Expression-related functions

In this section and the last, we have examined the lattice model of the Flory-Huggins theory for general expressions relating AHj and ASj to the composition of the mixture. The separate components can therefore be put together to give an expression for AGj as a function of temperature and composition ... 

If only one type of particle is present, mx = m2 however, the expressions relating the velocities before and after collision do not simplify to any great extent. If several types of particles are present, then there results one Boltzmann equation for the distribution function for each type of particle in each equation, integrals will appear for collisions with each type of particle. That is, if there are P types of particles, numbered i = 1,2,- , P, there are P distribution functions, ft /(r,vt, ), describing the system ftdrdvt is the number of particles of type i in the differential phase space volume around (r,v(). The set of Boltzmann equations for the system would then be ... 

This chapter makes extensive use of expressions derived from calculus. For a discussion of derivatives and related functions, see Appendix IF. 

This latter differential equation, coupled with the algebraic expression relating qout to h, may be solved to determine the fluid height as a function of time. The initial fluid height is 50.93 m, based upon the specified initial fluid volume and tank diameter. This serves as the initial condition to be used for the integration. The E-Z Solve syntax is ... 

The sound absorption coefficient, a, is increased when the dynamics of the chemical system are of the same order of magnitude as the frequency of the sound wave,41 and experimentally this quantity is measured as a function of frequency of the ultrasonic sound wave (Fig. 4). When the frequency of the sound wave is of the same order as the frequency for the relaxation process, effects due to relaxation of the equilibrium give rise to characteristic changes in the quantity a//2, where a is the sound absorption coefficient measured at frequency /40 The variation of a with frequency, /, has an inflection point at the relaxation frequency of the system, fr, which is related to 1/t, where r is the relaxation time (1/t = 27i/r).40,41 The expression relating the quantity... 

Abstract To better understand the relation between form and function in the complex olfactory communication system of the ringtailed lemur (Lemur catta), we integrated observational, experimental, and chemical approaches applied to a population of semi free-ranging animals at the Duke Lemur Center in Durham, North Carolina. Our aim was to examine sex-role reversal in the expression and function of scent marking and unravel the contribution of multimodal components of information transfer, with the unifying framework for all three avenues of our research being that multiplicity of form implies multiplicity of function. 

The leading coefficients are rather small for these functions. This is in part because the orbital set in terms of which we have expressed the functions is not the most felicitous. We have used cr, and tt, relating to the local geometry of each methylene. Alternatively, we can form hybrid orbitals... 

Hackett, W.P., Differential expression and functional significance of anthocyanins in relation to phasic development in Hedera helix L., in Anthocyanins in Leaves. Advances in Botanical Research, vol. 37, Gould, K.S. and Lee, D.W., Eds., Academic Press, Amsterdam, 2002, 95. 

The translation of the peptide sequence to functions in a protein molecule can be expressed as modular units (motifs and domains) that confer similar properties or functions in a variety of proteins. Based on characteristics of modular units, proteomes can be classified into families of proteins possessing related functions. For instance, some proteins play a key role in intercellular signaling pathways and some are structural, while others participate in metabolism. Up to 40% of proteins are encoded by the genome and carry out unknown functions, which still need to be discovered. 

The Langmuir adsorption isotherm describes the equilibrium between a single-component gas A and adsorbed species A(s) at a surface [237]. The expression relates the fraction of the surface 6a covered by adsorbed species as a function of the partial pressure pa exposed to the surface. The usual form of the Langmuir adsorption isotherm is... 

As for the previous two theories, we are interested in W(t)/t — k as a function of the energy separation Eai — Es. Robinson and Frosch have empirically correlated the square of the overlap integral [as in eq. (7)] with the energy separation for a singlet-triplet transition. From experimentally determined rate constants and an arbitrary but reasonable value for pel (0.01 cm-1) an expression relating < 0>2>tal to Eti ESo was deduced,... 

These equations can be also expressed as functions of the strength H of the main magnetic field by using a relation of = yH, were y is the nuclear gyromagnetic ratio. Such expressions may be more useful for the usual broad-line NMR spectrometry in which the main field is slowly swept under a constant rotating subfield. 

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