Sentence examples for equation exists from inspiring English sources
The master curve corresponding to that equation exists only for θ ⩾ θLC limit.
end{aligned} (3.3) The solution (x^{n}(t)) of the above equation exists according to Lemma 3.4.
The solution of the ASE-I scheme (12) for solving a nonlinear Leland equation exists and is unique.
We then show that if a solution to the HJB equation exists, then it must have a strictly positive uniform lower bound.
It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation.
We assume that the functions g,f,q i (i = 1,2) satisfy the conditions so that the solution of this equation exists and is unique.
To do so, we use submanifold geometry, and prove that the weak curvature tensor of the right invariantH1metric on Dsμis a bounded trilinear map in theHstopology, from which it follows that solutions to Jacobi's equation exist.
Moreover, we assume, as it is the case for all the models described in the 'Spiking conductance-based models' section, that the solutions of this stochastic differential equation exist for all time.
It is found that there are five exact traveling wave solutions (12 to 16) of K-dV equation exist for pretend model depends on different values related physical parameters.
Because of the relation between KdV and ZK equation, it is reasonable to consider the classical solitary wave solutions of the 'sech2' form; on the other hand, motivated by the research about rational solutions of soliton equation by professor Ma, we have to think deeply whether rational solutions of the ZK equation exist.
It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns.
