Sentence examples for matrix representation and from inspiring English sources

Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis.

The defining constraints are operator algebra without a matrix representation and semi-orthogonalization without storage of Krylov vectors.

The discretisation utilises the integral definition of the fractional derivatives, and we show that it leads to a diagonally dominant matrix representation, and a provably stable numerical scheme.

We obtain a special operator matrix representation and some necessary/sufficient conditions for an infinite-dimensional operator to be expressible as a sum of projections.

The aim of this paper is to give additional properties of such a matrix representation and to show how these findings can be applied to obtain binding energies and eigenfunctions for the hydrogen atom.

The simulation is carried out by solving in cylindrical coordinates the Laplace differential equation for the electrical field's potentials, using a matrix representation and a numerical solution for the fundamental system of boundary conditions.

The system conguration and design are discussed, and the energy and mass balances are obtained through the matrix representation method and integrated into a simulation program by MATLAB soft package.

The main improvements come from adopting a novel protein sequence representation by using discrete cosine transform (DCT) on substitution matrix representation (SMR) and from using weighted sparse representation based classifier (WSRC).

Because not all species investigated were sequenced for all genes used, we constructed trees from the various datasets and combined these source trees via a supertree with the aid of Rainbow [ 27], using matrix representation with parsimony and the Baum [ 28] and Ragan [ 29] coding scheme [ 30, 31].

Using linear algebra, we will see that this matrix representation is useful and gives interesting results.

(3.7) We take (mathbf{A}/h^{2}) to be approximation of differential operator (T=partial^{2}/partial x^{2}), then we set (m(T^{alpha/2})approx 1/h^{alpha}mathbf{A}^{alpha}) (an approximate matrix representation of T) and we approximate (3.5) by the equation frac{dmathbf{u}}{dt}=bar{delta} mathbf{A}^{alpha}mathbf{u}, (3.8) with (bar{delta}=D/h^{alpha}).