Sentence examples for principle to the case of from inspiring English sources

And now let us return for an illustration of our principle to the case of letters.

The basis of this analysis will be orbital variational principle for the intense wave beams-generalization of Fermat's principle to the case of a nonlinear medium (Molotkov and Vakulenko, 1988a, Molotkov and Vakulenko, 1988b, Molotkov, 2003, Molotkov, 2005).

These theorems are a normal generalization of the contraction principle to the case of self-mappings.

One of the most interesting studies is the extension of Banach's contraction principle to the case of non-self-mappings.

One of the most interesting is the study of the extension of Banach contraction principle to the case of non-self-mappings.

Recently, in [22], the authors used the notion of a cone metric space to generalize the Banach contraction principle to the case of cone metric spaces.

In part 1, we deduce the exponential stability of the basic solution of the homogeneous equation of (2.1), and in part 2, we employ the fixed point principle to discuss the case of the nonhomogeneous equation.

Machiavelli then applies this general principle directly to the case of France, remarking that "the people live securely (vivere sicuro) for no other reason than that its kings are bound to infinite laws in which the security of all their people is comprehended" (Machiavelli 1965, 237).

The application of these principles to the case before us is straightforward.

Application of these principles to the case at hand is straightforward.

In contrast to Post, Radder (1991) has claimed that the generalized correspondence principle does apply to the case of the quantum-classical relation (p. 215), and that Bohr's correspondence principle, which he interprets largely as a heuristic tool, can be seen as an instance of the generalized correspondence principle (p. 208).