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In calculations requiring satellite predictions, it is necessary to determine whether a year is a leap year or not, and the simple rule is: If the year number ends in two zeros and is divisible by 400 without remainder, it is a leap year. Otherwise, if the year number is divisible by 4 without remainder, it is a leap year.

Hex(ExprN) Returns a string that contains the hexadecimal representation of the integer resulting from ExprN. If ExprN is not numeric an error is issued. If ExprN is not integer it will be converted to integer. Bin(ExprN) Returns a string that contains the binary representation of the integer resulting from ExprN. If ExprN is not numeric an error is issued. If ExprN is not integer it will be converted to integer. The number of bits will depend on the value of ExprN. There will be no leading zeros. So Bin(7) will return 111 while Bin(3) will return 11 and Bin(4) gives 100. If the number must be a xed number of bits with leading zeros then use the sRepeat() and Length() functions below. For example, to return a 10-bit binary of a number with leading zeros do sRepeat( 0 ,10-length(bin(5))+bin(5) => 0000000101.

Example 2.8 Determine which of the following years are leap years: (a) 1987, (b) 1988, (c) 2000, (d) 2100.

Fig 23-3 From Fig 23-1 we see that if we move from left to right along a curve that is concave upward, the slope of the tangent line increases The slope either becomes less negative or more positive Conversely, if the tangent line has this property, the curve must be concave upward Now for a curve y = f (x), the tangent line will certainly have this property if f (x) > 0 since, in that case, Theorem 173 implies that the slope f (x) of the tangent line will be an increasing function By a similar argument, we see that if f (x) < 0, the slope of the tangent line is decreasing, and from Fig 23-2 we see that the curve y = f (x) is concave downward This yields: Theorem 23.

IsNumber(Expr) If Expr is a string that can be converted to a numeric or is a numeric returns 1, otherwise returns 0. IsString(Expr) If Expr is a string (regardless of whether it can be converted to a number or not) returns 1, otherwise returns 0. ToNumber(Expr) Returns the resulting string expression as a number if possible, otherwise it will return the string unconverted. If Expr results in a number then that number is returned. ToString(Expr) If Expr results in a number it converts the number to a string and returns the value as a string. If Expr results in a string then the string is returned. Ascii(ExprS) Returns the ASCII code of the rst character in ExprS.

(a) 1987/4 (b) 1988/4 (c) 2000/400

496.75 (therefore, 1987 is not a leap year) 497 (therefore, 1988 is a leap year) 5 (therefore, 2000 is a leap year)

Char(ExprN) Returns a string of one character which is the character whose ASCII code is ExprN. Format(ExprN,ExprS) Returns a string containing ExprN formatted according to ExprS. (See Sec. C.8.14) C.8.8 STRING MANIPULATION FUNCTIONS Length(ExprS) Trim(ExprS) Returns the length of the resulting string from ExprS.

1: If f (x) > 0 for all x in (a, b), then the graph of f is concave upward between x = a and x = b If f (x) < 0 for all x in (a, b), then the graph of f is concave downward between x = a and x = b For a rigorous proof of Theorem 231, see Problem 2317 Corollary 232: If the graph of f has an in ection point at x = c, and f exists and is continuous at x = c, then f (c) = 0 In fact, if f (c) = 0, then f (c) > 0 or f (c) < 0.

(d) 2100/400 5.25 (therefore, 2100 is not a leap year, even though 2100 is divisible by 4 without remainder)

Returns ExprS without leading or trailing spaces. Returns ExprS without leading space. Returns ExprS without trailing spaces.

Universal time coordinated (UTC) is the time used for all civil time keeping purposes, and it is the time reference which is broadcast by the National Bureau of Standards as a standard for setting clocks. It is based on an atomic time-frequency standard. The fundamental unit for UTC is the mean solar day (see App. J in Wertz, 1984). In terms of clock time, the mean solar day is divided into 24 h, an hour into 60 min, and a minute into 60 s. Thus there are 86,400 clock seconds in a mean solar day. Satellite-orbit epoch time is given in terms of UTC.