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The degree of a monomial is defined as the sum of all the exponents of the variables, including the implicit exponents of 1 for the variables which appear without exponent; e.g., in the example of the previous section, the degree is + +. The degree of is 1+1+2=4. The degree of a nonzero constant is 0.
This glossary of chemistry terms is a list of terms and definitions relevant to chemistry, including chemical laws, diagrams and formulae, laboratory tools, glassware, and equipment. Chemistry is a physical science concerned with the composition, structure, and properties of matter , as well as the changes it undergoes during chemical reactions ...
The leading term of a nonzero polynomial [,, …,], denoted by () is the monomial term of maximal order in and the leading term of = is . The ideal of leading terms , denoted by L T ( I ) {\displaystyle LT(I)} , is the ideal generated by the leading terms of every element in the ideal, that is, L T ( I ) = ( L T ( f ) ∣ f ∈ I ...
When a monomial order has been chosen, the leading monomial is the largest u in S, the leading coefficient is the corresponding c u, and the leading term is the corresponding c u u. Head monomial/coefficient/term is sometimes used as a synonym of "leading". Some authors use "monomial" instead of "term" and "power product" instead of "monomial".
Chemical nomenclature however (with IUPAC nomenclature as the best example) is necessarily more restrictive: Its purpose is to standardize communication and practice so that, when a chemical term is used it has a fixed meaning relating to chemical structure, thereby giving insights into chemical properties and derived molecular functions. These ...
The mole is widely used in chemistry as a convenient way to express amounts of reactants and amounts of products of chemical reactions. For example, the chemical equation 2 H 2 + O 2 → 2 H 2 O can be interpreted to mean that for each 2 mol molecular hydrogen (H 2) and 1 mol molecular oxygen (O 2) that react, 2 mol of water (H 2 O) form.
A monomial is a polynomial with one term while two- and three-term polynomials are called binomials and trinomials. The degree of a polynomial is the maximal value (among its terms) of the sum of the exponents of the variables (4 in the above example). [ 32 ]
Electrons in solids have a chemical potential, defined the same way as the chemical potential of a chemical species: The change in free energy when electrons are added or removed from the system. In the case of electrons, the chemical potential is usually expressed in energy per particle rather than energy per mole, and the energy per particle ...