Symbols equal

It follows from Eq. (6.2) that these coefficients are joined by the following symbolic equality ... 

Let s take F = eijkUi where 6, is the Levi-Civitta permutation symbol equal to 1 when indexes ijk form a qfdic permutation of numbers 123, equal to 0 when among ijk are two (or more) identical numbers from the set 123, and to —1 otherwise. Using this tensor, the components of a cross product can be written as (b X c) — SjjifbiCi. Then it follows from (5.1)... 

The valence electrons in the outermost energy level of an atom are responsible for the electron activity that occurs to form chemical bonds. The Lewis structure of an atom is a representation that shows the valence electrons for that atom. American chemist Gilbert N. Lewis (1875-1946) proposed using the symbol for the element and dots for electrons. The number of dots placed around the symbol equals the number of s and p electrons in the outermost energy level of the atom. Paired dots represent paired electrons unpaired dots represent unpaired electrons. For example, H" is the Lewis symbol for a hydrogen atom, Is B is the Lewis symbol for a boron atom, with valence electrons 2s 2p In the case of boron, the symbol B represents the boron nucleus and the Is electrons the dots represent only the 2s 2p electrons. 

In the EMR in Fig. 1.4, the enzyme acts as a biocatalyst in homogeneous solution, where diffusive resistances are minimized. It mainly consists of a continuously stirred tank, with a volume symbolically equal to V, equipped with a UF membrane and characterized by an exposed area A. llie membrane is chosen to ensure complete rejection of the enzyme. Tlie tank is loaded with the required amount of enzyme. It is then continuously fed with the substrate solution, at a given concentration of substrate So and... 

The two types of assignment equals signs and the evaluation equals sign are all available in the Evaluation toolbar. The symbolic equals sign is available under the Boolean toolbar. Please see Figure 5.2. 

Mathcad can solve problems numerically (approximately) as well as analytically (symbolically). The symbolic equality operator is It will be discussed below. 

Still undocumented is the tandem operators — and (local definition and symbolic equal sign, see point 3 in Fig. 6.17) which enable us to look dirough the variables in programs and is very useful for verification. 

The brackets symbolize fiinction of, not multiplication.) Smce there are only two parameters, and a, in this expression, the homogeneity assumption means that all four exponents a, p, y and S must be fiinctions of these two hence the inequalities in section A2.5.4.5(e) must be equalities. Equations for the various other thennodynamic quantities, in particular the singidar part of the heat capacity Cy and the isothemial compressibility Kp may be derived from this equation for p. The behaviour of these quantities as tire critical point is approached can be satisfied only if... 

The symbol M represents the masses of the nuclei in the molecule, which for simplicity are taken to be equal. The symbol is the Kionecker delta. The tensor notation is used in this section and the summation convention is assumed for all repeated indexes not placed in parentheses. In Eq. (91) the NACT appears (this being a matrix in the electronic Hilbert space, whose components are denoted by labels k, m, and a vector with respect to the b component of the nuclear coordinate R). It is given by an integral over the electron coordinates... 

Note that in Mathcad, both matrices must be defined above the problem to be worked. In Mathcad, the symbol A = means matrix A is set equal to. ... 

Photochemical energy is indi cated by writing light or hv above or below the ar row The symbol hv is equal to the energy of a light pho ton and will be discussed in more detail in Section 13 1... 

R (Section 4 1) Symbol for an alkyl group Racemic mixture (Section 7 4) Mixture containing equal quantities of enantiomers... 

Let s use a simple example to develop the rationale behind a one-way ANOVA calculation. The data in Table 14.7 show the results obtained by several analysts in determining the purity of a single pharmaceutical preparation of sulfanilamide. Each column in this table lists the results obtained by an individual analyst. For convenience, entries in the table are represented by the symbol where i identifies the analyst and j indicates the replicate number thus 3 5 is the fifth replicate for the third analyst (and is equal to 94.24%). The variability in the results shown in Table 14.7 arises from two sources indeterminate errors associated with the analytical procedure that are experienced equally by all analysts, and systematic or determinate errors introduced by the analysts. 

This last result includes the factor since all segments are counted twice by the combination of Eqs. (1.53) and (1.54). The double summation also makes the two terms in the brackets equal to two times either one of them. This procedure averages over all segments fulfilling the role of center of mass therefore it is appropriate to identify the quantity evaluated by Eq. (1.59) by the symbol rg. ... 

If a molecule has a plane of symmetry, for which the symbol is a, reflection of all the nuclei through the plane to an equal distance on the opposite side produces a configuration indistinguishable from the initial one. Figure 4.3(a) shows the two planes of symmetry, (7 (xz) and (yfyz), of H2O using conventional axis notation. Just as theyz plane, the plane of the molecule, is a plane of symmetry so any planar molecule has at least one plane of symmetry. The subscript u stands for vertical and implies that the plane is vertical with respect to the highest-fold axis, C2 in this case, which defines the vertical direction. 

Mass. The metric ton (symbol t), equal to 1000 kg, is used widely in commerce, although the megagram (Mg) is the appropriate SI unit. 

The conversion factors are presented for ready adaptation to computer readout and electronic data transmission. The factors are written as a number equal to or greater than one and less than 10, with six or fewer decimal places. The number is followed by E (for exponent), a plus or minus symbol, and two digits which indicate the power of 10 by which the number must be multiphed to obtain the correct value. Eor example ... 

In membrane separations, the product S Dj is referred to as the per-meabihty, p (kmoL/m s Pa). The rate of passage of material through a membrane is referred to as flux, with symbol J . Jj is equal to Ni in the equations given above. Generally Jj has the dimensions of velocity, m/s (more conveniently, Im/s), or conventionally as /m hr, gal/ft day, or ftVft day. For most apphcations, throughput is expressed in volumes instead of moles or mass. 

Sedimentation coefficients are a measure of the velocity witli which a particle sediments in a centrifugal force field. Sedimentation coefficients are typically expressed in Svedbergs (.symbolized S), named to honor The Svedberg, developer of the ultracentrifuge. One S equals 10 . sec. 

In order to make a body of mass m undergo an acceleration a, a force F is required that is equal to the product of the mass times the acceleration. In symbols... 

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