2) construction of a global solution by recursive extension of local solutions; 3) convergence of the global solution to the minimizing state for all initial values contained in the interior of the bounded level set; 4) eventual exact exponential decay of the gradient magnitude independent of the...
with the optical fields (Ep, Ec, Ed) taken to be Gaussian beams with the samez0andw0as the detection modeus. We also accounted for the relatively strong absorption of the probe field (Ep) by multiplying its amplitude by the exponential decay\(\exp (-\alpha z)\)with (measured)α...
While the neural network presented in equation (3) can be proven to be a universal approximator as it is an approximation of an ODE system1,2, in its current form, it has trainability issues which we point out and resolve shortly. Resolving the gradient issues The exponential term in ...
(x))u=μu3+\beuv2,x∈\rz3,−Δv+(1+\deb(x))v=νv3+\beu2v,x∈\rz3,u>0,v>0,x∈\rz3,u→0,v→0as|x|→+∞, where \de>0\de>0, μ>0μ>0, ν>0ν>0 and \be∈\rz\be∈\rz, a(x)a(x) and b(x)b(x) are two continuous, exponential decay functions without ...
It is stressed that the stretched Gaussian distribution extends the generalized gamma distribution with much thicker tail than exponential decay. Generally, μ is always equal to 0 and σ can be normalized, then β is the critical parameter which controls the tails and determines whether the peak ...
Only the retarded equation seems to be associated with quantum states that decay with time. If that is truly valid, we have an expression that could be used for phenomenologically determining the value of the chronon. Finally, we can conclude that the time discretization brings forth a formalism...
When the parameters involved satisfy certain conditions, the integral equation of this model has a solution in the space of continuous functions that grows ... C Yu,Thomas F,Cosimano,... - 《Journal of Economic Dynamics & Control》 被引量: 23发表: 2008年 Analyticity for one-dimensional syst...
However, this equation is written for our convenience. Carbon doesn't decay in jumps, politely waiting around 5700 years and suddenly decaying by half. We use (1/2) as the base becausewe humanswant to count the number of halvings (decaying into half, decaying into a quarter, decaying into...
Show abstract Exponential decay rate of planar switched positive linear systems 2017, International Conference on Control, Automation and Systems Exponential stability of impulsive positive systems with mixed time-varying delays 2014, IET Control Theory and ApplicationsView...
The decrease in the activity of the system was modeled as a function of time t using an exponential decay function: $$\begin{array}{*{20}{c}} {A_{\mathrm{b}} + b \cdot {\rm exp}\left( { - \displaystyle\frac{t}{{\tau _{{\mathrm{off}}} \right),} \end{array}$$ (6) ...