text:
Cookbook:Yu Choy

| Brassicas

Yu choy (also edible rape) is a green leafy vegetable used in Chinese and Southeast Asian cooking. Younger and/or more tender varieties are often called choy sum.

Characteristics
Yu choy consists of branching stalks with a couple broad leaves at the end of each and, sometimes, yellow flower heads. The texture when raw is somewhat crunchy, though it gets tougher as it ages. Most varieties are green, though purple/red cultivars exist as well. The flavor is grassy with a slight bitterness that, again, increases with age.

The vegetable looks very similar to gai lan, but it is more tender and has a slightly different flavor.

Seasonality
Technically, yu choy is a cooler weather vegetable, but it does tend to be available year-round.

Selection and storage
Like other leafy greens, look for bright green yu choy that has no wilting, browning, blemishes, or sliminess. The younger and smaller, the more tender the stems. Additionally, those with more flowers may be more bitter. It can be stored, unwashed, for a few days in a container in the fridge. If you want to freeze yu choy, it's best to blanch it before doing so.

Use
Yu choy is popular in Cantonese cuisine, where is is often steamed or stir-fried with strong flavors. Tougher stalks can be separated from the leaves and braised for longer in order to tenderize them, but don't overcook them. To prepare yu choy, trim any tough parts off the stem. Particularly thick or fibrous stems can be peeled.

Substitution
If you can't get your hands on yu choy, gai lan or tender bok choy will make for reasonable approximations. Rapini is also an option, though it is more bitter.

title: Cookbook:Yu Choy


text:
Cookbook:Rape

This is an ambiguous term. See one of:

 * Yu Choy (edible rape)
 * Canola Oil (low erucic acid rapeseed oil)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Cookbook:Rape


text:
Movie Making Manual/Sound Design

The job was originally referred to as "Sound Editor" but when legendary Film Editor Walter Murch worked for Coppola on Rain People he was not a part of the union so could not use the standard job description and thus coined the term "Sound Design".

Since then the two terms have served to identify the distinction between the technical skills needed to work in the audio strand of Post-production (the editor) and the artistic or academic skills and knowledge used to inform edits (the designer). Thus an editor would be able to employ equipment, such as a mixing desk, while the designer might employ Walter Murch's theory, 'The Color of Sound', to create a well balanced mix.

In practise, a working professional must be both a competent editor and designer.

The Importance of Sound
The sound in a motion picture is composed of dialogue, music and sound effects. The most important thing that film students must learn is 90% of a motion picture is sound. The picture is far less important than the sound. Here is why:

The audience can only look at one picture at a time. Yet the audience can hear dozens of distinct sounds all at the same time and separate and process all that information... if it is done correctly. Therefore, much more information can be transmitted from the filmmaker to the audience via sound than via picture.

The goal of a filmmaker is to give the audience as much information as possible. Too little information and the audience becomes bored. Example: If a shot remains on the screen for more than 5 seconds, it becomes boring. For the younger generation, the average time between cuts is 1.5 seconds where as movies made for an older generation will cut from one picture to the next on an average of once every three seconds. This is because the eye can examine and process all the information in a frame in about 3 seconds for an adult and 1.5 seconds for teenagers. So if you are going to have a shot longer than about 5 seconds, you must find some way to convey more information to the audience.

When a motion picture is delivered to a distributor (specially for distribution overseas), the sound must be on three completely separate tracks. The dialogue, music and sound effects must be kept separate on the final mix. But when you are editing a motion picture, you must always look at all the sound together. If you are doing sound, you cannot ignore the dialogue or the music. They all tie together. They all work together.

Here is something else you need to know:

 * 1. Sound effects make the scene seem real.

 * 2. Music creates the mood of the scene.

Another thing you need to know is:

 * 3. Sound and music create the continuity for a motion picture.

When you cut from one shot to another, you always create a discontinuity. If the sound remains consistent from one shot to the next, continuity is restored.

So let's get started:

Sound Effects
There are different types of sound effects.

 * 1. Ambience = Background sounds = Atmosphere
 * This is the sound in the background. There are two parts to this.

 * A. One part of ambience is room tone.  This is the background noise on the movie set.  When you erase dialog or unwanted noise (such as the director yelling, "Cut!", you must fill the gap with room tone.

 * B. After the scene is edited, a background sound is added from sound recorded in the field.  If you are editing a scene of three men in a cafeteria, you have to go to a cafeteria and record the background sounds from the real cafeteria and put in faintly in the background of the scene.

Many movies do not have background sound. When you watch "The Sound Of Music" and Maria is singing on the top of a mountain on a green meadow, there is no ambience sound. This scene sounds as if she is singing in a sterile sound booth... which she is. If you take that same sound track and add the sound of a meadow in spring, the audience hears both the singing and the meadow separately... and entire scenes sounds much more realistic and inviting. By not having ambiance, you limit the information that you give the audience.

 * 2. Walla
 * My favorite sound is walla. Where else but in motion pictures do you worry about how people mumble faintly in the background?  Walla is indistinguishable voices talking in a murmer.  It seems a bit dorky to record people mumbling but it really is great in scenes of a crowd.  The most annoying thing is I have not found a good sound effects library with walla.

 * 3. Pre-Recorded Sound Effects
 * For music, using pre-recorded music is frowned upon. But for sound effects, the fastest and easiest way of getting sound effects is from sound effects libraries.

 * 4. Field Recording of Sound Effects
 * Eventually, this is where most sound effects for motion pictures come from. It is not easy to record good, clean sound in the field.

 * 5. Foley Sound Effects
 * See the separate section on Foley sound.

Sound Sweetening
Sound Sweetening simply means enhancing a sound effect. This is easy to do if you have the right sound effects program. All you do is create copies of the sound and apply various sound effects filters (reverb, echo, pitch shifting compression etc.) and then combine them all together until it sounds good. You might have half a dozen different layers in a single sound effect. Total trial and error.

Sound Recording Hardware
There is no good sound recording device for low-budget filmmakers. Sony's MD (MiniDisc) recorders have strong limitations, because they compress the incoming signal very much like the compression of a mp3 is done. It also could only record in 32 Khz sampling rate. A good alternative is a DAT-recorder, which can record in 16 Bit and 48 Khz without any compression. Try to record the signal as loud as you can, without overshooting. This will ensure that you have a good signal to noise rate. There are also some hardware recorder on the market, which are able to record 2 channels at once in high quality 24 Bit 48Khz or 96Khz on a memory card. They are the best, you can get for the job, because they get the sounds as clean as possible and without compression. Some have build in microphones, which are quite good, but also allow to connect external microphones with symetric-wireing. The microphone that you use, makes a tremendous difference. Also, with sound effects, you will find that you need a wide selection of microphones since each one is designed for a specific application.

Sound Software
There are two kinds of software for sound.

1. DAW software is multi-track recording software which simulates a digital audio workstation.

2.  Sound editing software is a program which can work with individual sound samples.

Programs such as iMovie, Final Cut Pro and Final Cut Express include most of the functionality of a multi-track digital audio workstation. All three programs are useless for working with individual sound samples.

Long ago, there was a program called "SoundEdit 16" which was easy to use, easy to view, totally bug free, and produced wonderful results. A few years ago, Apple provides a free copy of BIAS Peak which is not easy to use, not easy to view and rather buggy in my humble opinion (r_purser-at-digipuppet.com). There is an upgrade path for a later version but I see little incentive in upgrading a program that they could not get right the first time. If you purchase an older version of Final Cut Pro, you will still get this program.

Now Apple sells a program called SoundTrack which will slice and dice any sound in a thousand different ways. However, first look at the program will convince you it is not designed for quick and simple sound effects sweetening.

A fairly simple and effective program for quick sound editing on Windows is Goldwave (http://www.goldwave.com). It is lightweight, and provides many effects to apply, along with options for volume, panning, and others. It is even possible to edit a wave on the sample level - you cannot get any more fine-grained. There is an expression evaluation effect which can be used for generating background hum, white noise, and various other frequencies. While it does not offer multi-track functionality, its sister product MultiQuence provides these features.

Audacity (http://audacity.sourceforge.net/) is another, totally free, sound editor for Windows, which provides many of the features of higher-level programs such as Cubase in a more accessible interface. This program has received many recommendations and good reviews.

/Audio /Post-production

title: Movie Making Manual/Sound Design


text:
Cookbook:Tempura

| Japanese Cuisine

Tempura is one of the fried foods of Japan. Various meats, fish, and vegetables are dipped in batter and then deep fried until lightly golden.

Ingredients

 * 1 egg
 * 1 cup ice cold water
 * 1 cup all-purpose flour
 * Oil for deep-frying (peanut oil is best)
 * Meat, vegetables, or seafood

Procedure

 * 1) Heat oil in a deep pan to 340–350°F (~171–176°C).
 * 2) Beat the egg in a bowl and add ice cold water. Warmer water will produce a sticky batter and more oily tempura.
 * 3) Add flour and mix lightly. Do not overmix batter—a few lumps actually improve the result, adding crispiness.
 * 4) Dip meat or vegetables briefly in the batter, and fry until brown.
 * 5) Remove from the oil and drain.
 * 6) Serve hot.

Notes, tips, and variations

 * If using shrimp, score them a few times crosswise on the underside, to prevent them from curling up during deep frying. Alternatively, skewer them before cooking. Remove the skewers before serving.
 * You may also wish to include 1 tablespoon of cornstarch in the batter.
 * Serve over white rice garnished with black sesame seeds, in a bowl of udon noodle soup, or in a bowl of soba noodle soup. Serving in soup will make the cooked batter get mushy, of course.

title: Cookbook:Tempura


text:
Gambas/Time

Back to Gambas

Usar la Propiedad Time
Time returns the current time. Example:

You need 1 button:

Private Sub Button1_click message(time) end

Te daria algo asi: 22:13:00.998 (En ubuntu me da asi :P)

Por ejemplo si queremos hacer que a determinada hora nos avise, seria algo asi:

Necesitas 2 Textbox, 1 Boton, 1 Timer y un modulo..

En textbox1 escribimos la Hora que queremos que nos avise. En textbox2 escribimos el minuto que queremos que nos avise.

Within the module write:

PUBLIC Hora as string[] PUBLIC Final as string[]

Within form Fmain, Button1 write:

Private Sub Button1_click dim tiempo as String tiempo=Time Module1.Hora=Split(tiempo,":") Timer1.enabled = true end

Private Sub Timer1_ dim tiempo as string Timer1.delay = 500 tiempo=Time Module1.Final=split(tiempo,":") if Module1.hora[0] = Module1.Final[0] and Module1.hora[1] = Module1.Final[1] then message.info("Ya es la hora que ingresaste antes") Timer1.enabled = false end if end

Wait Command
The Syntax is WAIT [ Delay ]

This command calls the event loop. If Delay is specified, it does not return until Delay seconds elapse. Delay is a floating point number. So, if you want to wait 100 ms, just do: WAIT 0.1 During the wait, no keyboard or mouse events are processed. Only drawing, timer and file descriptors events, like Process_Write are still running.

Example

You need a commandbutton and a textbox to get it going.

PUBLIC SUB Button1_Click WAIT 10 'waits 10 seconds WAIT 0.1 'waits 100 milliseconds textbox1.Text = "" END

title: Gambas/Time


text:
Gambas/Variable

Back to Gambas

Variable Declaration ( Dimensioning)
In Gambas it is necessary to declare every variable. To dimension a variable, the code is:

Dim variablename as type

You can just skip the word Dim, so the following is also correct:

variablename as type

The variable name could be whatever you want. The type however has to be chosen. You have a choice of integer, string, variant and some others. This tells the computer what type of information the variable holds. Singles and integers hold numbers, while strings hold text.

'Dimensioning Dim i as Integer Dim x as Variant 'assignment i = 31            'This is ok i = "i do"     'Error: type mismatch(i is an integer;"i do" is a string) x = 341           'This is ok x = "books"        'This is all right

In Gambas you cannot dim an array as you were used in VB. The following is wrong:

xxxxx Dim x(1 to 10) as integer  xxxxxx

Dimensioning can also be used to tell the computer that variables are public or private. When a variable is public, it may be used and changed in all sub-programs. To make a variable public you must dim it in the "declarations" area of the code. These declarations are placed on the very first lines in your code, above all sub programs and other code.

Examples: You need a command button on your form to get it going.

PUBLIC SUB Button1_Click 'Declaration x AS integer y AS float z AS String 'assignment x = 2 y = 2.378 z = "That ist correct" 'the use of variables print x,y,z,x*y END

The following program will cause an error: x already declared

'xxxxxxxxxxxxxxxxxxxx PUBLIC SUB Button1_Click DIM x AS integer DIM x AS float DIM x AS String x = 2 x = 2.378 y = "That ist not correct" print x,x,x END 'xxxxxxxxxxxxxxxxxxxxxx

In the following program you also cause some error warnings, as there is no difference between upcase and lowcase signs in Gambas.

PUBLIC SUB Button1_Click DIM x AS integer DIM X AS float DIM x$ AS String x = 2 X = 2.378 x$ = "that ist correct " print x,X,x$ END

List of Gambas predefined datatypes for the declaration of variables
 True or False    1 byte    False       0 ... 255   1 byte    0       -32768 ... +32767   2 bytes    0       -2147483648 ... +2147483647   4 bytes    0       Like the double datatype in C    8 bytes    0.0       Date and time, each stored in an integer.  8 bytes    Null       A reference to a variable length string.  4 bytes    Null       Any datatype.  12 bytes    Null       A anonymous reference to an object.  4 bytes    Null

Assignment
Once you have declared a variable, you can assign a value to it.

Variable = Expression

This will assign the value of an expression to one of the following elements :
 * A local variable.
 * A function parameter.
 * A global (class) variable.
 * An array slot.
 * An object public variable.
 * An object property.

Example

iVal = 1972 Name = "Gambas" hObject.Property = iVal cCollection[sKey] = Name

Structures
Some versions of basic, allow structured variables to be created by using TYPE definitions as follows:

' This will not work in gambas TYPE rhubarbstructure foo AS STRING * 32 bar AS INTEGER END TYPE

PUBLIC rhubarb AS rhubarbstructure

Currently, gambas does not support the TYPE keyword. However, it is possible to use class definitions for the same effect.

Creating a class
From the Integrated Development Environment file, create a class file rhubarbstructure.class as follows:

PUBLIC foo AS STRING PUBLIC bar AS INTEGER

It is now possible to define a variable utilizing that class, by creating an appropriate definition in the code module as follows:

DIM rhubarb AS rhubarbstructure

title: Gambas/Variable


text:
Gambas/Output

Back to Gambas

Simple output
The interaction between the user and the computer consists of the input and output of data. You wouldn't know what the computer is doing without seeing or hearing anything. That's the importance of output.

Printing
Note: The word "printing" here means using the Print statement, it's not about using the printer or printing files. Printing is a fairly simply part of gambas, but also essential. Most often printing is used to output information to the user, and can also prove a valuable troubleshooting tool. Whenever printing, you need an object, followed by of course, something to print. Printing may be used with various objects, however, the most common in the terminal window.

Example: You need a command button on your form:

PUBLIC SUB Button1_Click Print "Hello world!!!" END

This example prints a message in the terminal window, not on the current form like in VB

Output in Labels, Textlabels, Textboxes oder Textareas
You can also aim your output to different kind of text controls.

Example: You need a command button and a textbox on your form:

PUBLIC SUB Button1_Click Textbox1.text = "Hello world!!!" END

Message boxes
One of the easiest way of an output is the message box. This is what the code of a normal message box should look like.

Message.Info("Hallo")

Example:

PUBLIC SUB Button1_Click Message.Info("Hallo, this is your message", "OK") END

Spacing
There is various way to alter how text is spaced when printing. The most common is the comma. A comma will go to the next print zone. Print zones are 15 characters long. You can think of it like pressing the tab key when typing something out. Remember that print zones are fixed, so if you've typed 1 letter, and then used a comma, then it will be a big space. If you type 13 characters and use a comma, it will not be a large space. For example: Private Sub Form_Click Me.Print "Hello", "Next Zone" End Sub Several new things are introduced in this example. The subroutine(which is a function that does not return a value; you'll learn more about them later) Form_Click is called when the user clicks on the current Form(Form1). 'Me' is the same as the current form (Form1). Don't be afraid to experiment. No matter what you do in VB, its always reversible. Now, the comma isn't all that versatile. Another feature is tab. Tab will move so many spaces from the BEGINNING of the line. Followed by tab in parentheses is the amount of characters spaces. For example: Form1.Print "Hello"; Tab(10); "Yay" This will NOT print "yay" 10 spaces after the O of "Hello". Rather it will print 10 spaces from the beginning of the line. You may use as many tabs as you want in the same print command. Although tab is useful, sometimes it is better to spaces things in relation to what has already been printed. This is where the space function comes in. The syntax of space is identical to that of tab. Space will move the next printed text so many spaces over from its CURRENT location. For example: Pic.print "Hello"; Space(10); "Yay" This will print the first Y of "Yay" 10 spaces to the right of the O in "Hello". It is important to note, if you write: Pic.Print "Hello" Pic.Print "Hello" They will appear on separate lines as: Hello Hello This can be easily dealt with in the need of having separate print statements print on the same line. You merely have to change the code to: Pic.Print "Hello"; Pic.Print "Hello" This will appear as: HelloHello If you want to make a blank line in between the two hellos, then you may simply have a blank print statement WITHOUT a semicolon. For example: Pic.Print "Hello" Pic.Print Pic.Print "Hello" This will print as: Hello Hello It is important to remember that even if the first print has a semicolon at the end, often referred to as a trailing semicolon, the empty print will only reverse it, and print the second Hello on the next line, and no blank line will appear.

title: Gambas/Output


text:
User:Mplogan

My name is Michael Logan. I am an ASP.Net programmer working for the state of Virginia.--Mplogan 23:14, 11 Feb 2005 (UTC)

title: User:Mplogan


text:
ASP.NET/Database

ASP.NET Database
ASP.NET v1.1.4322

Introduction
A database is essentially a place to store data. However the key to understanding the term "database" is that a database is an electronic warehouse for storing data. Databases can contain any type of data (depending on the manufacturer/vendor). For example the Wikibooks website is maintained within a database.

There are many types of database. Hierarchy database, Network database, Relational database, Object database, XML database. Even a file system or Excel can be considered as a database.

The most common structure for storing the data is as a table. Each row in the table is a record and each column is a field. The table may relate to other tables by sharing a common field. This is known as a relational database.

Relational database is the dominant database in the database market today. There are proprietary ones like Oracle, IBM DB2, Microsoft SQL Server, Sybase, ANTs, and open source ones like PostgreSQL, MySQL, Derby, Berkeley DB (Sleepcat) etc.

There are typically limitations on length and width of database tables. SQL Server 2005 has an 8K row width limit for example, and many lengths are limited by 32-bit addressing, to at most approximately 4E9 records. This increases to approximately 1.8E19 records with 64-bit addressing.

The Microsoft .NET framework comes with several namespaces to manage data in databases. .NET also comes with SQL Server and Oracle native providers. A native provider will only work with one database product, and uses the native database more efficiently. There are several generic database classes, however if you are using a database that has a native provider, use it.

Performing database operations is fairly easy in ASP.NET. Below is a quick sample of how to connect to a database.

Connecting to a Database
VB.NET Class Page1 Public Sub Page_Load (byval sender as System.Object, byval eventars as System.EventArgs) Dim sqlconn as new SQLConnection("database connection string") sqlconn.Open End Sub

End Class C#.NET public class Page1

{   public void Page_Load(object sender, EventArgs e)    { string strConn = "database connection string"; // the italicized database connection string above should // be replaced by some real valid one. SqlConnection sqlConn = new SqlConnection(strConn); sqlConn.Open; } }

Comments on the C# example: using System; using System.Collections; using System.Web; using System.Web.UI; using System.Web.UI.WebControls; using System.Data; using System.Data.SqlClient;
 * Since the Page_Load event handler (i.e. the "void" method which handles this event) is declared inside a class declaration (named "Page1"), it means usually that in such case it is in a separate "code behind" file, and if the ASP.NET file of the page is named "Page1.aspx" it's code behind file is usually named "Page1.aspx.cs". Should it be declared in the same file as the source code of the page (i.e., inside ... tags) there would be no need to make a page class declaration.
 * In the case you are using the code behind coding model it is necessary to include the appropriate attributes in the @Page directive (look in the SDK documentation for details).
 * In the code behind file the class is to be declared inside a "namespace" declaration (named usually after the name of the application - namespace DataAccess{ ... }, for instance).
 * Above the namespace declaration it is advisable to add using declarations for the integrated namespaces of the .NET framework, so you will be able to refer to the .NET classes with short names, not System.Data.SqlClient.SqlConnection, for instance. In the case of single file code model, the appropriate @Import directives should be added.
 * The Page1 class should usually be inherited explicitly from System.Web.UI.Page. Thus our Page1 source code file might look like:

namespace DataAccess

{   public class Page1 : System.Web.UI.Page {       public void Page_Load(object sender, EventArgs e)        { ...       }    } }

 * The access modifier of the Page_Load event handler in the present example is "public". Usually it is customary to use a "protected", or even a "private" access modifier (for encapsulation reasons). In the present example though, the programmer might wish to access the sqlConn variable outside the Page1 class, so "public" it is...

See also: SQLConnection parameters

ADO.NET
class DBConnection {  public void Page_Load (System.Object sender, System.EventArgs eventars) {    try {        SqlConnection sqlconnection = new SqlConnection("database connection string"); sqlconnection.Open; }       catch(Exception ex) {        MessageBox.show(ex.message); }  } }

ADO.NET Connection String Example (Trusted Connection)
server=DBSERVER;database=DBName;Trusted_Connection=True;

Connection Pooling
In classic ASP, database connections were not managed very effectively. However with the advent of ASP.NET, database connection pooling is fairly translucent. If the same connection string is provided, connection pooling is handled automatically.

title: ASP.NET/Database


text:
Cookbook:Tomato Sauce

Tomato sauce is an ambiguous term that can mean many things, including:

 * tomato puree flavored with salt, garlic, onion, basil, and oregano (commonly sold in cans in the USA)
 * ketchup (Australia, and sometimes in the UK)
 * any tomato-based spaghetti sauce or pasta sauce

title: Cookbook:Tomato Sauce


text:
Talk:Discrete Mathematics/Axiomatic set theory

Dear Somebody Intelligent,

Please write this section.

Regards, -Me
 * As the foundation of nearly all of mathematics, axiomatic set theory obviously goes beyond the bounds of "Discrete Mathmatics" in the traditional sense, I'm going to change this to a redirect to Set Theory which seems to be the start of such a book. Siroxo 21:49, 15 Mar 2005 (UTC)


text:
Talk:Guitar/Chord Reference

"An open chord is any chord that has one or more strings sounded without being fretted."

This statement is contradicted by the F major and B minor chords shown below.

This page is not to be trusted.
 * The one chord that I looked up here turned out to be wrong:
 * The Eo7 Chord is [E G Bb Db], not: [D E G Bb]. And the supplied fingering is also wrong.
 * I am no guitar expert so I won't make any changes, but be warned!

(stestagg) 86.140.72.186 21:27, 1 September 2007 (UTC)

HQ diagrams
with GChords? Jd (talk) 11:26, 20 December 2008 (UTC)

Removing incorrect chord information
The chord reference section is incorrect. The notes in A major are "A - C sharp - E" not "A - D flat - E". This is also a very complicated way of presenting chords. I'm removing the whole section. I will be replacing this with simple chord diagrams that are key related.

Chords in C major
The proper chord form for B in a C major scale is B half-dim7 which has the notes B-D-F-A as opposed to B dim7, the chord shown, which has the notes B-D-F-Ab. It's worth noting that Ab is not a note within the C major scale. I recommend changing the B chord to a half-dim7 or a triadic voicing if practical.

-mike

title: Talk:Guitar/Chord Reference


text:
Logic for Computer Science/Applications

In the following we briefly consider some applied problems where the expressibility of languages matter. It easily becomes clear that FO does not suffice for many cases. To overcome the restrictions of FO there exist many extensions such as fixed-point logic, counting logic, miscellaneous flavours of second-order logic, etc. which are not covered in this chaper [chapter | paper].

Database Theory: SQL
Relations have named columns called attributes

frequents | drinker  bar --|---             |

serves   |  bar  beer --|---             |

likes    |  drinker  beer --|---             |

Standard Query Language:

Relational calculus variant of FO on relational vocabulary (no functions just relations).

Here constants have a fixed interpretation, this is slightly different than in FO logic.

Examples of relational queries:

(i) Find all bars that serve Bud

$$\{ b : bar  |  serves(b,Bud)\}$$

b is a free variable, Bud is a constant.

(ii) Find the drunkers [drinkers | drunkards] who frequent some bar that serves Bud $$\{ d : drinker | \exists b ( frequents(d,b) \wedge serves(b,Bud)) \}$$

(iii) Find the drinkers who frequent only bars serving Bud $$\{ d : drinker | \forall b [ frequents(d,b) \longrightarrow serves(b,Bud)] \}$$

(iv) Find drinkers who frequent only bars serving some beer they like $$\{ d : drinker | \forall b ( freq(d,b) \longrightarrow \exists c (serves(b,c) \wedge likes(d,c)))\}$$

SQL Representation of these queries:

SELECT s.bar FROM serves s   WHERE s.beer = 'Bud'

SELECT f.drinker FROM freq f, serves s   WHERE f.bar = s.bar and s.beer = 'Bud'

SELECT drinker FROM freq WHERE dr NOT IN   (        SELECT f.drinker        FROM frequents f        WHERE f.bar NOT IN            (SELECT bar FROM serves WHERE beer = 'Bud')   )

Relational Algebra

Is an alternative representation language used in SQL. What you can represent using relational algebra is absolutely the same as what you can represent in FO logic. It constitutes of simple operations on relations that allow you to specify queries.

Main Operations

$$\Pi$$ Projection : Project relations on a subset of its columns (attributes).

$$\sigma$$ Selection : Selects a subset of tuples from a particular relation, based upon a specified selection cond ition.

$$\cup$$, $$-$$ Union, Diff : similar to set operations.

 * ><| Join : allows you to combine tuples from two relations.

Rename : renames A to B.

Expressions built from these expressions are called a relational algebra query. Whatever you can express in algebra we can represent in FO.

Examples:

(i) $$\Pi_{bar} (\Sigma_{beer=Bud}(serves))$$

(ii) $$ \Pi_{dr} (freq |><| \sigma_{beer=Bud}(serves))$$

(iii) $$ \Pi_{d}(freq)- \Pi_{d}[freq |><| (\Pi_{bar}(freq) - \Pi_{bar}(\Sigma_{beer=Bud}(serves)))] $$

Expressive Power

Graph properties correspond to properties of datastructures in relational databases (see the chapter on database queries), e.g.:
 * Consider a companies database that contains all managers together with the 'is superordinate' relation amongst them. In a proper heirachy the database should contain no circles, i.e. a manager can not be a superordinate of his superordinate. Querying this corresponds to checking a graph for cyclicity. As from above this can not be done in FO.
 * Say two managers want to find out if one of them is more powerful than the other. So the want to query the database if the number of their subordinates is equal, i.e. the cardinalities of the sets of subordinates (say, directly and indirectly) is equal. This can't be done in FO ("FO can not count"). This is the reason why SQL is extended by a counting function.
 * Consider a database of airports and connection flights among them. In order to query the direct reachibility of airport b from airport a we can write

$$q_0(a, b) = F(a, b)$$.

Now in order to query connections with one change of plane we write

$$q_1(a, b) = \exists_c F(a, c) \land F(c, b)$$ and get $$Q_1(a, b) = q_1(a, b) \lor q_1(a, b)$$

for connections with zero or one change. Thus in order to extend this to reachibility (of no matter how many changes) we have to write

$$\bigvee_{k\in\mathbb{N}} q_k$$

what is not a FO expression. So we are fine with FO for a restricted reachibility up to a certain k but not for reachibility as it appears in graph theory. In fact it can be shown that reachibility can not be queried in FO.

Descriptive Complexity Theory
As mentioned above Hamiltonicity can not be expressed in FO. So now one can think of an extension of FO in order to express this property. This can be done like

$$\exists L \exists S (isLinOrd(L) \land isSucRelOf(S, L) \land \forall_x \exists_y (L(x, y) L\lor L(y, x)) \land \forall_x \forall_y(S(x, y) \implies E(x, y)))$$

where the quantifiers on the left state the existence of the binary relations L and S that satisfy the formula on the right. The realtion isLinOrd states that L is a linear order and isSucRelOf means that S is the successor relation of L. Both can be expressed in FO. The pattern as above, second-order existential quantifiers followed by a first order formula is called existential second order logic.

Now it is well known that Hamiltonicity is a NP-complete problem and one can ask: is there a natural connection between NP and second order logic? Indeed, there is a very amazing one: existential second-order logic corresponds exactly (!) to the class of NP-complete problems! This result is known as Fagin's theorem, it has lead to the new area of descriptive complexity where complexity classes are described by means of logical formalisms.

title: Logic for Computer Science/Applications


text:
Template:Computer Programming Navigation

All bookshelves > Science > Computer Science > Computer Programming >  - /Templates


text:
Cookbook talk:Chili con Carne

Why cookbook links and not interwiki wikipedia links? Reub2000 14:21, 12 Feb 2005 (UTC)

Why use Cookbook Links
The cookbook should not be a mere dumping ground for things that got kicked out of wikipedia.

The cookbook needs to be self-contained. If it is not, then that should be fixed. This is especially true for cooking-related stuff. Most other stuff simply does not belong. (for example, the chemistry lesson that somebody ripped out of the Cookbook:Fat module)

Links that stay within the cookbook will go to pages with cookbook links across the top and cookbook categories across the bottom. This is friendly. It allows for easy navigation within the cookbook.

Wikipedia does not normally provide links into the cookbook.

Links into wikipedia can be done via the wikipedia template, giving them a nice little box that invites the reader to learn more -- presumably about non-cooking aspects of something.

Likewise, for the gardening book. There is a template for it that gives a neat little box. (Un attributed edit)

No, this is EXACTLY what belongs on Wikibooks! It is a recipe. Recipe = Wikibooks. WhisperToMe 17:33, 19 Mar 2005 (UTC)

Kidney beans
I always put Cookbook:kidney beans in mine. Yum. Cdyson37 11:56, 31 August 2005 (UTC)

disambiguation page
I'd like to split the various recipes out of this page into their own modules, and convert this page into a disambiguation page, or a general chili discussion page. Any other thoughts? Gentgeen 20:08, 4 November 2005 (UTC)

title: Cookbook talk:Chili con Carne


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User:McCart42~enwikibooks

McCart42 on Wikipedia

title: User:McCart42~enwikibooks


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Template:Computer Programming/Variables/0

This computer programming article is available in pseudocode and Ada.


text:
Template:Computer Programming/Variables/1

Variables are references that stand in for a value that is contained at a certain memory address.

Variables are said to have a value and may have a data type. If a variable has a type, then only values of this type may be assigned to it. Variables do not always have a type.

A value can have many values of many different types: integers (7), ratios (1/2), (approximations of) reals (10.234), complex numbers (4+2i), characters ('a'), strings ("hello"), and much more.

Different languages use different names for their types and may not include any of the above.

Assignment statements
An assignment statement is used to set a variable to a new value.


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Ada Programming/Variables

Assignment statements are written as.

X = 10;

Ada is the same. The declaration is as follows:

X : Integer = 10; Do_Something (X); ;

Without variables, we would not be able to create programs that go much beyond the classic "Hello World!" example. Variables in Ada must be declared. They cannot just magically appear in a program without first having been declared. A variable declaration looks like this:

Variable_Name : Variable_Type [:=Optional Value]

If a variable is assigned a value when declared, it is said to be initialized. It is possible to declare more than one variable of the same  in one go by comma-separating the variable names:

Variable_A, Variable_B : Variable_Type [:=Optional Value]

As you can see, the assignment of a value to a variable is optional. All the compiler needs to know, is what kind of data (the ) you intend the variable to hold. It doesn't care if there's actual data in the variable or not. When you declare a variable, you're basically just asking for a specific amount of memory to be set aside. The actual amount of memory depends, of course, on the declared. An  might take up 4 bytes of memory, and a   might take up 10 bytes of memory. The variable name is nothing more than a symbolic name, associated with whatever value that is placed in the memory reserved to the variable.

If we were to assign a value to a variable during its declaration, it would look like this:

Variable_Name : Variable_Type := Variable_Value

Let's try it with some real Ada variables. As seen above, a variable in Ada **must** be declared as pointing to a specific  of data:

Here we declare the variable  as a   type, the length of which is 10 characters,. Lets see how it looks if we assign a value to  during its declaration:

Here we've first declared and then initialized the  variable.

In the case of the  type, the length can be omitted and we can instead simply write:

Here the assignment of  implicitly declares   to be of length , because that is the length of the assigned string.

Variables can be declared as any, be it  ,  ,  ,   or homegrown types. Lets try and declare a variety of variables:

Notice the homegrown  type. First we declare the new type, and then we declare the  variable the of that type. This is one of the biggest strengths of Ada: The ability to declare your own types and subtypes. More can be found on this subject in the Type System article.

Now, let's try and use the above declared variables in an actual program:

When executed, the above program should output the following:

A_String B_String String_A String_B 1: 1 2: 2  3: 3  1: 10  2: 20  3: 30  10  RED Thomas Løcke

Here we can actually see why variables are called variables: Their values vary.

Notice how we are able to change the data contained in, for example, the  variable. When we declare it, we assign the value  (the variable is said to be initialized), but a little later we assign another value to  :. That right there is the core concept of variables that every beginning programmer must understand: Variables vary. A variable name is just a reference to a place in memory where a a specified  of data resides. The exact data can, and probably will, change a lot during the run of a program, but the variable name and the  remains the same.

If a variable doesn't change during program execution, then we have a better option: A constant. These are the stiff upper lip siblings of variables.

Scope
Finally, let's take a short look at variable scope in regard to blocks. When and where are they visible? This is perhaps best understood by a simple program:

The output we get from the above looks like this:

1:Thomas Løcke 2:Dwight S. Miller 3:Thomas Løcke 4:Thomas Løcke

Note how  is declared as a local variable in the first block. The declaration in the first block does not in any way interfere with the "global"  variable. If no  variable is declared for a block, the "global"   variable is used, as can be seen in the final block, where   is printed, even though no such assignment has been done in the block.

So variable scope in regard to blocks is very straightforward: Blocks inherit variables from their parent(s) and these can then be overridden locally in the block by declaring the variable anew.

Ada Reference Manual

| Programación en Ada/Objetos

title: Ada Programming/Variables


text:
Template:Computer Programming/Variables/2

The example set the variable X to the integer value of 10. The assignment statement overwrites the contents of the variable and the previous value is lost.

In some languages, before a variable can be used, it will have to be declared, where the declaration specifies the type.


text:
Web Development

Table of Contents

 * 1) Introduction
 * 2) /The history of the Internet/
 * 3) /Why do people develop web pages?/
 * 4) /What is web development?/
 * 5) The Concept
 * 6) /Getting from vague idea to hammered-out concept/
 * 7) /Pre-design testing and other useful techniques/
 * 8) /The rationale of concepts: being careful/
 * 9) Resources
 * 10) /What's needed to develop a website?/
 * 11) /Setting up a reasonable web development budget/
 * 12) /Finding investors, advertisers, and supporters/
 * 13) /Making connections and selling your concept/
 * 14) The Image
 * 15) /The importance of a website's unified theme/
 * 16) /The design phase and the one-second test/
 * 17) /Compliance and audience reach/
 * 18) The Backend
 * 19) /What is a backend?/
 * 20) /To db or not to db?/
 * 21) /Choosing the right programming language/
 * 22) /Good coding procedures and adherence to standards/
 * 23) Gaining users
 * 24) /Finding your target audience/
 * 25) /Enticing advertisers/
 * 26) /Search engine optimization/
 * 27) /The common misconception: visits vs. hits/
 * 28) /Staying updated: why people come back/
 * 29) Adding a Forum
 * 30) The Follow-through
 * 31) /Updating a live website/
 * 32) /Providing support/
 * 33) /Continued dedication/
 * 34) Closing Shop
 * 35) /Life after death: selling your website/
 * 36) /An alternative to closing: going open-source/

Case Studies

 * 1) /PTM Training/

Développement web

title: Web Development


text:
Template:Computer Programming/Variables/3

Uses
Variables store everything in your program. The purpose of any useful program is to modify variables.


title: User:24.224.153.40


text:
A History of Japan: From Mythology to Nationhood/The Late Heian Period

The Heian Period ends with the Genpei War (源平合戦), fought between the Minamoto (源) and the Taira (平) clans. It occurs during the Late-Heian Period and marks the rise of the military class, and the formation of the Kamakura Shogunate under Minamoto Yoritomo.

Background
The Genpei War was the culmination of a decades-long conflict between the two clans over dominance of the Imperial court and control of Japan. In the Hōgen Rebellion and in the Heiji Rebellion of earlier decades, the Minamoto attempted to regain control from the Taira and failed. The Taira then began a series of executions, intended to eliminate their rivals.

In 1177, relations between the Taira clan and the retired Emperor Go-Shirakawa became highly strained, and the latter attempted a coup d'état to oust the Daijō Daijin (prime minister), Taira no Kiyomori. Kiyomori defeated the former emperor and abolished the Insei system. This provoked strong anti-Taira sentiment.

On March 21, 1180, Taira no Kiyomori put his grandson, Antoku (then only two years of age), on the throne, after the abdication of Emperor Takakura. Go-Shirakawa's son, Prince Mochihito, felt that he was being denied his rightful place on the throne and, with the help of Minamoto Yoritomo, sent out a call to arms to the various samurai families and Buddhist monasteries on May 5. In June, Kiyomori moved the seat of imperial power to Fukuhara (modern day Kobe), in the hope of promoting trade with Song Dynasty China, and on the fifteenth of that month, Prince Mochihito fled Kyoto to take refuge in Mii-dera.

Beginnings of the War
The actions of Taira no Kiyomori having deepened Minamoto hatred for the Taira clan, a call for arms was sent up by Minamoto no Yorimasa and Prince Mochihito. Not knowing who was behind this rally, Kiyomori called for the arrest of Mochihito, who sought protection at the temple of Mii-dera. The Mii-dera monks were unable to ensure him sufficient protection, so he was forced to move along. He was then chased by Taira forces to the Byōdō-in, just outside Kyoto. The war began thus, with a dramatic encounter on and around the bridge over the River Uji. This battle ended in Yorimasa's ritual suicide inside the Byōdō-in and Mochihito's capture and execution shortly afterwards.

It was at this point that Minamoto no Yoritomo took over leadership of the Minamoto clan and began traveling the country seeking to rendezvous with allies. Leaving Izu Province, heading for the Hakone Pass, he was defeated by the Taira in the battle of Ishibashiyama. However he successfully made it to the provinces of Kai and Kozuke, where the Takeda and other friendly families helped repel the Taira army. Meanwhile, Taira no Kiyomori, seeking vengeance against the Mii-dera monks and others, besieged Nara and burnt much of the city to the ground.

Fighting continued the following year. Minamoto no Yukiie launched an unsuccessful sneak attack attempt against the army of Taira no Tomomori at the Battle of Sunomatagawa. He was pursued by them to the Yahahigawa, destroying the bridge over the river in order to slow the Taira progress. He was defeated and forced to withdraw once again, but Taira no Tomomori fell ill and called off his pursuit of Yukiie's forces.

Taira no Kiyomori died from illness in the spring of 1181, and around the same time Japan began to suffer from a famine which would last through the following year. The Taira moved to attack Minamoto no Yoshinaka, a cousin of Yoritomo, who had raised forces in the north but were unsuccessful. For nearly two years, the war ceased, only to resume in the spring of 1183.

Turning of the tide
Minamoto no Yoritomo, suspicious of the strength of his cousin, launched a series of attacks against Yoshinaka. Yoshinaka had sought to take for himself lands controlled by Yoritomo, which had earlier belonged to Yoshinaka's father. Though the two reconciled with one another and agreed to focus on their common enemy, the Taira, this rivalry would remain strong throughout the war. Forced to recognize Yoritomo as the head of the clan and to send his son Yoshitaka to Kamakura as a hostage, Yoshinaka would not truly fight alongside his cousin for much of the war. He sought to defeat the Taira himself and to reach Kyoto before Yoritomo, claiming victory and the according honor and power.

Placating Yoritomo's suspicions of treachery or betrayal, Yoshinaka survived an assault on his fortress at Hiuchiyama by Taira no Koremori and engaged Koremori again at the battle of Kurikara. Yoshinaka's victory for the Minamoto at Kurikara, also known as the battle of Tonamiyama, would prove to be the turning point in the war. Through creative tactics, skillful division of his forces and a series of bluffs and diversions, Yoshinaka inflicted heavy losses on the Taira, who fled, confused and demoralized.

The Taira loss at Kurikara was so severe that they found themselves, several months later, under siege in Kyoto, with Yoshinaka approaching the city from the northeast and Yukiie from the east. Both Minamoto leaders had seen little or no opposition in marching to the capital and now forced the Taira to flee the city. Taira no Munemori, head of the clan since his father Kiyomori's death, led his army, along with the young Emperor Antoku and the Imperial regalia, to his clan's fortresses in western Honshū and Shikoku.

Internal Minamoto clan hostilities
The Taira clan set fire to their Rokuhara palace and the surrounding district, leaving Minamoto no Yoshinaka with the only force of any significant power in the Home Provinces surrounding the capital. Empowered with a mandate by Emperor Go-Shirakawa to pursue the Taira and destroy them, Yoshinaka once again sought to gain control of the Minamoto clan and regain his ancestral lands from his cousins Yoritomo and Yoshitsune.

Meanwhile, the fleeing Taira set up a temporary Court at Dazaifu in Kyūshū, the southernmost of Japan's main islands. They were forced out soon afterwards by local revolts, spurred by Emperor Go-Shirakawa and sought refuge at Yashima, a small island in the Inland Sea.

Yoshinaka sent a force to pursue the Taira, while he led a second force back to Kamakura to delay his cousins' actions. While his men lost to the Taira at Mizushima, Yoshinaka conspired with Yukiie to seize the capital and the Emperor, possibly even establishing a new Court in the north. However, Yukiie revealed these plans to the Emperor, who communicated them to Yoritomo. Betrayed by Yukiie, Yoshinaka took command of Kyoto and, at the beginning of 1184, set fire to the Hōjūjidono, taking the Emperor into custody. Minamoto no Yoshitsune arrived soon afterwards with his brother Noriyori and a considerable force, driving Yoshinaka from the city. After fighting his cousins at the bridge over the Uji, where the war began, Yoshinaka made his final stand at Awazu, in Ōmi province.

Final stages of the conflict
As the united Minamoto forces left Kyoto, the Taira began consolidating their position at a number of sites in and around the Inland Sea, which was their ancestral home territory. They received a number of missives from the Emperor offering that if they surrendered by the seventh day of the second month, the Minamoto could be convinced to agree to a truce. This was a farce, as neither the Minamoto nor the Emperor had any intentions of waiting until the eighth day to attack. Nevertheless, this tactic offered the Emperor a chance to regain the Regalia and to distract the Taira leadership.

The Minamoto army, led by Yoshitsune and Noriyori, made their first major assault at Ichi-no-Tani, one of the primary Taira fortresses on Honshū. The fortress was surrounded, and the Taira retreated to Shikoku. However, the Minamoto were not prepared to assault Shikoku; a six-month pause thus ensued during which the Minamoto took the proper steps. Though on the retreat, the Taira enjoyed the distinct advantages of being in friendly, home territories, and of being far more adept at naval combat than their rivals.

It was not until nearly a year after Ichi-no-Tani that the main Taira fortress at Yashima came under assault. Seeing bonfires on the mainland of Shikoku, the Taira expected a land-based attack and took to their ships. This was a deceptive play on the part of the Minamoto, however, who lay in wait with their own navy. The Yashima fortress fell, along with the improvised imperial palace built there by the Taira, many of whom however escaped along with the Imperial regalia and the Emperor Antoku.

The Genpei War came to an end one month later, following the battle of Dan-no-ura, one of the most famous and important battles in Japanese history. The Minamoto engaged the Taira fleet in the Straits of Shimonoseki, a tiny body of water separating the islands of Honshū and Kyūshū. After a series of archery duels, hand-to-hand fighting broke out. The tides played a powerful role in the development of the battle, granting the advantage first to the Taira, who were more experienced and abler sailors and later to the Minamoto. The Minamoto advantage was considerably enhanced by the defection of Taguchi Shigeyoshi, a Taira general who revealed the location of Emperor Antoku and the regalia. The Minamoto redirected their attention on the Emperor's ship, and the battle quickly swung in their favor.

Many of the Taira samurai, along with Emperor Antoku and his grandmother Taira no Tokiko, widow of Taira no Kiyomori, threw themselves into the waves rather than live to see their clan's ultimate defeat at the hands of the Minamoto.

Consequences
The Taira clan was destroyed, and the Minamoto victory was followed by the establishment of the Kamakura shogunate. Though Minamoto no Yoritomo was not the first to ever hold the title of Shogun, he was the first to wield it in a role of nationwide scope. The end of the Genpei War and beginning of the Kamakura shogunate marked the rise of military class and the suppression of the power of the emperor, who was compelled to preside without effective political or military power, until the Meiji Restoration over 650 years later.

In addition, this war and its aftermath established red and white, the colors of the Taira and Minamoto standards, respectively, as Japan's national colors. Today, these colors can be seen on the flag of Japan, and also in banners and flags in sumo and other traditional activities.

Battles

 * 1180 First Battle of Uji - regarded as the first battle in the Genpei Wars, the monks of the Byodoin fight alongside Minamoto no Yorimasa.
 * 1180 Siege of Nara - the Taira set fire to temples and monasteries, to cut supplies to their rivals.
 * 1180 Battle of Ishibashiyama - Minamoto no Yoritomo's first battle against the Taira. Minamoto Yoritomo loses the battle.
 * 1180 Battle of Fujigawa - the Taira mistake a flock of waterfowl for a sneak attack by the Minamoto in the night, and retreat before any fighting occurs.
 * 1181 Battle of Sunomatagawa - the Taira thwart a sneak attack in the night but retreat.
 * 1181 Battle of Yahagigawa - the Minamoto, retreating from Sunomata, attempt to make a stand.
 * 1183 Siege of Hiuchi - the Taira attack a Minamoto fortress.
 * 1183 Battle of Kurikara - the tide of the war turns, in the Minamoto's favor.
 * 1183 Battle of Shinohara - Yoshinaka pursues the Taira force from Kurikara
 * 1183 Battle of Mizushima - the Taira intercept a Minamoto force, heading for Yashima.
 * 1183 Siege of Fukuryuji - the Minamoto attack a Taira fortress.
 * 1183 Battle of Muroyama - Minamoto no Yukiie tries and fails to recoup the loss of the battle of Mizushima.
 * 1184 Siege of Hojujidono - Yoshinaka sets fire to the Hojuji-dono and kidnaps Emperor Go-Shirakawa.
 * 1184 Second Battle of Uji - Yoshinaka is pursued out of the capital by Yoshitsune and Noriyori.
 * 1184 Battle of Awazu - Minamoto no Yoshinaka is defeated and killed by Minamoto no Yoshitsune and Minamoto no Noriyori.
 * 1184 Battle of Ichi-no-Tani - the Minamoto attack one of the Taira's primary fortresses.
 * 1184 Battle of Kojima - Taira fleeing Ichi-no-Tani are attacked by Minamoto no Noriyori.
 * 1185 Battle of Yashima - the Minamoto assault their enemies' fortress, just off of Shikoku.
 * 1185 Battle of Dan-no-ura - the decisive naval battle ending the war.


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Category:Candidates for speedy deletion

__NOGALLERY__

These pages are candidates for speedy deletion because someone used or, or more than 7 days ago used ,  or. NB: there can be false positives with the print versions of more than seven days transcluding a new page with these templates.

ca:Categoria:Viquillibres:Elements a eliminar de:Kategorie:Wikibooks: Schnelllöschkandidaten es:Categoría:Wikilibros:Borrar gl:Categoría:Páxinas para borrar hy:Կատեգորիա:Արագ ջնջման թեկնածուներ it:Categoria:Da cancellare subito ka:კატეგორია:წასაშლელი გვერდები ja:カテゴリ:即時削除 ru:Категория:Викиучебник:К быстрому удалению tr:Kategori:Vikikitap:Silinecek sayfalar zh:Category:快速刪除候選

title: Category:Candidates for speedy deletion


text:
Cookbook:Neck Sweetbread

| Basic foodstuffs | Organ Meat

Neck sweetbread is the genteel name of the meat of the thymus of a young calf. Sweetbreads are noted and prized for their flavor and texture. Sweetbreads have nothing to do with bread and they are not sweet.

The thymus is known as neck sweetbread.

The pancreas is known as stomach sweetbread.

title: Cookbook:Neck Sweetbread


text:
Cookbook:Sweetbread II

| Organ Meat

Sweetbread is the culinary name for various glands from larger animals. Despite the name, sweetbread is not sweet.

title: Cookbook:Sweetbread II


text:
Cookbook:Stomach Sweetbread

| Basic foodstuffs | Organ Meat

Stomach sweetbread is the genteel name of the meat of the pancreas of a young calf. Sweetbreads are noted and prized for their flavor and texture. Sweetbreads have nothing to do with bread and they are not sweet.

The thymus is known as neck sweetbread.

The pancreas is known as stomach sweetbread.

title: Cookbook:Stomach Sweetbread


text:
User:24~enwikibooks

I am 24.

 * Go!

title: User:24~enwikibooks


text:
User:24~enwikibooks/go

Equal?

title: User:24~enwikibooks/go


text:
User talk:24~enwikibooks/go

 Welcome to the talk page of 24, user.

title: User talk:24~enwikibooks/go


text:
Cookbook:Vanilla

Vanilla is a flavoring derived from the vanilla bean. Vanillin is the distinctive chemical in vanilla. Vanilla is commonly used in desserts and in chocolate. Vanilla is often not noticeable as a distinct flavor, yet nevertheless greatly improves the taste of the dish it has been added to (much like salt and MSG).

Vanilla extract is alcohol containing flavor (vanillin) from the vanilla bean. Vanillin itself, produced by a modern chemical process, is widely sold in a form similar to vanilla extract. When a recipe specifies vanilla, usually the recipe is intended to work with either vanilla extract or vanillin. Such recipes will require modification if whole vanilla beans are used.

Vanilla is also used in the form of vanilla sugar. This can have different meanings depending upon the origin of the recipe. In Scandinavian countries, vanilla sugar is a powdered sugar with a strong vanilla flavour. In these countries, it is the main method of incorporating vanilla flavor into a recipe; vanilla extract is not commonly available. This form of vanilla sugar can be replaced by a roughly equivalent volume of vanilla extract. In other countries, including the United States, vanilla sugar usually is granulated white sugar that has been flavored over some time by a vanilla bean included in the sugar.

Kookboek/Vanille

title: Cookbook:Vanilla


text:
Japanese/Vocabulary/Numbers

Further reading: 数の比較 ("comparison of numbers") at Japanese Wikipedia.

Japonés/Vocabulario/Números Japonais/Vocabulaire/Nombres

title: Japanese/Vocabulary/Numbers


text:
User:Jun-Dai

http://jundai.kurutta.net

m:User:Jun-Dai

also,

User:Jun-Dai/Np/L1

title: User:Jun-Dai


text:
D'ni/Foreword

Shorah!

Welcome to the Wikibook grammar of the D'ni language. Perhaps this Wikibook is not ideal as a course for beginners, but will offer concise, complete information on the principles of D'ni language for reference.

Note that this Wikibook makes use of the 'New Transcription Standard', that means the way D'ni words are rendered with normal letters.

The language
D'ni (more properly spelled D'nee, D'ní), In the Myst series, is the race who came to Earth from Garternay. The word is used for

 * 1) A member of this race.
 * 2) The city in a subterranean cavern below New Mexico, populated by them.
 * 3) Their language.

The language was created by Cyan employee Richard A. Watson, or RAWA during the production of the game Riven. The game provided many D'ni spoken words and inscriptions that initially puzzled the fans, and some of them remain still untranslated.

Information about the language and vocabulary, have been provided in the three Myst books. Online communities study the language, sometimes with contribution by RAWA himself, who doesn't like to give out information easily, and prefers only to clarify matters rather than give translations. RAWA has contributed to the community, not only in the linguistic matters, but anything that has to do with the world of Myst.

Years after the publication of Riven, slowly more facts and words come to our knowledge with the subsequent games. Study of D'ni is more or less like an enormous puzzle that is filled now and then, after hunting of sporadic hints and evidence. This wikibook will attempt to describe our knowledge so far, and be updated whenever new facts show up.

title: D'ni/Foreword


text:
D'ni/Pronouns

Personal Pronouns
Personal Pronouns appear in 2 kinds: independent words (in accusative, like 'me, him, her' etc.) or suffixes (subjects to verbs or possessors).

Nominative
The nominative forms are suffixed to the verbs as subjects. e.g. to say 'he finds' we add suffix –en 'he' to verb stem húr- 'to find' to form húren.

There is no 1st person in nominative, and we use the bare verb stem. E.g. tégan to form 'I love'

Genitive
Genitive forms are suffixed to nouns to indicate possessors of that noun. E.g. korom ‘thy book’, navaot ‘our master’, únrétíos ‘their lords’.

The 3rd plural genitive form –os is irregular.

Accusative/Dative
Accusative is used when a pronoun is the direct object of a verb. English examples are 'I love him', 'I choose you'. Dative is when the pronoun is the indirect object, ex: 'I talk to you', 'You work for him'. Accusative/Dative pronouns unlike the others, are independent words. E.g. çev šem ‘I thank you’, tagema b’zú ‘give to me!’ (Note: Most examples of these pronouns occur in the dative case (i.e., as indirect objects) -- the case for the accusative is less strong.)

It is hypothetically assumed therefore that the accusative of 3rd person singular and plural can be sen and sít respectively.

Other pronouns
There are also other pronouns:

 * met 'this'. Indicative pronoun which follows the noun. E.g. bacana met, 'this map' but it is also prefixed to the noun e.g. a met m'la, 'this lizard' (a- is a "direct object indicator". The rules for using it are not quite clear, in translations it can be omitted.)
 * mot 'that, which'. Relative pronoun. E.g. rem'la sexen poant, mot tornen, ‘the lizard has saliva, which it spits’, also used with the element gor ‘time’ and forms gormot ‘then’

title: D'ni/Pronouns


text:
D'ni/Verbs

The common verb form is formed by 3 parts: the tense prefix, the verb stem and the pronoun suffix e.g. Do-húr-et 'We are finding'

Inflexion
As we said, pronoun suffixes are used for every person except the 1st singular. Here is for example the conjugation in simple present tense of the verb ken ‘to be’

 * Ken	'I am'
 * Kenem	'Thou art'
 * Kenen	'He is'
 * Kenet	'We are'
 * Kentí	'You-plural are'
 * Kenít	'They are'

Tenses
There are four basic tense prefixes:

 * le = perfect
 * ko = past
 * do = present progressive
 * bo = future

Present tense has no prefix.

Their combinations can provide other tenses. The rule of the prefixes series says that they must follow the priority bo-ko-do-l(e)

Attested tenses are the following:

 * Present
 * Húr	'I find'

 * Present cont.
 * Do-húr	'I am finding'

 * Present perfect
 * Le-húr	'I have found'

 * Past
 * Ko-húr	'I found'

 * Past cont.
 * Ko-do-húr	'I was finding

 * Past perfect
 * Ko-l-húr	'I had found'

 * Future
 * Bo-húr	'I will find'

 * Future cont.
 * Bo-do-húr	'I will be finding'

 * Future perfect
 * Bo-ko-húr	I will have found'

 * Future perfect cont.
 * Bo-do-l-húr	I will have been finding'

Other prefix combinations are possible, and some of them hint at tenses missing from the above... for example *do-l-húr 'I have been finding' etc.

Voice
We have conflicting information on how passive is formed. The Kenen Gor text shows that passive participles can be formed with ken and the ending -ij. This formation could be applied for present tense. Therefore 'I am known' can be translated as ken tagamij

Most other passive voice examples are in past tense; even then we have three different ways of passive formation

 * In one example, passive is expressed by simple past (Kotokituen lit. 'it determined', understood as 'it was determined'; kohúren lit. 'it found', understood as 'it was found')
 * Passive is also formed with past continuous (kodobarelen 'it was making/was made' and kodolasaen 'it was sealing/was sealed')
 * However there are some instances where the verb ken 'be' is also added to form the passive, as in English; ken is followed by the past tense of the verb in the 3rd person: kokenen kosayen lit. 'it was it designed' understood as 'it was designed'; kokenen kohúren 'was found'.

All the above attested examples have a problem: not only are passive but also refer to the past as well; therefore we can't determine if the tense expressed the voice, the time, or both.

The following possibilities can be considered: or
 * As in English, passive voice is formed always with the past tense.
 * No distinction between active and passive; For example dotagen means both 'I give' and 'I am given'. The above examples are found in past tense simply because they refer to a past time and this hasn't to do with the passive formation

Imperative
The suffix -a denotes Imperative.

 * húr-em-a! 'find!' (command to one person)
 * húr-tí-a! '[all of you] find!' (command to a group excluding you)
 * húr-et-a! 'let’s find!' (command to a group including you)

Negation
Negative phrases are formed with the word for ril which means 'no'. It contains all the English used of 'doesn't', 'isn't' etc.

 * Gen kenen renavaox Riven, rúb ril bokenen navaot 'Gen is the master of Riven, but will not be our master'
 * Étrus ril lesel Myst. Étrus lesel Edanna 'Atrus did not write Myst; Atrus wrote Edanna'

Formation
Note that verbs can become adjectives, nouns and persons with -al, -tav and -tan respectively

 * marn-al 'creating' (e.g. the creating spirit)
 * húr-tav 'finding' (e.g. the finding of the book)
 * lon-tan 'discoverer'

title: D'ni/Verbs


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D'ni/Nouns

The noun is the basic form of speech in D'ni. Nouns that are basic words, usually have 2 syllables, but many have 3 as well.

Some which are compounds can reach 4 or 5. Those usually have derived endings and are derived from other parts of speech, like verbs.

Articles
The articles are prefixes to the nouns. Like in English, there are two kind of articles: definite re ('the') and indefinite erþ ('a'); unlike English, they stay the same whether the noun is singular or plural:

 * kor 'book
 * re-kor 'the book'
 * erþ-kor 'a book' (and possibly erþ-kortí 'some books')

Numbers
As in many languages, there are two numbers of the D'ni noun: singular and plural.

Plural is formed with the ending -tí

 * kor-tí 'books'

title: D'ni/Nouns


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D'ni/Adverbs

D'ni has adverbs, both original or derived from adjectives. Adverbs generally follow the verb they describe, except the temporal ones which precede the verb.

There are a few adverbs attested:

Mode

 * þoe 'how?'
 * megóré 'straight (out of)'
 * ril 'not'

Quantity

 * blo 'about, approximately'

Temporal

 * gormot 'then'. Maybe gormot is a compound of gor ‘time’ and mot ‘that, which’.
 * gormet 'now'. Not attested, but a hypothised compound of gor ‘time’ and met ‘this’.
 * gaþ 'still'
 * can 'always'

Derivation from adjectives
The adverbs can be derived by ''-sh suffixed to an adjective

 * kera 'brave' > kera-š 'bravely'
 * garo 'might' > garo-š 'mightily'

title: D'ni/Adverbs


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D'ni/Prepositions

Like English, D'ni is a non-inflected language. Therefore, prepositions are very important. They are mostly prefixes connected to words with apostrophes.

The prepositions attested are

 * be 'to', which can used if someone is giving something to someone (dotagen b'set ‘is giving to us’), to express amount with numbers (b'vat ‘to five’), to show direction (relena b'retalío ‘the journey to the surface’) and, like English, to form the infinitive of verbs (rebišta kodoséen b'mes ‘the tunnel was designed to require’)
 * fe 'along/at', to show something be done on the surface of something (tornen f'reprædtí ‘it spits at the rocks’) and the expression f'túgo, ‘on foot’ is attested
 * xe 'for' when it means 'towards the goal of', in xregicaþ ‘for the safety’
 * me 'from/of', to show origin (dorísloen remarg melin m'repræd ‘dissolving the outer layer from the rock’) or composition (erþbæntí me kílentí ‘a series of steps’)
 * ne 'around', to show direction of motion
 * te 'by/with/in/of', which has the same function as the Latin ablative. It expresses instrument, or something that happens with something else (trebigto ‘with the blessing’, tre'irvæntí ‘along with the minerals’) and place (regalpotí tretalío ‘the caves at the surface’)
 * ben is a different kind of preposition; it means 'during, for (a time)' or 'instead' when it means 'in exchange or equivalence with', in ferem ben erþgor tona ‘dry for a long time’

Contraction
Oftentimes, prepositions are contracted.

 * When the word does not begin with an article, the preposition's becomes a prefix and the e is replaced with an apostrophe (re'irvæntí, t'Gen, b'Yavo, kortí'nea)
 * When the word does begin with an article (re or erþ), the preposition becomes a prefix and loses the e altogether (trebigto 'with the blessing', terþtes 'of a group')

The above rules also apply to the conjunction ga, 'and'.

Ben is never contracted.

Genitive
The word ox 'of' is an individual word when the noun is modified with a following adjective, otherwise it is a suffix. It means direct possession.

 * rekorox Gen 'the book of Gehn'
 * rekor prin ox Gen 'the small book of Gehn' (here the adjective prin intervenes between the noun and ox)

The word co also means 'of' but in the meaning of characteristics/properties.

title: D'ni/Prepositions


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D'ni/Derivations

Noun to adjective
A noun with the suffix -ec becomes an adjective

 * vog 'nature' > vog-ec 'natural'
 * fa 'one' > faec 'first'

Adjective to noun
An adjective with the suffix -(e)þ becomes a noun

 * gica 'safe' > gica-þ 'safety'
 * sógi 'stable' > sógi-þ 'stability'

Note that the name Kerath means ‘[the] Brave One’ formed by the adjective kera ‘brave’ indicating a titulary function of this suffix.

Adjective to adverb
Similarly, -(e)š is always suffixed onto adjectives and changes them to adverbs.

 * ten 'simple' > teneš 'simply'
 * garo 'mighty' > garoš 'mightily'
 * kera 'brave' > keraš 'bravely'

Verb to noun
The -tav suffix is used with verbs and is understood to form common nouns.

 * tégan 'to love' > re-tégan-tav 'the love'
 * cav 'to live' > re-cav-tav 'the life'

The -tan suffix is used with verbs to make the actor.

 * re-tégan-tan 'the lover'

The adverbs can be derived by -š suffixed to an adjective

 * Kera 'brave' > Kera-š 'bravely'

title: D'ni/Derivations


text:
D'ni/Idioms

There are some idioms to the D'ni that differentiate it from English. A D'ni fanfic writer should have these rules handy:

Word order

 * The adjectives follow the noun they describe. 'Small rock' is Præd prin
 * Articles always precede the noun they refer to, never the adjective: 'the natural rock' is 'the-rock natural', so we must say repræd vogec, and not **re-vogec præd.
 * When a word has several modifiers (adjectives, adverbs), the closer a modifier is to that word, the greater its significance. While English has them scattered on both sides of the noun, D'ni arranges them all afterwards in descending order of significance, single-word adjectives first, then adjectival phrases.
 * The bond between verb and object is very strong and can never be broken. Thus, when adverbs are introduced into a sentence that has both verb and object, they don't come directly after the verb as would be expected but rather are placed after the object.

Commas

 * The repeating ‘and’ ga between a series of words is correct, so it is okay to say 'I walked between rocks and plants and trees and mountains and caves and animals' while in English it might be annoying...

Quantity

 * Quantity factor such as 'a bit', 'very' or 'a lot' are expressed with preposition b'  followed by a number between 1 and 25. B'fasí ('to 25') means 'absolutely'. Numbers above 25 are used for exaggeration. See also ../Numbers/

title: D'ni/Idioms


text:
Template:Computer Programming/Statements/0

This computer programming article is available in pseudocode, Ada, C, C++, and Delphi.


text:
Template:Computer Programming/Statements/1

''Note: there are some simplifications in the explanations below. Don't take anything too literally.''

Most programming languages have the concept of a statement. A statement is a command that the programmer gives to the computer. For example:


text:
Ada Programming/Statements

Ada.Text_IO.Put_Line ("Hi there!");

Ada.Text_IO.Put_Line ("Hi there!"); Ada.Text_IO.Put_Line ("Strange things are afoot...");

This does seem like a lot of typing but don't worry: Ada allows you to declare shorter aliasnames if you need a long statement very often.

|Statements

title: Ada Programming/Statements


text:
C Programming/Statements

A statement is a command given to the computer that instructs the computer to take a specific action, such as display to the screen, or collect input. A computer program is made up of a series of statements.

In C, a statement can be any of the following:

Labeled Statements
A statement can be preceded by a label. Three types of labels exist in C.

A simple identifier followed by a colon is a label. Usually, this label is the target of a  statement.

Within  statements,   and   labeled statements exist.

A statement of the form

constant-expression  statement

indicates that control will pass to this statement if the value of the control expression of the  statement matches the value of the constant-expression. (In this case, the type of the constant-expression must be an integer or character.)

A statement of the form

statement

indicates that control will pass to this statement if the control expression of the  statement does not match any of the constant-expressions within the   statement. If the  statement is omitted, the control will pass to the statement following the   statement. Within a  statement, there can be only one   statement, unless the   statement is within another   statement.

Compound Statements
A compound statement is the way C groups multiple statements into a single statement. It consists of multiple statements and declarations within braces (i.e.  and  ). In the ANSI C Standard of 1989-1990, a compound statement contained an optional list of declarations followed by an optional list of statements; in more recent revisions of the Standard, declarations and statements can be freely interwoven through the code. The body of a function is also a compound statement by rule.

Expression Statements
An expression statement consists of an optional expression followed by a semicolon. If the expression is present, the statement may have a value. If no expression is present, the statement is often called the null statement.

The  function calls are expressions, so statements such as   are expression statements.

Selection Statements
Three types of selection statements exist in C:

expression  statement

In this type of if-statement, the sub-statement will only be executed iff the expression is non-zero.

expression  statement   statement

In this type of if-statement, the first sub-statement will only be executed iff the expression is non-zero; otherwise, the second sub-statement will be executed. Each  matches up with the closest unmatched , so that the following two snippets of code are not equal:

because in the first, the  statement matches up with the if statement that has   for a control, but in the second, the braces force the   to match up with the if that has   for a control.

Switch statements are also a type of selection statement. They have the format

expression  statement

The expression here is an integer or a character. The statement here is usually compound and it contains case-labeled statements and optionally a default-labeled statement. The compound statement should not have local variables as the jump to an internal label may skip over the initialization of such variables.

Iteration Statements
C has three kinds of iteration statements. The first is a while-statement with the form

expression  statement

The substatement of a while runs repeatedly as long as the control expression evaluates to non-zero at the beginning of each iteration. If the control expression evaluates to zero the first time through, the substatement may not run at all.

The second is a do-while statement of the form

statement    expression

This is similar to a while loop, except that the controlling expression is evaluated at the end of the loop instead of the beginning and consequently the sub-statement must execute at least once.

The third type of iteration statement is the for-statement. In ANSI C 1989, it has the form

expressionopt  expressionopt   expressionopt   statement

In more recent versions of the C standard, a declaration can substitute for the first expression. The opt subscript indicates that the expression is optional.

The statement

is the rough equivalent of

except for the behavior of  statements within.

The  expression represents an initial condition;   a control expression; and   what to happen on each iteration of the loop. If  is missing, the expression is considered to be non-zero on every iteration, and only a   statement within   (or a call to a non-returning function such as   or  ) will end the loop.

Jump Statements
C has four types of jump statements. The first, the  statement, is used sparingly and has the form

identifier

This statement transfers control flow to the statement labeled with the given identifier. The statement must be within the same function as the.

The second, the break statement, with the form

is used within iteration statements and  statements to pass control flow to the statement following the while, do-while, for, or switch.

The third, the continue statement, with the form

is used within the substatement of iteration statements to transfer control flow to the place just before the end of the substatement. In  statements the iteration expression (  above) will then be executed before the controlling expression (  above) is evaluated.

The fourth type of jump statement is the  statement with the form

expressionopt

This statement returns from the function. If the function return type is, the function may not return a value; otherwise, the expression represents the value to be returned.

title: C Programming/Statements


text:
Template:Computer Programming/Statements/2

This command has a verb ("") and other details (what to print). In this case, the command "" means "show on the screen," not "print on the printer." The programmer either gives the statement directly to the computer (by typing it while running a special program), or creates a text file with the command in it. You could create a file called "hi.txt", put the above command in it, and give the file to the computer.

If you have more than one command in the file, each will be performed in order, top to bottom. So the file could contain:


text:
Template:Computer Programming/Statements/3

The computer will perform each of these commands sequentially. It's invaluable to be able to "play computer" when programming. Ask yourself, "If I were the computer, what would I do with these statements?" If you're not sure what the answer is, then you are very likely to write incorrect code. Stop and check the manual for the programming language you're using.

In the above case, the computer will look at the first statement, determine that it's a  statement, look at what needs to be printed, and display that text on the computer screen. It'll look like this:

Hi there!

Note that the quotation marks aren't there. Their purpose in the program is to tell the computer where the text begins and ends, just like in English prose. The computer will then continue to the next statement, perform its command, and the screen will look like this:

Hi there! Strange things are afoot...

When the computer gets to the end of the text file, it stops. There are many different kinds of statements, depending on which programming language is being used. For example, there could be a beep statement that causes the computer to output a beep on its speaker, or a window statement that causes a new window to pop up.

Also, the way statements are written will vary depending on the programming language. These differences are fairly superficial. The set of rules like the first two is called a programming language's syntax. The set of verbs is called its library.

This article is available in pseudocode, Ada, C, C++, and Delphi - do have a look at the other languages as well.


text:
Calculus/Improper Integrals

The definition of a definite integral:
 * $$\int\limits_a^b f(x)dx$$

requires the interval $$[a,b]$$ be finite. The Fundamental Theorem of Calculus requires that $$f$$ be continuous on $$[a,b]$$. In this section, you will be studying a method of evaluating integrals that fail these requirements—either because their limits of integration are infinite, or because a finite number of discontinuities exist on the interval $$[a,b]$$. Integrals that fail either of these requirements are improper integrals. (If you are not familiar with L'Hôpital's rule, it is a good idea to review it before reading this section.)

Improper Integrals with Infinite Limits of Integration
Consider the integral
 * $$\int\limits_1^\infty\frac{dx}{x^2}$$

Assigning a finite upper bound $$b$$ in place of infinity gives
 * $$\lim_{b\to\infty}\int\limits_1^b\frac{dx}{x^2}=\lim_{b\to\infty}\left(\frac11-\frac{1}{b}\right)=\lim_{b\to\infty}\left(1-\frac{1}{b}\right)=1$$

This improper integral can be interpreted as the area of the unbounded region between $$f(x)=\frac{1}{x^2}$$, $$y=0$$ (the $$x$$-axis), and $$x=1$$.

Definition
1. Suppose $$\int\limits_a^b f(x)dx$$ exists for all $$b\ge a$$. Then we define
 * $$\int\limits_a^\infty f(x)dx=\lim_{b\to\infty}\int\limits_a^b f(x)dx$$, as long as this limit exists and is finite.

If it does exist we say the integral is convergent and otherwise we say it is divergent.

2. Similarly if $$\int\limits_a^b f(x)dx$$ exists for all $$a\le b$$ we define
 * $$\int\limits_{-\infty}^b f(x)dx=\lim_{a\to-\infty}\int\limits_a^b f(x)dx$$

3. Finally suppose $$c$$ is a fixed real number and that $$\int\limits_{-\infty}^c f(x)dx$$ and $$\int\limits_c^\infty f(x)dx$$ are both convergent. Then we define
 * $$\int\limits_{-\infty}^\infty f(x)dx=\int\limits_{-\infty}^c f(x)dx+\int\limits_c^\infty f(x)dx$$

We claim that
 * $$\int\limits_0^\infty e^{-x}dx=1$$

To do this we calculate

 * $$\int\limits_0^\infty e^{-x}dx$$
 * $$=\lim_{b\to\infty}\int\limits_0^b e^{-x}dx$$
 * $$=\lim_{b\to\infty}(-e^{-x})\Bigr|_0^b$$
 * $$=\lim_{b\to\infty}\left(-e^{-b}+1 \right)$$
 * $$=1$$
 * }
 * $$=\lim_{b\to\infty}\left(-e^{-b}+1 \right)$$
 * $$=1$$
 * }
 * $$=1$$
 * }
 * }

We claim that the integral
 * $$\int\limits_1^\infty \frac{dx}{x}$$ diverges.

This follows as

 * $$\int\limits_1^\infty\frac{dx}{x}$$
 * $$=\lim_{b\to\infty}\int\limits_1^b \frac{dx}{x}$$
 * $$=\lim_{b\to\infty}\ln(x)\Bigr|_1^b$$
 * $$=\lim_{b\to\infty}\left(\ln(b)-0\right)$$
 * $$=\infty$$
 * }
 * $$=\lim_{b\to\infty}\left(\ln(b)-0\right)$$
 * $$=\infty$$
 * }
 * $$=\infty$$
 * }
 * }

Therefore
 * $$\int\limits_1^\infty\frac{dx}{x}$$ diverges.

Find $$\int\limits_0^\infty x^2e^{-x}dx$$.

To calculate the integral use integration by parts twice to get

 * $$\int\limits_0^b x^2e^{-x}dx$$
 * $$=(-x^2e^{-x})\Bigr|_0^b+2\int\limits_0^b xe^{-x}dx$$
 * $$=-b^2e^{-b}+2\left((-x e^{-x})\Bigr|_0^b+\int\limits_0^b e^{-x}dx\right)$$
 * $$=-b^2e^{-b}+2\left(-be^{-b}-(e^{-x})\Bigr|_0^b\right)$$
 * $$=-b^2 e^{-b}+2(-be^{-b}-e^{-b}+1)$$
 * }
 * $$=-b^2e^{-b}+2\left(-be^{-b}-(e^{-x})\Bigr|_0^b\right)$$
 * $$=-b^2 e^{-b}+2(-be^{-b}-e^{-b}+1)$$
 * }
 * $$=-b^2 e^{-b}+2(-be^{-b}-e^{-b}+1)$$
 * }
 * }

Now $$\lim_{b\to\infty}e^{-b}=0$$ and because exponentials overpower polynomials, we see that $$\lim_{b\to\infty}b^2e^{-b}=0$$ and $$\lim_{b\to\infty}be^{-b}=0$$ as well. Hence,
 * $$\int\limits_0^\infty x^2e^{-x}dx=\lim_{b\to\infty}\int\limits_0^b x^2e^{-x}dx=0+2(0-0+1)=2$$

Show $$\int\limits_1^\infty\frac{dx}{x^p}=\begin{cases}\frac{1}{p-1},&\text{if }p>1\\ \text{diverges},&\text{if }p\le1\end{cases}$$

If $$p\ne 1$$ then

 * $$\int\limits_1^\infty \frac{dx}{x^p}$$
 * $$=\lim_{b\to\infty}\int\limits_1^b x^{-p}dx$$
 * $$=\lim_{b\to\infty}\left(\frac{x^{-p+1}}{-p+1}\right)\Bigg|_1^b$$
 * $$=-\frac{1}{1-p}\lim_{b\to\infty}\left(b^{-p+1}-1\right)$$
 * $$=\begin{cases}\frac{1}{p-1},&\text{if }p>1\\ \text{diverges},&\text{if }p<1\end{cases}$$
 * }
 * $$=-\frac{1}{1-p}\lim_{b\to\infty}\left(b^{-p+1}-1\right)$$
 * $$=\begin{cases}\frac{1}{p-1},&\text{if }p>1\\ \text{diverges},&\text{if }p<1\end{cases}$$
 * }
 * $$=\begin{cases}\frac{1}{p-1},&\text{if }p>1\\ \text{diverges},&\text{if }p<1\end{cases}$$
 * }
 * }

Notice that we had to assume that $$p\ne 1$$ to avoid dividing by 0. However the $$p=1$$ case was done in a previous example.

Improper Integrals with a Finite Number Discontinuities
First we give a definition for the integral of functions which have a discontinuity at one point.

Definition of improper integrals with a single discontinuity
If $$f$$ is continuous on the interval $$[a,b)$$ and is discontinuous at $$b$$, we define
 * $$\int\limits_a^b f(x)dx=\lim_{c\to b^-}\int\limits_a^c f(x)dx$$

If the limit in question exists we say the integral converges and otherwise we say it diverges.

Similarly if $$f$$ is continuous on the interval $$(a,b]$$ and is discontinuous at $$a$$, we define
 * $$\int\limits_a^b f(x)dx=\lim_{c\to a^+}\int\limits_c^b f(x)dx$$

Finally suppose $$f$$ has an discontinuity at a point $$c\in(a,b)$$ and is continuous at all other points in $$[a,b]$$. If $$\int\limits_a^c f(x)dx$$ and $$\int\limits_c^b f(x)dx$$ converge we define
 * $$\int\limits_a^b f(x)dx$$=$$\int\limits_a^c f(x)dx+\int\limits_c^b f(x)dx$$

Show $$\int\limits_0^1\frac{dx}{x^p}=\begin{cases}\frac{1}{1-p},&\text{if }p<1\\ \text{diverges},&\text{if }p\ge1\end{cases}$$

If $$p\ne1$$ then

 * $$\int\limits_0^1\frac{dx}{x^p}$$
 * $$=\lim_{a\to 0^+}\int\limits_a^1 x^{-p}dx$$
 * $$=\lim_{a\to 0^+}\left(\frac{x^{-p+1}}{-p+1}\right)\Bigg|_a^1$$
 * $$=-\frac{1}{1-p}\lim_{a\to 0^+}\left(1-a^{-p+1}\right)$$
 * $$=\begin{cases}\frac{1}{1-p},&\mbox{if }p<1\\ \text{diverges},&\text{if }p>1\end{cases}$$
 * }
 * $$=-\frac{1}{1-p}\lim_{a\to 0^+}\left(1-a^{-p+1}\right)$$
 * $$=\begin{cases}\frac{1}{1-p},&\mbox{if }p<1\\ \text{diverges},&\text{if }p>1\end{cases}$$
 * }
 * $$=\begin{cases}\frac{1}{1-p},&\mbox{if }p<1\\ \text{diverges},&\text{if }p>1\end{cases}$$
 * }
 * }

Notice that we had to assume that $$p\ne1$$ do avoid dividing by 0. So instead we do the $$p=1$$ case separately,
 * $$\int\limits_0^1 \frac{dx}{x}=\lim_{a\to 0^+}\left[\ln\big(|x|\big)\Big|_a^1\right]=\lim_{a\to 0^+}\Big[-\ln(a)\Big]$$

which diverges.

The integral $$\int\limits_{-1}^3\frac{dx}{x-2}$$ is improper because the integrand is not continuous at $$x=2$$. However had we not noticed that we might have been tempted to apply the fundamental theorem of calculus and conclude that it equals
 * $$\ln\big(|x-2|\big)\Big|_{-1}^3=\ln(5)-\ln(3)=\ln\left(\tfrac{5}{3}\right)$$

which is not correct. In fact the integral diverges since
 * $$\begin{align}\int\limits_{-1}^3\frac{dx}{x-2}&=\lim_{b\to2^-}\int\limits_{-1}^b \frac{dx}{x-2}+\lim_{a\to2^+}\int\limits_a^3\frac{dx}{x-2}\\

&=\lim_{b\to2^-}\ln\big(|x-2|\big)\Big|_{-1}^b+\lim_{a\to2^+}\ln\big(|x-2|\big)\Big|_a^3\\ &=\lim_{b\to2^-}\Big[\ln(2-b)-\ln(3)\Big]+\lim_{a\to2^+}\Big[\ln(1)-\ln(a-2)\Big]\\ &=\lim_{b\to2^-}\Big[\ln(2-b)\Big]-\ln(3)+\lim_{a\to2^+}\Big[-\ln(a-2)\Big]\\ \end{align}$$ and $$\lim_{b\to2^-}\Big[\ln(2-b)\Big]$$ and $$\lim_{a\to2^+}\Big[-\ln(a-2)\Big]$$ both diverge.

We can also give a definition of the integral of a function with a finite number of discontinuities.

Definition: Improper integrals with finite number of discontinuities
Suppose $$f$$ is continuous on $$[a,b]$$ except at points $$c_1<c_2<\ldots<c_n$$ in $$[a,b]$$. We define $$\begin{align}\int\limits_a^b f(x)dx=\int\limits_a^{c_1}f(x)dx+\int\limits_{c_1}^{c_2}f(x)dx+\int\limits_{c_2}^{c_3}f(x)dx+\cdots+\int\limits_{c_{n-1}}^{c_n} f(x)dx+\int\limits_{c_n}^b f(x)dx\end{align}$$ as long as each integral on the right converges.

Notice that by combining this definition with the definition for improper integrals with infinite endpoints, we can define the integral of a function with a finite number of discontinuities with one or more infinite endpoints.

Comparison Test
There are integrals which cannot easily be evaluated. However it may still be possible to show they are convergent by comparing them to an integral we already know converges.

 Theorem (Comparison Test) Let $$f,g$$ be continuous functions defined for all $$x\ge a$$.
 * 1) Suppose $$g(x)\ge f(x)\ge0$$ for all $$x\ge a$$ . Then if $$\int\limits_a^\infty g(x)dx$$ converges so does $$\int\limits_a^\infty f(x)dx$$.
 * 2) Suppose $$f(x)\ge h(x)\ge0$$ for all $$x\ge a$$ . Then if $$\int\limits_a^\infty h(x)dx$$ diverges so does $$\int\limits_a^\infty f(x)dx$$.

A similar theorem holds for improper integrals of the form $$\int\limits_{-\infty}^b f(x)dx$$ and for improper integrals with discontinuities.

Show that $$\int\limits_1^\infty\frac{\sin(x)+2}{x^2}dx$$ converges.

For all $$x$$ we know that $$-1\le\sin(x)\le 1$$ so $$1\le\sin(x)+2\le3$$. This implies that
 * $$0\le\frac{\sin(x)+2}{x^2}\le\frac{3}{x^2}$$.

We have seen that $$\int\limits_1^\infty\frac{3}{x^2}dx=3\int\limits_1^\infty\frac{dx}{x^2}$$ converges. So putting $$f(x)=\frac{\sin(x)+2}{x^2}$$ and $$g(x)=\frac{3}{x^2}$$ into the comparison test we get that the integral $$\int\limits_1^\infty\frac{\sin(x)+2}{x^2}dx$$ converges as well.

Show that $$\int\limits_1^\infty\frac{\sin(x)+2}{x}dx$$ diverges.

Just as in the previous example we know that $$\sin(x)+2\ge1$$ for all $$x$$. Thus
 * $$\frac{\sin(x)+2}{x}\ge\frac{1}{x}\ge0$$

We have seen that $$\int\limits_1^\infty\frac{dx}{x}$$ diverges. So putting $$f(x)=\frac{\sin(x)+2}{x}$$ and $$g(x)=\frac{1}{x}$$ into the comparison test we get that $$\int\limits_1^\infty\frac{\sin(x)+2}{x}dx$$ diverges as well.

An extension of the comparison theorem
To apply the comparison theorem you do not really need $$g(x)\ge f(x)\ge0$$ for all $$x\ge a$$. What we actually need is this inequality holds for sufficiently large $$x$$ (i.e. there is a number $$c$$ such that $$g(x)\ge f(x)$$ for all $$x\ge c$$). For then
 * $$\int\limits_a^\infty f(x)dx=\int\limits_a^c f(x)dx+\int\limits_c^\infty f(x)dx$$

so the first integral converges if and only if third does, and we can apply the comparison theorem to the $$\int\limits_c^\infty f(x)dx$$ piece.

Show that $$\int\limits_1^\infty\sqrt{\frac{x^7}{e^{3x}}}dx$$ converges.

The reason that this integral converges is because for large $$x$$ the $$e^{-x}$$ factor in the integrand is dominant. We could try comparing $$x^\frac{7}{2}e^{-x}$$ with $$e^{-x}$$, but as $$x\ge1$$ , the inequality
 * $$x^\frac{7}{2}e^{-x}\ge e^{-x}$$

is the wrong way around to show convergence.

Instead we rewrite the integrand as $$x^\frac{7}{2}e^{-\frac{3x}{2}}dx=x^\frac{7}{2}e^{-\frac{x}{2}}e^{-x}dx$$.

Since the limit $$\lim_{x\to\infty}\Big[x^\frac{7}{2}e^{-\frac{x}{2}}\Big]=0$$ we know that for $$x$$ sufficiently large we have $$x^\frac{7}{2}e^{-\frac{x}{2}}\le1$$. So for large $$x$$ ,
 * $$x^\frac{7}{2}e^{-\frac{7x}{2}}=x^\frac{7}{2}e^{-\frac{x}{2}}e^{-x}\le e^{-x}$$

Since the integral $$\int\limits_1^\infty e^{-x} dx$$ converges the comparison test tells us that $$\int\limits_1^\infty\sqrt{\frac{x^7}{e^{3x}}}dx$$ converges as well.

title: Calculus/Improper Integrals


text:
Cookbook:Sponge Cake II

Sponge cake is the most commonly recognised variety of baked confectionery in Britain. It has a sweet taste, often flavoured with vanilla, chocolate or other additions, and can be cut and displayed in a number of different ways.

An easier version of this recipe is available that does not require a kitchen scale.

Cake

 * 200 g caster sugar
 * 200 g butter
 * 200 g (4 whole) eggs
 * 1–2 tsp vanilla extract

 * 200 g self-raising flour
 * 2 tsp baking powder

Filling

 * 2–4 tbsp jam, stirred
 * Buttercream frosting

Topping (pick one)

 * 75 g icing sugar
 * 70 g superfine sugar
 * 65 g granulated sugar
 * 55 g demerara sugar

Equipment

 * 1 large mixing bowl
 * 1 set of scales
 * 1 wooden spoon

Procedure

 * 1) Preheat an oven to 200°C.
 * 2) Cream together the sugar and butter until they are light and fluffy. The fluffier this mixture, the lighter the finished cake.
 * 3) Add both eggs and vanilla, and mix well.
 * 4) Add all the flour and baking powder, and mix well.
 * 5) Beat with wooden spoon in a circular motion, trying to incorporate as much air as possible.
 * 6) Grease 2 round cake tins with butter.
 * 7) Evenly divide the batter between the 2 pans—make sure the pans are no more than ¾ full.
 * 8) Bake the cakes in the preheated oven for about 15 minutes until they are golden. Start checking the cakes after 10 minutes.
 * 9) Cool the cakes in the pans, then unmold.
 * 10) Spread the frosting and jam over one of the cake layers. Top with the other cake layer. Sprinkle well with the sugar of choice.

Notes, tips, and variations

 * A few drops of concentrated food colouring or flavoring may be added along with the eggs.
 * Unsweetened cocoa powder may be added to taste. For every 4 g of cocoa you add, remove 3 g of the flour.
 * If your eggs don't come out to 200 g, simply adjust the flour, butter, and sugar so that they each weigh the same as the eggs.

title: Cookbook:Sponge Cake II


text:
Talk:Logic for Computer Science/First-Order Logic

There is an axiom for mod missing, something like

mod(m,n,s) <=> (exists r: Nat . m = n*r + s /\ s < n).

This axiom also implies NT 14.

Moreover, the 14 axioms should not be called "the axioms" for numbers, but only "some axioms". After all, the Peano axiom is missing. NT3 is only a very weak form of it, and not even the strongest possible first-order form. Till

 * Feel free to make the changes. MShonle 22:46, 13 Feb 2005 (UTC)


text:
Gambas/Branch

Back to Gambas

What are branches in a program?
A branch is a point at which your program must make a choice. With these structures, it is possible to make programs that can have multiple outcomes. There are mainly two branching methods:
 * if then and ist variations
 * select case

If...Then statement
The if then branch works quite the same as it is used in natural language. If something is true, then make something. If it is not true then just continue.

Try this little example: You just need a command button on your form to get it going. The output is shown in the terminal window.

PUBLIC SUB Button1_Click k AS Integer FOR k = 1 TO 10000 IF k = 5000 THEN PRINT "5000 has been reached !" NEXT END

Try to alter the program so that the output is shown in a textbox. You have to add a textbox to your form. You will find it with F6 in your toolbox. Then you have to change the code, so that the print command is exchanged.

PUBLIC SUB Button1_Click k AS Integer FOR k = 1 TO 10000 IF k = 5000 THEN textbox1.text = "5000 has been reached !" NEXT END

If...Then...Else...End if
You can modify the if-then construction by adding some other commands like else and end if. Here is another example with an else and end if command in it. You just need a command button on your form to get it going.

PUBLIC SUB Button1_Click k AS Integer FOR k = 1 TO 6000 IF k < 5000 THEN PRINT k   ELSE PRINT "5000 has been reached!" END IF NEXT END

The program counts from 1 to 6000. When the number 5000 is reached, you get a message in the terminal window.

You have to be aware of the right outline, otherwise it wont work.

Here is another example using the toggle button: It shows a message without a messagebox and the message can be copied into the clipboard. You need a toggle button and a textarea to get it going. You should change the property of the textarea to
 * Visible = false

When you click the button then the text will appear. When you click once again, the text will disappear.

PUBLIC SUB ToggleButton1_Click DIM Help AS String IF TextArea1.Visible = FALSE THEN ToggleButton1.Text = "Close Info " Help = "Hello, this is a info" & Chr(13) & Chr(10) Help = Help & "www.madeveryeasy.de" & Chr(13) & Chr(10) Help = Help & "rho55@gmx.de" TextArea1.Visible = TRUE TextArea1.text = Help ELSE TextArea1.Visible = FALSE ToggleButton1.Text = "Show Info" ENDIF END

Select Case
If you want to branch and you have more than 2 possible answers, then you can use the select-case command. Try this little example to get used to it. You just need an empty form to get it going. The output will be done in the terminal window.

PUBLIC SUB Form_Open PRINT Now PRINT WeekDay(Now) SELECT CASE WeekDay(Now) CASE 1 PRINT "Monday" CASE 2 PRINT "Tuesday" CASE 3 PRINT "Wednesday" CASE 4 PRINT "Thursday" CASE 5 PRINT "Friday" CASE 6 PRINT "Saturday" CASE 7 PRINT "Sunday" END SELECT END

title: Gambas/Branch


text:
Climate Change/Mitigation Strategies/Transport

There are many alternatives to automobile transport. For example, you can walk, bike, or take public transit whenever possible. Don't idle your vehicle. Carpool. Take the bus or train instead of driving long distances. Fill up your tires - improves mileage. Buy a gas-electric hybrid (it never needs to be plugged in), or a diesel.

Automobile Maintenance for a Greener Ride

 * Maintain your car properly
 * Clean your air system by periodically replacing your car's air filter
 * Clean your throttle body/air intake with a strong auto detergent like SeaFoam, STP Throttle body/Air Intake cleaner (1/2 hr job for a person new to cars). Remember to get the right spray can, ask the manager of the store. If you have a fuel injected car, using the carburated cleaner can cause unpleasant surprise.
 * Clean your fuel system by using a fuel system cleaner like Techron, Amsoil's PI
 * Use synthetics for your engine oil, transmission, power steering etc. I recommend Amsoil products as they last much much longer than any well known brands like Castrol. For the typical car (with automatic transmission) use of Series 2000 0W-30 for engine oil, ATF for transmission and power steering. Ask Amsoil technical support for help.
 * Keep tires inflated. Under-inflated tires reduce gas passage.
 * Do tire rotation, balancing and alignment regularly as prescribed in user's manual. This will increase lifetime or tire which are rarely restored or recycled and most likely burnt.
 * Do oil changes promptly. Clean oil reduces carbon dioxide emission. Change oil as prescribed in car user's manual, not every 3,000 miles as recommended by oil changing services.
 * If you're in the market for a new car anyway, consider getting a car with an order of magnitude better mileage.
 * Drive less:
 * Designate one day each week as a car-free day.
 * If possible, consider one car-free weekend each month.
 * Share ride to work with colleges. Carpool lines are also faster during traffic time.