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Using qualitative analysis we prove theorems on which we base a new method of regularity analysis of the firing map, that, contrasting with methods previously reported in the literature, does not requires analytic knowledge of the solutions of the differential equation and therefore it is also applicable to non-linear integrate and fire systems.
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We showed that the method of p-regularity may have an effective application to the study of solutions of advanced differential equations.
We study the structure of solutions to the Duffing oscillation equation of the form F x,mu, beta)=x"+x+mu x^{3}-betasin t = 0,quad beta > 0, muneq0, (1) where (F: mathcal{C}^{2}[0,2pi]timesmathbb{R}times mathbb{R}rightarrowmathcal{C}[0,2pi]) and (x 0)=x(2pi)=0) applying some methods of p-regularity theory [2 5].
The existence of local solutions can be obtained by utilizing the method of the standard regularization, and the regularities of the solutions can be derived by the argument similar to that in [18].
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The design method of the materials component distributing regularity in the part entity is studied.
In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.
More recently, Liu, Zhao and Cui [28] have adapted the method of [27] to establish a similar regularity criterion for the 3D nematic liquid crystal flow.
An alternative method of computing coordination known as the regularity index (RI) has been reported in rats [ 28] and can be calculated readily from our data by multiplying the number of footsteps taken in a normal stepping sequence by 4 to give the total number of coordinated steps and dividing by the total number of steps taken [ 28].
So, we have proposed alternative versions of the proposed methods that exploit regularity of clock zones in design and have compared them to each other.
I want to create that kind of regularity.
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