## Mathematical Formulas, Units, and Time and Date

### Mathematical Formulas and Terms

Mathematical formulas can appear as display equations or in-line equations. Display equations are centered on their own line and are usually numbered but do not have to be. In-line equations appear in running text. When citing display equations in text, use either Eq. ( ) or ( ) consistently; do not mix the two styles.

When using Microsoft Word to prepare a manuscript, use MathType for display equations and other complicated mathematical expressions. Equation numbers should be given outside of MathType and surrounded by parentheses, such as (1). In-line equations and uncomplicated expressions may be entered using MathType or typing directly from the keyboard. In-line equations should not be built up or stacked; instead, use fencing to make clear the order of calculation.

The AMS fencing hierarchy is {[( )]}: for instance, (a + 10){[b + (c + 5)]/(d − 12)}. Deviations are allowed only if the usage is defined (e.g., “square brackets indicate a time mean”). The sequence may be repeated if more than three levels of fencing are needed.

Use AMS style for variables consistently in text, equations, figures, and tables. They should be set as Times New Roman, although some exceptions apply such as script letters and matrix characters.

Character type
Typeface
Example
Notes/exceptions
Single-character scalar variable, index, or constant
Italic
t, u, w, x, y, z, υ, θ, i, j, CD
Greek upsilon is used for the lowercase italic vee (v) to avoid confusion with the Greek letter nu (𝜈).
Multiple-character scalar variable, abbreviation, nondimensional number, or acronym
Regular/nonitalic
Re, Ro, abs, max, min, Re, Im

Vector (Roman letters)
Boldface nonitalic
V, v, x, i, j, k
Boldface type replaces an arrow above a vector.
Matrix (Roman letters)
Boldface Arial or Helvetica
A, B, M

Vector and matrix (Greek letters)
Boldface
𝛌, 𝛕, 𝚪, 𝛀
Italic if lowercase and nonitalic if uppercase. Boldface type replaces an arrow above a vector.
Operators
Regular/nonitalic
sin, cos, arctan, tanh, sgn, const, c.c.
“On the order of” or "Order of" is set italic: O( ). Units are placed outside the parentheses. For complicated arguments to exponential functions, use exp( ) instead of e( ).

### Units, Time, and Date

Units should be SI with the exception of several approved non-SI units (e.g., cfs, mb). Use unit abbreviations only when preceded by a numeral. Set units in Times New Roman font with spaces between components of compound units. Use negative signs for denominators. For example, 5 meters per second should be set as 5 m s−1.

It is AMS style to hyphenate number–unit pairs when they are used to modify a noun, for example, “10-km length; 5-day intervals”; we omit the hyphen in number–unit pairs that are not used as modifiers, for example, “the trench is 75 m deep; a height of 12 m.”

The recommended time annotation is coordinated universal time. Please use UTC instead of Z or GMT. Other time zones are permitted if they are defined. Four-digit astronomical or military time (i.e., 24-hour clock) is required.

Dates must be written in “Day Month Year” format. Abbreviations for months are permitted only in figures, tables, and their captions.

For example, AMS style for May 3, 2015 at 3:00 p.m. GMT is 1500 UTC 3 May 2015.