Equations

Centre in the column (except Biol Lett, Proc B and Trans B, left-align). Break at a mathematically appropriate place, such as an operator, and align the next line(s) at the start of the equation right-hand side, on an operator or cascade the equation lines rightward. In addition, for sets of equations, vertically align qualifying statements, such as ‘if…’ or ‘when…’ with each other.

Where there are sets of equations that start in a similar way, align the equations by equals. e.g.

x₁ + y₁ = z_1,

x₂ + y₂ = z₂ + a

and x₃ + y₃ = z₃ + b + c.

Number chronologically within each section (e.g. 3.1) and right-justify the equation number in parenthesis.

• In the text, cite as, for instance, ‘equation (3.5)’, unless referring to another work, when ‘eqn’ should be used. However, if unsure, follow author’s usage as the ‘equations’ may be inequalities or matrices etc. in which case, for example, 'inequality (3.6)' or 'matrix (3.7)' should be used. 12/5/10
• Equations split into parts should be set with a right-hand brace ( } ) to encompass all the parts with one equation number.
• If one equation number is used for more than one equation, centre the number vertically across all equations to encompass all equations with the one equation number and insert a right-hand brace. However, confirm with author if necessary as it may only refer to one of the equations.
• Cite equation parts as, for instance, ‘equation (4.2)₂’ when referred to individually.
• (However, author may have a logical reason for labelling differently, for instance, ‘equation (3.4a)’ – in which case, leave as is.)
• When referred to collectively, reference as, for instance, ‘equations (6.24)’. In an appendix, use, for instance, ‘equation (B 4)’ (note the fixed – but not full – space) and for equation parts ‘equation (B 4a)’.
• If one equation runs over more than one line, align the equation number with the last line of the equation.

Do not add equation numbers. An equation number can be removed (add author query) if it appears there is no need for it; however, reference to the equation may not occur in the article itself, but might be useful for other publications.

Equations are read as part of a sentence. If display equations follow one another, use commas between them and the conjunction ‘and’ before the last one. NOTE, if there are three or more equations, place the ‘and’ aligned with the last equation, do not insert a line space. e.g.

x₁ + y₁ = z₁,

x₂ + y₂ = z₂ + a

and x₃ + y₃ = z₃ + b + c.

Punctuate within and around displayed equations; additionally, check whether the sentence following a displayed equation that ends a sentence should or should not start a new paragraph. Avoid the use of colons before equations unless the term “following” precedes it. e.g.

...the following equation:

x = y + z.

Theorem and proof environments

Theorem-like environments—theorem, lemma, corollary, assumption and proposition—should be presented as follows (first number: §; second number: counter in §; use lower-case first letter in text; no parenthesis around numbers in text):

Theorem 1.1. Let E be an orbifold C^ast-bundle over the closed spin_c orbifold Q and let D be the generalized Dirac operator on Q with coefficients in E.

Proof. Use K_λ > S_λ to translate combinators into λ-terms. For the converse, translate λx … by [x < y] … and use induction and the lemma. ■ The end-of-proof square should be flush right.

Make sure the proof is closed (and confirm with author when ‘■’ is introduced). Make sure there is sufficient spacing above and below these environments to set them apart from the body text. The end-of-proof mark should be the same size as the body of text it falls in.

Commas inside mathematical parentheses should NOT be italics, e.g. x = {y₁, y₂, y₃, …}.

The other theorem-like environments—definition, remark and example—should be presented as above, but the text should not be italic.

Subheading style is as follows:

Theorem 3.1 (Carr & da Costa (1994), theorem 6.1). Assume hypotheses 2.6–2.9 hold. Suppose that c is an admissible solution to the generalized Becker–Döring equations.