Double equal sign

The name of the variable to be solved for must be included at the end of the equation and separated from it by a comma. Mathematica s third kind of equal sign, a double equal sign, must be used in equations to be solved. Another use of this equal sign is in asking Mathematica to test whether an equality if true or false. The resulting output is the standard quadratic formula ... 

The Eliminate statement is used to eliminate one or more of the variables in a set of simultaneous equations. For example, to obtain a single equation in x from the set of equations above, you would type the input entry (note the double equal signs) ... 

Most of the examples of chemical equations presented in Table 4.1 include an arrow ( ) symbol. This implies a direction to the chemical change represented this is a process of reactant(s) becoming produces). However, sometimes students meet reactions where an equality sign (=) or a double-headed arrow symbol is... 

The worksheet can be made easier to look at by adding lines that separate the column labels and numbers. To create a line under the labels one moves the cell pointer to cell C7, type then =. In LOTUS the backslash ( ) serves as a repeating label prefix. Whatever is typed after the backslash is repeated until it fills the cell. After pressing RETURN cell C7 now contains a row of equal signs ( = ). To continue the double line across the worksheet from cell C7 to cell 07 one can use the / Copy Command. 

Bonds are specified using hyphens (-) for single bonds, equals signs (=) for double bonds, hash marks ( ) for triple bonds, and colons ( ) for aromatic bonds. Single bonds may be omitted and are implied between two following atom symbols. For example, both C-C=C and CC=C represent propene. 

In terms of the boundary-layer variable Y, the outer edge of the boundary-layer corresponds to a very large value of Y, but, as we can see from (4-167), this corresponds to an arbitrarily small value of the core variable y. The symbolic representation for matching is the double-ended arrow <=>. This is intended to distinguish it from a numerical equal sign. 

Bonds single bonds are represented by a simple dash (-), double bonds by an equal sign, and triple bonds by the symbol. Thus, C=C is ethylene C C is acetylene and hydrogen cyanide IS C N. 

The zeta-potential is frequently used to predict the stability of a suspension or the adhesion of suspended particles on macroscopic surfaces (e.g. cellulose fibres, tubing). This is because double layer interaction between particles or between particles and surfaces is governed by the ion distribution in the diffuse layer, which primarily depends on the Debye-Hiickel parameter k and the diffuse layer potential i/ d- The latter, however, is commonly approximated by the zeta potential f (Lyklema 2010, cf. Fig. 3.3). It is quite obvious that repulsion requires high zeta-potential values of equal sign, whereas adhesion occurs in the absence of surface charge or for oppositely charged surfaces. 

To emphasise the analogy with mathematical equations, so far the equality sign (=) was always used for chemical equations. From now on, arrows will be used for one-way or irreversible chemical reactions (like A —> B). Reversible reactions will be denoted by double arrows (like A B). 

Note 2.2 - It should be noted that in an elementary reaction, the equals sign (=) between the reactants and the products is replaced by a double arrow (< =>), which means that we are dealing with two opposite elementary reactions. A single arrow (—> ) is often used in order to indicate the preferred direction of progress of the reaction. So, a chemical equation with arrows, for an elementary step, is a molecular equation (then the molecules can be cut). This is not a molar equation like the classical chemical reactions. 

The total charge of the compact and diffuse layers equals (and is opposite in sign to) the net charge on the electrode side. The potential-distance profile across the double-... 

Here, the sign of equality (=) has been replaced by the double oppositely directed arrows (s=) called a sign of reversibility. Such a reaction is called a reversible reaction. The reversibility of reactions can be detected when both the forward and the reverse reactions occur to a noticeable extent. Generally, such reactions are described as reversible reactions. The most important criterion of a reaction of this type is that none of the reactants will become exhausted. When the reaction is allowed to take place in a closed system from where none of the substances involved in the reaction can escape, one obtains a mixture of the reactants and the products in the reaction vessel. Every reversible reaction, depending on its nature, will after some time reach a stage when the reactants and the products coexist in a state of balance, and their amounts will remain unaltered for unlimited time. Such a state of a chemical reaction is called chemical equilibrium, and the point of such an equilibrium varies only with temperature. 

Note that the sum must be doubled because there are two electrons in every occupied MO, as this analysis assumes that the system has equal numbers of electrons with spins of opposite sign. 

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