All show a progressive diminishment of function with degree of truncation, including a plateau phase, as in our studies.
This paper studies the population control problem associated with the equilibrium states of mixed-state quantum systems by using a Lyapunov function with degrees of freedom.
To get a smooth flux profile, i.e., a function with continuous first derivative, the degree of the spline function should be at least two, and for this reason the degree will be fixed to two in this work, i.e., k=2.
The basic kernel functions are : K (x → i, x → j ) = (x i → · x → j + c ) d K (x i →, x → j ) = exp (− γ | | x i → − x j → | | 2 ) K (x → i, x → j ) = tanh (γ x i T x j + r ) Equation (i) is the polynomial kernel function with degree d >1, acts as a linear function when degree d =1.
For each ACT and coverage level, prevalence means at all EIR levels for ACT alone and ACT + PQ were correlated using the Python 2.7 polyfit function with degree 1.
The initial models for the three response variables were: SINDVI = s(ESM) + s AIRGS) + s(PARGS) + s RAINGS) + s SINDVIPREV) + s AIRGSPREV) DOYmax = s(ESM) + s AIRUP) + s(PARUP) + s RAINUP) + s SINDVIPREV) + s AIRGSPREV) MaxNDVI = s(ESM) + s AIRUP) + s(PARUP) + s RAINUP) + s SINDVIPREV) + s AIRGSPREV) where s is a function with smoothing of up to 3 degrees of freedom.
The values obtained of C and L as a function of degree K were compared with the theoretical values of C and L for ordered (C = 3/4, L = N/2K) and random (C = K/N, L = ln(N /ln(K)) graphs.
The thermodynamic driving force of enamel de- or remineralization is a function of the degree of saturation with respect to HA DSHAA) [ 59, 60], and the degree of saturation of a solution (DS) can be defined by dividing the product of the ion activities (IP) by K, and exposing this result to the number of ions in the formula unit [ 61].
Note that E 1 and E 2 are not dependent on ΔX, h 1 ( Δ X ) is a linear function of ΔX, and h 2 ( Δ X ) is a function of ΔX with degree at most 2. Assume that the linear operator L c of (4) is invertible.
On the other hand, many studies have proved that the T-S fuzzy model can approximate a continuous function with any degree of accuracy.
Each element Ω k is obtained by a transformation F k from a reference (or parent) element Ω ^ = [ - 1,1 ] 3. On the reference element, we consider the space ℚ p of polynomial functions with degree less than or equal to p in each variable x i, i = 1,2, 3.
