Sentence examples for exist equation from inspiring English sources

Although an analytical solution does not exist, equation (2) can be solved numerically [ 37].

Moreover, there exist equations in the Calogero list of C-integrable PDEs belonging to the class of solvable through hodograph transformations which do not satisfy the Painlevé property at all.

In the superlinear case (alpha0) for any (Tgeq1), there may exist equations of type (1) with uncontinuable solutions; see, e.g., [16], p.343.

Only for M1/M0 a theoretical value for a well ventilated volume exists (equation 4).

Since two unknown variables exist in equation (11), an alternating minimization scheme is used to minimize the cost function (11).

Consequently, considerable research efforts have been devoted, especially within the past 40 years or so, to methods for finding approximate solutions (when they exist) of equation (1.2).

If the solution Φ ( x ( t, ω ) ) is found to exist for equation (16), then we have the results given below.

Combining the new proposed design equation and the existed stiffness equation, a new proportion compliant mechanism with corner-filleted flexure hinges is designed by means of the least squares optimization.

Based on results of [24] (see also [25, 26]), the conjecture is given in our previous paper [5] that the border case (M ( {{r_{k}^{-1}} } ) M {s_{k}}) = 1/4 ) from Corollary 1 is not solvable for general coefficients; i.e., in the border case, there exist oscillatory equations in the form of (3.41) and, at the same time, there exist non-oscillatory equations in this form.

We will show that the left-hand and right-hand limits of the function m k at λ0 also exist and Equations (2.8) and (2.9) are satisfied.

At the same time, there exist differential equations that can be transformed to the Cauchy-Euler type, and the entire procedure that leads to constant coefficients must then be applied to them as well.