Basis definition

Basie definitions of terms relating to polymerization reactions [1,2] and stereochemical definitions and notations relating to polymers [3] have been published, but no reference was made explieitly to reaetions involving the asymmetric synthesis of polymers. It is the aim of the present doeument to recommend classification and definitions relating to asymmetrie polymerizations that may produce optically active polymers. 

Polymers having monomeric units differing in constitutional or configurational features, but derived from a single monomer, are not regarded as eopolymers, in accordance with the basie definitions [4]. Examples of sueh polymers, whieh are not copolymers, are ... 

For most materials, the particle size hes somewhere between these two extremes, and the torques required in two properly designed thickeners of the same size but in distinct applications can differ greatly. Unfortunately, test methods to specify torque from small-scale tests are of questionable value, since it is difficult to duplicate actual conditions. Manufacturers of sedimentation equipment select torque ratings from experience with similar substances and will recommend a torque capability on this basis. Definitions of operating torque vary with the manufacturer, and the user should ask the supplier to specify the B-10 life for bearings and to reference appropriate mechanical... 

Thus, as long as p < 0.5, the monomer always predominates on a weight basis (definition of p), while later, the primary substance aggregated in the higher polymers must inevitably far exceed the monomer by weight. 

Plant data for selected case scenarios agreed in the basis definition. 

In the above basis, the Hamiltonian Hen is off-diagonal, while the damping matrix is diagonal. From the basis definition (see Equation A19), it is evident that the effective Hamiltonian is non-Hermitian. This can be rationalized by noting that we consider only a subspace of the Hilbert space, consisting of the above discrete zero-order basis set. In fact, the effective Hamiltonian of Equation Gl can be written as a sum... 

In the definition phase options are narrowed down and a preferred solution is proposed. The project becomes better defined in terms of what should be built and how it should be operated, and an assessment of how the project may be affected by changes beyond the control of the company (for example the oil price) should be made. Normally a clear statement should be prepared, describing why the option is preferred and what project specifications must be met, to be used as a basis for further work. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

A third definition of surface mobility is essentially a rheological one it represents the extension to films of the criteria we use for bulk phases and, of course, it is the basis for distinguishing states of films on liquid substrates. Thus as discussed in Chapter IV, solid films should be ordered and should show elastic and yield point behavior liquid films should be coherent and show viscous flow gaseous films should be in rapid equilibrium with all parts of the surface. 

Mead C A and Truhlar D G 1982 Conditions for the definition of a strictly diabatic electronic basis for molecular systems J. Chem. Rhys. 77 6090... 

Figure C3.4.4. Definition of the dimer transition dipole moments and p on tire basis of tire monomer transition dipole moments p and P2-...

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. 

These new wave functions are eigenfunctions of the z component of the angular momentum iij = —with eigenvalues = +2,0, —2 in units of h. Thus, Eqs. (D.l 1)-(D.13) represent states in which the vibrational angular momentum of the nuclei about the molecular axis has a definite value. When beating the vibrations as harmonic, there is no reason to prefer them to any other linear combinations that can be obtained from the original basis functions in... 

The unit vectors Ci, whose exact definition, meaning and interpretation depend on the particular application at hand, are called basis vectors and form the elements of a basis. They are particularly simple to work with because they are orthogonal. This means that... 

Capacity. Capacity is a measure of the quantity of ions, acid, or base removed (adsorbed) by an ion-exchange material. The quantity removed is direcdy correlated with the number of functional groups. Capacity is reported ia several different ways, but requites further definition because the word by itself does not cover ad situations. Total capacity is a measure of ad the functional groups on a resia and is recorded on a weight as wed as a volume basis. 

A reliability block diagram can be developed for the system from the definition of adequate performance. The block diagram represents the effect of subsystem or component failure on system performance. In this preliminary analysis, each subsystem is assumed to be either a success or failure. A rehabihty value is assigned to each subsystem where the appHcation and a specified time period are given. The reUabiUty values for each subsystem and the functional block diagram are the basis for the analysis. 

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