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end{aligned} (6.7 The tautological embedding (lambda :Delta _+ X rightarrow Delta _< X = lambda ^*Delta _+ X) is left-adjoint to (rho _X), and the composition (a_X circ rho _X:Delta _+ X = rho ^* Delta X rightarrow Delta X) is the tautological embedding (rho ).

For any simplicial set X with the discrete fibration (Delta X rightarrow Delta ), denote (Delta _+X = rho ^*Delta X) and (Delta _

( Delta x ) is the step length.

(Delta X), (sigma ^*mathcal {C}) resp.

Table 2 Simulation domains corresponding to the initial grain size r for multigrain simulations Grains Grain size r Simulation domain size Fine (20Delta x) (300 Delta x times 300 Delta x times 300 Delta x) Medium (25Delta x) (375 Delta x times 375 Delta x times 375 Delta x) Coarse (30Delta x) (450 Delta x times 450 Delta x times 450 Delta x).

Then (Delta X) is a Reedy category.

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Similar(36)

textstylebegin{array}{l} x'(t)=-dx-delta x, y'(t)=delta x-dy, end{array}displaystyle right} quad tneq nT,y(t)< h, left.

textstylebegin{array}{l} x'(t)=-dx-delta x, y'(t)=delta x-dy, end{array}displaystyle right}quad tneq nT, left.

We set again (Delta t=0.15~Delta x).

Moreover, for any simplicial set X, let (Delta _flat X = Delta _flat times _Delta Delta X), with the induced cofibration (nu :Delta _flat X rightarrow Delta X).

textstylebegin{array}{l} {Delta x t) =-alpha(x) x t),} {Delta y(t)=-beta(x) y(t)+delta(x),} end{array}displaystyle right } quad x=h_{2}.

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