A subscript index

With applications to protein solution thermodynamics in mind, we now present an alternative derivation of the potential distribution theorem. Consider a macroscopic solution consisting of the solute of interest and the solvent. We describe a macroscopic subsystem of this solution based on the grand canonical ensemble of statistical thermodynamics, accordingly specified by a temperature, a volume, and chemical potentials for all solution species including the solute of interest, which is identified with a subscript index 1. The average number of solute molecules in this subsystem is... 

The numeric codes for structures of an inhomogeneous structure series are more complicated in comparison to the codes for structures of homogeneous structure series. A numeral (digit) indicates the succeeding number of segments of one kind. A subscripted index shows from what parent structure(s) the segment is taken. A superscripted index specifies the symmetry of the segment. 

Thus, all possible ways to unite a link pair using smallest rings are counted and then added as a subscript index to the ring size as M>i-Ny2 0y,... The connectivity p is now deduced from the number of link pairs, each of these having a Mji symbol assigned to it. Thus summing the number of link pairs is equal to / (/ -1 )/2 (equation 4.1). For example for a three-connected net there will be three link pairs (Myi-Nyj-Oys) and for a four-connected net there will be six (My -Ny2-Oy3 Py4-Qy5-Ry[Pg.63]

Subscript i identifies species, and J is a dummy index all summations are over all species. Note that Xp however, when i = J, then Xu = = 1. In these equations / (a relative molecular volume) and (a relative molecular surface area) are pure-species parameters. The influence of temperature on g enters through the interaction parameters Xp of Eq. (4-261), which are temperature dependent ... 

The orbitals <]) j(k r) are Bloch functions labeled by a wave vector k in the first Brillouin zone (BZ), a band index p, and a subscript i indicating the spinor component. The combination of k and p. can be thought of as a label of an irreducible representation of the space group of the crystal. Thequantity n (k)is the occupation function which measures... 

Note that here bracket does not mean just any round, square, or curly bracket but specifically the symbols and > known as the angle brackets or chevrons. Then ( /l is called a bra and Ivp) is a ket, which is much more than a word play because a bra wavefunction is the complex conjugate of the ket wavefunction (i.e., obtained from the ket by replacing all f s by -i s), and Equation 7.6 implies that in order to obtain the energies of a static molecule we must first let the Hamiltonian work to the right on its ket wavefunction and then take the result to compute the product with the bra wavefunction to the left. In the practice of molecular spectroscopy l /) is commonly a collection, or set, of subwavefunctions l /,) whose subscript index i runs through the number n that is equal to the number of allowed static states of the molecule under study. Equation 7.6 also implies the Dirac function equality... 

Let us consider a case of one enclosed partition. There are two levels of partitioning in the considered PS. The upper level of partitioning includes partitions 1 and 2 (corresponding subscript indexes are 1 and 2). The lower level of partitioning includes partitions 11 and 12 (corresponding subscript indexes are 11 and 12) that form partition 1. At each level of partitioning, Equation 9.23 through Equation 9.28 are correct, thus... 

Therefore, conventionally the temperature at which the refractive index is measured is usually designated as a superscript numerical on n whereas the wave-length of light employed as a subscript capital. 

Thus in Eq. (98), to consider the modes mentioned above, p = X — 0 and v, p = 0,1,2,3 need to considered, where 0 represents the density, 1 the longitudinal current, 2 the transverse current, and 3 the temperature. Please note that the subscript p is a dummy index and is not to be confused with the density. C 1 for different values of v are... 

Here, we shall discuss the implications of cosmological expansion for the searches of a quantum-gravity-induced refractive index and a stochastic effect. We will consider Friedman-Robertson-Walker (FRW) metrics as an appropriate candidate for standard homogeneous and isotropic cosmology. Let R be the FRW scale factor, and a subscript 0 will denote the value at the present era. Ho is the present Hubble expansion parameter, and the deceleration parameter qo is defined in terms of the curvature k of the FRW metric by k ( 2[Pg.588]

In Equation (9.6), x is the direction of flux, nt [mol m-3 s 1 ] is the total molar density, X [1] is the mole fraction, Nd [mol m-2 s 1] is the mole flux due to molecular diffusion, D k [m2 s 1] is the effective Knudsen diffusion coefficient, D [m2 s 1] is the effective bimolecular diffusion coefficient (D = Aye/r), e is the porosity of the electrode, r is the tortuosity of the electrode, and J is the total number of gas species. Here, a subscript denotes the index value to a specific specie. The first term on the right of Equation (9.6) accounts for Knudsen diffusion, and the following term accounts for multicomponent bulk molecular diffusion. Further, to account for the porous media, along with induced convection, the Dusty Gas Model is required (Mason and Malinauskas, 1983 Warren, 1969). This model modifies Equation (9.6) as ... 

Link types are characterized by their crossing numbers according to a convention in which c K) is superscripted by the number of components in the link and subscripted by a numerical index, needed because two or more nonequivalent links may share the same crossing number for links with c(K) > 5. For the case of one-component links, that is, for knots, the superscript 1 is omitted. If directions (denoted by arrows along the curves) are assigned to all the component curves that constitute a link, that link is said to be oriented. Otherwise it is nonoriented. We begin our discussion by a consideration of nonoriented links. 

Subscript i identifies species, and j is a dummy index running over all species. Subscript k identifies subgroups, and m is a dummy index running over all subgroups. The quantity v(k) is the number of subgroups of type k in a molecule of species i. Values of the subgroup parameters Rk and Qk and of the group... 

The occurrence of the imino and hydroxyl forms in which the H atom can be on either side of the 0-C6 or N-C2 bond, in the molecular plane, like in phenol, gives rise to twin forms, sometimes referred to as rotamers, in spite of a significant barrier between them which is probably not easily overcome at room temperature ( 10kcal/mol for the 9AH rotamers [28, 29]). These forms are labelled by the same short name with a subscript indicating the index of the N atom the hydroxy or imino H atom is pointing. 

A more compact notation [58] may be used to label vibronic (or vibrational) transitions in polyatomic molecules with many normal modes, in which each vibration index r is given a superscript v r and a subscript v, indicating the upper and lower state values of the quantum number. When v r = v, = 0 the corresponding index is suppressed. 

In all expressions the Einstein repeated index summation convention is used. Xi, x2 and x3 will be taken to be synonymous with x, y and z so that o-n = axx etc. The parameter B will be temperature-dependent through an activation energy expression and can be related to microstructural parameters such as grain size, diffusion coefficients, etc., on a case-by-case basis depending on the mechanism of creep involved.1 In addition, the index will depend on the mechanism which is active. In the linear case, n = 1 and B is equal to 1/3t/ where 17 is the linear shear viscosity of the material. Stresses, strains, and material parameters for the fibers will be denoted with a subscript or superscript/, and those for the matrix with a subscript or superscript m. 

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It is convenient at this stage to redefine the notation for energy. We drop the channel index from the total energy E, since it is the same in all channels. This is expressed for example by the energy-conserving delta function in (6.39). We now use a subscripted energy variable to refer to the kinetic energy of an electron, for example in channel 0 or i. The density of... 

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The Universal Quasi-chemical Theory or UNIQUAC method of Abrams and Prausnitz divides the excess Gibbs free energy into two parts. The dominant entropic contribution is described by a combinatorial part ( ). Intermolecular forces responsible for the enthalpy of mixing are described by a residual part ( ). The sizes and shapes of the molecule determine the combinatorial part, which is thus dependent on the compositions and requires only pure component data. Since the residual part depends on the intermolecular forces, two adjustable binary parameters are used to better describe the intermolecular forces. As the UNIQUAC equations are about as simple for multi-component solutions as for binary solutions, the UNIQUAC equations for multicomponent solutions are given below. Species are identified by subscript i, subscript j is a dummy index. Here, is a relative molecular surface area and r, is a relative molecular volume. Both of these quantities are pure-species parameters. 

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