Sentence examples for degree continuation from inspiring English sources

Now let us recall some notation about the coincidence degree continuation theorem.

Now let us recall some notations as regards the coincidence degree continuation theorem.

These three notions, namely Greater Degree, Continuation, and Decrement, all correlate to properties or states, with the predicate location occupied by adjectives or stative verbs.

For ImQ is isomorphic to KerL, there exists an isomorphism J N L : Im Q → Ker L. Then we shall give the coincidence degree continuation theorem, which is proved in [21].

To solve this interesting and important problem and to overcome the difficulties caused by the impulses, we will construct some Banach spaces, then we shall obtain the new solvability results for the coupled system (1.1) with the help of a coincidence degree continuation theorem.

They argue that, contrary to what might be expected, and despite financial cuts and scarce resources, immigrant integration policy paradigms have witnessed a substantial degree of continuation as a result of local perseverance and determination, social contexts, structural features and organisational patterns.

This study, however, had high degrees of continuation of cART at the end of the study in both arms (73 vs 75%%), suggesting an overall high degree of persistence on therapy.

The findings of most of these studies are mainly achieved through some such theories as fixed point theory, topological degree theory (including continuation method and coincidence degree theory) and comparison method (including upper and lower solutions method and monotone iterative method) (see, for example, [12 15] and references therein).

But to what degree this means a continuation of the cultural role that Islamic literatures have played in the formation and education of society over the centuries is not yet clear.

The existence of positive solutions for p-Laplacian equation boundary value problems has been studied by many authors applying various nice methods such as topological degree, the Leray-Schauder continuation theorem, coincidence degree theory and so on (see [2, 4, 5, 8 24]).

In the following consequence of Theorem 3.1 we further assume that M is nonsingular and use the properties of the Brouwer degree to get a continuation result with the sole assumption that Ω # ∩ ( { 0 } × [ g ( 0, ⋅ ) ] − 1 ( 0 ) ) is a nonempty and compact subset of R m × R s.