factorize

To factorize Schrodinger equation, there are pairs of linear differential operator as

and we can factorize further the b-dependence from the a-dependence by the substitution

Quantum computer allows us to factorize a number consisting of N digits for [N.sup.2] operations.

There is an infinite number of forms to factorize f(x) as A(x)x(t), so this property increases the flexibility of the SDRE.

In this paper, to further improve the efficiency, the sparse solver of the multifrontal direct method [20] is first employed to factorize the FEM matrix [[K.sub.m]] to obtain the expression of [E.sub.m] by using [mathematical expression not reproducible], then the finite element tearing and tearing and interconnecting method (FETI) [17] is employed to handle the FEM matrix of the radome before solving (5).

If a is a perfect square, one can easily factorize 4q instead of factorising 4aq.

Consequently, there are just arithmetic operations necessary to factorize chromatic differences in final intensity of the image, so the image processing speed is raised up considerably.

permutations, in turn, factorize a SIF permutation.

Factorize C = -[LL.sup.T], where L is lower bidiagonal.

Thus, the methodological requirements to factorize matrices cannot be overlooked.

Knowing a proxy public key [d.sub.p] hacker cannot create a proxy private key given as it is hard to factorize. Thus the proposed scheme resists the above attacks.

Hence, we introduced and tested an alternative growth accounting method to factorize the components of output based on a production function approach.

Symeonidis, Nanopoulos, and Manolopoulos (2008) proposed to factorize Y through minimizing the element-wise loss on the elements of f by optimizing the square loss, that is,