With the formula of electric flux, the net charge that is enclosed in the surface can be calculated. This can be achieved by charge multiplication for the electron with the entire electrons that appear on the surface. Using this, the free space permittivity and the electric flux can be known...
It is shown that in Artin's characterization of Γ as the unique continuous function : R + → R + satisfying the functional equation ( F ): ( x + 1) = x ( x ) and the multiplication formula, the condition ( F ) can be replaced by a simple normalization. Related results are ...
Bug fix: multi-dimensional array matrix multiplication in certain cases with complex matrices would return an error message instead of computing the product.Bug fix: possible crash when opening files with very long lines.Bug fix: Fix plotBox() with only 1 value....
21). In the following, whenever R is commutative, as in Example 2.10, we write a∧ b and a∨ b respectively for an lcm and a gcd of a, b∈ R if they exist (in which case they are unique up to multiplication by units in R). The proof of the following results is an exercise*...
= n2n + 2 12 13 Similarly, from formula 12 it follows that the quantity of multiplication operations for the second strategy is estimated by formula: X3 nᝇ1 n =0 ᝇ 2 = nn + 12n 2 + 1: 14 To illustrate the theoreti...
Find the inverse of the given matrix if the matrix is invertible, and check the answer by multiplication. A=\begin{bmatrix} \frac{1}{5}&\frac{1}{5}&-\frac{2}{5}\ \frac{1}{5} &\frac{1}{5}&\frac{1}{10} Find the inverse using an augmented matrix. \begin{...
We propose a fomula that directly gives an estimate of the value of a Gaussian integral through only one multiplication. Using this formula, we may neglect about 60%–80% of integrals in quantum chemical ab initio calculations, without any loss in precision theoretically. Such a large molecule ...
formula (3.5). Corollary 3.8 If the pair (C(x), a) is unbalanced for x ∈ Cn − , then the operator of multiplication aj fj ∗x in O(CC(x),a) equals the operator K j (x) : O(CC(x),a) → O(CC(x),a) defined in (3.20). 3.9 Corollary of Theorem 3.7 For a ...
Such a collection is unique up to multiplication by a nonzero number. For every circuit C, we fix such a collection and denote fC = ∑i∈C λiCzi. The equation fC = 0 defines a hyperplane HC in Cn. It is convenient to assume that λiC = 0 for i ∈ J − C and write fC =...
Inspired by the computation of one and two dimensional image moments,a new fast computation algorithm is proposed,which realizes multi-nest by multiplication of matrices. 受一维和二维图像矩的计算启发,提出了一种新的快速计算方法,利用矩阵相乘实现多重循环。 更多例句>> 5...