Sentence examples for evolution is given by from inspiring English sources

We consider a discrete time linear dynamic system, whose state evolution is given by left{begin{array}{lll} mathbf{x}(t+1)&=&mathbf{A}mathbf{x}(t)+mathbf{B} mathbf{u}(t)+ mathbf{n}(t) mathbf{y}(t)&=&mathbf{C}mathbf{x}(t)+ mathbf{w}(t) end{array}right.

We will also assume for simplicity in the development that the battery never reaches its maximum limit, (C^{i}_{max }) and, thus, the battery dynamics equation that governs the battery evolution is given by C_{i} tau+1) = C_{i} tau) - E_{i} tau) + H_{i} tau) = (1-alpha) C_{i} tau) + H_{i} tau), (29).

The internal energy evolution is given by the expression [28] d E i dt = 1 2 ∑ j = 1 N m j p i ρ i 2 + p j ρ j 2 v i β − v j β ∂ W ij ∂ x i β + μ i 2 ρ i ϵ i αβ ϵ i αβ, Open image in new window (17).

The evolution operator is obtained in the interaction picture where time evolution is given by the interaction Hamiltonian, which is the integral over space of the second term in the Lagrangian density given above: V=e\int d^3x\bar\psi\gamma^\mu\psi A_\mu and so, one has U=T\exp\left[-\frac{i}{\hbar}\int_{t_0}^tdt'V(t')\right] where T is the time ordering operator.

The final system of the equations for the perturbation evolution is given by two Orr-Sommerfeld equations, one for each fluid, together with suitable boundary conditions [ 31].

The relative rate of antigenic evolution is given by the fraction of arising antigenic mutants that establish under the deleterious mutation load relative to the fraction of arising antigenic mutants that would establish under a no-load scenario.

Damage evolution was given by {d}_i=left{begin{array}{cc}hfill frac{{leftlangle sqrt{Y_i}-sqrt{Y_0}rightrangle}_{sqrt{Y_c}} hfill & hfill if {d}_i<1hfill hfill 1hfill & hfill otherwisehfill end{array}left(i=1,2right)right., (43 where Y 0 controls the damage initiation, Y c the damage evolution.

If you have to pull out 30,000?" Sometimes evolution is given a nudge by a notorious incident, like Todd Bertuzzi's retaliatory attack in 2004 that ended the career of Steve Moore and has resulted in lawsuits that are still pending.

Hamiltonian formulation of various energy conservative evolution equations is given by means of wavelet expansion of solutions on the whole real axis R. The KdV equation, wave equations and Schrödinger equations are treated in a unified similar manner.

If the evolution equation is given by the inviscid Euler equation, the equation is reduced to frac{partial omega}{partial t} = 0 (18).

The weight of a solution is used for determining the attractiveness of a solution to be chosen in the next evolution and is given by Eq. (22) (Schlueter 2012) w_{j} = frac{1}{{qksqrt {2pi } }}exp left( {frac{{ - ({text{rank}}(j) - 1)^{2} }}{{2q^{2} k^{2} }}} right) (22)In the equation, the term ({text{rank}}(j)) is given the rank of the solution.