Sentence examples for for singular cases from inspiring English sources

For singular cases a prediction with detailed calculations based on the Fresnel Kirchhoff approximation is also given.

Except for singular cases where parameters are directly measured experimentally, parameter estimation from experimental data is an inevitable step in the process of constructing models [ 2].

This zero set formulation allows for a better treatment of singular cases while these characteristic curves are crucial for various applications, from visualization through interrogation to design and manufacturing.

While the NCCN guidelines recommend the testing of singular cases suggestive for LFS, even in the absence of family history, others negate the necessity for testing because of low mutation rates (0 7%) and high psychological burden.

We also provide related examples that the functional equations (1.7) and (1.8) are not stable for the singular cases.

Some related examples for the singular cases of these new functional equations on an Archimedean field are indicated.

Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed.

The illustrative examples of drum brake, translating punch and rotating annular punch (disc brake) provide the distribution of contact pressure and wear rate for regular and singular cases associated with the optimality conditions.

By the same reason as for Example 2.6, the function f is a counterexample for the singular case p = n of Theorem 2.7.

and got -estimates of the degenerate parabolic equation with -growth conditions for, where is a constant, then in [16] the authors established the Hölder continuity of the equation for the singular case, and in [17] the authors discussed Harnack estimates for the bounded solutions of the above parabolic equation for.

The nonsingular and singular cases for the nonlinearities are investigated.