Combination definition

Combine definitions of the activity coefficient and the fugacity coefficients ... 

Combining Definition 4.5.1.3 with Theorem 4.4.1.9, we reach the following immediate yet significant result. 

Combining definitions 8.33 and 8.34 leads to a more generalized expression for /response,... 

Alternatively, in combination with the definition of work of adhesion (Eq. XII-... 

Alternatively, the electron can exchange parallel momentum with the lattice, but only in well defined amounts given by vectors that belong to the reciprocal lattice of the surface. That is, the vector is a linear combination of two reciprocal lattice vectors a and b, with integer coefficients. Thus, g = ha + kb, with arbitrary integers h and k (note that all the vectors a,b, a, b and g are parallel to the surface). The reciprocal lattice vectors a and are related to tire direct-space lattice vectors a and b through the following non-transparent definitions, which also use a vector n that is perpendicular to the surface plane, as well as vectorial dot and cross products ... 

Over the next few years, both the mid-infrared and the far-infrared spectra for Ar-HF and Ar-HCl were extended to numerous other bands and to other isotopic species (most importantly those containing deuterium). In 1992, Hutson [18, 39] combined all the available spectroscopic data to produce definitive potential energy surfaces that included both the angle dependence and the dependence on the HF/HCl monomer vibrational quantum number v... 

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... 

We have seen that a base can be defined as combining with a proton and, therefore, requires at least one lone pair of electrons. A more general definition of acids and bases, due to G. N. Lewis, describes a base as any species (atom, ion or molecule) which can donate an electron pair, and an acid as any species which can accept an electron pair— more simply, a base is an electron-pair donor, an acid an electron-pair acceptor. Some examples of Lewis acids and bases are ... 

Identification of Aromatic Hydrocarbons. Picric acid combines with many aromatic hydrocarbons, giving addition products of definite m.p. Thus with naphthalene it gives yellow naphthalene picrate, C oHg,(N08)jCeHiOH, m.p. 152°, and with anthracene it gives red anthracene picrate, C 4Hio,(NOj)jCeHjOH, m.p. 138 . For practical details, see p. 394. 

To resolve the problems associated with structured and unstructured grids, these fundamentally different approaches may be combined to generate mesh types which partially posses the properties of both categories. This gives rise to block-structured , overset and hybrid mesh types which under certain conditions may lead to more efficient simulations than the either class of purely structured or unstructured grids. Detailed discussions related to the properties of these classes of computational grid.s can be found in specialized textbooks (e.g, see Liseikin, 1999) and only brief definitions are given here. 

Section 2 combines the former separate section on Mathematics with the material involving General Information and Conversion Tables. The fundamental physical constants reflect values recommended in 1986. Physical and chemical symbols and definitions have undergone extensive revision and expansion. Presented in 14 categories, the entries follow recommendations published in 1988 by the lUPAC. The table of abbreviations and standard letter symbols provides, in a sense, an alphabetical index to the foregoing tables. The table of conversion factors has been modified in view of recent data and inclusion of SI units cross-entries for archaic or unusual entries have been curtailed. 

Atoms combine in definite proportions to give molecules. For example, natural gas is mostly composed of methane, a substance in which four hydrogen atoms (H) are combined with one carbon (C) the molecular formula is written as CH4. Similarly, water, ammonia, ethanol, and glucose have... 

The elastic and viscoelastic properties of materials are less familiar in chemistry than many other physical properties hence it is necessary to spend a fair amount of time describing the experiments and the observed response of the polymer. There are a large number of possible modes of deformation that might be considered We shall consider only elongation and shear. For each of these we consider the stress associated with a unit strain and the strain associated with a unit stress the former is called the modulus, the latter the compliance. Experiments can be time independent (equilibrium), time dependent (transient), or periodic (dynamic). Just to define and describe these basic combinations takes us into a fair amount of detail and affords some possibilities for confusion. Pay close attention to the definitions of terms and symbols. 

By combining random flight statistics from Chap. 1 with the statistical definition of entropy from the last section, we shall be able to develop a molecular model for the stress-strain relationship in a cross-linked network. It turns out to be more convenient to work with the ratio of stretched to unstretched lengths L/Lq than with y itself. Note the relationship between these variables ... 

In Chap. 5, p was defined as the fraction (or probability) of functional groups that had reacted at a certain point in the polymerization. According to the current definition provided by Eq. (6.66), p is the fraction (or probability) of propagation steps among the combined total of propagation and termination steps. The quantity 1 - p is therefore the fraction (or... 

The inherent viscosity (I/C2) In (77/770). A plot of inherent viscosity versus concentration also extrapolates to [77] in the limit of C2 0. That this is the case is readily seen by combining Eq. (9.12) with the definition of the inherent viscosity and then expanding the logarithm ... 

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