Superscript notations

Figure 6.14 Schematic representation of the scoring system the example illustrated uses the Reference Center set of HER2/Chl7 ratios obtained for the SK-BR3 cell line at Run 4. In this case the lowest ratio obtained by a Reference Center was 3.19, and the highest was 4.10 participants submitting ratios within this range were judged to have achieved an appropriate result (score = 3). The lower cutoff for acceptable ratios (score = 2) was calculated as 3.19 minus 10% of 3.19, that is 2.87 and the upper cutoff was calculated as 4.10 plus 10% of 4.10, that is 4.51. Participants who submitted ratios outside these 10% cutoffs were judged to have achieved an inappropriate result and received a score of 1. Except in the case of the MDA-MB-453 cell line, misdiagnosis (amplified reported as nonamplified, and vice versa) resulted in a score of 0. Superscript notation and abbreviation used in figure Does not apply to results obtained for MDA-MB-453 cell line RC, Reference Center. See color insert.

The L are the familiar L matrix elements the coefficients L" and L u, etc., will be called the second and third derivative elements of the L tensor, following the notation introduced by Hoy et al,12 In equation (44) an unrestricted summation is to be understood over all indices repeated as a superscript and a subscript in the terms on the right-hand side this convention will be followed in all the later equations of this section. The use of subscript/ superscript notation for the indices on the L matrix and L tensor elements, which is used throughout the equations of this section, simplifies the rather complex algebra involved in the non-linear co-ordinate transformations. Equation (44) may be compared with equation (39) for the co-ordinates Ri, which contains only linear terms. 

We retain the superscript notation from the preceding section to designate the order of each variable in terms of the small parameter e. The governing equations, which we obtained by substituting these expansions into (6-202)-(6-204), plus (6-213), are thus, at 0(1),... 

For simplicity the superscript (5 in 17, is omitted we have also used the notation... 

As in our previous notations, the species superscript 0 is for the matrix component and the species superscript 1 denotes the fluid component. The fluid-matrix interaction is chosen between a fluid particle and a monomer belonging to a chain by using the model of additive hard spheres. The fluid-matrix and fluid-fluid interactions are... 

The superscript t denotes a transposition of the r-vector, i.e. converting it from a column to a row vector. The rr notation for the quadmpole moment therefore indicates a 3 x 3 matrix containing the products of the x-, y- and z-coordinates, e.g. the Qxy component is calculated as the expectation value of xy. 

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

The variants are distinguished by the locants of those ring atoms that lie outside a reference plane (defined below) and are listed for some examples in Table 1. The locants of ring atoms that lie on the side of the reference plane from which numbering appears clockwise (i.e. the upper side in the normal Haworth representation of furanoses and pyranoses) are written as superscripts and precede the letter those that lie on the other side are written as subscripts and follow the letter. Heteroatoms (e.g. O, S) are indicated by their subscript or superscript atomic symbols. Table 1 gives the notations and Chart III some examples. 

Let us pass, time and again, to the notations without subscripts and superscripts, which are good enough for our purposes ... 

It should be noted that, in this notation, the order of the superscripts is irrelevant ab... is the entire perturbed energy term linear in ab. .. z and there is no... 

The coordination conditions can be expressed in a chemical formula using a notation suggested by F. Machatschki (and extended by several other authors for recommendations see [35]). The coordination number and polyhedron of an atom are given in brackets in a right superscript next to the element symbol. The polyhedron is designated with a symbol as listed in Fig. 2.2. Short forms can be used for the symbols, namely the coordination number alone or, for simple polyhedra, the letter alone, e.g. t for tetrahedron, and in this case the brackets can also be dropped. For example ... 

To distinguish partition coefficients of neutral species from ionized species, the notation log PN and log/j/ may be used, respectively, or the symbol C or A may be used as a substitute for superscript /, denoting a cation or anion, respectively. [362],... 

The fluorescent components are denoted by / (intensity) followed by a capitalized subscript (D A or s, for respectively Donors, Acceptors, or s.e.) to indicate the particular population of molecules responsible for emission and a lower-case superscript ( " or ) that indicates the detection channel (or filter cube). For example, I denotes the intensity of the donors as detected in the donor channel and reads as Intensity of donors in the donor channel, etc. Notes (1) The excitation in the s.e. channel is generally set up to be equal to that in the donor channel. In case a separate filter cube is used, slight differences may occur, which is denoted by Don(S). See the text and appendix for further details. (2) The s.e. emission filter is usually the same as the acceptor emission filter in confocal determinations. We here designate a different filter to accommodate those wide-field/digital camera experiments that employ different filters for A and S. (3) Here the notation D-S indicates the residual (quenched) donor fluorescence in the presence of the acceptor. In the other chapters this is indicated as DA. Hence ... 

For hydrogen, the notation Is1 is used, where the superscript denotes a single electron in the Is state. Because an electron can have a spin quantum number of +1/2 or -1/2, two electrons having opposite spins can occupy the Is state. The helium atom, having two electrons, has the configuration Is2 with the electrons having spins of +1/2 and —1/2. 

Superscripts a c refer to the footnotes subscripts a and b refer to notation used in Eq. (25). 

This example focuses on the design and optimization of a steady-state staged column. Figure El 2.1 shows a typical column and some of the notation we will use, and Table El2.1 A lists the other variables and parameters. Feed is denoted by superscript F. Withdrawals take the subscripts of the withdrawal stage. Superscripts V for vapor and L for liquid are used as needed to distinguish between phases. If we number the stages from tihe bottom of the column (the reboiler) upward with k= 1, then V0 = L1 = 0, and at the top of the column, or the condenser, Vn = Ln+l = 0. We first formulate the equality constraints, then the inequality constraints, and lastly the objective function. 

In this notation, the upper line of superscripts refers to the mass of the particles in Daltons, and the subscripts refer to the charge. The resulting electron is then ejected from the nucleus as the (3 particle. 

D (7y notation employed for block copolymers, where the subscripts (w and y) denote the composition in weight percent and the superscripts (x and z) the number-average molecular mass in kilograms per mole. In the case of PPDX-fr-PCL diblock copolymers, the letter D is used for PPDX and the letter C for PCL... 

In order to simplify the notation, we drop the superscript (k). Nevertheless, the reader should keep in mind that Sjp will depend on the linear-mixture basis chosen to define the mixture-fraction vector. 

Thus, in analogy to (5.341), 0 will replace (0) in the multi-environment LES model. Hereinafter, in order to simplify the notation, we will denote all conditional variables with a superscript as follows (s) = (s U, 0 ) . 

The nomenclature usually assumes R = Me, and substitution of methyl groups is indicated by a superscript suffix, e.g. Dph represents the unit Me(Ph)SiO(o.5)2, or with the substituted group following a prime notation and enclosed in brackets, e.g. M(D A)M. 

Whewell criticized Berzelius s original superscript symbols on the grounds that they contravened the most elementary rules of algebra. NH4C1 means (x y4 Cl), not, as Berzelius intends, (N + 4H + Cl).64 Whewell complained of the new notation,... 

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