物，另一个冰箱则是存放泡菜，泡菜会因为不同温度呈现不同的风味。

By using the group-chain, the wavefunctions of the 4f〓 configuration for RE ions are also expressed as linear combinations of group-chain basis functions in Butler's irreducible representation notation. The matrix elements of the CF Hamiltonian then are calculated by means of the Wigner-Eckart theorem and factorization lemma of the jm factors. Before the CF level fitting, a point-charge calculation of the conventional CF parameters B〓 has been performed by means of the lattice-sum technique from the known crystal structure data. The corresponding parameters in the group-chain are calculated by the conversion relationship between two schemes that proved identical in essence, which are usually used as initial values in the fit to the experimental levels. The ratios of the same k-value CF parameters are suggested as the constraint conditions in the fit, in order to utilize fully the symmetry distortion degree of the studied system.

利用群链理论，属稀土离子4f〓组态的波函数表示为以不可约表示标记的群链基波函数的线性组合；借助Wigner-Eckart定理和2jm和3jm因子的分解定律计算了晶场哈密顿的矩阵元；根据点电荷模型和已知晶体结构数据，利用点阵求和技术计算得到传统晶场参数B〓初值，相应的非传统形式的群链参数初值则由两种方案下的转换关系求得；这些初值通常作为非线性拟合晶场能级计算的初值，系统的对称性畸变信息则反映在以同阶晶场参数的比值作为能级拟合的约束条件。

The resulting surface has a degree 4 parametric polynomial representation and is represented as a network of tangent plane continuous triangular Bézier patches.

生成的曲面有一个4次参数多项式表示并且被表示成一个切平面连续的三角形Bézier片网。

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我们讨论了具有自交数为+1的嵌入环面〓的4—流形的Donladson不变量，运用环面上欧拉数为-1的圆丛的单个不可约SU（2）表示给出了Donaldson不变量在环面表示的同调类上的一个粘合公式（定理2.4.1），这一结果补充了P。

In ARM a basic unit of the domain-specific knowledge representation is characterized by a triad in which P is a fuzzy assertion;β∈[0,1] is the degree of confidence; LTV is the degree of self-confidence, that is,the linguistic truth .

在ARM中，我们把领域专家知识表示的基本单元表征为一个三元组，其中P是一个模糊断言；β∈[0，1]是可信度；LTV是自信度，即语言真值。

The mass fraction of Fe2O3 in the mixture was calculated and used as a representation of mixedness degree. The results of the study show that the new method provides similar precision and accuracy for...

结果表明，该法与重铬酸钾法比较，精密度和准确度均无显著性差异，测定混匀度的相对误差在±2%，且方法简便、快速、准确、对环境友好，可用于生产实时监控。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。