A bias analysis of Weibull models under heaped data by Augustin T., Wolff J.

By Augustin T., Wolff J.

Retrospectively accrued length facts are frequently mentioned incorrectly. a massive form of such an mistakes is heaping - respondents are inclined to round-off or round-up the knowledge based on a few rule of thumb. for 2 distinctive instances of the Weibull version we learn the behaviour of the 'naive estimators', which easily forget about the dimension errors as a result of heaping, and derive closed expressions for the asymptotic bias. those effects supply a proper justification of empirical facts and simulation-based findings stated within the literature. also, events the place a amazing bias should be anticipated may be pointed out, and a precise bias correction could be played.

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6 and (2) a spin polarization is too small at room temperature, as we discussed in Sec. 5. Despite of these limitations, the NMR-QC is considered as a model of other true quantum computers, and thus its understanding should be useful for researchers, especially for new comers who have just started their study on quantum computer. 9 Qubit 3 No RP RP z x 10:0 WSPC - Proceedings Trim Size: 9in x 6in Fig. 14. Spectra after quantum teleportation when the initial state is I0 + Iz . RP (No RP) denotes with (without) a read pulse (R(π/2, π/2)) applying to qubit 3.

4 T is taken as an example of heteronucleus molecules. In this case, ω0,1 /2π = 125 MHz for 13 C, ω0,2 /2π = 500 MHz for proton, tp ∼ 20 µs, ω1,1 /2π ∼ 25 kHz, and ω1,2 /2π ∼ 100 kHz are typical figures for a π pulse on 13 C. Then, tp ω1,2 /2 ∼ 2 × 10−3 . A cytosine molecule in the same magnetic filed is taken as an example of homonucleus molecules with two proton spins. In this case, ∆/2π ∼ 700 Hz, tp ∼ 6 ms, and ω1,2 /2π ∼ 80 Hz are typical figures for a π-pulse on one of the protons. 2. May 6, 2009 10:0 WSPC - Proceedings Trim Size: 9in x 6in master 20 We transform Hdrift by the unitary operator Ui = e−iω0,1 Iz t ⊗ e−iω0,2 Iz t and obtain ˜ i = Ui Hdrift U † − iUi d U † = JIz ⊗ Iz + J M (∆ t), H i dt i 2 (20) where  0 0 M (x) =  0 0  0 0 0 0 e−ix 0  .

Therefore the density matrix at t = 2τ is i i R(π, π/2) Ufp (τ )R(π/2, 0) ρ(M, 0, 0, 1) = ρ(M, 0, −1, 0), Ad Ufp regardless of the index i. We interpret this result as R(π, π/2) refocused ρ. We note i i (τ ) R(π, φ) Ufp (τ ) = I R(−π, φ) Ufp which means that a pair of 180◦ -pulses can null the effect of the Larmor frequency differences. 6. 6 here. We only need to remember M = Tr(µρ), and thus γ Tr(σx ρ) Mx = γ Tr(Ix ρ) = 2 which is observed as an absorptive signal in NMR measurements. My corresponds to a dispersive signal.

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