Generalized Formulation

Ahn C B and Cho Z H 1989 A generalized formulation of diffusion effects in pm resolution nuclear magnetic-resonance imaging Med. Rhys. 16 22-8... 

Ciccotti G, Ferrario M and Ryckaert J-P 1982 Molecular dynamics of rigid systems in cartesian coordinates. A general formulation Mol. Phys. 47 1253-64... 

The inks formulated for jet printing must be very fluid, stable, and free of any particles that could cause clogging of the jet nozzles, and be capable of depositing and adhering to a substrate with a minimum of character fogging. They are generally formulated with soluble dye colorants in a suitable aqueous or solvent-based vehicle (9). 

Fig. 10. Generalized formulation design outline for radiation-curable coatings and adhesive systems. The cross-linker is a multifimctional unsaturated cross-linking agent or oligomer, rj = viscosity CR = cure rate S = shrinl ge H = hardness F = flexibility A = adhesion 7 = surface energy ...

Products for use on the skin are designed to improve skin quality, to maintain (or restore) skin s youthful appearance, and to aid in alleviating the symptoms of minor diseases of the skin. Many of these products are subject to different regulations in different countries. Skin products are generally formulated for a specific consumer purpose. 

Equation (7) is a second-order differential equation. A more general formulation of Newton s equation of motion is given in terms of the system s Hamiltonian, FI [Eq. (1)]. Put in these terms, the classical equation of motion is written as a pair of coupled first-order differential equations ... 

Irwin [23] developed an expression for the mode I stress intensity factor around an elliptical crack embedded in an infinite elastic solid subjected to uniform tension. The most general formulation is given by ... 

Thus in a mixed system, as e.g. in a stirred tank, the rate of agglomeration additionally depends on the shear field and therefore on the energy dissipation e in the vessel. Furthermore, in precipitation systems solution supersaturation plays an important role, as the higher the supersaturation, the stickier the particles and the easier they agglomerate (Mullin, 2001). This leads to a general formulation of the agglomeration rate... 

Hymes (1983) presents a fireball-specific formulation of the point-source model developed from the generalized formulation (presented in Section 3.5.1) and Roberts s (1982) correlation of the duration of the combustion phase of a fireball. According to this approach the peak thermal input at distance L is given by... 

In 1931, comparative study of photosynthesis in bacteria led van Niel to a more general formulation of the overall reaction ... 

Here W(a,(i) is the p a transition probability for which we accept the conventional thermally activated atomic exchange model . Below we briefly review several recent works on the general formulation of this approach and on its applications to studies of alloy phase transformatious. 

Generally formulated with mild solvents, such as white spirit ... 

The cyclitols are a group of carbocyclic sugar derivatives having the general formulation 1,2,3,4,5,6-cyclohexanehexol. How many stereoisomeric cyclitols are possible Draw them in their chair forms. 

Nozieres, P., and Pines, D., Phys. Rev. 109, 741, Electron interaction in solids. I. General formulation."... 

Programs containing lignins as the primary polymeric dispersant are generally formulated to provide 30 to 50 ppm of active lignin product in the BW. 

For a general formulation of mean bubble sizes see Eqs. (261M264). 

In this section, a general formulation will be given for the effect of bubble residence-time and bubble-size distributions on simultaneous and thermodynamically coupled heat- and mass-transfer in a multicomponent gas-liquid dispersion consisting of a large number of spherical bubbles. Here one can... 

The most general formulation is in terms of real parameters, as any complex paramet -ization can always expanded into real and imaginary parts, while the converse construction (complex parameto S from combination of real... 

Chapter 11 treats reactors where mass and component balances are needed for at least two phases and where there is interphase mass transfer. Most examples have two fluid phases, typically gas-liquid. Reaction is usually confined to one phase, although the general formulation allows reaction in any phase. A third phase, when present, is usually solid and usually catalytic. The solid phase may be either mobile or stationary. Some example systems are shown in Table 11.1. 

Before proposing a general formulation, we illustrate a DIFF with a simple case, in which we consider bone collagen as the body component, and the diet as containingjust two components, protein and non-protein. In the notation, B stands for body 5 values, and D for diet 8 values suffixes distinguish the particular component specified. Thus Bcolla stands for the collagen 8 C, Dp and Dn for the dietary protein and non-protein 6 C values. 

If the explicit solution cannot be used or appears impractical, we have to return to the general formulation of the problem, given at the beginning of the last section, and search for a solution without any simplifying assumptions. The system of normal equations (34) can be solved numerically in the following simple way (164). Let us choose an arbitrary value x(= T ) and search for the optimum ordinate of the point of intersection y(= log k) and optimum values of slopes bj to give the least residual sum of squares Sx (i.e., the least possible with a fixed value of x). From the first and third equations of the set eq. (34), we get... 

Since EPDM is a cheaper elastomer, it is often added to SBR to reduce cost. Zhao et al. have studied the effects of curative and accelerator concentration as well as the effect of mixing on the properties of ablend compound containing 70 parts of SBR and 30 parts of EPDM [41]. Table 11.18 gives the general formulation of the blend compounds. 

Difference schemes as operator equations. General formulations 117... 

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