PHP Date add 1 month
This example shows you how one month can be added to a PHP Date object. Date manupulation is one of the basic requirement of any business application. Example explained here can be used easily.
Code example to add 1 month:
//PHP Example code to add one moth to a date
$todayDate = date("Y-m-d");// current date
echo "Today: ".$todayDate;
//Add one day to today
$dateOneMonthAdded = strtotime(date("Y-m-d", strtotime($todayDate)) . "+1 month");
echo "After adding one month: ".date('l dS \o\f F Y', $dateOneMonthAdded);
The output of the program:
Today: 2009-08-25
After adding one month: Friday 25th of September 2009
Sai Gopal Wordpress Blog
Saigopal's website
My Daughter Website
Palwow
Friday, September 17, 2010
HTML Forms : RADIO BUTTON
RADIO BUTTON - Printable Version
- Send Page To Friend
Radio buttons are used when you want to let the visitor select one - and just one - option from a set of alternatives. If more options are to be allowed at the same time you should use
check boxes instead.
--------------------------------------------------------------------------------
SETTINGS:
Below is a listing of valid settings for radio buttons:
The name setting tells which group of radio buttons the field belongs to. When you select one button, all other buttons in the same group are unselected.
If you couldn't define which group the current button belongs to, you could only have one group of radio buttons on each page.
The value setting defines what will be submitted if checked.
The align setting defines how the field is aligned.
Valid entries are: TOP, MIDDLE, BOTTOM, RIGHT, LEFT, TEXTTOP, BASELINE, ABSMIDDLE, ABSBOTTOM.
The alignments are explained in the image section. You can learn about the different alignments here.
The tabindex setting defines in which order the different fields should be activated when the visitor clicks the tab key.
- Send Page To Friend
Radio buttons are used when you want to let the visitor select one - and just one - option from a set of alternatives. If more options are to be allowed at the same time you should use
check boxes instead.
--------------------------------------------------------------------------------
SETTINGS:
Below is a listing of valid settings for radio buttons:
The name setting tells which group of radio buttons the field belongs to. When you select one button, all other buttons in the same group are unselected.
If you couldn't define which group the current button belongs to, you could only have one group of radio buttons on each page.
The value setting defines what will be submitted if checked.
The align setting defines how the field is aligned.
Valid entries are: TOP, MIDDLE, BOTTOM, RIGHT, LEFT, TEXTTOP, BASELINE, ABSMIDDLE, ABSBOTTOM.
The alignments are explained in the image section. You can learn about the different alignments here.
The tabindex setting defines in which order the different fields should be activated when the visitor clicks the tab key.
set commands in oracle sql plus
SQL*PLUS - SET Statement
Set sqlplus system settings and defaults.
Syntax:
SET option value
SHO[W] option
Options: most of the options listed below have an abbreviated and a long form
e.g. APPINFO or APPI will do the same thing
APPI[NFO]{ON|OFF|text}
Application info for performance monitor (see DBMS_APPLICATION_INFO)
ARRAY[SIZE] {15|n}
Fetch size (1 to 5000) the number of rows that will be retrieved in one go.
AUTO[COMMIT] {OFF|ON|IMM[EDIATE]|n}
Autocommit commits after each SQL command or PL/SQL block
AUTOP[RINT] {OFF|ON}
Automatic PRINTing of bind variables.(see PRINT)
AUTORECOVERY [ON|OFF]
Configure the RECOVER command to automatically apply
archived redo log files during recovery - without any user confirmation.
AUTOT[RACE] {OFF|ON|TRACE[ONLY]} [EXP[LAIN]] [STAT[ISTICS]]
Display a trace report for SELECT, INSERT, UPDATE or DELETE statements
EXPLAIN shows the query execution path by performing an EXPLAIN PLAN.
STATISTICS displays SQL statement statistics.
Using ON or TRACEONLY with no explicit options defaults to EXPLAIN STATISTICS
BLO[CKTERMINATOR] {.|c|OFF|ON}
Set the non-alphanumeric character used to end PL/SQL blocks to c
CMDS[EP] {;|c|OFF|ON}
Change or enable command separator - default is a semicolon (;)
COLSEP { |text}
The text to be printed between SELECTed columns normally a space.
COM[PATIBILITY] {V5|V6|V7|V8|NATIVE}
Version of oracle - see also init.ora COMPATIBILITY=
You can set this back by up to 2 major versions e.g. Ora 9 supports 8 and 7
CON[CAT] {.|c|OFF|ON}
termination character for substitution variable reference
default is a period.
COPYC[OMMIT] {0|n}
The COPY command will fetch n batches of data between commits.
(n= 0 to 5000) the size of each fetch=ARRAYSIZE.
If COPYCOMMIT = 0, COPY will commit just once - at the end.
COPYTYPECHECK {OFF|ON}
Suppres the comparison of datatypes while inserting or appending to DB2
DEF[INE] {&|c|OFF|ON}
c = the char used to prefix substitution variables.
ON or OFF controls whether to replace substitution variables with their values.
(this overrides SET SCAN)
DESCRIBE [DEPTH {1|n|ALL}][LINENUM {ON|OFF}][INDENT {ON|OFF}]
Sets the depth of the level to which you can recursively describe an object
(1 to 50) see the DESCRIBE command
ECHO {OFF|ON}
Display commands as they are executed
EMB[EDDED] {OFF|ON}
OFF = report printing will start at the top of a new page.
ON = report printing may begin anywhere on a page.
ESC[APE] {\|c|OFF|ON}
Defines the escape character. OFF undefines. ON enables.
FEED[BACK] {6|n|OFF|ON}
Display the number of records returned (when rows >= n )
OFF (or n=0) will turn the display off
ON will set n=1
FLAGGER {OFF|ENTRY|INTERMED[IATE]|FULL}
Checks to make sure that SQL statements conform to the ANSI/ISO SQL92 standard.
non-standard constructs are flagged as errors and displayed
See also ALTER SESSION SET FLAGGER.
FLU[SH] {OFF|ON}
Buffer display output (OS)
(no longer used in Oracle 9)
HEA[DING] {OFF|ON}
print column headings
HEADS[EP] {||c|OFF|ON}
Define the heading separator character (used to divide a column heading onto > one line.)
OFF will actually print the heading separator char
see also: COLUMN command
INSTANCE [instance_path|LOCAL]
Change the default instance for your session, this command may only be issued when
not already connected and requires Net8
LIN[ESIZE] {150|n}
Width of a line (before wrapping to the next line)
Earlier versions default to 80, Oracle 9 is 150
LOBOF[FSET] {n|1}
Starting position from which CLOB and NCLOB data is retrieved and displayed
LOGSOURCE [pathname]
Change the location from which archive logs are retrieved during recovery
normally taken from LOG_ARCHIVE_DEST
LONG {80|n}
Set the maximum width (in chars) for displaying and copying LONG values.
LONGC[HUNKSIZE] {80|n}
Set the fetch size (in chars) for retrieving LONG values.
MARK[UP] HTML [ON|OFF]
[HEAD text] [BODY text] [TABLE text]
[ENTMAP {ON|OFF}][SPOOL {ON|OFF}]
[PRE[FORMAT] {ON|OFF}]
Output HTML text, which is the output used by iSQL*Plus.
NEWP[AGE] {1|n}
The number of blank lines between the top of each page and the top title.
0 = a formfeed between pages.
NULL text
Replace a null value with 'text'
The NULL clause of the COLUMN command will override this for a given column.
NUMF[ORMAT] format
The default number format.
see COLUMN FORMAT.
NUM[WIDTH] {10|n}
The default width for displaying numbers.
PAGES[IZE] {14|n}
The height of the page - number of lines.
0 will suppress all headings, page breaks, titles
PAU[SE] {OFF|ON|text}
press [Return] after each page
enclose 'text' in single quotes
RECSEP {WR[APPED]|EA[CH]|OFF}
Print a single line of the RECSEPCHAR between each record.
WRAPPED = print only for wrapped lines
EACH=print for every row
RECSEPCHAR {_|c}
Define the RECSEPCHAR character, default= ' '
SCAN {OFF|ON}
OFF = disable substitution variables and parameters
SERVEROUT[PUT] {OFF|ON} [SIZE n] [FOR[MAT] {WRA[PPED]|WOR[D_WRAPPED]|TRU[NCATED]}]
whether to display the output of stored procedures (or PL/SQL blocks)
i.e., DBMS_OUTPUT.PUT_LINE
SIZE = buffer size (2000-1,000,000) bytes
SHOW[MODE] {OFF|ON}
Display old and new settings of a system variable
SPA[CE] {1|n}
The number of spaces between columns in output (1-10)
SQLBL[ANKLINES] {ON|OFF}
Allow blank lines within an SQL command. reverts to OFF after the curent command/block.
SQLC[ASE] {MIX[ED]|LO[WER]|UP[PER]}
Convert the case of SQL commands and PL/SQL blocks
(but not the SQL buffer itself)
SQLPLUSCOMPAT[IBILITY] {x.y[.z]}
Set the behavior or output format of VARIABLE to that of the
release or version specified by x.y[.z].
SQLCO[NTINUE] {> |text}
Continuation prompt (used when a command is continued on an additional line using a hyphen -)
SQLN[UMBER] {OFF|ON}
Set the prompt for the second and subsequent lines of a command or PL/SQL block.
ON = set the SQL prompt = the line number.
OFF = set the SQL prompt = SQLPROMPT.
SQLPRE[FIX] {#|c}
set a non-alphanumeric prefix char for immediately executing one line of SQL (#)
SQLP[ROMPT] {SQL>|text}
Set the command prompt.
SQLT[ERMINATOR] {;|c|OFF|ON}|
Set the char used to end and execute SQL commands to c.
OFF disables the command terminator - use an empty line instead.
ON resets the terminator to the default semicolon (;).
SUF[FIX] {SQL|text}
Default file extension for SQL scripts
TAB {OFF|ON}
Format white space in terminal output.
OFF = use spaces to format white space.
ON = use the TAB char.
Note this does not apply to spooled output files.
The default is system-dependent. Enter SHOW TAB to see the default value.
TERM[OUT] {OFF|ON}
OFF suppresses the display of output from a command file
ON displays the output.
TERMOUT OFF does not affect the output from commands entered interactively.
TI[ME] {OFF|ON}
Display the time at the command prompt.
TIMI[NG] {OFF|ON}
ON = display timing statistics for each SQL command or PL/SQL block run.
OFF = suppress timing statistics
TRIM[OUT] {OFF|ON}
Display trailing blanks at the end of each line.
ON = remove blanks, improving performance
OFF = display blanks.
This does not affect spooled output.
SQL*Plus ignores TRIMOUT ON unless you set TAB ON.
TRIMS[POOL] {ON|OFF}
Allows trailing blanks at the end of each spooled line.
This does not affect terminal output.
UND[ERLINE] {-|c|ON|OFF}
Set the char used to underline column headings to c.
VER[IFY] {OFF|ON}
ON = list the text of a command before and after replacing substitution variables with values.
OFF = dont display the command.
WRA[P] {OFF|ON}
Controls whether to truncate or wrap the display of long lines.
OFF = truncate
ON = wrap to the next line
The COLUMN command (WRAPPED and TRUNCATED clause) can override this for specific columns.
The items in Gray on this page are deprecated from Oracle 9 onwards - also note that several of the options above have 'gone missing' from the official documentation set - HELP SET is a more accurate reference.
Get a list of these SET options in sql*plus with the command:
SQLPLUS> HELP SET
Example
A demo SQL script with the most common SET options
Related:
SQL*Plus commands
/*
Multiple line comments
Can go between these delimiters
*/
SET TERM OFF
-- TERM = ON will display on terminal screen (OFF = show in LOG only)
SET ECHO ON
-- ECHO = ON will Display the command on screen (+ spool)
-- ECHO = OFF will Display the command on screen but not in spool files.
-- Interactive commands are always echoed to screen/spool.
SET TRIMOUT ON
-- TRIMOUT = ON will remove trailing spaces from output
SET TRIMSPOOL ON
-- TRIMSPOOL = ON will remove trailing spaces from spooled output
SET HEADING OFF
-- HEADING = OFF will hide column headings
SET FEEDBACK OFF
-- FEEDBACK = ON will count rows returned
SET PAUSE OFF
-- PAUSE = ON .. press return at end of each page
SET PAGESIZE 0
-- PAGESIZE = height 54 is 11 inches (0 will supress all headings and page brks)
SET LINESIZE 80
-- LINESIZE = width of page (80 is typical)
SET VERIFY OFF
-- VERIFY = ON will show before and after substitution variables
-- Start spooling to a log file
SPOOL C:\TEMP\MY_LOG_FILE.LOG
--
-- The rest of the SQL commands go here
--
SELECT * FROM GLOBAL_NAME;
SPOOL OFF
Oracle SQL*Plus
Version 11.1
General
Note: Oracle in its near infinite wisdom dropped sqlplusw.exe from the initial release of 11gR1. If want it you can copy in the executable from 10.2.0.1 and in most cases rename the DLL oraclient11.dll to oraclient10.dll. Then you will again have a usable interface. If you are as thrilled as we are about this send us an email and we will pass it along to Oracle.
Constants Constant Usage Example
SQL.LNO Line Number SELECT COUNT(*)
FROM all_objects
WHERE SUBSTR(object_name,1,1) BETWEEN 'A' AND 'W';
show lno
SQL.PNO Page Number SELECT object_name
FROM all_objects
WHERE SUBSTR(object_name,1,1) BETWEEN 'A' AND 'W';
show pno
SQL.RELEASE Oracle Version show release
SQL.SQLCODE Current error code show sqlcode
SQL.USER Currently connected user show user
Startup Parameters: Usage 1 Flags
Description
-H Displays the SQL*Plus version and the usage help
-V Displays the SQL*Plus version
sqlplus -C | -H
Startup Parameters: Usage 2 Flags
Description
-C Sets the compatibility of affected commands to the version specified. The version has the form "x.y[.z]. For example -C 10.2.0
-L Attempts to log on just once, instead of reprompting on error
-M
Set sqlplus system settings and defaults.
Syntax:
SET option value
SHO[W] option
Options: most of the options listed below have an abbreviated and a long form
e.g. APPINFO or APPI will do the same thing
APPI[NFO]{ON|OFF|text}
Application info for performance monitor (see DBMS_APPLICATION_INFO)
ARRAY[SIZE] {15|n}
Fetch size (1 to 5000) the number of rows that will be retrieved in one go.
AUTO[COMMIT] {OFF|ON|IMM[EDIATE]|n}
Autocommit commits after each SQL command or PL/SQL block
AUTOP[RINT] {OFF|ON}
Automatic PRINTing of bind variables.(see PRINT)
AUTORECOVERY [ON|OFF]
Configure the RECOVER command to automatically apply
archived redo log files during recovery - without any user confirmation.
AUTOT[RACE] {OFF|ON|TRACE[ONLY]} [EXP[LAIN]] [STAT[ISTICS]]
Display a trace report for SELECT, INSERT, UPDATE or DELETE statements
EXPLAIN shows the query execution path by performing an EXPLAIN PLAN.
STATISTICS displays SQL statement statistics.
Using ON or TRACEONLY with no explicit options defaults to EXPLAIN STATISTICS
BLO[CKTERMINATOR] {.|c|OFF|ON}
Set the non-alphanumeric character used to end PL/SQL blocks to c
CMDS[EP] {;|c|OFF|ON}
Change or enable command separator - default is a semicolon (;)
COLSEP { |text}
The text to be printed between SELECTed columns normally a space.
COM[PATIBILITY] {V5|V6|V7|V8|NATIVE}
Version of oracle - see also init.ora COMPATIBILITY=
You can set this back by up to 2 major versions e.g. Ora 9 supports 8 and 7
CON[CAT] {.|c|OFF|ON}
termination character for substitution variable reference
default is a period.
COPYC[OMMIT] {0|n}
The COPY command will fetch n batches of data between commits.
(n= 0 to 5000) the size of each fetch=ARRAYSIZE.
If COPYCOMMIT = 0, COPY will commit just once - at the end.
COPYTYPECHECK {OFF|ON}
Suppres the comparison of datatypes while inserting or appending to DB2
DEF[INE] {&|c|OFF|ON}
c = the char used to prefix substitution variables.
ON or OFF controls whether to replace substitution variables with their values.
(this overrides SET SCAN)
DESCRIBE [DEPTH {1|n|ALL}][LINENUM {ON|OFF}][INDENT {ON|OFF}]
Sets the depth of the level to which you can recursively describe an object
(1 to 50) see the DESCRIBE command
ECHO {OFF|ON}
Display commands as they are executed
EMB[EDDED] {OFF|ON}
OFF = report printing will start at the top of a new page.
ON = report printing may begin anywhere on a page.
ESC[APE] {\|c|OFF|ON}
Defines the escape character. OFF undefines. ON enables.
FEED[BACK] {6|n|OFF|ON}
Display the number of records returned (when rows >= n )
OFF (or n=0) will turn the display off
ON will set n=1
FLAGGER {OFF|ENTRY|INTERMED[IATE]|FULL}
Checks to make sure that SQL statements conform to the ANSI/ISO SQL92 standard.
non-standard constructs are flagged as errors and displayed
See also ALTER SESSION SET FLAGGER.
FLU[SH] {OFF|ON}
Buffer display output (OS)
(no longer used in Oracle 9)
HEA[DING] {OFF|ON}
print column headings
HEADS[EP] {||c|OFF|ON}
Define the heading separator character (used to divide a column heading onto > one line.)
OFF will actually print the heading separator char
see also: COLUMN command
INSTANCE [instance_path|LOCAL]
Change the default instance for your session, this command may only be issued when
not already connected and requires Net8
LIN[ESIZE] {150|n}
Width of a line (before wrapping to the next line)
Earlier versions default to 80, Oracle 9 is 150
LOBOF[FSET] {n|1}
Starting position from which CLOB and NCLOB data is retrieved and displayed
LOGSOURCE [pathname]
Change the location from which archive logs are retrieved during recovery
normally taken from LOG_ARCHIVE_DEST
LONG {80|n}
Set the maximum width (in chars) for displaying and copying LONG values.
LONGC[HUNKSIZE] {80|n}
Set the fetch size (in chars) for retrieving LONG values.
MARK[UP] HTML [ON|OFF]
[HEAD text] [BODY text] [TABLE text]
[ENTMAP {ON|OFF}][SPOOL {ON|OFF}]
[PRE[FORMAT] {ON|OFF}]
Output HTML text, which is the output used by iSQL*Plus.
NEWP[AGE] {1|n}
The number of blank lines between the top of each page and the top title.
0 = a formfeed between pages.
NULL text
Replace a null value with 'text'
The NULL clause of the COLUMN command will override this for a given column.
NUMF[ORMAT] format
The default number format.
see COLUMN FORMAT.
NUM[WIDTH] {10|n}
The default width for displaying numbers.
PAGES[IZE] {14|n}
The height of the page - number of lines.
0 will suppress all headings, page breaks, titles
PAU[SE] {OFF|ON|text}
press [Return] after each page
enclose 'text' in single quotes
RECSEP {WR[APPED]|EA[CH]|OFF}
Print a single line of the RECSEPCHAR between each record.
WRAPPED = print only for wrapped lines
EACH=print for every row
RECSEPCHAR {_|c}
Define the RECSEPCHAR character, default= ' '
SCAN {OFF|ON}
OFF = disable substitution variables and parameters
SERVEROUT[PUT] {OFF|ON} [SIZE n] [FOR[MAT] {WRA[PPED]|WOR[D_WRAPPED]|TRU[NCATED]}]
whether to display the output of stored procedures (or PL/SQL blocks)
i.e., DBMS_OUTPUT.PUT_LINE
SIZE = buffer size (2000-1,000,000) bytes
SHOW[MODE] {OFF|ON}
Display old and new settings of a system variable
SPA[CE] {1|n}
The number of spaces between columns in output (1-10)
SQLBL[ANKLINES] {ON|OFF}
Allow blank lines within an SQL command. reverts to OFF after the curent command/block.
SQLC[ASE] {MIX[ED]|LO[WER]|UP[PER]}
Convert the case of SQL commands and PL/SQL blocks
(but not the SQL buffer itself)
SQLPLUSCOMPAT[IBILITY] {x.y[.z]}
Set the behavior or output format of VARIABLE to that of the
release or version specified by x.y[.z].
SQLCO[NTINUE] {> |text}
Continuation prompt (used when a command is continued on an additional line using a hyphen -)
SQLN[UMBER] {OFF|ON}
Set the prompt for the second and subsequent lines of a command or PL/SQL block.
ON = set the SQL prompt = the line number.
OFF = set the SQL prompt = SQLPROMPT.
SQLPRE[FIX] {#|c}
set a non-alphanumeric prefix char for immediately executing one line of SQL (#)
SQLP[ROMPT] {SQL>|text}
Set the command prompt.
SQLT[ERMINATOR] {;|c|OFF|ON}|
Set the char used to end and execute SQL commands to c.
OFF disables the command terminator - use an empty line instead.
ON resets the terminator to the default semicolon (;).
SUF[FIX] {SQL|text}
Default file extension for SQL scripts
TAB {OFF|ON}
Format white space in terminal output.
OFF = use spaces to format white space.
ON = use the TAB char.
Note this does not apply to spooled output files.
The default is system-dependent. Enter SHOW TAB to see the default value.
TERM[OUT] {OFF|ON}
OFF suppresses the display of output from a command file
ON displays the output.
TERMOUT OFF does not affect the output from commands entered interactively.
TI[ME] {OFF|ON}
Display the time at the command prompt.
TIMI[NG] {OFF|ON}
ON = display timing statistics for each SQL command or PL/SQL block run.
OFF = suppress timing statistics
TRIM[OUT] {OFF|ON}
Display trailing blanks at the end of each line.
ON = remove blanks, improving performance
OFF = display blanks.
This does not affect spooled output.
SQL*Plus ignores TRIMOUT ON unless you set TAB ON.
TRIMS[POOL] {ON|OFF}
Allows trailing blanks at the end of each spooled line.
This does not affect terminal output.
UND[ERLINE] {-|c|ON|OFF}
Set the char used to underline column headings to c.
VER[IFY] {OFF|ON}
ON = list the text of a command before and after replacing substitution variables with values.
OFF = dont display the command.
WRA[P] {OFF|ON}
Controls whether to truncate or wrap the display of long lines.
OFF = truncate
ON = wrap to the next line
The COLUMN command (WRAPPED and TRUNCATED clause) can override this for specific columns.
The items in Gray on this page are deprecated from Oracle 9 onwards - also note that several of the options above have 'gone missing' from the official documentation set - HELP SET is a more accurate reference.
Get a list of these SET options in sql*plus with the command:
SQLPLUS> HELP SET
Example
A demo SQL script with the most common SET options
Related:
SQL*Plus commands
/*
Multiple line comments
Can go between these delimiters
*/
SET TERM OFF
-- TERM = ON will display on terminal screen (OFF = show in LOG only)
SET ECHO ON
-- ECHO = ON will Display the command on screen (+ spool)
-- ECHO = OFF will Display the command on screen but not in spool files.
-- Interactive commands are always echoed to screen/spool.
SET TRIMOUT ON
-- TRIMOUT = ON will remove trailing spaces from output
SET TRIMSPOOL ON
-- TRIMSPOOL = ON will remove trailing spaces from spooled output
SET HEADING OFF
-- HEADING = OFF will hide column headings
SET FEEDBACK OFF
-- FEEDBACK = ON will count rows returned
SET PAUSE OFF
-- PAUSE = ON .. press return at end of each page
SET PAGESIZE 0
-- PAGESIZE = height 54 is 11 inches (0 will supress all headings and page brks)
SET LINESIZE 80
-- LINESIZE = width of page (80 is typical)
SET VERIFY OFF
-- VERIFY = ON will show before and after substitution variables
-- Start spooling to a log file
SPOOL C:\TEMP\MY_LOG_FILE.LOG
--
-- The rest of the SQL commands go here
--
SELECT * FROM GLOBAL_NAME;
SPOOL OFF
Oracle SQL*Plus
Version 11.1
General
Note: Oracle in its near infinite wisdom dropped sqlplusw.exe from the initial release of 11gR1. If want it you can copy in the executable from 10.2.0.1 and in most cases rename the DLL oraclient11.dll to oraclient10.dll. Then you will again have a usable interface. If you are as thrilled as we are about this send us an email and we will pass it along to Oracle.
Constants Constant Usage Example
SQL.LNO Line Number SELECT COUNT(*)
FROM all_objects
WHERE SUBSTR(object_name,1,1) BETWEEN 'A' AND 'W';
show lno
SQL.PNO Page Number SELECT object_name
FROM all_objects
WHERE SUBSTR(object_name,1,1) BETWEEN 'A' AND 'W';
show pno
SQL.RELEASE Oracle Version show release
SQL.SQLCODE Current error code show sqlcode
SQL.USER Currently connected user show user
Startup Parameters: Usage 1 Flags
Description
-H Displays the SQL*Plus version and the usage help
-V Displays the SQL*Plus version
sqlplus -C | -H
Startup Parameters: Usage 2 Flags
Description
-C
-L Attempts to log on just once, instead of reprompting on error
-M
Wednesday, September 15, 2010
Javascript RegExp Object
JavaScript RegExp Object
RegExp, is short for regular expression.
Complete RegExp Object Reference
For a complete reference of all the properties and methods that can be used with the RegExp object, go to our complete RegExp object reference.
The reference contains a brief description and examples of use for each property and method!
What is RegExp?
A regular expression is an object that describes a pattern of characters.
When you search in a text, you can use a pattern to describe what you are searching for.
A simple pattern can be one single character.
A more complicated pattern can consist of more characters, and can be used for parsing, format checking, substitution and more.
Regular expressions are used to perform powerful pattern-matching and "search-and-replace" functions on text.
Syntax
var txt=new RegExp(pattern,modifiers);
or more simply:
var txt=/pattern/modifiers;
• pattern specifies the pattern of an expression
• modifiers specify if a search should be global, case-sensitive, etc.
RegExp Modifiers
Modifiers are used to perform case-insensitive and global searches.
The i modifier is used to perform case-insensitive matching.
The g modifier is used to perform a global match (find all matches rather than stopping after the first match).
Example 1
Do a case-insensitive search for "w3schools" in a string:
var str="Visit W3Schools";
var patt1=/w3schools/i;
The marked text below shows where the expression gets a match:
Visit W3Schools
Example 2
Do a global search for "is":
var str="Is this all there is?";
var patt1=/is/g;
The marked text below shows where the expression gets a match:
Is this all there is?
Example 3
Do a global, case-insensitive search for "is":
var str="Is this all there is?";
var patt1=/is/gi;
The marked text below shows where the expression gets a match:
Is this all there is?
test()
The test() method searches a string for a specified value, and returns true or false, depending on the result.
The following example searches a string for the character "e":
Example
var patt1=new RegExp("e");
document.write(patt1.test("The best things in life are free"));
Since there is an "e" in the string, the output of the code above will be:
true
exec()
The exec() method searches a string for a specified value, and returns the text of the found value. If no match is found, it returns null.
The following example searches a string for the character "e":
Example 1
var patt1=new RegExp("e");
document.write(patt1.exec("The best things in life are free"));
Since there is an "e" in the string, the output of the code above will be:
e
RegExp, is short for regular expression.
Complete RegExp Object Reference
For a complete reference of all the properties and methods that can be used with the RegExp object, go to our complete RegExp object reference.
The reference contains a brief description and examples of use for each property and method!
What is RegExp?
A regular expression is an object that describes a pattern of characters.
When you search in a text, you can use a pattern to describe what you are searching for.
A simple pattern can be one single character.
A more complicated pattern can consist of more characters, and can be used for parsing, format checking, substitution and more.
Regular expressions are used to perform powerful pattern-matching and "search-and-replace" functions on text.
Syntax
var txt=new RegExp(pattern,modifiers);
or more simply:
var txt=/pattern/modifiers;
• pattern specifies the pattern of an expression
• modifiers specify if a search should be global, case-sensitive, etc.
RegExp Modifiers
Modifiers are used to perform case-insensitive and global searches.
The i modifier is used to perform case-insensitive matching.
The g modifier is used to perform a global match (find all matches rather than stopping after the first match).
Example 1
Do a case-insensitive search for "w3schools" in a string:
var str="Visit W3Schools";
var patt1=/w3schools/i;
The marked text below shows where the expression gets a match:
Visit W3Schools
Example 2
Do a global search for "is":
var str="Is this all there is?";
var patt1=/is/g;
The marked text below shows where the expression gets a match:
Is this all there is?
Example 3
Do a global, case-insensitive search for "is":
var str="Is this all there is?";
var patt1=/is/gi;
The marked text below shows where the expression gets a match:
Is this all there is?
test()
The test() method searches a string for a specified value, and returns true or false, depending on the result.
The following example searches a string for the character "e":
Example
var patt1=new RegExp("e");
document.write(patt1.test("The best things in life are free"));
Since there is an "e" in the string, the output of the code above will be:
true
exec()
The exec() method searches a string for a specified value, and returns the text of the found value. If no match is found, it returns null.
The following example searches a string for the character "e":
Example 1
var patt1=new RegExp("e");
document.write(patt1.exec("The best things in life are free"));
Since there is an "e" in the string, the output of the code above will be:
e
Tuesday, September 14, 2010
mathematical articles
Formatting Mathematical Articles with Cascading
Style Sheets
George Chavchanidze
Department of Theoretical Physics, A. Razmadze Institute of Mathematics, 1
Aleksidze Street, Tbilisi 0193, Georgia
Abstract. This page shows how to format mathematical articles with
Cascading Style Sheets (CSS). Simple XML 1.0 markup is used to capture
basic structure of math expressions while rendering is specified via CSS
2.0/2.1. Abilities and limitations of present approach are discussed.
Keywords: eXtensible Markup Language, Cascading Style Sheets,
Mathematics in XML
Date: Sun, 10 Oct 2004 (revised version)
1. Introduction
CSS is the simplest way to control formatting of XML and SGML
documents. Today it is mainly used in web design to render and style
(X)HTML documents, but its applications spread far beyond ordinary web
design and one can use XML and CSS to embed mathematical expressions
in web pages. Generally speaking it is easy to control general layout and
style of scientific documents with CSS, the only problem is rendering of
complex mathematical formulæ. So in this article we will mainly focus on
this problem and suggest relatively simple approach for rendering of
mathematical expressions that may appear in scientific papers. We use
simple XML 1.0 markup to capture basic structure of math expressions and
CSS 2.0/2.1 to specify their rendering (see [2]-[4] for specs).
Each mathematical expression may be formatted as inline equation like
z = 1/c or as block level (displayed) equation
z = 1/c (1)
Rendering of inline equations is more specific as one has to care about
height of line box.
2. Indices in display mode
In mathematical expressions indices are probably the most widespread
objects so it is essential to keep corresponding markup as simple as possible,
otherwise compactness and readability of XML source will be seriously
undermined. The simpliest way is to use CSS relative positioning to shift
indices up/downwards. Most of the browsers support relative positioning
and thus can easily process simple indices. Here are some examples of top
dzk = dxk + idyk (2)
ch2(x) − sh2(x) = 1 (3)
ch(3x) = 4ch3(x) − 3ch(x) (4)
Na − e− = Na+ (5)
and lower indices taken from mathematics and chemistry
Tmn = − Tnm (6)
Fe3O4 + 4H2 ? 3Fe + 4H2 (7)
Simple indices may be combined. Subscripts may precede superscripts and
vise versa.
Tmn = εnm
kSk
(8)
Tmn = εnm
kSk (9)
13Al27 + 2He4 = 15P30 + 0n1 (10)
Indices may be also positioned one over another in this way
∇mRn
ikl + ∇lRn
imk + ∇kRn
ilm = 0 (11)
However to archive correct alignment of such an indices one has to put them
in inline table. Here browser compatibility issues show up as some browsers
does not support inline tables. Nesting of simple indices is allowed.
dzk1 = dxk1 + idyk1 (12)
dzk(1) = dxk(1) + idyk(1) (13)
Tk1k2
= − Tk2k1
(14)
Tk(1)k(2) = − Tk(2)k(1) (15)
eA(1)eA(2) = eA(1) + A(2) (16)
Xh(F) = LXh
F (17)
∇k1Rk5
k2k3k4 + ∇k4Rk5
k2k1k3 + ∇k3Rk5
k2k4k1 = 0 (18)
∇ŝ1
Rŝ5 ŝ2ŝ3ŝ4
+ ∇ŝ4
Rŝ5 ŝ2ŝ1ŝ3
+ ∇ŝ3
Rŝ5 ŝ2ŝ4ŝ1
= 0 (19)
So rendering indices with CSS2 is not a big problem. Their rendering can be
controlled in details by both author and user through adjusting relative
positioning offsets, font-size and style in author and user style sheets.
3. Indices in inline mode
Here similar math expression appear inline. Note that relatively positioned
indices should not affect line height Tmn = − Tnm. Alternatively one can shift
indices using CSS vertical-align property used to control vertical alignment.
However, unlike relative positioning, vertical alignment may affect height of
line box. So it is better to use relative positioning εnm
kSk. Line breaks inside
equations are prohibited as browsers may generate line break in
inappropriate place (after all, there is no reliable algorithm for handling line
breaks in mathematical equations). Thus the simplest solution is to prohibit
all line breaks inside math expressions εnm
kSk (this can be done by setting
CSS 'white-space' property to 'nowrap') and mark those few points where
line breaks are allowed with an element that has CSS 'white-space' property
set to 'auto'. More complex indices ∇mRn
ikl can be used in inline mode as
well, but again some browsers does not like them. This happens due to weak
CSS support in those browsers. One can nest indices as follows ∇k1Rk5
k2k3k4 .
Nested indices are also shifted using relative positioning and thus they
should not change height of line box. Here are another samples of nested
superscripts eA(1)eA(2) and nested subscripts Xh(F) = LXh
F.
4. Fractions in display mode
Fractions are quite frequent in mathematical articles, so it is preferable to
have simple markup for fractions. Making it too simple results poor
rendering quality so we think that the minimal reasonable approach is to take
two elements, to mark fraction and its rows (numerator/denominator).
Fractions can be formatted as vertically centered inline tables. To reduce
markup anonymous table objects may be exploited. Below you see example
from statistics
A =
Tr(AW)
Tr(W)
(20)
another example from gravity
Rnm −
1
2
Rgnm = 0 (21)
and some samples from analysis and trigonometry
ln(2) = 1 −
1
2
+
1
3
−
1
4
+ ... (22)
B6 =
3617
510
(23)
ch(x) =
1
2
(ex + e− x) (24)
th(x ± y) =
th(x) ± th(y)
1 ± th(x)th(y)
(25)
Fractions may contain nested indices. Here are some samples from
mechanics
I =
m1m2
m1 + m2
x2 (26)
D =
4B3
ω2
(27)
examples from field theory
Fmn =
∂Am
∂xn
−
∂An
∂xm
(28)
Fmn =
∂Am
∂xn
−
∂An
∂xm
(29)
and other mathematical expressions
th(2x) =
2th(x)
1 + th2(x)
(30)
G = 1 −
1
32
+
1
52
−
1
72
+ ... (31)
Nesting of fractions is possible but limited to second order
g = 1 −
1
1 − ar
(32)
m =
1
1
m1
+ 1
m2
(33)
More deep nesting is also possible, but may require extra markup so at the
moment it is reasonable to limit nesting to second order as in real world
articles deeper nesting is rarely used and can be always avoided.
5. Fractions in inline mode
In inline mode fractions are rendered in the same manner as in block level
equations Tr(AW)
Tr(W) . The only difference is that inline fractions are slightly
compactified (height of numerator/denominator is reduced) th(x) ± th(y)
1 ± th(x)th(y) to
avoid possible line-height enlargement and nesting of fractions in inline
mode is not allowed but nesting of indices is possible so inline fractions may
contain nested indices m1m2
m1 + m2
x2 . Here is another example with nested
superscripts 2th(x)
1 + th2(x)
6. Operators in display mode
Rendering of indexed operators is much more complicated issue as in
general number of under and over scripts may be arbitrary and in addition
one needs to rearrange all this stuff when operators are nested in fractions or
appear inline. Also shape and baseline of glyphs may vary. At the moment
we will assume that only single under and over scripts are used (multiple
under scripts are really rarely used while multiple over scripts are almost
never used). One can format operators as inline tables. Below are some
sample integrals
B(m , n) =
1∫0
xm − 1(1 − x)n − 1dx (34)
Here are some sums
p =
nΣ
m=1
pm
(35)
G = Σ
p, s ∈ Z
ApBs (36)
Product
Ω = Π
m ∈ N
Ω(m) (37)
Unification operator
A =
∞∪
m=1
A(m) (38)
and intersection
B(s) =
2n
∩
m=1
B(m) (39)
Direct sum and tensor products are rendered in the same manner
Q
n⊕
k=1
xk =
n⊕
k=1
xQ[k]
(40)
 =
n⊗
k=1
m⊗
s=1
NksMs
(41)
Under and over scripts may contain nested indices
G = Σ
m1m2
Am1Bm2 (42)
F = Σ
m1 ≠ m2
pm1
pm2
(43)
Operators can be combined with indices and fractions to form complex
expressions
∞∫0
e− ax − e− bx
x
dx = ln
b
a
(44)
∞∫0
xne− axdx =
n!
an + 1
(45)
1∫0
dx
1 + 2x + x2
=
1
2
(46)
1∫0
sin2mx
c2 + x2
dx =
π
4c
(1 − e−2mc) (47)
1∫0
x2p − 1ln(1 + x)dx =
1
2p
2p
Σ
n=1
(− 1)n − 1
n
(48)
Nested fractions should not affect vertical alignment of parent fraction
1∫0
xm(1 − xn)pdx =
Γ(p + 1)Γ( m + 1
n )
nΓ(p + 1 + m + 1
n )
(49)
∞∫0
sin(mx)
eax + 1
dx =
1
2m
−
π
2ash( πm
a )
(50)
∞∫0
th( πx
2 )
1 + x2
sin(mx)dx =
m
em
− sh(m)ln(1 − e−2m) (51)
∞∫0
cos(mx)cos(nx)
ch(ax)
dx =
πch( πm
2a ) ch( πn
2a )
a(ch( πm
a ) + ch( πn
a ))
(52)
Operators can be nested inside fractions. But in this case it is better to
replace under/over scripts with sub/superscripts placed after operator
A = Σ n
k=1W(k)A(k)
Σ n
k=1 A(k)
(53)
S = Π n
k=1 Pk
Π n
k=1 Qk
(54)
F = Σ m
k=1 F(m)W(m)
Σ m
k=1W(m)
= Σ m
k=0 F(m)W(m)
Ŵ
(55)
So it is possible to render common operators with CSS.
7. Operators in inline mode
In inline mode it is better to replace under/over scripts with indices placed
after operator, Σ n
m=1 pm in this way possible line height distortions are
reduced Π s
m=0 Ω(m). The additional problem is that in different fonts glyphs
that correspond to mathematical operators like sums, products and intergals
have different shapes, baselines and sizes Σm1 ≠ m2
pm1
pm2
so if in one font
operators look perfectly centered in others they may appear to be distorted.
The problem will be partly resolved when we will have single font with
good coverage of all mathematical ranges (maybe STIX).
8. Under and Over scripts
Rendering of generic under and over scripted expressions is easier then
rendering of indexed operators. They are formatted as inline tables. Here is
for example limit
c−3 = lim
x → 0
x3s(x) (56)
Residue
I(z0) = Res
z = z0
F(z) (57)
Under script with brace (rendering of such a simple square under/over braces
is not a problem but making them round, or curly or allowing overlaps is
much more difficult to achieve, so currently it is better to stick to simplest
case).
V(n) = W ∧ W ∧ ⋯ ∧ W
n times
(58)
Below you see some samples from chemistry
+IV
Na2SO3 +
0
J2 + H2O =
+VI
Na2SO4 +
−I
2HJ (59)
+IV
MnO2 +
−I
4HCl =
+II
MnCl2 +
0
Cl2 + 2H2O (60)
+2e−
Zn + H2 SO4 = ZnSO4 + H2
(61)
Here is example from nuclear physics
Ra
226
→ Rn
222
+ He
4
(62)
Under over scripts are really rarely used. Below is rather artificial example
from chemistry.
27
Al
13
+
4
He
2
=
30
P
15
+
1n0
(63)
9. Vectors, Matrices and Cases
Vectors, matrices and cases can be formatted as inline tables. Here are
sample matrices and vectors. 'Hooks' are produced by inserting extra cells at
edges using CSS generated content and removing inner borders via border
collapse mechanism.
c11 c12 c13
c21 c22 c23
c31 c32 c33
x1
x2
x3
=
b1
b2
b3
(64)
Matrices may contain nested fractions, indices and operators
M3 =
M11 M12 M13
M21 M22 M23
M31 M32 M33
=
a2
b2 + c2 a3 − b2
c4 a2 + b2
12c 8a
12c b4 2a2
7b3
(65)
rendering of determinants is much easier as no 'hooks' are necessary.
det(M3) =
M11 M12 M13
M21 M22 M23
M31 M32 M33
=
a2
b2 + c2 a3 − b2
c4 a2 + b2
12c 8a
12c b4 2a2
7b3
(66)
Rendering of multivalues is slightly simplified.
ε(x) =
+1 {if x > 0}
0 {if x = 0}
−1 {if x < 0}
(67)
10. Large Brackets
Simple square brackets can be imitated using generated content and borders.
This is the simplest and most reliable way to handle them.
D = G(z) +
1
S(z)
3 (68)
Ĉ(m) =
m2
Π
k=m
kFk3(x) +
k5
Π
s = c4
Fs(x) + 12
Gs(x)
Fs(x) − 12Gs(x)
3k (69)
Ŝ± =
4θ2
6z3 + z2
3u
4b2
∫
2c2
e± 3uc2ŵ2 + Σ
m1 ≠ m2
e±m1m2ŵ dŵ (70)
As an alternative solution one can compose brackets by combining Unicode
characters 239B-23AD (located in Misc. Technical range). Task can be
simplified using CSS generated content.
11. Diacritical Marks
Rendering of diacritical marks is not governed by CSS. This issue is
addressed by Unicode standard [1] that defines so called combining
diacritical marks like __?__??__?__̃_?__?__ that being combined with
ordinary Unicode characters must produce characters with over dots, hats,
tildes, bars etc.
q? + q?2 + q4 = c̃ (71)
but at the moment browsers does not support combining diacritical marks
properly and it is better to use precomposed characters
[Â , Ĥ] = 0 (72)
located in the following Unicode ranges: Latin-1 Supplement, Latin
Extended-A, Latin Extended-B, Latin Extended Additional.
12. Radicals
The most reliable way to settle issue with radicals is to use more simple
power notations
x =
− b ± (b² − 4ac)½
2a
(73)
R± = m2 ±
12c5
29w7
3/2 (74)
In this way one avoids dependence on font metrics.
13. Nesting Limitations
Our present style sheet uses simple 'shrink to fit' nesting scheme to ensure
that nested element does not affect height of its parent. Such a rendering
naturally imposes limits on nesting of certain expressions. In overall these
limitations are not severe and does not affect real world articles. For
example simple nesting of fractions is allowed
Q = B0 +
A0
B1 + A1
B2 + A2 / B3
(75)
but those who try to nest fractions deeper will encounter nesting limitation.
It is possible to remove this and other nesting limitations by using more
complex markup, but at the moment we don't want to do this as limitation
are not severe.
14. Conclusions
CSS2 is basically simple style language, but in spite of its simplicity it is
powerful enough to afford rendering of most of mathematical expressions.
So one can start using CSS for formatting of scientific and technical XML
documents already today. Rendering of some things like for instance
radicals, and deeply nested expressions are not fully addressed in the present
article. However it happened just because current CSS2 based solutions for
rendering of radicals are slightly artificial, while support for deep nesting
requires slightly more detailed markup then we currently use, so taking into
account that this issues are not urgent we think it is better to address them
later when we will have more natural solutions (like CSS3 math module).
References
1. B. Beeton et al.,Unicode Support for Mathematics, 2003
2. B. Bos et al., Cascading Style Sheets, level 2 revision 1, 2004
3. T. Bray et al., Extensible Markup Language (XML) 1.0, 2004
4. J. Clark, Associating Style Sheets with XML documents, 1999
for more reference go through this website
http://www.princexml.com/samples/math.pdf
Style Sheets
George Chavchanidze
Department of Theoretical Physics, A. Razmadze Institute of Mathematics, 1
Aleksidze Street, Tbilisi 0193, Georgia
Abstract. This page shows how to format mathematical articles with
Cascading Style Sheets (CSS). Simple XML 1.0 markup is used to capture
basic structure of math expressions while rendering is specified via CSS
2.0/2.1. Abilities and limitations of present approach are discussed.
Keywords: eXtensible Markup Language, Cascading Style Sheets,
Mathematics in XML
Date: Sun, 10 Oct 2004 (revised version)
1. Introduction
CSS is the simplest way to control formatting of XML and SGML
documents. Today it is mainly used in web design to render and style
(X)HTML documents, but its applications spread far beyond ordinary web
design and one can use XML and CSS to embed mathematical expressions
in web pages. Generally speaking it is easy to control general layout and
style of scientific documents with CSS, the only problem is rendering of
complex mathematical formulæ. So in this article we will mainly focus on
this problem and suggest relatively simple approach for rendering of
mathematical expressions that may appear in scientific papers. We use
simple XML 1.0 markup to capture basic structure of math expressions and
CSS 2.0/2.1 to specify their rendering (see [2]-[4] for specs).
Each mathematical expression may be formatted as inline equation like
z = 1/c or as block level (displayed) equation
z = 1/c (1)
Rendering of inline equations is more specific as one has to care about
height of line box.
2. Indices in display mode
In mathematical expressions indices are probably the most widespread
objects so it is essential to keep corresponding markup as simple as possible,
otherwise compactness and readability of XML source will be seriously
undermined. The simpliest way is to use CSS relative positioning to shift
indices up/downwards. Most of the browsers support relative positioning
and thus can easily process simple indices. Here are some examples of top
dzk = dxk + idyk (2)
ch2(x) − sh2(x) = 1 (3)
ch(3x) = 4ch3(x) − 3ch(x) (4)
Na − e− = Na+ (5)
and lower indices taken from mathematics and chemistry
Tmn = − Tnm (6)
Fe3O4 + 4H2 ? 3Fe + 4H2 (7)
Simple indices may be combined. Subscripts may precede superscripts and
vise versa.
Tmn = εnm
kSk
(8)
Tmn = εnm
kSk (9)
13Al27 + 2He4 = 15P30 + 0n1 (10)
Indices may be also positioned one over another in this way
∇mRn
ikl + ∇lRn
imk + ∇kRn
ilm = 0 (11)
However to archive correct alignment of such an indices one has to put them
in inline table. Here browser compatibility issues show up as some browsers
does not support inline tables. Nesting of simple indices is allowed.
dzk1 = dxk1 + idyk1 (12)
dzk(1) = dxk(1) + idyk(1) (13)
Tk1k2
= − Tk2k1
(14)
Tk(1)k(2) = − Tk(2)k(1) (15)
eA(1)eA(2) = eA(1) + A(2) (16)
Xh(F) = LXh
F (17)
∇k1Rk5
k2k3k4 + ∇k4Rk5
k2k1k3 + ∇k3Rk5
k2k4k1 = 0 (18)
∇ŝ1
Rŝ5 ŝ2ŝ3ŝ4
+ ∇ŝ4
Rŝ5 ŝ2ŝ1ŝ3
+ ∇ŝ3
Rŝ5 ŝ2ŝ4ŝ1
= 0 (19)
So rendering indices with CSS2 is not a big problem. Their rendering can be
controlled in details by both author and user through adjusting relative
positioning offsets, font-size and style in author and user style sheets.
3. Indices in inline mode
Here similar math expression appear inline. Note that relatively positioned
indices should not affect line height Tmn = − Tnm. Alternatively one can shift
indices using CSS vertical-align property used to control vertical alignment.
However, unlike relative positioning, vertical alignment may affect height of
line box. So it is better to use relative positioning εnm
kSk. Line breaks inside
equations are prohibited as browsers may generate line break in
inappropriate place (after all, there is no reliable algorithm for handling line
breaks in mathematical equations). Thus the simplest solution is to prohibit
all line breaks inside math expressions εnm
kSk (this can be done by setting
CSS 'white-space' property to 'nowrap') and mark those few points where
line breaks are allowed with an element that has CSS 'white-space' property
set to 'auto'. More complex indices ∇mRn
ikl can be used in inline mode as
well, but again some browsers does not like them. This happens due to weak
CSS support in those browsers. One can nest indices as follows ∇k1Rk5
k2k3k4 .
Nested indices are also shifted using relative positioning and thus they
should not change height of line box. Here are another samples of nested
superscripts eA(1)eA(2) and nested subscripts Xh(F) = LXh
F.
4. Fractions in display mode
Fractions are quite frequent in mathematical articles, so it is preferable to
have simple markup for fractions. Making it too simple results poor
rendering quality so we think that the minimal reasonable approach is to take
two elements, to mark fraction and its rows (numerator/denominator).
Fractions can be formatted as vertically centered inline tables. To reduce
markup anonymous table objects may be exploited. Below you see example
from statistics
A =
Tr(AW)
Tr(W)
(20)
another example from gravity
Rnm −
1
2
Rgnm = 0 (21)
and some samples from analysis and trigonometry
ln(2) = 1 −
1
2
+
1
3
−
1
4
+ ... (22)
B6 =
3617
510
(23)
ch(x) =
1
2
(ex + e− x) (24)
th(x ± y) =
th(x) ± th(y)
1 ± th(x)th(y)
(25)
Fractions may contain nested indices. Here are some samples from
mechanics
I =
m1m2
m1 + m2
x2 (26)
D =
4B3
ω2
(27)
examples from field theory
Fmn =
∂Am
∂xn
−
∂An
∂xm
(28)
Fmn =
∂Am
∂xn
−
∂An
∂xm
(29)
and other mathematical expressions
th(2x) =
2th(x)
1 + th2(x)
(30)
G = 1 −
1
32
+
1
52
−
1
72
+ ... (31)
Nesting of fractions is possible but limited to second order
g = 1 −
1
1 − ar
(32)
m =
1
1
m1
+ 1
m2
(33)
More deep nesting is also possible, but may require extra markup so at the
moment it is reasonable to limit nesting to second order as in real world
articles deeper nesting is rarely used and can be always avoided.
5. Fractions in inline mode
In inline mode fractions are rendered in the same manner as in block level
equations Tr(AW)
Tr(W) . The only difference is that inline fractions are slightly
compactified (height of numerator/denominator is reduced) th(x) ± th(y)
1 ± th(x)th(y) to
avoid possible line-height enlargement and nesting of fractions in inline
mode is not allowed but nesting of indices is possible so inline fractions may
contain nested indices m1m2
m1 + m2
x2 . Here is another example with nested
superscripts 2th(x)
1 + th2(x)
6. Operators in display mode
Rendering of indexed operators is much more complicated issue as in
general number of under and over scripts may be arbitrary and in addition
one needs to rearrange all this stuff when operators are nested in fractions or
appear inline. Also shape and baseline of glyphs may vary. At the moment
we will assume that only single under and over scripts are used (multiple
under scripts are really rarely used while multiple over scripts are almost
never used). One can format operators as inline tables. Below are some
sample integrals
B(m , n) =
1∫0
xm − 1(1 − x)n − 1dx (34)
Here are some sums
p =
nΣ
m=1
pm
(35)
G = Σ
p, s ∈ Z
ApBs (36)
Product
Ω = Π
m ∈ N
Ω(m) (37)
Unification operator
A =
∞∪
m=1
A(m) (38)
and intersection
B(s) =
2n
∩
m=1
B(m) (39)
Direct sum and tensor products are rendered in the same manner
Q
n⊕
k=1
xk =
n⊕
k=1
xQ[k]
(40)
 =
n⊗
k=1
m⊗
s=1
NksMs
(41)
Under and over scripts may contain nested indices
G = Σ
m1m2
Am1Bm2 (42)
F = Σ
m1 ≠ m2
pm1
pm2
(43)
Operators can be combined with indices and fractions to form complex
expressions
∞∫0
e− ax − e− bx
x
dx = ln
b
a
(44)
∞∫0
xne− axdx =
n!
an + 1
(45)
1∫0
dx
1 + 2x + x2
=
1
2
(46)
1∫0
sin2mx
c2 + x2
dx =
π
4c
(1 − e−2mc) (47)
1∫0
x2p − 1ln(1 + x)dx =
1
2p
2p
Σ
n=1
(− 1)n − 1
n
(48)
Nested fractions should not affect vertical alignment of parent fraction
1∫0
xm(1 − xn)pdx =
Γ(p + 1)Γ( m + 1
n )
nΓ(p + 1 + m + 1
n )
(49)
∞∫0
sin(mx)
eax + 1
dx =
1
2m
−
π
2ash( πm
a )
(50)
∞∫0
th( πx
2 )
1 + x2
sin(mx)dx =
m
em
− sh(m)ln(1 − e−2m) (51)
∞∫0
cos(mx)cos(nx)
ch(ax)
dx =
πch( πm
2a ) ch( πn
2a )
a(ch( πm
a ) + ch( πn
a ))
(52)
Operators can be nested inside fractions. But in this case it is better to
replace under/over scripts with sub/superscripts placed after operator
A = Σ n
k=1W(k)A(k)
Σ n
k=1 A(k)
(53)
S = Π n
k=1 Pk
Π n
k=1 Qk
(54)
F = Σ m
k=1 F(m)W(m)
Σ m
k=1W(m)
= Σ m
k=0 F(m)W(m)
Ŵ
(55)
So it is possible to render common operators with CSS.
7. Operators in inline mode
In inline mode it is better to replace under/over scripts with indices placed
after operator, Σ n
m=1 pm in this way possible line height distortions are
reduced Π s
m=0 Ω(m). The additional problem is that in different fonts glyphs
that correspond to mathematical operators like sums, products and intergals
have different shapes, baselines and sizes Σm1 ≠ m2
pm1
pm2
so if in one font
operators look perfectly centered in others they may appear to be distorted.
The problem will be partly resolved when we will have single font with
good coverage of all mathematical ranges (maybe STIX).
8. Under and Over scripts
Rendering of generic under and over scripted expressions is easier then
rendering of indexed operators. They are formatted as inline tables. Here is
for example limit
c−3 = lim
x → 0
x3s(x) (56)
Residue
I(z0) = Res
z = z0
F(z) (57)
Under script with brace (rendering of such a simple square under/over braces
is not a problem but making them round, or curly or allowing overlaps is
much more difficult to achieve, so currently it is better to stick to simplest
case).
V(n) = W ∧ W ∧ ⋯ ∧ W
n times
(58)
Below you see some samples from chemistry
+IV
Na2SO3 +
0
J2 + H2O =
+VI
Na2SO4 +
−I
2HJ (59)
+IV
MnO2 +
−I
4HCl =
+II
MnCl2 +
0
Cl2 + 2H2O (60)
+2e−
Zn + H2 SO4 = ZnSO4 + H2
(61)
Here is example from nuclear physics
Ra
226
→ Rn
222
+ He
4
(62)
Under over scripts are really rarely used. Below is rather artificial example
from chemistry.
27
Al
13
+
4
He
2
=
30
P
15
+
1n0
(63)
9. Vectors, Matrices and Cases
Vectors, matrices and cases can be formatted as inline tables. Here are
sample matrices and vectors. 'Hooks' are produced by inserting extra cells at
edges using CSS generated content and removing inner borders via border
collapse mechanism.
c11 c12 c13
c21 c22 c23
c31 c32 c33
x1
x2
x3
=
b1
b2
b3
(64)
Matrices may contain nested fractions, indices and operators
M3 =
M11 M12 M13
M21 M22 M23
M31 M32 M33
=
a2
b2 + c2 a3 − b2
c4 a2 + b2
12c 8a
12c b4 2a2
7b3
(65)
rendering of determinants is much easier as no 'hooks' are necessary.
det(M3) =
M11 M12 M13
M21 M22 M23
M31 M32 M33
=
a2
b2 + c2 a3 − b2
c4 a2 + b2
12c 8a
12c b4 2a2
7b3
(66)
Rendering of multivalues is slightly simplified.
ε(x) =
+1 {if x > 0}
0 {if x = 0}
−1 {if x < 0}
(67)
10. Large Brackets
Simple square brackets can be imitated using generated content and borders.
This is the simplest and most reliable way to handle them.
D = G(z) +
1
S(z)
3 (68)
Ĉ(m) =
m2
Π
k=m
kFk3(x) +
k5
Π
s = c4
Fs(x) + 12
Gs(x)
Fs(x) − 12Gs(x)
3k (69)
Ŝ± =
4θ2
6z3 + z2
3u
4b2
∫
2c2
e± 3uc2ŵ2 + Σ
m1 ≠ m2
e±m1m2ŵ dŵ (70)
As an alternative solution one can compose brackets by combining Unicode
characters 239B-23AD (located in Misc. Technical range). Task can be
simplified using CSS generated content.
11. Diacritical Marks
Rendering of diacritical marks is not governed by CSS. This issue is
addressed by Unicode standard [1] that defines so called combining
diacritical marks like __?__??__?__̃_?__?__ that being combined with
ordinary Unicode characters must produce characters with over dots, hats,
tildes, bars etc.
q? + q?2 + q4 = c̃ (71)
but at the moment browsers does not support combining diacritical marks
properly and it is better to use precomposed characters
[Â , Ĥ] = 0 (72)
located in the following Unicode ranges: Latin-1 Supplement, Latin
Extended-A, Latin Extended-B, Latin Extended Additional.
12. Radicals
The most reliable way to settle issue with radicals is to use more simple
power notations
x =
− b ± (b² − 4ac)½
2a
(73)
R± = m2 ±
12c5
29w7
3/2 (74)
In this way one avoids dependence on font metrics.
13. Nesting Limitations
Our present style sheet uses simple 'shrink to fit' nesting scheme to ensure
that nested element does not affect height of its parent. Such a rendering
naturally imposes limits on nesting of certain expressions. In overall these
limitations are not severe and does not affect real world articles. For
example simple nesting of fractions is allowed
Q = B0 +
A0
B1 + A1
B2 + A2 / B3
(75)
but those who try to nest fractions deeper will encounter nesting limitation.
It is possible to remove this and other nesting limitations by using more
complex markup, but at the moment we don't want to do this as limitation
are not severe.
14. Conclusions
CSS2 is basically simple style language, but in spite of its simplicity it is
powerful enough to afford rendering of most of mathematical expressions.
So one can start using CSS for formatting of scientific and technical XML
documents already today. Rendering of some things like for instance
radicals, and deeply nested expressions are not fully addressed in the present
article. However it happened just because current CSS2 based solutions for
rendering of radicals are slightly artificial, while support for deep nesting
requires slightly more detailed markup then we currently use, so taking into
account that this issues are not urgent we think it is better to address them
later when we will have more natural solutions (like CSS3 math module).
References
1. B. Beeton et al.,Unicode Support for Mathematics, 2003
2. B. Bos et al., Cascading Style Sheets, level 2 revision 1, 2004
3. T. Bray et al., Extensible Markup Language (XML) 1.0, 2004
4. J. Clark, Associating Style Sheets with XML documents, 1999
for more reference go through this website
http://www.princexml.com/samples/math.pdf
Wednesday, September 8, 2010
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