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## Mathematical Formulas, Units, and Time and Date

Because of AMS typesetting requirements, authors who use Microsoft Word to prepare their manuscripts are asked to use MathType to prepare display equations, rather than making entries directly from the keyboard. If you do not have access to MathType, please DO NOT use the “Insert ribbon, Equation/Symbol” feature of Word 2007 or newer (i.e., “Equation Builder,” which is not compatible with our typesetting system and will lead to hand rekeying of equations that may introduce errors and delay papers). Instead use the “Insert ribbon, Object pulldown, Object, Create New, Microsoft Equation 3.0” feature (i.e., “Equation Editor,” which is the default in Word 2003 and older).

Authors should attempt to visualize mathematical expressions as they will appear in print. Avoid built-up fractions and other complicated equation structures in text. Instead, have complicated expressions appear as display equations, centered on their own line. Display equations are usually numbered consecutively to facilitate their citation in text, which is done by placing the equation number in parentheses set off to the right of the equation; do this from the keyboard outside of MathType rather than as part of the MathType equation. In referring to display equations in text, please consistently use either “Eq. ()” style or just “()” style, and do not mix the two. Equations that appear in-line in running text should be kept on the line by using nesting fences and should not be built up or stacked {e.g., [(a + b)^{2} + e]/(c + d)}. Equations that are too complicated to lend themselves to this approach but do not require an equation number may be set as unnumbered display equations on their own line.

Authors can facilitate the correct typesetting of their equations by using the correct typeface for variables and by using it consistently in both text and display equations. Figures should be prepared to match. Scalar single-character symbols are set italic, Greek, or script. Examples are *u*, *υ* [note that Greek upsilon is used for italic vee (*v*) to avoid confusion with the Greek nu (*ν*) often used for viscosity, etc.], *w, x, y, z, f, g, r,* and indices such as *i* or *j*, and constants such as *C _{D}*,

*k*, or

*K*. Multiple-character scalar variables, abbreviations, nondimensional numbers, and acronyms for variables are set regular nonitalic: LWC, Re, Ro, BT, abs, obs, max, min, Re/Im (real/imaginary), and so on. For vectors, use boldface nonitalic Times Roman as in

**V**,

**v**, or

**x**and the

**i**,

**j**, and

**k**unit vectors. For matrix notation use nonitalic Ariel or Helvetica boldface font as in

**A**,

**B**, or

**M**. Make greek vectors and matrices boldface (and italic if lowercase). All mathematical operator abbreviations/acronyms are set lower case regular Roman font, except

*O*(on the order of): sin, cos, tan, tanh, cov, Pr (for probability; note same as Prandtl number), const (for constant), c.c. (complex conjugate), etc.

The following hierarchy for nesting fences is used by AMS: {[()]}, repeating the sequence as necessary if more than three levels of nesting are required. An author may deviate from this style if the usage is defined in the text (e.g., brackets for set notation or angle brackets to indicate an averaged or mean quantity). Complicated arguments to exponential functions should be expressed using “exp(…)” rather than

*e*raised to an exponent.

Units should be SI with the exception of a few approved non-SI units of wide meteorological or oceanographic usage. Units should be set in roman font using exponents (negative for denominator) rather than the forward slash and with a space between each unit in a compound set (e.g., m s^{-1} rather than m/s or ms^{-1}; note that the latter is the unit for “per millisecond”).

Day, month, and year are written in the form “26 May 1998” in AMS publications. Do not abbreviate the names of months except in figure captions or tables. The recommended time zone annotation system is universal time and is abbreviated UTC. Time, time zone, day, month, and year are written in the form “1619 UTC 26 May 1998.” The use of other time zones (please define acronym) is permissible—for instance, EST, EDT, PST, LST (local standard time), or LT (local time). Do not use Z or GMT in place of UTC. Four-digit astronomical or military time (i.e., a 24-hour clock) is required.