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This generalized concept to blend physical systems with their virtual counterparts, being their computer-internal representation or a functional continuation will be presented.
By Lyapunov functional, continuation theorem of topological degree, inequality technique and matrix analysis, sufficient conditions guaranteeing the existence and globally exponential convergence of periodic solutions are obtained, without assuming the boundedness and differentiability of activation functions.
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Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method.
Functional problems affect the continuation of communication, i.e., the possibility of the sustainment of social reality.
Here, we examine beat finding, adjustment, and continuation using functional magnetic resonance imaging (fMRI) to assess the role of the cortex and basal ganglia.
Long-term ventilation in patients with stroke is not futile; recovery of functional independence is possible and continuation of full level of care seems warranted.
Riemann proved that the zeta-function has a meromorphic continuation to the complex plane and satisfies the Riemann functional equation (see [[5], p. 13 (2.1.1)]) ζ ( s ) = 2 ( 2 π ) - ( 1 - s ) cos π 2 ( 1 - s ) Γ ( 1 - s ) ζ ( 1 - s ).
In [48, 49], the authors propose a continuation on the cost functional, starting from the minimum-energy problem.
It is the continuation of the same functional organization and thus the same life which is the criterion of identity for sameness of living thing, be it an oak or a horse.
This process allowed caregivers to be informed of patient preferences about continued advanced supportive technology when its continuation would result in a compromised functional outcome or death.
end{aligned} They showed the existence of 2π-periodic solution by developing a new continuation theorem with two functionals.
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