Sentence examples for initial equations from inspiring English sources

Start with initial equations as: begin{array}rcl@ mathbf{P}_{M}=mathbf{I}_{N}, end{array} (10).

The sequential equations of the SCA algorithm are as follows: Start with initial equations as: begin{array}rcl@ mathbf{P}_{M}=mathbf{I}_{N}, end{array} (10) begin{array}rcl@ bar{mathbf{s}}_{text{sur}}^{(M }=mathbf{s}_{text{sur}}.

The Therrien and Henderson study has been criticized for the choice of theropods used for comparison (e.g., most of the theropods used to set the initial equations were tyrannosaurids and carnosaurs, which have a different build than spinosaurids), and for the assumption that the Spinosaurus skull could be as little as 1.5 m in length.

Initial equations for various models are given below: (3) Zero order model : X = K t (4) First order model : log X = K t / 2.303 (5) Higuchi release model : X = K (t ) 1 / 2 where X is the amount of drug released, K is the release rate constant, and t is time.

This conclusion poses questions about the meaning of the initial equation (18), because for mathematical Brownian motion the term dA t) does not exist in the usual sense of a derivative.

We shall now get to solving (4), i.e. 'the simplified' variant of the initial equation (1).

The initial equation (1) is reduced to the Abel integral equation (23) by the regularization method of Carleman-Vekua [4], which was developed for solving singular integral equations.

By the Carleman-Vekua regularization method (Vekua in Generalized Analytic Functions, 1988) the initial equation is reduced to the Abel equation.

Our method is based on a "two scale" reformulation of the initial equation, with the introduction of an additional periodic variable.

In the present paper, we are concerned with a class of stochastic functional differential delay equations with the Poisson jump, whose coefficients are general Taylor expansions of the coefficients of the initial equation.

We note that after the multiplication of (44) by exp { t / ( 4 a 2 ) } (i.e. with the substitution after (33)), we obtain the solution φ ∗ ( t ) of the homogeneous equation corresponding to the initial equation (30) φ ∗ ( t ) = 1 − t exp { t 4 a 2 } + π 2 a [ 1 + erf ( − t 2 a ) ]. (45).