From the proof of Theorem 3 it follows that if x is a q-periodic solution of (1), then x has the following form x(n)=(c_{1}, c_{2}, dots, c_{q},c_{1}, c_{2}, dots, c_{q}, dots), where ((c_{1}, c_{2}, dots, c_{q})) is a certain solution of system (18).
Those tiny granules are formed by exposing a certain solution to a nanolithographic process (but of course we all knew that already).
For the periodic solution case, i.e., (Qequiv I_{n}), as shown in [15], one can transform the problem into one of finding certain solutions of the Cauchy problem by introducing a homotopy parameter (lambdain[0,1]).
The observation that certain solutions of ruthenium complexes can absorb atmospheric nitrogen has led to hope that one day a simpler and better method of nitrogen fixation may be found.
Continuing former experiments with microelectrolysis of certain solutions of metallic salts we could confirm the assumption that production of dendrites were caused by electric forces.
In order to overcome the difficulty, combining an argument of contradiction, property of convex function ([7]) and important inequalities in [15] (cf. Lemma 2.1), we consider problem (1)–(4) and prove a blow-up result of certain solutions at a high energy level.
The first fitness function f 1 evaluates the coverage for a certain literature capacity of a certain solution and will often be the most important requirement.
This design uses the ion-selective electrode method to measure the pH, or the ion concentration of a certain solution.
