Respectively resp

Lemma 3. Let p M be a probability measure and let X and Y be disjoint sets which are dx- resp. dy-almost invariant with respect to p. Moreover suppose that f (X) n Y = 0 and f Y) n A = 0. Then X UY is 6xuy-almost invariant with respect to p where... 

Figure 2 Orbital magnetic moments in bcc-Fe Coi-a . The triangles pointing up-and downwards represent the theoretical moments of Fe and Co, respectively, while the concentration weighted sum is given by circles. Full and open symbols stand for results obtained with and without the OP-term included (SOPR- and SPR-KKR-CPA, resp.). Experimental data [15] for the average magnetic moment (bottom) stemming from magneto mechanical and spectroscopic g-factors are given by full squares and diamonds.

Figure 1.15. Student s f-distiibutions for 1 (bottom), 2, 5, and 100 (top) degrees of freedom /. The hatched area between the innermost marks is in all cases 80% of the total area under the respective curve. The other marks designate the points at which the area reaches 90, resp. 95% of the total area. This shows how the r-factor varies with /. The t-distribution for / = 100 already very closely matches the normal distribution. The normal distribution, which corresponds to t(f = o), does not depend on/.

Figure 2.8. The slopes and residuals are the same as in Figure 2.4 (50,75,100, 125, and 150% of nominal black squares), but the A -values are more densely clustered 90, 95, 100, 105, and 110% of nominal (gray squares), respectively 96, 98, 100, 102, and 104% of nominal (white squares). The following figures of merit are found for the sequence bottom, middle, top the residual standard deviations +0.00363 in all cases the coefficients of determination 0.9996, 0.9909, 0.9455 the relative confidence intervals of b +3.5%, +17.6%, 44.1%. Obviously the extrapolation penalty increases with decreasing Sx.x, and can be readily influenced by the choice of the calibration concentrations. The difference in Sxx (6250, 250 resp. 40) exerts a very large influence on the estimated confidence limits associated with a, b, Y(x), and X( y ).

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

Catalytic activity tests have been performed in a quartz microreactor (I.D.=0.8 cm) filled with 0.45 g of fine catalyst powders (dp=0 1 micron). The reactor has been fed with lean fiiel/air mixtures (1.3% of CO, 1.3% of H2 and 1% of CH4 in air resp ively) and has been operated at atmospheric pressure and with GHSV= 54000 Ncc/gcath The inlet and outlet gas compositions were determined by on-line Gas Chromatography. A 4 m column (I D. =5mm) filled with Porapak QS was used to separate CH4, CO2 and H2O with He as carrier gas. Two molecular sieves (5 A) columns (I D.=5 mm) 3m length, with He and Ar as carrier gases, were used for the separation and analysis of CO, N2, O2, CH4, and H2, N2, O2 respectively... 

If separate D-RESP charge sets are fitted for every single one of the 36 frames, the standard deviation of the electrostatic field generated varies between 3.5 and 5% with respect to the full quantum reference. This accuracy is the best (in the least-squares sense) that can be obtained if the system is modeled with time-dependent atomic point-charges and represents the accuracy limit for a fluctuating point charge model of the dipeptide. 

The QM dipole moment of the Gly-Ala dipeptide is, furthermore, reproduced by the D-RESP set within 2%. The predictivity of any D-RESP set on the dipole along the full trajectory is approximately 4%. This compares with predictivities of 6% and 7% for the dipoles computed with the AMBER 1995 and GRO-MOS96 force field charges, respectively. 

The reservations with respect to the existence of Re03-t5 e trifluorides free of oxygen include the case of tantaliun 269). The phases of oxide fluorides Me(0, F)3, which we have to conceive instead, are limited by the compounds Nb02F and Ta02F resp., which adapt the ReOa-type structure 105). 

Here p iaa occ, L() (respectively p iaa unocc, L()) represents the probability of the atomic configuration of site i, where the orbital a with spin a is occupied (resp. unoccupied) and where L[ is a configuration of the remaining orbitals of this site. This result is similar to the expression obtained by Biinemann et al. [22], but it is obtained more directly by the density matrix renormalization (5). To obtain the expression of the qiaa factors, an additional approximation to the density matrix of the uncorrelated state was necessary. This approximation can be viewed as the multiband generalization of the Gutzwiller approximation, exact in infinite dimension [23]... 

Let us take up first the issue concerning the existence of some common feature to different characters. We say a character (n, >, F) (or the corresponding type resp. formation rule) is sensible with respect to aspects, if it has the following property if for any two alternatives x and and for any bundle (Rj,.. . t Rn) in the domain >, x is preferred to with respect to all Rh then jt is also preferred to with respect to F RX,. . . , Rn) moreover, if in addition x is strictly preferred to with respect to some R then also x is strictly preferred to with respect to F(RX,. .. Rn). It turns out that almost all characters mentioned thus far are sensible in this sense. More precisely, we have the following proposition ... 

The consecutive reactions have been investigated by the method of preparative voltammetry, namely by analyzing the product mixture, which is essentially composed of the anodic monomer and dimer independence of working potential or current density resp. Correlating the respective current and mass yields of monomers and dimers with current density allows the kinetic laws governing the selectivities at different anode materials to be obtained. 

The pseudo-first order rate constants (resp. coefficients) for the direct reaction of some compounds may almost be in the order of typical hydroxyl rate constants (kR > 10 M s ), due to high concentrations of the pollutants as well as mass transfer enhancement. For example, Sotelo et al. (1991) measured values of 6.35 106 and 2.88 106 M l s"1 for the dissociating hydroxylated phenols, resorchinol (1,3-dihydroxybenzene) and phlorogluci-nol (1,3,5-tn hydroxybenzene) respectively (pH = 8.5 and T= 20 °C). 

Let us postulate that we live in a 3D hypersurface that slides along the u axis with speed v°u = ca, where the u axis coincides with the arrow of time. The 4-velocity is then a (row or column) vector 1 a = ( ca,vx,vy,vz). The plus (resp. minus) sign corresponds to the speed of preons that enter (resp. leave) our 3D world, parallel (resp. antiparallel) to the time arrow. It will be seen below that this constant ca is the one that enters Einstein s mass-energy equation, and corresponds to the speed of our 3D world along the time axis (interpretation 2 in Fig. 1). The speed of electromagnetic radiation in free space is a different constant c. The value of the latter may be either identical or numerically close to c , depending of whether one adopts a relativistic or an emission theory for photons, respectively (see Section V). 

Already 15 min after oral administration, radioactivity concentrations in blood and plasma (5.90 and 10.67 ig equivalents/g, resp.) were found indicating a fast absorption. The maximum concentrations (Cmax) occurred 0.5 hours after administration and amounted to a mean of 9.34 pg equivalents/g (blood) and 16.95 pg equivalents/g (plasma). The elimination of radioactivity from blood and plasma was biphasic. The half-lives for the first phase amounted to 1.1 h (blood) and 0.9 h (plasma), for the second phase half-lives of 7.5 h and 6.3 h were calculated. In all animals, radioactivity concentrations were detectable up to the last measuring time 48 h after dosing and showed averages of 0.025 and 0.024 pg equivalents/g (blood and plasma, respectively). 

Na is the Avogadro constant, Too is the electron energy at rest at infinite distance, Tp is the -> Fermi energy or the molar Fermi energy, respectively, T is the -> Faraday constant, fM and (pM are the outer electric and inner electric -> potentials of the metal phase (M), resp., and pf is the -> electrochemical potential of electrons in the metal phase. 

III. Salt of Weak Acid and Weak Base.-Hf both the acid and base from which a given salt is made are weak, the resp( ctive conjugate base and acid will have appreciable strength and consequently will tend to interact with the amphiprotic solvent water. When a salt such as ammonium acetate is dissolved in water, it dissociates almost completely into NH " and Ac" ions, and these acting as acid and base, respectively, take part in the hydrolytic equilibria... 

Figure 1.27. Histograms of a data set containing n - 19 values, the r-range depicted is in all cases -0.5 to 5.5 inclusive, leaving one event to the left of the lower boundary. The number of classes is 6, 12, resp. 24 in the latter case the observed frequency never exceeds two per class, which is clearly insufficient for a x -test. (See text.) The superimposed normal distribution has the same area as the sum of events, n, times the bin width, namely 19, 8.5, respectively 4.25.

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