If we denote by πe1m,πe2m the equilibrium distribution of the m gate and by πe1h,πe2h, the equilibrium distribution of the h gate, we obtain the equilibrium distribution of the eight state sodium channel model by the same combinatorial argument used to derive Figure 17.3. The correspond...
We can now derive a differential equation for R2 in a similar manner as for pij above: R2(t+Δt)=R2(t)P(X(t+Δt)=1|X(t)=1)=R2(t)(1−βΔt). Hence, as Δt→ 0, R′2 = −βR2, and R2(t) = exp(−βt), since R2(0) = 1. This implies F2(t) = 1 −...
State the work-energy theorem and show that W_{tot}=K_2-K_1. In one cycle of the engine, the net change in the entropy of both reservoirs (hot and cold together) is what? Using written explanations...
Infinite-state games are a commonly used model for the synthesis of reactive systems with unbounded data domains. Symbolic methods for solving such games need to be able to construct intricate arguments to establish the existence of winning strategies. O
In calculations, we use the formula μ = MY2 − (2Mc)2 to determine the optimal energy scales of the QCD spectral densities, more- over, we take the experimental values of the masses of the Y (4260/4220), Y (4360/4320), Y (4390) and Y (4660/4630) as input parameters and fit...
Here we formalize the extremality notion and derive a lower bound on the fidelity F for non post-selected target states. All the non post-selected target states we consider are of the form where is an arbitrary Gaussian unitary and an arbitrary Fock-basis state. First, we derive a fidelity...
By letting the estimation error be ek xk − xˆk, it is easy to derive from (1) and (2) that ek+1 = (A − LC)ek + Bωk − Lνk − Lok , rk = Cek + νk + ok (3) which implies that ⎧ ⎪⎪⎪⎪⎪⎪⎨ek = A¯ ke0 + k−1 i=0 A¯ ...
Mechanical advantage refers to the force amplification, and it is used to reduce the input force to get the same output force as before by using the simple machines. It helps to convert complex work into the easy one.Answer and Explanation: ...
and derive upper bounds for magic distillation. These bounds are shown to be tighter than other bounds, such as from mana and thauma, and can be used to incorporate hardware physics, such as temperature dependence and system Hamiltonians. We also show that a subset of single-shot Rényi ...
Derive the r and θ equations of motion in cylindrical coordinates and compare the equations with those given in Section 4.8. 4.37 Verify that the following stress field satisfies the z-equation of equilibrium in the absence of body forces: Trr=A(zR3−3r2zR5),Tθθ=AzR3,Tzz=−A(zR3+...