Matrix, first cumulant

Mobility matrix Tube survival probability Neutron wavelength First cumulant matrix Rouse variable Osmometic pressure Conductivity... 

The first two terms on the right-hand side (rhs) of Eq. (68) together satisfy properties (10)-(13) of the 2-RDM. Therefore the cumulant matrix F should satisfy these relations too. We further see that matrix elements of F are nonvanishing only if all its labels refer to partially occupied NSOs with ON different from 0 or 1. For a single Slater determinant, the cumulant matrix vanishes. 

It is clear that the strong form of the QCT is impossible to obtain from either the isolated or open evolution equations for the density matrix or Wigner function. For a generic dynamical system, a localized initial distribution tends to distribute itself over phase space and either continue to evolve in complicated ways (isolated system) or asymptote to an equilibrium state (open system) - whether classically or quantum mechanically. In the case of conditioned evolution, however, the distribution can be localized due to the information gained from the measurement. In order to quantify how this happ ens, let us first apply a cumulant expansion to the (fine-grained) conditioned classical evolution (5), resulting in the equations for the centroids (x = (t), P= (P ,... 

Two variables are fundamental to assessing the flow across complex fault zones. The first variable is the cumulative fault-rock thickness across the fault zone, i.e., the total thickness of fault-rock from all faults along the flow path. This depends upon the fault frequency along the flow path and is not equivalent to the fault damage zone thickness (cf. Knott, 1993) unless the fault zone is invaded by cements. The second variable is the connectivity of the faults or deformation features with low permeabilities in the fault zone. In the case of a completely connected array with no windows of undeformed material along possible flow paths, the flow is controlled by the permeability of the fault rocks. Where a more open network of faults is present then the flow will depend upon the tortuosity associated with flow around the low permeability zones and the ratio of matrix to fault-rock permeability. The interaction of these two factors will control the effective transmissivity of the zone. We have constructed a database on... 

Now we compare the variation of the brush thickness L with P, as predicted by Eq. (59), with the available data. The first experimental study of this problem [265], performed by SIMS for a series of very short (as compared to a standard depth resolution of this technique) (COOH)dPS (N=125-413) end-anchored chains annealed at different temperatures and with different matrices used (T= 108 °C for P=63, and 160 °C for P=4460), revealed identical unswollen brush conformation for both used matrix molecular weights. The variation of the brush height L with P, at a constant coverage other groups in experiments performed later [241,243]. On the basis of the cumulative data for the Pl-dPS (N=893) brush in the PS host matrix (P=88,495, and 3173), presented in Fig. 37, we were able to achieve an equi-o situation (o=3.7.10 3, see arrow in Fig. 37 and corresponding symbols (A, ) in Fig. 38 as described in... 

The rate of release decreases with time since drug molecules near the surface are released first (they have the shortest distance to travel by diffusion). The common matrix form of a slab has a cumulative release proportional to the square root of time therefore, the release rate decreases with the square root of time (this fact can be demonstrated by taking the first derivative of Equation 9-19). However, if the matrix is formed as a hemisphere with an... 

Figure 3a. Cumulative mass ofZn extracted from contaminated soils using SC CO2 with Cyanex 302 ligand at 60 C and varying pressures and moisture additions. A quantity of 0.5 g of Cyanex was added per extraction cycle. Wet samples were obtained by addition of 10 joL of water to the soil matrix prior to first extraction. 

Sivaramakrishnan a/. (1989) described BST matrix implants consisting of either BST/ethyl cellulose or BST/poly(lactic acid) (Hi2700) contained within microporous polyethylene sleeves (average pore size 30-70 m). The in vitro dissolution studies showed significant initial release from uncoated tablets (70% cumulative release in the first 4 days to a total of 80% in 8 days) the coated tablets had sustained release over 14 days with 35% cumulative release over that time. 

Fig. 3. Cumulative release provided by various release kinetics. A, Constant release, independent of time (zero order), such as that possible from a membrane reservoir device free of lag time or initial burst effects. B, Matrix or monolithic sphere with square root time release. C, First-order release A-zero order C-first order B-square root.

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