Probability-conserving

The second condition is clearly necessary to achieve any consistent (i.e. probability conserving) quantum dynamics. It has the additional effect of restricting the number of classical rules for which a quantum analogue can be constructed (see k — 2 example below). 

The physical meaning of and f L.., is obvious they govern the relaxation of rotational energy and angular momentum, respectively. The former is also an operator of the spectral exchange between the components of the isotropic Raman Q-branch. So, equality (7.94a) holds, as the probability conservation law. In contrast, the second one, Eq. (7.94b), is wrong, because, after substitution into the definition of the angular momentum correlation time... 

This equation does not conserve probability. However, probability conservation can be restored by adding an equation for the probability p that the... 

Equations (5.4) and (5.5) together are a probability conserving master equation. The dissociated state is an absorbing state and consequently P (°°) = l,Pv(°°) = 0- However, the chemist wants to know how fast this dissociation occurs. Suppose one has solved (5.4) with initial condition pv(0) = 5v0 i.e., the molecule starts in its ground state. Then the probability that it dissociates between t and M-dt is /) ( ) dt.The average dissociation time is, compare (VI.7.5),... 

Although the shortest way to the tunneling gap 8 is the solution of Landau and Lifshits [27], here we consider the problem from a different perspective. Like in the theory of electric circuits, instead of a detailed consideration of each particle, one can apply some simple rules that provide enough equations to solve the problem. One is the junction rule. It is based upon the probability conservation law for a stationary state, PiQ, t). At any point Q in the domain of 77(2, t), the probability density, I PiQ, t) 2 remains constant, dl P(Q. f)P/df = 0. Consider the part of a vibronic state that is located in a potential well. In this region, the probability density, P(Q, t) 2, looks like an octopus with its tentacles extended into the restricted areas under the barriers.2 If we construct a closed surface S around the body of the octopus , then, due to conservation of probability density, the total flux of probability through the surface S must be equal to zero,... 

Nole. Patch- (grass and various woody communities) and soil-specific SR rates measured monthly over an annual cycle at La Copita (McCulley, 1998) were multiplied by the area of respective commrmity types (Scanhui a]id Archer, 1991). Effects of mean annual temperature change (MAT, "C) on SR were estimated from (A) equations in Raich and Schlesinger (1992) for La Copita (MAT - 22.4°C and MAP - 720 mm) a. 0 and 6°C increase in MAT would produce a 3.9 and 7.8% increase, respectively, in soil respiration and (B) Q,o values of in sitti, community-specific soil respiration from McCulley (1998). Estimates are probably conservative, as respiration rates used in computations w ere measured during a below-normal rainfall year. 

The total membrane area in the plant would be reduced to 75% of the original. Membrane life would be reduced from 300 days at a 60% minimum coulomb efficiency to 270 days at 65% efficiency. This is probably conservative, because plant membrane efficiencies as checked on small laboratory cells averaged 70% after 10 months use. There is, thus, a net saving of approximately 17% on the annual requirement of membranes. 

Equation (6.14) again can be viewed in our general framework by defining the probability conserving generalization of Eq. (6.4)... 

Probably conserving their strength," Silvano Richmann said. "It s what I would do."... 

For initial screening, we have operated our micro-catalytic reactor in a pulsed mode. As is shown below (Results Discussion, Figure 2), the catalyst appears to rather quickly achieve steady-state response, after the first few samples of wood (e.g., <100 mg wood per gram of catalyst). This is confirmed by the approximate mass closures (>80 % typically) from summation of all gaseous species evolving from each wood-vapor pulse, plus measured char yields for each pulse, and overall coke yields of 5-10 weight percent (See Table II under Results Discussion). There is some evidence of absorption of water and light aromatics when vapor first contacts the catalyst, so that the reported yields of liquid products are probably conservative. We plan to insert wood dowels in a continuous manner to verify the behavior under steady state of wood addition. 

The consideration of up to six targets is based on the daily processing rate representative of 100% of U.S. demand for Mo-99. Since residual materials are typically solidified each day, it would be unrealistic to consider more than six targets to be at risk at the same time. While it could be conservatively assumed that all spill events involve a maximum of 6 targets, the stated likelihoods are considered more realistic, and are probably conservative. 

For the complex crystals with the carboxyl group, I and IX, the carboxyl groups make a dimer structure directly or through solvent water molecules. When the aromatic crystals with the dimer structure were ground in a mortar, the dimer structure is probably conserved. Since the dimer structure is too large, it may be difficult to be inserted between the anti-parallel alkyl chains. When the aromatic compounds with a carboxyl group are dissolved in aqueous solution, the dimer structure may be loosened allowing easy insertion between the alkyl chains. 

The resulting schedule indicates a total construction time of 42 months for the plant -from pouring of the first concrete to start commercial operation, or 36 months to fuel loading. This time is probably conservative since the possibilities of reducing it by onsite or ofifeite prefabrication (or modularization) have not been taken into account. 

There is a non linear relationship between coverage and faults. A coverage growth model can be fitted to the observed data to estimate residual faults, but it is probably conservative to assume a linear relationship between coverage and faults found, and then devise a test strategy that maximises the coverage (like MCDC random testing). 

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