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.
We can see that if α changes from 0 to ∞, the left side of Equation 20 will monotonically decrease from ∞ to 0. Hence, it is ensured that a unique positive solution α exists for Equation 20, and the optimal α can be found using bisection method.
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.
They are familiar enough with the economy as it exists in equations and official statistics, but are fair strangers to the economy as it exists behind cash tills and on assembly lines.
If the condition (H51) holds, then there exists (omega_{2}^>0) satisfying equation (20) and equation (3) has a pair of purely imaginary roots (pm iomega_{2}^).
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.
