We present the basics of number theory emphasizing the striking similarity between the properties of usual integers and those of polynomials over a finite field. This leads to understanding that number theory and algebraic geometry is in fact one and the same domain. The core of number theory being an elementary problem, we stick to concrete examples. ... P-adic numbers. ... Algebraic number fields. ... Geometry of numbers. ... S. Lang, Algebraic number theory, Springer, 1994. ...

This document describes how number input can be given to tasks which request numbers from Hermes. ... list selection The following constants are implemented: pi 3.14159.... c speed of light (SI) h Planck (SI) k Boltzmann (SI) g gravitation (SI) s Stefan-Boltzman (SI) m mass of sun (SI) p parsec (SI) BLANK Universal undefined value The following mathematical functions are implemented: abs(x) absolute value of x sqrt(x) square root of x sin(x) sine of x asin(x) inverse sine ...

... Abstract Convert a spacecraft clock format string to number of "ticks". ... Detailed_Input sc is the NAIF ID number for the spacecraft whose clock string is being converted. clkstr is a character string representing a spacecraft clock time, WITHOUT PARTITION NUMBER. ... scencd_c converts a clock string to the number of ticks it represents since the beginning of the mission, and so uses partition information. sctiks_c just converts to absolute ticks. ... The SCLK string includes a partition number. ...

... Basic time functions . ... Example 2: Set a random number seed . ... Uses of time functions include: . ... time_t time(time_t *tloc) -- returns the time since 00:00:00 GMT, Jan. 1, 1970 , measured in seconds. ... timer.c */ #include <stdio.h> #include <sys/types.h> #include <time.h> main() { int i; time_t t1,t2; (void) time(&t1); for (i=1;i<=300;++i) printf(``%d %d %d n'',i, i*i, i*i*i); (void) time(&t2); printf(`` n Time to do 300 squares and cubes= %d seconds n'', (int) t2-t1); } . ...

... The event object contains properties that describe a JavaScript event, and is passed as an argument to an event handler when the event occurs. Client-side object . ... See Chapter 3, "Event Handlers," for complete information about event handlers. For more information on handling events, see the Client-Side JavaScript Guide . ... Setting any property of this object requires the UniversalBrowserWrite privilege. ... For information on security, see the Client-Side JavaScript Guide . ... event . ...

... Counts) for an RGS source, overlaying the source dependent energy and wavelength scales. The data can be represented in original format, or rebinned, to contain a minimum number of counts (speci ed by the user) per bin, with a minimum of 1 count/bin and a minimum number of bins equal to ve otherwise a warning is raised and no rebinning takes place, see Section 5. ... The error values are plotted in gray and are always the square root of the counts. ...

... Co-ordinate systems description . Directories structure . The file names' construction . The file set description . ... The orbital information for each month is presented in the separate directory. The INTERBALL orbital data are located on the STDA server, for each month in the separate subdirectory, which name consists from the year (YYYY) and month (MM) numbers. The Parent Directory of the Tail Probe orbital data is http://www.iki.rssi.ru/da/interball/tail/orbit/ . ...

... The numbers of three types of compact binaries containing accreting NSs and BHs, which are most interesting from the point of view of their observational appearances, have been calculated as a function of time: i) X-ray transient source containing a NS in an eccentric orbit around a main sequence Be-star (the observed prototype: A0535+26), ii) BH The evolution of the selected types of X-ray binaries during the first 10 million years after the starburst onset is presented in Fig. ...

... MAXLEN parameter specifies maximum length of the number considered as a 'good' integer. ... If REJECTLONG = FALSE (default), than dictionary returns prefixed part of integer number with length MAXLEN . ... This is a dict_tmpl.c file. # include postgres.h # include utils/builtins.h # include fmgr.h #ifdef PG_MODULE_MAGIC PG_MODULE_MAGIC; #endif # include utils/ts_locale.h # include utils/ts_public.h # include utils/ts_utils.h typedef struct { int maxlen ; bool rejectlong ; } ...

Present section contains two Tables: the first one lists the names of all minor planets in alphabetic order as of the last updating of the Table. ... For each minor planet the Table, apart from number represents also the name of minor planet, if any, and its principal preliminary designation. ... Apart these preliminary designations special ones are used for minor planets discovered in the course of special surveys, undertaken between 1960 and 1977. ... Survey . ... Second Trojan Survey (1973) . ...

... Circle area is proportional to the number of tweets + retweets tweets retweets . Order accounts: by user number (effectively random) by number of tweets (includes retweets) by number of followers by number of followers that also tweeted about AAS223 by number of friends that also tweeted about AAS223 . ... The top/left position is for the user with the largest number of followers, and the bottom/right is for the smallest number of followers. by number of followers that also tweeted about AAS223 . ...

Unknown numbers are usually represented by letters of the alphabet . ... However, different letters are also used, often hinting at the quantity they represent-- v for an unknown velocity, T for an unknown time, m or M for unknown masses and F for an unknown force. ... An example of case (#1) is the ratio between the length of a circle and its diameter, a universal constant appearing in many equations (for example, Kepler's equation in section (12a)), whose value to 11 decimals is 3.14159265359.. ...

... Document Title | Document Number | ... The code uses fields: category, system, subsystem, EMA, vendor, and a sequential number. ... Previous Document Number This is a TEXT field and represents the document number that preceeds the found document in the set of original documents supplied by the engineer/vendor. ... Next Document Number This is a TEXT field and represents the document number that follows the found document in the set of original documents supplied by the engineer/vendor. ...

... The tension in members of the telescope changes as we move the dome, ch, azimuth, and tiedown tensions. The lifetime of a beam is counted in the number of times the change in tension goes through a cycle. ... Examples of telescope motion with corresponding unbalanced moment. ... The number of cycles were computed for : 5000, 10000, 15000, 20000 kipFeet momemnt change. ... The number of cycles on the telescope was computed using the change in the unbalanced moment (at a corner). ... cycles . ...

... This chapter describes the functions that allow a plug-in to display a message on the status line, get agent information, and check on the current version of the Plug-in API and Communicator. ... Displaying a Status Line Message . ... The Communicator and Plug-in API major version numbers represent code release numbers, and their minor version numbers represent point release numbers. ... Differing version numbers may mean that the current Plug-in API and Communicator versions are incompatible. ...

... The begining of program -- Target function: a * b with TEXT_IO ; use TEXT_IO ; procedure EXAMPLE is package IO_INT is new INTEGER_IO ( INTEGER ) ; use IO_INT ; r,b,a: INTEGER ; begin put ( Enter unsigned number 'b', please ... unsigned number 'a', please: ) ; get ( a ) ; declare VAR0 , VAR1 : INTEGER ; begin VAR0 := a; VAR1 := b; declare VAR3 , VAR2 , VAR4 : INTEGER ; begin VAR3 := 0 ; VAR2 := VAR0 ; VAR4 := VAR1 ; while VAR2 /= 0 loop begin if ...

... Three is a magic number. ... You get three as a magic number. ... Give you three. That's a magic number. It takes three legs to make a tri-pod or to make a table stand. ... When it's three you can see it's a magic number. ... Multiply backwards from three times ten.> Three time ten is.. ... Three times nine is.. ... Three times six is 18, three times five is 15 . Three times four is twelve . And three times three is nine and three times two is six. ... Yeah> That's a magic number. ...

... The Dust InfraRed ToolBox (DIRT - a part of the Web Infrared ToolShed, or WITS, located at http://dustem.astro.umd.edu ) is a Java applet for modeling astrophysical processes in circumstellar shells around young and evolved stars. ... DIRT uses results from a number of numerical models of astrophysical processes, and has an AWT based user interface. ... Before refactoring, model data was represented within the user interface using Database and Record objects. ...

Permitted Context: %math . ... This is represented in HTML math by: <array> <row><item>a_11_<item>a_12_<item> <item>a_1n_ <row><item> <item> <item> <item> <row><item>a_n1_<item>a_n2_<item> <item>a_nn_ </array> . ... This is represented by: <array coldef="C+C+C+C=C"> <row><item>a_11_x_1_<item>a_12_x_2_<item> <item>a_1n_x_n_<item>b_1_ <row><item>a_21_x_1_<item>a_22_x_2_<item> <item>a_2n_x_n_<item>b_2_ <row><item colspan=5> <row><item>a_n1_x_1_<item>a_n2_x_2_<item> <item>a_nn_x_n_<item>b_n_ </array> . ...