Multiplying coefficient

Reciprocal of heat transfer coefficient multiplied by 1,000. A term employed when designing surface condensers. 

In other words, the stoichiometric coefficients multiplying the chemical formulas in any balanced chemical equation tell us the relative number of moles of each substance that reacts or is produced in the reaction. 

We note that n in the summand of Eq. (20) annuls terms with n = 0 and permits the sum to start with n > 1. Thus, Eq. (20) can be rearranged to have an explicit leading factor of zi. This colligative property was noted above. Of course, a determination of Z establishes the solute chemical potential //1 we seek. We are motivated, therefore, to examine the coefficient multiplying zi. To that end, we bring forward the explicit extra factor in zj and rearrange Eq. (20) to obtain... 

Example PET. Let us consider polyethylene terephthalate) (PET, C oHK(h n, Ppet=1-35 g/cm3) of tpET =2 mm thickness and an X-radiation wavelength X= 0.15418 nm (CuKa). We set up a table with one row for each chemical element and sum both the masses and the mass absorption coefficients multiplied by the masses. After normalization to the molecular mass of the PET monomer, 192.17 amu, we find (p/p)pet = 1291.97/192.17 cm2/g a value 6.72 cm2/g. Considering the density ppet we find for the linear absorption coefficient Ppet =... 

Table 57-2 The Savitzky-Golay convolution coefficients multiplied out. All coefficients are for a quadratic fitting function. See text for meaning of SSK...

C[, corresponding to the Stokes diffusional process, can be written as the product of the Stokes friction coefficient multiplied by a correcting factor fr taking into account the finite thickness of the solvent layers... 

This type of equation, used in Volume 1 for the rate of vaporisation into an air stream, simply states that the rate of transfer is equal to the transfer coefficient multiplied by the driving force. It may be noted, however, that (Ps — Pw) is not only a driving force, but it is also related to the capacity of the air stream to absorb moisture. 

For most design purposes, it may be assumed that the rate of drying is proportional to the transfer coefficient multiplied by (Ps — P, ). Chakravorty(10) has shown that, if the temperature of the surface is greater than that of the air stream, then Pw may easily reach a value corresponding to saturation of the air. Under these conditions, the capacity of the air to take up moisture is zero, while the force causing evaporation is (Ps — Pw). As a result, a mist will form and water may be redeposited on the surface. In all drying equipment, care must therefore be taken to ensure that the air or gas used does not become saturated with moisture at any stage. 

Note that the radial and vertical components are out of phase, and that the coefficient multiplying r is only half that multiplying z. Thus, the effect of the ac field is to exert an oscillatory force on the particle with an effective field strength in the vertical direction that is twice the radial field strength. As a result of the larger field strength in the z-direction, the onset of instability is governed by the z-component of the equation of motion, so we need examine only that component. 

Coefficients multiply a normalized radial functions (not shown), complex spherical harmonics Yj jjj, and spin functions as indicated. Values for the ligand are for a single atom. Coefficients smaller than 0.01 are not shown. 

An even more radical yet effective approximation to the R12 method was proposed by Ten-no [28,43], in which the coefficients multiplying the correlation function were held fixed at the values implied by the first-order cusp condition and hence were not to be determined iteratively or noniteratively. Several variants of the CCSD(T)-R12 methods were developed on the basis of this promising approximation by Adler et al. [68], Tew et al. [69], Bokhan et al. [70], and Torheyden et al. [66]. 

Huang and Guan have reported an ultraviolet spectrophotometric and coefficient-multiplied method for the determination of procaine hydrochloride in compounded zinc sulfate eye drops [36]. 3 mL of sample was shaken with 1.5 mL of ethyl ether and water, and after removal of the organic phase, water was added to achieve a final volume of 50 mL. The absorbance of this solution was measured at 291 and 344.5 nm. The recovery (n = 6) for procaine was found to be 99.9%, with a relative standard deviation equal to 0.44%. 

II. Linear differential equations in which one or more of the coefficients multiplying u are random functions. They have been called multiplicative and can be solved only in special cases, but a rather general approximation method will be given in sections 2 and 3.w... 

We also noted [15] that the OAI and OAIT [11] theories are crucially different. In OAI, the coefficients multiplying s and d boson operators are constant thus OAI can be an IBA. In OAIT, however, the coefficients depend on v, and thus OAIT is not an IBA. (With OAIT, the SU(6) symmetry, which is the key ingredient of the phenomenological IBA, may largely be lost.) In any case, the (somewhat better looking) OAIT numerical results, rather than the (poorer) OAI results, were presented in OAI tables, without mentioning at all that this was done. 

Leaving out the z0 column, these coefficients multiplied by 2 immediately yield the effects in the statistical or variance analytical sense. This difference in the computation of the regression coefficients and the effects comes from the different models used in regression analysis and in analysis of variance. The first refers to the zero or medium level, the second refers to the lowest level. 

Once the intensity has been measured, it is left to analyze the Fourier content of the signal to extract the coefficients multiplying the desired terms,, Sg c20 and Sg,s2e ... 

Two methods are used to perform the Fourier analysis. If the signal is digitally recorded over at least one period of the lowest frequency, a fast Fourier transform (FFT) can be applied [36]. This will produce the time independent, or DC component, (f Cg -.ESg c20 ), and the coefficients multiplying the harmonics of the signal (the... 

Cronin Goldsmith have provided some uniquely precise information on the photoreceptors of the crayfish, Orconnectes, procambarus153. They give a peak spectral absorption as 535 nm for what they define as rhodopsin. They quantify this peak in terms of a molecular absorption coefficient multiplied by a quantum efficiency for photoconversion of 0.69. This wavelength does not correspond to the frequently quoted peak of 502 for Rhodopsin. Historically, the 535 nm peak has been associated with porphyropsin. If the expression rhodopsin metarhodopsin transition is replaced with Rhodonine=> Rhodoninc transition, the material fits the model of this work precisely. They also present a peak at 510 nm that is based on difference measurements following an adaptation process. 

The expressions for circular polarized P- or 72-absorption may also be easily obtained by substitution of the respective actbp (presented in the Table C.2 of Appendix C) into (3.11) (the explicit form of (C b/3)2 can be found in Table 3.6 as coefficients multiplied by x). The cases of linear and circular polarized P-absorption are demonstrated in Fig. 3.6(6) and 3.6(c). 

It has been shown that when pungency is determined through the just outlined procedure, and the total capsaicinoids content has been obtained by a reliable method, there is a highly significant linear regression (P<0.00l). The coefficient multiplying the dependent variable in the regression equation will reflect the acuity of the panel. 

Equation (15), which is based on a model, must, however, be equivalent to Eq. (12), which is based on the traditional thermodynamics of a multicomponent mixture. For the free energy changes given by Eqs. (12) and (15) to be the same for arbitrary changes in the independent variables V, , r, and Nit the respective coefficients multiplying dV, d, dr, and dNt must be equal. It should be emphasized, however, that depends on the distribution at equilibrium of tire moles Ni of species i between the two media of the microemulsion and their interface,... 

The variational treatment of hydration confinement by Podgomik and Parsegian5 provided an expression similar to eq 18 in the limit of small a however the coefficient multiplying the exponential of the second term was dependent on a. 

Table XVI gives recent values of the thermionic work functions for several clean metals and also (for discussion later) the accepted values of the standard electrode potential of the metal in contact with an activity molar aqueous solution of one of its salts, where the concentration is such that the activity coefficient multiplied by the molarity is unity.

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