Generalization of terms

Cells can draw on a large number of types of raw material to modify the functional properties of membranes in temperature-adaptive manners. In the most general of terms, there are two fundamental ways in which phase transition temperatures and localized order can be altered. These are (1) intrinsic changes in the lipid composition of the membrane, notably in lipid class, molecular species, and cholesterol content, and (2) extrinsic changes, alterations in the solution bathing the inner and outer surfaces of the bilayer. The latter changes include... 

A related family of hosts that Cram first synthesized were the velcrands [14,31]. In the most general of terms, velcrands are cavitands in which the bridges between resorcinol moieties are comprised of ori/io-substituted aromatic rings. Scheme 9.4 shows the first velcrand with quinoxaline walls (11). As we will see in Sect. 9.5, a wide variety of velcrands have since been synthesized, but in general these hosts exist in two forms the vase and the kite. 

Application of the weighted residual method to the solution of incompressible non-Newtonian equations of continuity and motion can be based on a variety of different schemes. Tn what follows general outlines and the formulation of the working equations of these schemes are explained. In these formulations Cauchy s equation of motion, which includes the extra stress derivatives (Equation (1.4)), is used to preseiwe the generality of the derivations. However, velocity and pressure are the only field unknowns which are obtainable from the solution of the equations of continuity and motion. The extra stress in Cauchy s equation of motion is either substituted in terms of velocity gradients or calculated via a viscoelastic constitutive equation in a separate step. 

The acetoacetic ester condensation (involving the acylation of an ester by an ester) is a special case of a more general reaction term the Claisen condensation. The latter is the condensation between a carboxylic ester and an ester (or ketone or nitrile) containing an a-hydrogen atom in the presence of a base (sodium, sodium alkoxide, sodamide, sodium triphenylmethide, etc.). If R—H is the compound containing the a- or active hydrogen atom, the Claisen condensation may be written ... 

This works for any veetor f, and we eould write the proeess in general in terms of the resolution of the identity as... 

The Poisson-Boltzmann equation is a modification of the Poisson equation. It has an additional term describing the solvent charge separation and can also be viewed mathematically as a generalization of Debye-Huckel theory. 

A big step forward came with the discovery that bombardment of a liquid target surface by abeam of fast atoms caused continuous desorption of ions that were characteristic of the liquid. Where this liquid consisted of a sample substance dissolved in a solvent of low volatility (a matrix), both positive and negative molecular or quasi-molecular ions characteristic of the sample were produced. The process quickly became known by the acronym FAB (fast-atom bombardment) and for its then-fabulous results on substances that had hitherto proved intractable. Later, it was found that a primary incident beam of fast ions could be used instead, and a more generally descriptive term, LSIMS (liquid secondary ion mass spectrometry) has come into use. However, note that purists still regard and refer to both FAB and LSIMS as simply facets of the original SIMS. In practice, any of the acronyms can be used, but FAB and LSIMS are more descriptive when referring to the primary atom or ion beam. 

Ionizing collision. An ion/neutral reaction in which an electron or electrons are stripped from the ion and/or the neutral species in the collision. Generally, this term describes collisions of fast-moving ions or atoms with a neutral species in which the neutral species is ionized. Care should be taken to emphasize if charge stripping of the ion has taken place. 

For special high strength appHcations, ie, up to 69 MPa (10,000 psi), special formulations of Pordand cement concretes have been developed. These ate based on the use of chemical and mineral admixtures. The typical mineral admixtures ate fumed siUca and other po22olanics. The chemical admixtures ate generally chemicals termed supetplastici2ets that allow very low water to cement ratios, ie, between 0.4 and 0.25, and reduce the amount of water needed to provide plasticity or dow to the concrete. PubHc works appHcations take just under 32% of the total Pordand cement market streets and highways represent 68% of this usage, and water and waste account for 23%. 

An alternative to the use of generalized charts is an analytical equation of state. Equations of state which are expressed as a function of reduced properties and nondimensional variables are said to be generalized. The term generalization is in reference to the wide appHcabiHty to the estimation of fluid properties for many substances. 

Most ethers are potentially ha2ardous chemicals because, in the presence of atmospheric oxygen, a radical-chain process can occur, resulting in the formation of peroxides that are unstable, explosion-prone compounds (7). The reaction maybe generalized in terms of the following steps involving initiation, propagation, and termination. 

The effectiveness is known from experiment for important industrial catalysts and is correlated, in general, in terms of pore characteristics, concentrations, and specific rate equations. 

Several generalizations of the inelastic theory to large deformations are developed in Section 5.4. In one the stretching (velocity strain) tensor is substituted for the strain rate. In order to make the resulting constitutive equations objective, i.e., invariant to relative rotation between the material and the coordinate frame, the stress rate must be replaced by one of a class of indifferent (objective) stress rates, and the moduli and elastic limit functions must be isotropic. In the elastic case, the constitutive equations reduce to the equation of hypoelastidty. The corresponding inelastic equations are therefore termed hypoinelastic. 

Tabic 9-1 is a handy little chart to visualize a vertical, single-cylinder compressor and the basic functions. The functions are normalized to keep them in a dimensionless form [4]. With the following set of equations, the X and y components of the inertia forces for a single cylinder can be calculated. For the derivation, the reader is referred to references [4,. 5], Figure 9-4 depicts the generalized stage to aid in the definitioii of terms... 

Kinetic studies of the reaction of alcohols with acyl chlorides in polar solvents in the absence of basic catalysts generally reveal terms both first-order and second-order in alcohol. Transition states in which the second alcohol molecule acts as a proton acceptor have been proposed ... 

The term annulene was coined to refer to the completely conjugated monocyclic polyenes. The synthesis of annulenes has been extended well beyond the first two members of the series [4]annulene (cyclobutadiene) and [6]annulene (benzene). The generality of the Hiickel rule can be tested by considering the properties of members of the annulene series. 

Hansen [137-139], and later van Krevelen [114] proposed the generalization of the solubility parameter concept to attempt to include the effects of strong dipole interactions and hydrogen bonding interactions. It was proposed that the cohesive energy density be written as the sum of three terms, viz. 

It is evident that, under certain conditions, an unusual shape of q]/ r) functions may be expected. This is a result of the blocking term contribution. Some rearrangement of terms is necessary for the case where kj = kq, but no peculiar behavior is observed under these conditions. It is worth emphasizing that our result for q]l(r) generalizes the expression obtained by Bratko and Chakraborty for infinite dilution of fluid particles [35]. The q]/ r) functions coincide with their result for p 0. 

Historically, this phenomenon was referred to as unconfined vapor cloud explosion, but, in general, the term unconfined is a misnomer. It is more accurate to call this type of explosion simply a vapor cloud explosion. ... 

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