Shorthand

Dirac showed in 1928 dial a fourth quantum number associated with intrinsic angidar momentum appears in a relativistic treatment of the free electron, it is customary to treat spin heiiristically. In general, the wavefimction of an electron is written as the product of the usual spatial part (which corresponds to a solution of the non-relativistic Sclnodinger equation and involves oidy the Cartesian coordinates of the particle) and a spin part a, where a is either a or p. A connnon shorthand notation is often used, whereby... 

The shorthand notation in the rhs of equation (A3.6.5) is frequently referred to as the Leffler-Gnmwald operator [7]. 

A quite successful integrator for (16), which is based on the idea of operator splitting, is the PICKABACK scheme of Nettesheim et al. [19]. With the shorthand notation... 

Besides specifications on atoms, bonds, branches, and ring closure, SLN additionally provides information on attributes of atoms and bonds, such as charge or stereochemistry. These are also indicated in square [ ] or angle < > brackets behind the entity e.g., trans-butane CH3CH=[s=t]CHCH3). Furthermore, macro atoms allow the shorthand specification of groups of atoms such as amino adds, e.g., Ala, Protein2, etc. A detailed description of these specifications and also specifications for 2D substructure queries or combinatorial libraries can be found in the literature [26]. 

The commercial 2D structure editor. Chemistry 4D-Draw, from Chemlnnovativc Software Inc., includes two additional special modules besides conventional chemical drawing tools. NamExpert provides the interpretation ofa compound name according to the lUPAC nomenclature to create the corresponding chemical structure. The latter can be represented in three different styles the shorthand. Kckulc. or semi-structural formula. In contrast to NamExpert, the Nomenclature module assigns lUPAC names to drawn structures. 

For any sizeable system the Slater determinant can be tedious to write out, let alone the equivalent full orbital expansion, and so it is common to use a shorthand notation. Various notation systems have been devised. In one system the terms along the diagonal of the matrix are written as a single-row determinant. For the 3x3 determinant we therefore have ... 

We have used the shorthand notation for the integrals in the final expression. Note that the two-electron integrals may involve up to four different basis functions /x, v, A, a), which may in turn be located at four different centres. This has important consequences for the way in which we try to solve the equations. 

The full Hamiltonian H thus eontains differential operators over the 3N eleetronie eoordinates (denoted r as a shorthand) and the 3M nuelear eoordinates (denoted R as a shorthand). In eontrast, the eleetronie Hamiltonian Hg is a Hermitian differential operator in... 

The circle m a hexagon symbol was first suggested by the British chemist Sir Robert Robinson to represent what he called the aromatic sextet —the six delocalized TT electrons of the three double bonds Robinson s symbol is a convenient time saving shorthand device but Kekule type formulas are better for counting and keeping track of electrons especially m chemical reactions... 

The strength of this bonding depends on the kind of ether Simple ethers form relatively weak complexes with metal ions but Charles J Pedersen of Du Pont discovered that cer tain polyethers form much more stable complexes with metal ions than do simple ethers Pedersen prepared a series of macrocyclic polyethers cyclic compounds contain mg four or more oxygens m a ring of 12 or more atoms He called these compounds crown ethers, because their molecular models resemble crowns Systematic nomencla ture of crown ethers is somewhat cumbersome and so Pedersen devised a shorthand description whereby the word crown is preceded by the total number of atoms m the ring and is followed by the number of oxygen atoms... 

The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

A shorthand method for expressing very large or very small numbers by indicating powers of ten for example, 1000 is 1 X 103. 

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... 

What are the anodic, cathodic, and overall reactions responsible for the potential in the electrochemical cell shown here Write the shorthand notation for the electrochemical cell. 

Potentiometric electrochemical cells are constructed such that one of the half-cells provides a known reference potential, and the potential of the other half-cell indicates the analyte s concentration. By convention, the reference electrode is taken to be the anode thus, the shorthand notation for a potentiometric electrochemical cell is... 

Standard Hydrogen Electrode The standard hydrogen electrode (SHE) is rarely used for routine analytical work, but is important because it is the reference electrode used to establish standard-state potentials for other half-reactions. The SHE consists of a Pt electrode immersed in a solution in which the hydrogen ion activity is 1.00 and in which H2 gas is bubbled at a pressure of 1 atm (Figure 11.7). A conventional salt bridge connects the SHE to the indicator half-cell. The shorthand notation for the standard hydrogen electrode is... 

The saturated calomel electrode (SCE), which is constructed using an aqueous solution saturated with KCl, has a potential at 25 °C of -hO.2444 V. A typical SCE is shown in Eigure 11.8 and consists of an inner tube, packed with a paste of Hg, HgiCli, and saturated KCl, situated within a second tube filled with a saturated solution of KCl. A small hole connects the two tubes, and an asbestos fiber serves as a salt bridge to the solution in which the SCE is immersed. The stopper in the outer tube may be removed when additional saturated KCl is needed. The shorthand notation for this cell is... 

A typical Ag/AgCl electrode is shown in figure 11.9 and consists of a silver wire, the end of which is coated with a thin film of AgCl. The wire is immersed in a solution that contains the desired concentration of KCl and that is saturated with AgCl. A porous plug serves as the salt bridge. The shorthand notation for the cell is... 

Membrane Potentials Ion-selective electrodes, such as the glass pH electrode, function by using a membrane that reacts selectively with a single ion. figure 11.10 shows a generic diagram for a potentiometric electrochemical cell equipped with an ion-selective electrode. The shorthand notation for this cell is... 

Force per unit area along the axis of the deformation is called the uniaxial tension or stress. We shall use the symbol a as a shorthand replacement for F/A and attach the subscript t to signify tension. The elongation, expressed as a fraction of the original length AL/Lq is called the strain. We shall use 7j as the symbol for the resulting strain (subscript t for tension). Both o... 

A shorthand designation for fatty acids is used. For example, 18 0 = saturated C g 18 1 = acid with one double bond 18 2 = Cjg acid with two... 

Similarly, the relationship between the n outputs, and the current values of the controlled variables,i, can be written as a matrix comparable to the inputs, which in matrix shorthand is... 

Fig. 9. Partial structural formulas and shorthand notations for principal hemiceUuloses found in wood, where the sugar units ate noted as P-D-xylopyranose (Xylp), 4-Omethyl-a-D-glucopyranosyluronic acid (GlupU), a-L-arabinofuranose (Araf), P-D-glucopyranose (Glup), P-D-mannopyranose (Manp), and P-D-galactopyranose (Galp) for (a) arabino-4-O-methylglucuronoxylan from softwood, (b) 0-acetyl-galactoglucomannan from softwood, and...

Although equation 35 is a simple expression, it tends to be confusing. In this equation the enthalpy difference appears as driving force in a mass-transfer expression. Enthalpy is not a potential, but rather an extensive thermodynamic function. In equation 35, it is used as enthalpy pet mole and is a kind of shorthand for a combination of temperature and mass concentration terms. 

Shorthand notations have been developed to avoid repetitive systematic names of unsaturated fatty acids. Eor example, linolenic or (7j -9,i7j -12-,i7j -15-octadecatrienoic acid can be represented by 18 3(9, 12, 15 ). The Greek letter A has been used to indicate presence and position of double bonds, eg a fatty acid, but it should never be used in a systematic name. An equally inappropriate but popular designation is derived by counting... 

Technical language and jargon are useful as professional shorthand, but they are barriers to successful communication with the public. Use simple, nontechnical language and vivid, concrete images that communicate on a personal level. Avoid distant, abstract, unfeeling language about deaths, injuries, and illnesses. 

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