Sentence examples for high energy solutions from inspiring English sources
Theorem 3.2 is about the existence of high energy solutions for (1.1) when the nonlinearity f is superlinear.
Hence, all the assumptions of Theorem 3.2 are satisfied and therefore BVP (3.38) has infinitely many high energy solutions.
Liu and He [7] discussed the existence of infinitely many high energy solutions of problem (1.1) under superlinear case by variant version of fountain theorem.
Under more relaxed assumptions on the nonlinear term f, we will present a new proof technique to construct high energy solutions for the problem (1.1).
In [8], Zhang and Tang also considered the problem (1.2) under the assumption ((V)), and they obtained infinitely many high energy solutions of the problem (1.2).
By Lemma 2.4, Lemma 2.6, Lemma 2.7 and the fountain theorem (Theorem 3.6 [16]), problem (1.3) possesses infinitely many high energy solutions.
The ultrasound protocol must be designed to operate at the solution associated with the higher mechanical energy – thus the start-up conditions should be in the domain of attraction of the high energy solution.
The muting step makes it likely that local minima are avoided in the optimization process by moving into higher energy solutions with some temperature-dependent probability.
This mixing of states allows the best results to propagate, but also allows nodes to explore higher energy solutions.
The analysis maintains full consideration of the electromechanical coupling and electrical impedance effects and predicts that for range of dimensionless electrical impedance values, the threshold for chaotic motion and other high-energy solutions is significantly influenced.
The GA is used to generate possible design solutions, which are evaluated in terms of passive heating and cooling of building, using a detailed thermal analysis of non air-condition building environment The results from the simulations are subsequently used to further guide the GA search to find the high-energy solutions for optimized design parameters.
