Mensural notation recoverable from the modern text. While 19th and early 20th century editions of Renaissance music often preserved the large note values of the originals, including breves and longs, most modern editions will use scaled-down note values in order to match modern reading habits regarding tempo and beat structure. For 16th century music, a frequent scheme is diminution by a factor of 2 (i.e., rendering semibreves as modern minims), in a modern "alla breve" bar. Older music might be diminished by a factor of 4 (rendering semibreves as crotchets) or sometimes 8 (rendering breves as crotchets). For 13th-century pieces, diminution by
Time value of money is to emphasize that "u" is a "parameter" (fixed in any instance—the time when the cash flow will occur), while "t" is a "variable" (time). In other words, future cash flows are exponentially discounted (exp) by the sum (integral, formula_44) of the future discount rates (formula_45 for future, "r"("v") for discount rates), while past cash flows are worth 0 (formula_46), because they have already occurred. Note that the value "at" the moment of a cash flow is not well-defined – there is a discontinuity at that point, and one can use a convention (assume cash flows have already occurred, or