Sentence examples for The principal solution from inspiring English sources

The principal solution mechanism is ZrO2 + 4NaOH = Na4ZrO4 + 2H2O with ∆H ~ 200 kJ/mol.

The principal solution mechanism is 2ZrO2 + 2NaOH + 2SiO2 = Na2Zr2Si2O9 + H2O with ∆H ~ 40 kJ/mol.

The principal solution u is unique up to a constant multiple.

The economic program of the HSP was vague, maintaining that the principal solution to all social and economic problems was the creation of a Greater Croatia.

As a result, this novel EC" mechanism possesses autocatalytic properties so that even a trace amount of bromine in the bulk solution may result in very high current densities, up to the those limited by the diffusion of the principal solution components, bromate and protons.

A general asymptotic analysis of the bifurcated equilibrium path about the principal solution's lowest critical load is presented using Lagrangian kinematics.

The principal solutions to teen pregnancy lie in traditional policy areas: better sex education and greater availability of contraception.

Corollary 2.2 Let Y i ( 0 ) and Y ˆ i ( N + 1 ) be the principal solutions of (2.1) and (2.2) associated with symplectic fundamental matrices Z i ( 0 ), Z ˆ i ( N + 1 ) such that conditions (2.4) hold.

For the particular case when Y i, Y ˆ i are the principal solutions of (2.1), (2.2), we have the following corollary from Theorem 2.1 (see [[13], Corollary 2.4]).

Remark 2.4 (i) Assume that Y i, Y ˆ i are conjoined bases and Y i ( M ), Y ˆ i ( M ) are the principal solutions of (2.1), (2.2) at M ∈ Z.

and the conjoined bases Y i ( M ), Y ˆ i ( M ) of (2.1), (2.2) with the initial conditions Y M ( M ) = [ 0 I ] T, Y ˆ M ( M ) = [ 0 I ] T at i = M are said to be the principal solutions at M. Note that for conjoined bases Y i, Y ˆ i of (2.1), (2.2) there exist symplectic fundamental matrices Z i, Z ˆ i such that Y i = Z i [ 0 I ] T, Y ˆ i = Z ˆ i [ 0 I ] T (2.4).