Re square

Re/= square matrix of stoichiometric coefficients for R reference components in R reactions Re/ = column vector of mole fractions for the R reference components in the liquid phase v oT = row vector composed of the sum of the stoichiometric coefficients for each reaction... 

Figure 10.7 The hydrodynamic radii (Rh), diamond, and the radii of the core of spherical-like micelles (r re), square, in EC, for SIhCsEOss i systems (a) and for SinCjE05i,6 systems (b) at 60°C as a function of the number of EG unit, x, for EG,.

Babadi, M., Ejtehadi, M. R., and Everaers, R. 2006. Analytical first derivatives of the RE-squared interaction potential, 219(2), 770-779. 

Example Crippen and Snow reported their success in developing a simplified potential for protein folding. In their model, single poin Ls rep resell t am in o acids. For th e avian pan creatic polypeptide, th c n ative structure is not at a poten tial m in imum. However, a global search fotin d that the most stable poten tial m in im urn h ad only a 1.8, An gstrom root-m ean-square deviation from thenative structu re. 

A few industrial catalysts have simple compositions, but the typical catalyst is a complex composite made up of several components, illustrated schematically in Figure 9 by a catalyst for ethylene oxidation. Often it consists largely of a porous support or carrier, with the catalyticaHy active components dispersed on the support surface. For example, petroleum refining catalysts used for reforming of naphtha have about 1 wt% Pt and Re on the surface of a transition alumina such as y-Al203 that has a surface area of several hundred square meters per gram. The expensive metal is dispersed as minute particles or clusters so that a large fraction of the atoms are exposed at the surface and accessible to reactants (see Catalysts, supported). 

Other types of bonding include donation by Ligand TT-orbitals, as in the classical Zeiss s salt ion [Pt( 7 -CH2=CH2)Cl3] [12275-00-2] and sandwich compounds such as ferrocene. Another type is the delta (5) bond, as in the Re2Clg ion, which consists of two ReCl squares with the Re—Re bonding and echpsed chlorides. The Re—Re 5 bond makes the system quadmply bonded and holds the chlorides in sterically crowded conditions. Numerous other coordination compounds contain two or more metal atoms having metal—metal bonds (11). 

The discharge coefficient for the screen C with aperture D, is given as a function of screen R nolds number Re = D,(V/d) /[L in Fig. 6-16 for plain square-mesfi screens, Ot = 0.14 to 0.79. This cui ve fits most of the data within 20 percent. In the laminar flow region, Re < 20, the discharge coefficient can be computed from... 

Nr = Rows of tubes per shell pass (Nr is always equal to the number of minimum clearances through which the fluid flows in series. For square staggered pitch the maximum velocity, Umax, which is required for evaluating Re may occur in the transverse clearances a or the diagonal clearances c. In the latter case Nr is one less than the number of tube rows.)... 

With the total number of monomers and the volume of the system fixed, a number of statistical averages can be sampled in the course of canonical ensemble averaging, like the mean squared end-to-end distance Re), gyration radius R g), bond length (/ ), and mean chain length (L). 

TetrakisidithioacetatoivanadiumCIV) was originally classified as dodecahedral. Re-examination has shown that its unit cell in fact contains two independent metal sites. One is indeed dodecahedral but the other is square antiprismatic C. W. Haigh, Polyhedron 14, 2871-8 (1995). 

This oxidation state is sparse in the case of Mn but is important in the pharmaceutical applications of Tc, and an extensive chemistry has been developed. Some fluoro complexes of Tc and Re such as the salts of [MFe] are known, but oxo compounds predominate and, in [MOCls] and [MOX4] (X = Cl, Br, I) for instance, other halides are also able to coordinate. [MOX4] is square pyramidal with apical M=0 and the moiety is reminiscent... 

The simplest of the ir-bondcd Re-C compounds is the green, paramagnetic, crystalline, therm ly unstable ReMen, w ich, after WMe, was only the second hexamethyl transition metal compound to be synthe zed 11976). It reacts with LiMe to give the unstable, pyrophoric, Lii[ReMe(,, which has a square-antiprismatic structure, and incorporation of oxygen into the coordination sphere greatly H reases the stability, wit e,ss Re CMe, which is thermally stable up to 200 C, and Re "0[Pg.1068]

Fig. 4.11 Temperature gradients due to viscous dissipation at Re = 300. Flow in rectangular (7 = 0.1), and square (7= 1) micro-channel. Reprinted from Morini (2005) with permission...

Taking the square root of Vres. one obtains the residual standard deviation, i res, a most useful measure ... 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

Model of ID dissipation spectrum from Pope [19] (line) and measured, noise-corrected spectrum of the square of the radial gradient of fluctuating temperature in a CH4/I-I2/N2 jet flame (Re = 15,200) (symbols). Each spectrum is normalized by its maximum value. The arrow indicates the 2% level, which corresponds to the normalized wavenumber k = 1 according to the model spectrum. (From Barlow, R.S., Proc. Combust. Inst., 31, 49,2007. With permission.)... 

Rosipal R, Trejo LJ. Kernel partial least squares regression in reproducing Kernel Hilbert space. J Machine Learning Res 2001 2 97-123. 

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