Means notation

The existence conditions of the solutions e, q, C2) can be jointly placed in a system formed through considering also simplifying yet with physical meaning notations ... 

Figure B3.5.2. Example Z matrix for fliioroethylene. Notation for example, line 4 of the Z matrix means that a H atom is bonded to earbon atom Cl with bond length L3 (angstroms), making an angle with earbon atom...

When constructing more general molecular wave functions there are several concepts that need to be defined. The concept of geometry is inhoduced to mean a (time-dependent) point in the generalized phase space for the total number of centers used to describe the END wave function. The notations R and P are used for the position and conjugate momenta vectors, such that... 

Stereochemistry can also be expressed in the SMILES notation [113]. Depending on the clockwise or anti-clockwise ordering of the atoms, the stereocenter is specified in the SMILES code with or respectively Figure 2-78). The atoms around this stereocenter are then assigned by the sequence of the atom symbols following the identifier or (g). This means that, reading the SMILES code from the left, the three atoms behind the identifiers ( ) or ( )( )) describe the stereochemistry of the stereocenter. The sequence of these three atoms is dependent only on the order of writing, and independent of the priorities of the atoms. 

Figure 6-2. Mappings between the que7 graph (Cq) and the target graph (Cr). Notation such as (2, 1, 3, 4) means that atom 2 of the que subgraph Gq is mapped to atom 1 from the target graph Cp...

Quantum chemists have devised efficient short-hand notation schemes to denote the basis set aseti in an ab initio calculation, although this does mean that a proliferation of abbrevia-liijii.s and acronyms are introduced. However, the codes are usually quite simple to under-sland. We shall concentrate on the notation used by Pople and co-workers in their Gaussian aerie-, of programs (see also the appendix to this chapter). 

Now, making only the change in notation of SSM for SST to indicate the total deviation from the mean and changing from upper to lower case r, we have... 

The operators F eorresponding to all physieally measurable quantities are Hermitian this means that their matrix representations obey (see Appendix C for a deseription of the bra I > and kef < notation used below) ... 

The notation for denoting this type of calculation is sometimes more specihc. For example, the acronym MCSCF+1+2 means that the calculation is a MRCI calculation with single and double Cl excitations out of an MCSCF reference space. Likewise, CASSCF+1+2 and GVB+1+2 calculations are possible. 

Another family of basis sets, commonly referred to as the Pople basis sets, are indicated by the notation 6—31G. This notation means that each core orbital is described by a single contraction of six GTO primitives and each valence shell orbital is described by two contractions, one with three primitives and the other with one primitive. These basis sets are very popular, particularly for organic molecules. Other Pople basis sets in this set are 3—21G, 4—31G, 4—22G, 6-21G, 6-31IG, and 7-41G. 

As the Pople basis sets have further expanded to include several sets of polarization functions, / functions and so on, there has been a need for a new notation. In recent years, the types of functions being added have been indicated in parentheses. An example of this notation is 6—31G(dp,p) which means that extra sets of p and d functions have been added to nonhydrogens and an extra set of p functions have been added to hydrogens. Thus, this example is synonymous with 6—31+G. ... 

An older, but still used, notation specihes how many contractions are present. For example, the acronym TZV stands for triple-zeta valence, meaning that there are three valence contractions, such as in a 6—311G basis. The acronyms SZ and DZ stand for single zeta and double zeta, respectively. A P in this notation indicates the use of polarization functions. Since this notation has been used for describing a number of basis sets, the name of the set creator is usually included in the basis set name (i.e., Ahlrichs VDZ). If the author s name is not included, either the Dunning-Hay set is implied or the set that came with the software package being used is implied. 

An extension of this last notation is aug—cc—pVDZ. The aug denotes that this is an augmented basis (diffuse functions are included). The cc denotes that this is a correlation-consistent basis, meaning that the functions were optimized for best performance with correlated calculations. The p denotes... 

Glycine is the simplest ammo acid and the only one m Table 27 1 that is achiral The a carbon atom is a chirality center m all the others Configurations m ammo acids are normally specified by the d l notational system All the chiral ammo acids obtained from proteins have the l configuration at their a carbon atom meaning that the amine group IS at the left when a Fischer projection is arranged so the carboxyl group is at the top... 

The notation here means that electron 1 occupies a spatial orbital /i with spin up (no bar on top) electron 2 occupies spatial orbital / with spin down (a bar on top), and so on. An RHF description... 

Introducing this notation means that Eqs. (1.3) and (1.4) may be written as... 

Until now we have been purposely vague about the quantity Aw. Since we shall use the notation of Eq. (8.42) from now on, it is convenient to say a few more things about Aw before we lose sight of it entirely. Reaction (8.A) is clear enough what is unspecific are the conditions under which this reaction takes place. Several possibilities come to mind, and each imparts a slightly different meaning to the energy w ... 

Eig. 4. The bulk oxygen isotopic composition of different meteorite classes where (—) is the terrestial fractionation line. The 5 notation refers to the normalized difference between or ratios to those in standard mean ocean water (SMOW) in relative units of parts per thousand. The... 

Mea.il Diameters. Several mean diameters are frequendy used to represent the statistical properties of droplets produced by Hquid atomizers. These mean diameters may be expressed according to the following proposed notation (27) ... 

Extracted from U.S. Standard Atmosphere, 1976, National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration and tte U.S. Air Force, Washington, 1976. Z = geometric altitude, T = temperature, P = pressure, g = acceleration of gravity, M = molecular weight, a = velocity of sound, i = viscosity, k = thermal conductivity, X = mean free path, p = density, and H = geopotential altitude. The notation 1.79.—5 signifies 1.79 X 10 . ... 

Condensed from Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1967 and 1972. Reproduced by permission. Tbe validity of many standard reference tables bas been critically reviewed by Jancso, Pupezin, and van Hook, J. Fhys. Chem., 74 (1970) 2984. Tbis source is recommended for further study. Tbe notation 4.949.-8, 3.607.-I-9, etc., means 4.949 x 10 , 3.607 x 10, etc. 

The notation a/ means the /th component of a evaluated on the /cth iteration. If a is a poor approximation to the optimum, we might use steepest descent instead. 

For an adequate interferenee fit seleeted on the basis of the hole, the toleranees are taken from BS 4500A (1970) as H7-s6. This translates to a toleranee on the hub bore H7 =+0.030, +0.000 mm and for the shaft diameter, s6 =+0.072, +0.053 mm. Given the notation for hub bore diameter is d, and eonverting to mean values and bilateral toleranees, these dimensions beeome ... 

The random nature of most physieal properties, sueh as dimensions, strength and loads, is well known to statistieians. Engineers too are familiar with the typieal appearanee of sets of tensile strength data in whieh most of the individuals eongregate around mid-range and fewer further out to either side. Statistieians use the mean to identify the loeation of a set of data on the seale of measurement and the variance (or standard deviation) to measure the dispersion about the mean. In a variable x , the symbols used to represent the mean are /i and i for a population and sample respeetively. The symbol for varianee is V. The symbols for standard deviation are cr and. V respeetively, although a is often used for both. In this book we will always use the notation /i for mean and cr for the standard deviation. 

The original work by NACA and NASA is the basis on which most modern axial-flow compressors are designed. Under NACA, a large number of blade profiles were tested. The test data on these blade profiles is published. The cascade data conducted by NACA is the most extensive work of its kind. In most commercial axial-flow compressors NACA 65 series blades are used. These blades are usually specified by notation similar to the following 65-(18) 10. This notation means that the blade has a lift coefficient of 1.8, a profile shape 65, and a thickness/chord ratio of 10%. The lift coefficient can be directly related to the blade camber angle by the following relationship for 65 series blades ... 

The 65 series blades are speeified by an airfoil notation similar to 65-(18) 10. This speeifieation means that an airfoil has the profile shape 65 with a eamber line eorresponding to a lift eoeffieient (Cr.) = 1.8 and approximate thiekness of 10% of the ehord length. The relationship between the eamber angle and the lift eoeffieient for the 65 series blades is shown in Figure 7-29. 

Dimensionless groups for a proeess model ean be easily obtained by inspeetion from Table 13-2. Eaeh of the three transport balanees is shown (in veetor/tensor notation) term-by-term under the deseription of the physieal meanings of the respeetive terms. The table shows how various well-known dimensionless groups are derived and gives the physieal interpretation of the various groups. Table 13-3 gives the symbols of the dimensions of the terms in Table 13-2. 

The term issue in the context of documents means that copies of the document are distributed. You will of course wish to issue draft documents for comment but obviously they cannot be reviewed and approved beforehand. The sole purpose of issuing draft documents is to solicit comments. The requirement should be that the documents are reviewed and approved prior to use. Some organizations insist that even drafts are approved for issue. Others go further and insist that copies cannot be taken from unapproved documents. This is nonsense and not what is intended by the standard. Your draft documents need to look different from the approved versions either by using letter issue notation (a common convention) or by printing on colored or watermark paper. If the approved document would carry signatures, the absence of any signature indicates that the document is not approved. 

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