Roman Letters

Lasorstein, m. lapis lazuli. — unechter —, false lapis lazuli, chessylite. lateinisch, a. Latin roman (letters). 

It is important to know that the Greek letters a and p refer to the standard deviation and mean respectively of a total population, whilst the Roman letters s and x are used for samples of populations, irrespective of the values of the population mean and the population standard deviation. 

It is convention to use Greek letters for a subscript that runs over all four coordinates, and Roman letters for subscripts only over the space components. 

Fig. 35. Projection in the be crystal plane of an /-alanine single crystal. Proposed positions for the Cu(II) impurities are marked with Roman letters. (Adapted from Ref. 63)...

In a few cases, however, certain Greek and Roman letters have assumed a more general meaning as symbols of groups of similar phases for instance, the name... 

Five key steps for the transformations are indicated by the roman letters. In step I, normal paraffins adsorb on Pt sites and undergo dehydrogenation to form small... 

The elements are given names, of which some have origins deep in the past and others are relatively modem. The names are trivial. The symbols consist of one, two or three roman letters, often but not always related to the name in English. 

These are constructed on a principle similar to that for A-La203 and Th3N4, except that the C1 layers are now devoid of anions, i.e. they are simply cations in cubic eutaxy. All the anions are in octahedral coordination, and a similar avoidance rule applies (c layers of cations except at B1/A1 boundaries where they are h). Hence, the stacking sequence of eutactic layers of cations is, h c in s-Hf3N2 and hV in -Hf4N3 so that the complete sequences are (roman letters = anion layers, greek letters = cation layers)... 

This is an eigenvalue equation for the Floquet exponents and the coefficients To see this more clearly, let us introduce the basis of states an), where the Greek letter labels the molecular states and the Roman letter the Fourier components. Then, Eq. (8.19) can be written as... 

Matrix elements 5 are the overlap matrix elements we have seen before. For a general matrix element (we here adopt a convention that basis functions are indexed by lowercase Greek letters, while MOs are indexed by lower-case Roman letters) we compute... 

Vectors are denoted by bold letters and their magnitudes by corresponding roman letters. Such a differentiation is not used when only the magnitudes are important. 

Atoms common to two or more rings are designated by adding roman letters a , b , c , etc., to the number of the position immediately preceding. Interior atoms follow the highest number, taking a clockwise sequence wherever there is a choice. 

For instance, a length may be expressed as a multiple of the unit of length, the meter, m so we write / = 2.0 m if the length is the product of 2.0 (the multiple) times the unit. All units are denoted by Roman letters, such as m for meter and s for second, that distinguish them from the physical quantity to which they refer. 

Therefore, k+bm and k label the same representation and are said to be equivalent (=). By definition, no two interior points can be equivalent but every point on the surface of the BZ has at least one equivalent point. The k = 0 point at the center of the zone is denoted by T. All other internal high-symmetry points are denoted by capital Greek letters. Surface symmetry points are denoted by capital Roman letters. The elements of the point group which transform a particular k point into itself or into an equivalent point constitute the point group of the wave vector (or little co-group of k) P(k) C P, for that k point. 

Fig. 41.—Diagram for calculating potential energies for the addition of a bromine molecule to a carbon-carbon double bond. Roman letters refer to coulombic or electrostatic exchange. Greek letters refer to attraction or exchange energy calculated on the basis of the semi-empirical method.

Superatoms are designated by roman letters R for any set of substituents or residues, for example, or Ar for a list of aromatic substituents. Superatoms may be distinguished by the addition of designation digits, typically a subscript following the superatom RA, RB, and Rc could specify the residue of reagents A, B,... 

Denote electron shells with the uppercase roman letters K, L, M, and N. 

Name electron subshells and atomic orbitals with the lowercase roman letters s, p, d, and f. Write principal energy levels 1-7 on the line and to the left of the letter give the number of electrons in the orbital as a superscript to the right of the letter. Specify orbital axes with italic subscripts. 

Name the electronic states of atoms with the uppercase roman letters S, P, D, F, G, H, I, and K, corresponding to quantum numbers l = 0-7. Use the corresponding lowercase letters to indicate the orbital angular momentum of a single electron. The left superscript is the spin multiplicity the right subscript is the total angular momentum quantum number /. 

Name the electronic states of molecules with the uppercase roman letters A, B, E, and T the ground state is X. Use the corresponding lowercase letters for one-electron orbitals. A tilde ( ) is added for polyatomic molecules. The subscripts describe the symmetry of the orbital. 

Abbreviate reaction types with capital roman letters and arabic numerals. 

Chemical reactions set as equations should be labeled with lightface roman letters, numerals, or combinations in parentheses in the right margin (see Chapter 13). Depending on the text, it may be appropriate to use one set of labels for both chemical reactions and mathematical equations, or two separate and distinct numbering sequences (for instance, eqs 1,2,3,... and reactions I, II, III,. ..). The numbering sequences for structures and for reactions should always remain separate. 

We generally denote scalars by lowercase Greek letters (e.g., P), column vectors by boldface lowercase Roman letters (e.g., x), and matrices by capital italic Roman letters (e.g., H). A superscriptT denotes a vector or matrix transpose. Thus xT is a row vector, xTy is an inner product, and AT is the transpose of the matrix A. Unless stated otherwise, all vectors belong to R , the u-dimen-sional vector space. Components of a vector are typically written as italic letters with subscripts (e.g., xux2,.. . , ). The standard basis vectors in R" are the n vectors ei,e2,. . . , e , where e has the entry 1 in the th component and 0 in all others. Often, the associated vector norm is the standard Euclidean norm, j 2, defined as... 

We will use Greek letters to label charged species (a, / ,. ..) and Roman letters (n, m,. ..) to label neutral particle species. 

Note that the symbols for SI units and derived units are all represented by roman letters, with an initial capital letter used when the unit is named after a person. These symbols are never expressed as plurals (with an added s) and are never followed by a period except at the end of a sentence. A sequence of symbols should alternate with spaces as shown above. The format a/b can be used in place of a b (e.g., J/K instead of J for entropy), but the exponent format is preferable since it is unambiguous for compound units (e.g., there is some possibility of confusion with W/mK for thermal conductivity but none with W m K ). 

Roman letters are used for representations of electronic states and greek letters for vibrational modes... 

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