Comma notation

It is useful at this point to observe that in this context frequently the so-called comma notation is employed for partial derivatives with respect to the different coordinates which means writing for the partial derivative of 4 with respect to the spatial coordinate xk and I jc for the partial derivative of I with respect to the material coordinate Xk where I stands for aity arbitrary frmetion of the coordinates and where 4 can itself be a derivative. This makes it necessary to distinguish spatial and material coordinates by their indices, which is most easily accomplished by using upper case indices for material coordinates. This explains the choice of upper and lower case indices in (6.2) which, using the comma notation henceforth we can rewrite as... 

Regarding the use of upper and lower case subscripts it must be borne in mind that in some instances it is not without ambiguity, as in the case of displacements. Strictly speaking, the distinction is mandatory only for the coordinates themselves in combination with the comma notation for derivatives. In all other contexts upper case indices serve as a useful reminder that a material frame representation is used. This reminder, of course, is superfluous if only Unear effects are considered. 

The ROSDAL syntax is characterized by a simple coding of a chemical structure using alphanumeric symbols which can easily be learned by a chemist [14]. In the linear structure representation, each atom of the structure is arbitrarily assigned a unique number, except for the hydrogen atoms. Carbon atoms are shown in the notation only by digits. The other types of atoms carry, in addition, their atomic symbol. In order to describe the bonds between atoms, bond symbols are inserted between the atom numbers. Branches are marked and separated from the other parts of the code by commas [15, 16] (Figure 2-9). The ROSDAL linear notation is rmambiguous but not unique. 

Shorthand Notation for Electrochemical Cells Although Figure 11.5 provides a useful picture of an electrochemical cell, it does not provide a convenient representation. A more useful representation is a shorthand, or schematic, notation that uses symbols to indicate the different phases present in the electrochemical cell, as well as the composition of each phase. A vertical slash ( ) indicates a phase boundary where a potential develops, and a comma (,) separates species in the same phase, or two phases where no potential develops. Shorthand cell notations begin with the anode and continue to the cathode. The electrochemical cell in Figure 11.5, for example, is described in shorthand notation as... 

The cell notation is Zn Zn2+1 Co3+, Co2+ Pt Note that a comma separates the half-cell components that are in the same phase. The symbol Pt is used to indicate the presence of an inert platinum electrode. A single vertical line separates Pt (a solid) from the components of the half-cell, which are in the liquid phase. 

Complex scalar products arise naturally in quantum mechanics because there is an experimental interpretation for the complex scalar product of two wave functions (as we saw in Section 1.2). Students of physics should note that the traditional brac-ket notation is consistent with our complex scalar product notation—just put a bar in place of the comma. The physical importance of the bracket will allow us to apply our intuition about Euclidean geometry (such as orthogonality) to states of quantum systems. 

According to this notation, the main symbol in a formula shows the species (usually elements) present in a certain site. The -> vacancies are normally denoted by the italicized symbol V. Sometimes the vacant sites may also be indicated by other symbols, such as square box ( ), especially when the symbol ofvanadium (V) is present. The right lower indexes may indicate the species occupying this crystallographic site in an ideal lattice, or may show that this position is interstitial (subscript i). The second right lower index, if any, indicates the occupancy and should be separated by a comma. 

To avoid any misinterpretations concerned with the digit style of numbers, the decimal point is used throughout the book instead of a comma (i.e. computer notation 1.03 instead of 1,03, except for some graphical representations). In representative molecular structures, spin-paired non-bonding electrons around an atom of a molecule are represented (if necessary) by a bold line —in accord with commonly used leivis-structures. Single electrons are represented by a dot A full arrow (-> ) indicates shifts of electron pairs, whereas single electron shifts are... 

In general, however, a notation in which there are variables which define composition should be used. The ranges of the variables can also be indicated. Thus, a phase involving substitution of atom A for B is written Am+xB xCp (0 < x < n). The commas and parentheses called for above are not then required. 

These states are described by the notation (3) +, + > and —, — >. where the sign before the comma refers to the I states, and after the comma to the proton states. These states are coherent a proton in the + ) state is coupled to a + > state I. After the second (2J) 1 period, the H and I states again evolve the resulting states can then be described as superpositions of the original +, + > and —, — > states [Eq. (6)]. Note that... 

A single vertical line represents a phase boundary. For example, Zn(s) Zn iaq) indicates that the solid Zn is a different phase from the aqueous Zn " ". A comma separates the half-cell components that are in the same phase. For example, the notation for the voltaic cell housing the reaction between I and Mn04 shown in Figure 21.6 is... 

In this notation, a slash represents a phase boundary, and a comma separates two components in the same phase. A double slash, not yet used here, represents a phase boundary whose potential is regarded as a negligible component of the overall cell potential. When a gaseous phase is involved, it is written adjacent to its corresponding conducting element. For example, the cell in Figure 1.1.1/ is written schematically as... 

We begin by writing down the conservation or balance laws (Ericksen ). We shall employ the cartesian tensor notation, repeated tensor indices being subject to the usual summation convention. The comma denotes partial differentiation with respect to spatial coordinates and the superposed dot a material time derivative. For example,... 

Ideally, this should have a (formal ) double bond twisted through 90° by the rigid scaffolding and exhibit Du symmetry. The molecule was conceived by Maier and Jeffrey, who examined it theoretically [1] and actually tried to synthesize it, a somewhat rare act of daring in this field [2]. Orthogonene has, in principle, the stereoisomers 1-6, which are shown in Fig. 7.1 using a schematic representation. In isomer 1 all the bridgehead C-H bonds point outward (away) from the molecule, which can be labeled (Fig. 7.1) oo,oo (or all-out). In 2 one of these bonds points inward (toward) the molecule, which we can label io,oo, and so on. In this notation the stereochemistry at the two ends of the double bond is separated by a comma, and i precedes o, alphabetically. To be systematic, the stmctures are drawn with any in C-H bonds preferentially at the top left and bottom front (above the plane of the paper), see e.g. io,io. The stereochemical situation is somewhat aMn to that in the ladderane 7 [3, 4] (an io,oo isomer is shown). 

Permutations are usually entered in a computer using the list notation, this is, up to commas, the second row of the notation introduced above. For example... 

The complete amino acid sequence of a P. is shown by linking the 3-letter amino acid symbols by hyphens. If only part of a sequence is shown, the terminal symbols must also carry a second hyphen, e.g. -Ala-Ile-Val-Lys-. If part of a sequence is unknown the symbols are enclosed in parentheses and separated by commas, e.g. Ser-Phe-Gly-(Tyr, Asn, Val)-Pro-Ala. Using the one-letter notation (see Amino acids), this peptide would be represented as SFG(Y,B,V)PA, where the absence of punctuation between letters indicates a known sequence. 

Regarding the ports notation, it will be described with a subscript indicating the number of the element, a comma, and another subscript that indicates the analyzed direction (i.e., i 4,i). 

Only those substances whose compositions were known at least qualitatively have been included. For the notation of the formulae see section 1.2. In the formulae for solid solutions, paraitheses have been used with the host atom or host compound listed first and separated by a comma firom the additive, e.g. (Te, Se)Sn. Phases which cannot be assigned to a specific stoichiometry, for whatever reason, and which cannot be explained as a solid solution, are identified by the symbols of their atoms, separated by a comma, and not enclosed in parentheses, e.g. Sb,Te. 

Here are several additional examples of this notation for electrodes (written as cathodes). A comma separates ions present in the same solution. We will write the cathode with oxidized species before reduced species, in the same order as in the half-reaction. 

In some voltaic cells, there is no component in the half-reactions that can be used as an electrode. When this is the case, inert electrodes made of graphite or platinum are used for the transfer of electrons. If there are two ionic components in a cell, their symbols are separated by a comma. For example, suppose a voltaic cell consists of a platinum anode placed in a Sn " solution, and a silver cathode placed in a Ag solution. The notation for the ceU would be written as... 

Note that in this and the following equations the comma is used in the subscripts on stress to be able to write both the radial and hoop stresses in one equation. Since the form of these stresses differs only by a minus sign, it is preferred to emphasize their similarity by this nonstandard notation rather than write the two equations separately. 

When numbers have four or more digits to the left of the decimal point, they must have commas to help the reader to see quickly the thousands, millions, and so on, places. Only if the numbers are too cumbersome should powers-of-10 notation be used. When it is used, so-called engineering notation is preferred to scientific notation. In engineeiii notation, the power of 10 is always divisible by 3 (analogous to the commas mentioned above). In a column of num-bers that all refer to the same kind of property, the format should be the same for each entry. 

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