qchapp/MNLP_M3_rag_documents · Datasets at Hugging Face

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wiki_41_chunk_17	AIM (software)	Chat robots AOL and various other companies supplied robots (bots) on AIM that could receive messages and send a response based on the bot's purpose. For example, bots could help with studying, like StudyBuddy. Some were made to relate to children and teenagers, like Spleak.	wikipedia
wiki_41_chunk_18	AIM (software)	Others gave advice. The more useful chat bots had features like the ability to play games, get sport scores, weather forecasts or financial stock information. Users were able to talk to automated chat bots that could respond to natural human language. They were primarily put into place as a marketing strategy and for unique advertising options. It was used by advertisers to market products or build better consumer relations.	wikipedia
wiki_41_chunk_19	AIM (software)	Before the inclusions of such bots, the other bots DoorManBot and AIMOffline provided features that were provided by AOL for those who needed it. ZolaOnAOL and ZoeOnAOL were short-lived bots that ultimately retired their features in favor of SmarterChild.	wikipedia
wiki_41_chunk_20	AIM (software)	URI scheme AOL Instant Messenger's installation process automatically installed an extra URI scheme ("protocol") handler into some Web browsers, so URIs beginning "aim:" could open a new AIM window with specified parameters. This was similar in function to the mailto: URI scheme, which created a new e-mail message using the system's default mail program. For instance, a webpage might have included a link like the following in its HTML source to open a window for sending a message to the AIM user notarealuser: <a href="aim:goim?screenname=notarealuser">Send Message</a>	wikipedia
wiki_41_chunk_21	AIM (software)	To specify a message body, the message parameter was used, so the link location would have looked like this: aim:goim?screenname=notarealuser&message=This+is+my+message To specify an away message, the message parameter was used, so the link location would have looked like this: aim:goaway?message=Hello,+my+name+is+Bill When placing this inside a URL link, an AIM user could click on the URL link and the away message "Hello, my name is Bill" would instantly become their away message.	wikipedia
wiki_41_chunk_22	AIM (software)	To add a buddy, the addbuddy message was used, with the "screenname" parameter aim:addbuddy?screenname=notarealuser This type of link was commonly found on forum profiles to easily add contacts.	wikipedia
wiki_41_chunk_23	AIM (software)	Vulnerabilities AIM had security weaknesses that have enabled exploits to be created that used third-party software to perform malicious acts on users' computers. Although most were relatively harmless, such as being kicked off the AIM service, others performed potentially dangerous actions, such as sending viruses. Some of these exploits relied on social engineering to spread by automatically sending instant messages that contained a Uniform Resource Locator (URL) accompanied by text suggesting the receiving user click on it, an action which leads to infection, i.e., a trojan horse. These messages could easily be mistaken as coming from a friend and contain a link to a Web address that installed software on the user's computer to restart the cycle.	wikipedia
wiki_41_chunk_24	AIM (software)	Users also have reported sudden additions of toolbars and advertisements from third parties in the newer version of AIM. Multiple complaints about the lack of control of third party involvement have caused many users to stop using the service. Extra features	wikipedia
wiki_41_chunk_25	AIM (software)	iPhone application On March 6, 2008, during Apple Inc.'s iPhone SDK event, AOL announced that they would be releasing an AIM application for iPhone and iPod Touch users. The application was available for free from the App Store, but the company also provides a paid version, which displays no advertisements. Both were available from the App Store. The AIM client for iPhone and iPod Touch supported standard AIM accounts, as well as MobileMe accounts. There was also an express version of AIM accessible through the Safari browser on the iPhone and iPod Touch.	wikipedia
wiki_41_chunk_26	AIM (software)	In 2011, AOL launched an overhaul of their Instant Messaging service. Included in the update was a brand new iOS application for iPhone and iPod Touch that incorporated all the latest features. A brand new icon was used for the application, featuring the new cursive logo for AIM. The user-interface was entirely redone for the features including: a new buddy list, group messaging, in-line photos and videos, as well as improved file-sharing.	wikipedia
wiki_41_chunk_27	AIM (software)	Version 5.0.5, updated in March 2012, it supported more social stream features, much like Facebook and Twitter, as well as the ability to send voice messages up to 60 seconds long. iPad application On April 3, 2010, Apple released the first generation iPad. Along with this newly released device AOL released the AIM application for iPad. It was built entirely from scratch for the new version iOS with a specialized user-interface for the device. It supports geo location, Facebook status updates and chat, Myspace, Twitter, YouTube, Foursquare and many social networking platforms.	wikipedia
wiki_41_chunk_28	AIM (software)	AIM Express AIM Express ran in a pop-up browser window. It was intended for use by people who are unwilling or unable to install a standalone application or those at computers that lack the AIM application. AIM Express supported many of the standard features included in the stand-alone client, but did not provide advanced features like file transfer, audio chat, video conferencing, or buddy info. It was implemented in Adobe Flash. It was an upgrade to the prior AOL Quick Buddy, which was later available for older systems that cannot handle Express before being discontinued. Express and Quick Buddy were similar to MSN Web Messenger and Yahoo! Web Messenger. This web version evolved into AIM.com's web-based messenger.	wikipedia
wiki_41_chunk_29	AIM (software)	AIM Pages AIM Pages was a free website released in May 2006 by AOL in replacement of AIMSpace. Anyone who had an AIM user name and was at least 16 years of age could create their own web page (to display an online, dynamic profile) and share it with buddies from their AIM Buddy list.	wikipedia
wiki_41_chunk_30	AIM (software)	Layout AIM Pages included links to the email and Instant Message of the owner, along with a section listing the owners "buddies", which included AIM user names. It was possible to create modules in a Module T microformat. Video hosting sites like Netflix and YouTube could be added to ones AIM Page, as well as other sites like Amazon.com. It was also possible to insert HTML code. The main focus of AIM Pages was the integration of external modules, like those listed above, into the AOL Instant Messenger experience.	wikipedia
wiki_41_chunk_31	AIM (software)	Discontinuation By late 2007, AIM Pages had been discontinued. After AIM Pages shutdown, links to AIM Pages were redirected to AOL Lifestream, AOL's new site aimed at collecting external modules in one place, independent of AIM buddies. AOL Lifestream was shut down February 24, 2017.	wikipedia
wiki_41_chunk_32	AIM (software)	AIM for Mac AOL released an all-new AIM for the Macintosh on September 29, 2008 and the final build on December 15, 2008. The redesigned AIM for Mac is a full universal binary Cocoa API application that supports both Tiger and Leopard — Mac OS X 10.4.8 (and above) or Mac OS X 10.5.3 (and above). On October 1, 2009, AOL released AIM 2.0 for Mac.	wikipedia
wiki_41_chunk_33	AIM (software)	AIM real-time IM This feature is available for AIM 7 and allows for a user to see what the other is typing as it is being done. It was developed and built with assistance from Trace Research and Development Centre at University of Wisconsin–Madison and Gallaudet University. The application provides visually impaired users the ability to convert messages from text (words) to speech. For the application to work users must have AIM 6.8 or higher, as it is not compatible with older versions of AIM software, AIM for Mac or iChat.	wikipedia
wiki_41_chunk_34	AIM (software)	AIM to mobile (messaging to phone numbers) This feature allows text messaging to a phone number (text messaging is less functional than instant messaging). Discontinued features	wikipedia
wiki_41_chunk_35	AIM (software)	AIM Phoneline AIM Phoneline was a Voice over IP PC-PC, PC-Phone and Phone-to-PC service provided via the AIM application. It was also known to work with Apple's iChat Client. The service was officially closed to its customers on January 13, 2009. The closing of the free service caused the number associated with the service to be disabled and not transferable for a different service. AIM Phoneline website was recommending users switch to a new service named AIM Call Out, also discontinued now.	wikipedia
wiki_41_chunk_36	AIM (software)	Launched on May 16, 2006, AIM Phoneline provided users the ability to have several local numbers, allowing AIM users to receive free incoming calls. The service allowed users to make calls to landlines and mobile devices through the use of a computer. The service, however, was only free for receiving and AOL charged users $14.95 a month for an unlimited calling plan. In order to use AIM Phoneline users had to install the latest free version of AIM Triton software and needed a good set of headphones with a boom microphone. It could take several days after a user signed up before it started working.	wikipedia
wiki_41_chunk_37	AIM (software)	AIM Call Out AIM Call Out is a discontinued Voice over IP PC-PC, PC-Phone and Phone-to-PC service provided by AOL via its AIM application that replaced the defunct AIM Phoneline service in November 2007. It did not depend on the AIM client and could be used with only an AIM screenname via the WebConnect feature or a dedicated SIP device. The AIM Call Out service was shut down on March 25, 2009.	wikipedia
wiki_41_chunk_38	AIM (software)	Security On November 4, 2014, AIM scored one out of seven points on the Electronic Frontier Foundation's secure messaging scorecard. AIM received a point for encryption during transit, but lost points because communications are not encrypted with a key to which the provider has no access, i.e., the communications are not end-to-end encrypted, users can't verify contacts' identities, past messages are not secure if the encryption keys are stolen, (i.e., the service does not provide forward secrecy), the code is not open to independent review, i.e., the code is not open-source), the security design is not properly documented, and there has not been a recent independent security audit. BlackBerry Messenger, Ebuddy XMS, Hushmail, Kik Messenger, Skype, Viber, and Yahoo! Messenger also scored one out of seven points.	wikipedia
wiki_41_chunk_39	AIM (software)	See also Comparison of cross-platform instant messaging clients List of defunct instant messaging platforms References External links 1997 software Android (operating system) software Instant Messenger BlackBerry software Classic Mac OS instant messaging clients Computer-related introductions in 1997 Cross-platform software Defunct instant messaging clients Instant messaging clients Internet properties disestablished in 2017 IOS software MacOS instant messaging clients Online chat Symbian software Unix instant messaging clients Videotelephony Windows instant messaging clients	wikipedia
wiki_42_chunk_0	Ackermann function	In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann-Péter function is defined as follows for nonnegative integers m and n:	wikipedia
wiki_42_chunk_1	Ackermann function	Its value grows rapidly, even for small inputs. For example, is an integer of 19,729 decimal digits (equivalent to 265536−3, or 22222−3).	wikipedia
wiki_42_chunk_2	Ackermann function	History In the late 1920s, the mathematicians Gabriel Sudan and Wilhelm Ackermann, students of David Hilbert, were studying the foundations of computation. Both Sudan and Ackermann are credited with discovering total computable functions (termed simply "recursive" in some references) that are not primitive recursive. Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function (the Greek letter phi). Ackermann's three-argument function, , is defined such that for , it reproduces the basic operations of addition, multiplication, and exponentiation as	wikipedia
wiki_42_chunk_3	Ackermann function	and for p > 2 it extends these basic operations in a way that can be compared to the hyperoperations: (Aside from its historic role as a total-computable-but-not-primitive-recursive function, Ackermann's original function is seen to extend the basic arithmetic operations beyond exponentiation, although not as seamlessly as do variants of Ackermann's function that are specifically designed for that purpose—such as Goodstein's hyperoperation sequence.)	wikipedia
wiki_42_chunk_4	Ackermann function	In On the Infinite, David Hilbert hypothesized that the Ackermann function was not primitive recursive, but it was Ackermann, Hilbert's personal secretary and former student, who actually proved the hypothesis in his paper On Hilbert's Construction of the Real Numbers. Rózsa Péter and Raphael Robinson later developed a two-variable version of the Ackermann function that became preferred by almost all authors. The generalized hyperoperation sequence, e.g. , is a version of Ackermann function as well.	wikipedia
wiki_42_chunk_5	Ackermann function	In 1963 R.C. Buck based an intuitive two-variable variant on the hyperoperation sequence: Compared to most other versions Buck's function has no unessential offsets: Many other versions of Ackermann function have been investigated. Definition Definition: as m-ary function Ackermann's original three-argument function is defined recursively as follows for nonnegative integers and : Of the various two-argument versions, the one developed by Péter and Robinson (called "the" Ackermann function by most authors) is defined for nonnegative integers and as follows:	wikipedia
wiki_42_chunk_6	Ackermann function	The Ackermann function has also been expressed in relation to the hyperoperation sequence: or, written in Knuth's up-arrow notation (extended to integer indices ): or, equivalently, in terms of Buck's function F: Definition: as iterated 1-ary function Define as the n-th iterate of : Iteration is the process of composing a function with itself a certain number of times. Function composition is an associative operation, so . Conceiving the Ackermann function as a sequence of unary functions, one can set .	wikipedia
wiki_42_chunk_7	Ackermann function	The function then becomes a sequence of unary functions, defined from iteration: As function composition is associative, the last line can as well be Computation The recursive definition of the Ackermann function can naturally be transposed to a term rewriting system (TRS). TRS, based on 2-ary function The definition of the 2-ary Ackermann function leads to the obvious reduction rules Example Compute The reduction sequence is To compute one can use a stack, which initially contains the elements . Then repeatedly the two top elements are replaced according to the rules Schematically, starting from :	wikipedia
wiki_42_chunk_8	Ackermann function	WHILE stackLength <> 1 { POP 2 elements; PUSH 1 or 2 or 3 elements, applying the rules r1, r2, r3 } The pseudocode is published in . For example, on input , Remarks The leftmost-innermost strategy is implemented in 225 computer languages on Rosetta Code. For all the computation of takes no more than steps. pointed out that in the computation of the maximum length of the stack is , as long as . Their own algorithm, inherently iterative, computes within time and within space.	wikipedia
wiki_42_chunk_9	Ackermann function	TRS, based on iterated 1-ary function The definition of the iterated 1-ary Ackermann functions leads to different reduction rules As function composition is associative, instead of rule r6 one can define Like in the previous section the computation of can be implemented with a stack. Initially the stack contains the three elements . Then repeatedly the three top elements are replaced according to the rules Schematically, starting from : WHILE stackLength <> 1 { POP 3 elements; PUSH 1 or 3 or 5 elements, applying the rules r4, r5, r6; } Example	wikipedia
wiki_42_chunk_10	Ackermann function	On input the successive stack configurations are The corresponding equalities are When reduction rule r7 is used instead of rule r6, the replacements in the stack will follow The successive stack configurations will then be The corresponding equalities are	wikipedia
wiki_42_chunk_11	Ackermann function	Remarks On any given input the TRSs presented so far converge in the same number of steps. They also use the same reduction rules (in this comparison the rules r1, r2, r3 are considered "the same as" the rules r4, r5, r6/r7 respectively). For example, the reduction of converges in 14 steps: 6 × r1, 3 × r2, 5 × r3. The reduction of converges in the same 14 steps: 6 × r4, 3 × r5, 5 × r6/r7. The TRSs differ in the order in which the reduction rules are applied. When is computed following the rules {r4, r5, r6}, the maximum length of the stack stays below . When reduction rule r7 is used instead of rule r6, the maximum length of the stack is only . The length of the stack reflects the recursion depth. As the reduction according to the rules {r4, r5, r7} involves a smaller maximum depth of recursion, this computation is more efficient in that respect.	wikipedia
wiki_42_chunk_12	Ackermann function	TRS, based on hyperoperators As — or — showed explicitly, the Ackermann function can be expressed in terms of the hyperoperation sequence: or, after removal of the constant 2 from the parameter list, in terms of Buck's function Buck's function , a variant of Ackermann function by itself, can be computed with the following reduction rules: Instead of rule b6 one can define the rule To compute the Ackermann function it suffices to add three reduction rules	wikipedia
wiki_42_chunk_13	Ackermann function	These rules take care of the base case A(0,n), the alignment (n+3) and the fudge (-3). Example Compute The matching equalities are when the TRS with the reduction rule is applied: when the TRS with the reduction rule is applied:	wikipedia
wiki_42_chunk_14	Ackermann function	Remarks The computation of according to the rules {b1 - b5, b6, r8 - r10} is deeply recursive. The maximum depth of nested s is . The culprit is the order in which iteration is executed: . The first disappears only after the whole sequence is unfolded. The computation according to the rules {b1 - b5, b7, r8 - r10} is more efficient in that respect. The iteration simulates the repeated loop over a block of code. The nesting is limited to , one recursion level per iterated function. showed this correspondence. These considerations concern the recursion depth only. Either way of iterating leads to the same number of reduction steps, involving the same rules (when the rules b6 and b7 are considered "the same"). The reduction of for instance converges in 35 steps: 12 × b1, 4 × b2, 1 × b3, 4 × b5, 12 × b6/b7, 1 × r9, 1 × r10. The modus iterandi only affects the order in which the reduction rules are applied. A real gain of execution time can only be achieved by not recalculating subresults over and over again. Memoization is an optimization technique where the results of function calls are cached and returned when the same inputs occur again. See for instance . published a cunning algorithm which computes within time and within space.	wikipedia
wiki_42_chunk_15	Ackermann function	Huge numbers To demonstrate how the computation of results in many steps and in a large number: Table of values Computing the Ackermann function can be restated in terms of an infinite table. First, place the natural numbers along the top row. To determine a number in the table, take the number immediately to the left. Then use that number to look up the required number in the column given by that number and one row up. If there is no number to its left, simply look at the column headed "1" in the previous row. Here is a small upper-left portion of the table:	wikipedia
wiki_42_chunk_16	Ackermann function	The numbers here which are only expressed with recursive exponentiation or Knuth arrows are very large and would take up too much space to notate in plain decimal digits. Despite the large values occurring in this early section of the table, some even larger numbers have been defined, such as Graham's number, which cannot be written with any small number of Knuth arrows. This number is constructed with a technique similar to applying the Ackermann function to itself recursively. This is a repeat of the above table, but with the values replaced by the relevant expression from the function definition to show the pattern clearly: Properties	wikipedia
wiki_42_chunk_17	Ackermann function	General remarks It may not be immediately obvious that the evaluation of always terminates. However, the recursion is bounded because in each recursive application either decreases, or remains the same and decreases. Each time that reaches zero, decreases, so eventually reaches zero as well. (Expressed more technically, in each case the pair decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of single non-negative integers; this means one cannot go down in the ordering infinitely many times in succession.) However, when decreases there is no upper bound on how much can increase — and it will often increase greatly. For small values of m like 1, 2, or 3, the Ackermann function grows relatively slowly with respect to n (at most exponentially). For , however, it grows much more quickly; even is about 2, and the decimal expansion of is very large by any typical measure. An interesting aspect is that the only arithmetic operation it ever uses is addition of 1. Its fast growing power is based solely on nested recursion. This also implies that its running time is at least proportional to its output, and so is also extremely huge. In actuality, for most cases the running time is far larger than the output; see above. A single-argument version that increases both and at the same time dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi- and superfactorial functions, and even functions defined using Knuth's up-arrow notation (except when the indexed up-arrow is used). It can be seen that is roughly comparable to in the fast-growing hierarchy. This extreme growth can be exploited to show that which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.	wikipedia
wiki_42_chunk_18	Ackermann function	Not primitive recursive The Ackermann function grows faster than any primitive recursive function and therefore is not itself primitive recursive. Specifically, one shows that to every primitive recursive function there exists a non-negative integer such that for all non-negative integers , Once this is established, it follows that itself is not primitive recursive, since otherwise putting would lead to the contradiction The proof proceeds as follows: define the class of all functions that grow slower than the Ackermann function	wikipedia
wiki_42_chunk_19	Ackermann function	and show that contains all primitive recursive functions. The latter is achieved by showing that contains the constant functions, the successor function, the projection functions and that it is closed under the operations of function composition and primitive recursion. Inverse Since the function considered above grows very rapidly, its inverse function, f, grows very slowly. This inverse Ackermann function f−1 is usually denoted by α. In fact, α(n) is less than 5 for any practical input size n, since is on the order of .	wikipedia
wiki_42_chunk_20	Ackermann function	This inverse appears in the time complexity of some algorithms, such as the disjoint-set data structure and Chazelle's algorithm for minimum spanning trees. Sometimes Ackermann's original function or other variations are used in these settings, but they all grow at similarly high rates. In particular, some modified functions simplify the expression by eliminating the −3 and similar terms. A two-parameter variation of the inverse Ackermann function can be defined as follows, where is the floor function:	wikipedia
wiki_42_chunk_21	Ackermann function	This function arises in more precise analyses of the algorithms mentioned above, and gives a more refined time bound. In the disjoint-set data structure, m represents the number of operations while n represents the number of elements; in the minimum spanning tree algorithm, m represents the number of edges while n represents the number of vertices. Several slightly different definitions of exist; for example, is sometimes replaced by n, and the floor function is sometimes replaced by a ceiling. Other studies might define an inverse function of one where m is set to a constant, such that the inverse applies to a particular row.	wikipedia
wiki_42_chunk_22	Ackermann function	The inverse of the Ackermann function is primitive recursive. Use as benchmark The Ackermann function, due to its definition in terms of extremely deep recursion, can be used as a benchmark of a compiler's ability to optimize recursion. The first published use of Ackermann's function in this way was in 1970 by Dragoș Vaida and, almost simultaneously, in 1971, by Yngve Sundblad.	wikipedia
wiki_42_chunk_23	Ackermann function	Sundblad's seminal paper was taken up by Brian Wichmann (co-author of the Whetstone benchmark) in a trilogy of papers written between 1975 and 1982. See also Computability theory Double recursion Fast-growing hierarchy Goodstein function Primitive recursive function Recursion (computer science) Notes References Bibliography	wikipedia
wiki_42_chunk_24	Ackermann function	External links An animated Ackermann function calculator Ackerman function implemented using a for loop Scott Aaronson, Who can name the biggest number? (1999) Ackermann functions. Includes a table of some values. Hyper-operations: Ackermann's Function and New Arithmetical Operation Robert Munafo's Large Numbers describes several variations on the definition of A. Gabriel Nivasch, Inverse Ackermann without pain on the inverse Ackermann function. Raimund Seidel, Understanding the inverse Ackermann function (PDF presentation). The Ackermann function written in different programming languages, (on Rosetta Code) Ackermann's Function (Archived 2009-10-24)—Some study and programming by Harry J. Smith.	wikipedia
wiki_42_chunk_25	Ackermann function	Arithmetic Large integers Special functions Theory of computation Computability theory	wikipedia
wiki_43_chunk_0	AMOS (programming language)	AMOS BASIC is a dialect of the BASIC programming language implemented on the Amiga computer. AMOS BASIC was published by Europress Software and originally written by François Lionet with Constantin Sotiropoulos in the year 1990. AMOS was considered to be a fast language. It also had 3D capabilities. History AMOS is a descendant of STOS BASIC for the Atari ST. AMOS BASIC was first produced in 1990.	wikipedia
wiki_43_chunk_1	AMOS (programming language)	AMOS competed on the Amiga platform with Acid Software's Blitz BASIC. Both BASICs differed from other dialects on different platforms, in that they allowed the easy creation of fairly demanding multimedia software, with full structured code and many high-level functions to load images, animations, sounds and display them in various ways.	wikipedia
wiki_43_chunk_2	AMOS (programming language)	The original AMOS was a BASIC interpreter which, whilst working fine, suffered the same disadvantages of any language being run interpretively. By all accounts, AMOS was extremely fast among interpreted languages, being speedy enough that an extension called AMOS 3D could produce playable 3D games even on plain 7 MHz 68000 Amigas. Later, an AMOS compiler was developed that further increased speed. AMOS could also run MC68000 machine code, loaded into a program's memory banks.	wikipedia
wiki_43_chunk_3	AMOS (programming language)	To simplify animation of sprites, AMOS included the AMOS Animation Language (AMAL), a compiled sprite scripting language which runs independently of the main AMOS BASIC program. It was also possible to control screen and "rainbow" effects using AMAL scripts. AMAL scripts in effect created CopperLists, small routines executed by the Amiga's Agnus chip.	wikipedia
wiki_43_chunk_4	AMOS (programming language)	After the original version of AMOS, Europress released a compiler (AMOS Compiler), and two other versions of the language: Easy AMOS, a simpler version for beginners, and AMOS Professional, a more advanced version with added features, such as a better IDE, ARexx support, a new UI API and new flow control constructs. Neither of these new versions was significantly more popular than the original AMOS. AMOS was used mostly to make multimedia software, video games (platformers and graphical adventures) and educational software. The language was mildly successful within the Amiga community. Its ease of use made it especially attractive to beginners.	wikipedia
wiki_43_chunk_5	AMOS (programming language)	Perhaps AMOS BASIC's biggest disadvantage, stemming from its Atari ST lineage, was its incompatibility with the Amiga's operating system functions and interfaces. Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of hardware. Today, the language has declined in popularity along with the Amiga computer for which it was written. Despite this, a small community of enthusiasts are still using it. The source code to AMOS was released around 2001 under a BSD style license by Clickteam, a company that includes the original programmer.	wikipedia
wiki_43_chunk_6	AMOS (programming language)	On the 4 April 2019, François Lionet announced the release of AMOS2 on his website amos2.org. AMOS2 replaces STOS and AMOS together, using JavaScript as its code interpreter, making the new development system independent and generally deployed in internet browsers. Amos 2 is now called AOZ Studio. Its website is at https://www.aoz.studio/. Software Software written using AMOS BASIC includes:	wikipedia
wiki_43_chunk_7	AMOS (programming language)	Miggybyte Scorched Tanks Games by Vulcan Software, amongst which was the Valhalla trilogy Amiga version of Ultimate Domain (called Genesia) by Microïds Flight of the Amazon Queen, by Interactive Binary Illusions Extreme Violence, included on an Amiga Power cover disk Jetstrike, a commercial game by Rasputin Software References	wikipedia
wiki_43_chunk_8	AMOS (programming language)	External links Source code for AMOS Professional 68000 ASM from pianetaamiga.it (archived, ZIP) Source code for AMOS and STOS 68000 ASM from clickteam.com (archived, ZIP) The AMOS Factory (an AMOS support/community site) Amigacoding website (contains in-depth info and references for AMOS) History of STOS and AMOS: how they came to be published in the UK Amos Professional group on Facebook (one of the members is AMOS' original developer François Lionet)	wikipedia
wiki_43_chunk_9	AMOS (programming language)	BASIC programming language family Video game development software Amiga development software Software using the BSD license Programming languages created in 1990	wikipedia
wiki_44_chunk_0	Adoptionism	Adoptionism, also called dynamic monarchianism, is an early Christian nontrinitarian theological doctrine, which holds that Jesus was adopted as the Son of God at his baptism, his resurrection, or his ascension.	wikipedia
wiki_44_chunk_1	Adoptionism	Definition Adoptionism is one of two main forms of monarchianism (the other is modalism which considers God to be one while working through the different "modes" or "manifestations" of God the Father, God the Son, and God the Holy Spirit, without limiting his modes or manifestations). Adoptionism denies the eternal pre-existence of Christ, and although it explicitly affirms his deity subsequent to events in his life, many classical trinitarians claim that the doctrine implicitly denies it by denying the constant hypostatic union of the eternal Logos to the human nature of Jesus. Under adoptionism Jesus is currently divine and has been since his adoption, although he is not equal to the Father, per "my Father is greater than I" and as such is a kind of subordinationism. Adoptionism is sometimes, but not always, related to denial of the virgin birth of Jesus.	wikipedia
wiki_44_chunk_2	Adoptionism	History Early Christianity Adoptionism and High Christology	wikipedia
wiki_44_chunk_3	Adoptionism	Bart Ehrman holds that the New Testament writings contain two different Christologies, namely a "low" or adoptionist Christology, and a "high" or "incarnation Christology." The "low Christology" or "adoptionist Christology" is the belief "that God exalted Jesus to be his Son by raising him from the dead," thereby raising him to "divine status." The other early Christology is "high Christology," which is "the view that Jesus was a pre-existent divine being who became a human, did the Father’s will on earth, and then was taken back up into heaven whence he had originally come," and from where he appeared on earth. The chronology of the development of these early Christologies is a matter of debate within contemporary scholarship.	wikipedia
wiki_44_chunk_4	Adoptionism	According to the "evolutionary model" c.q. "evolutionary theories," as proposed by Bousset, followed by Brown, the Christological understanding of Christ developed over time, from a low Christology to a high Christology, as witnessed in the Gospels. According to the evolutionary model, the earliest Christians believed that Jesus was a human who was exalted, c.q. adopted as God's Son, when he was resurrected, signaling the nearness of the Kingdom of God, when all dead would be resurrected and the righteous exalted. Adoptionist concepts can be found in the Gospel of Mark. As Daniel Johansson notes, a majority consensus holds Mark's Jesus as "an exalted, but merely human figure", especially when read in the apparent context of Jewish beliefs. Later beliefs shifted the exaltation to his baptism, birth, and subsequently to the idea of his eternal existence, as witnessed in the Gospel of John. Mark shifted the moment of when Jesus became the son to the baptism of Jesus, and later still Matthew and Luke shifted it to the moment of the divine conception, and finally John declared that Jesus had been with God from the beginning: "In the beginning was the Word".	wikipedia
wiki_44_chunk_5	Adoptionism	Since the 1970s, the late datings for the development of a "high Christology" have been contested, and a majority of scholars argue that this "High Christology" existed already before the writings of Paul. This "incarnation Christology" or "high Christology" did not evolve over a longer time, but was a "big bang" of ideas which were already present at the start of Christianity, and took further shape in the first few decades of the church, as witnessed in the writings of Paul.	wikipedia
wiki_44_chunk_6	Adoptionism	According to Ehrman, these two Christologies existed alongside each other, calling the "low Christology" an "adoptionist Christology, and "the "high Christology" an "incarnation Christology."	wikipedia
wiki_44_chunk_7	Adoptionism	New Testamental epistles Adoptionist theology may also be reflected in canonical epistles, the earliest of which pre-date the writing of the gospels. The letters of Paul the Apostle, for example, do not mention a virgin birth of Christ. Paul describes Jesus as "born of a woman, born under the law" and "as to his human nature was a descendant of David" in the Epistle to the Galatians and the Epistle to the Romans. Many interpreters, however, take his statements in Philippians 2 to imply that Paul believed Jesus to have existed as equal to God before his incarnation.	wikipedia
wiki_44_chunk_8	Adoptionism	The Book of Hebrews, a contemporary sermon by an unknown author, describes God as saying "You are my son; today I have begotten you." Shepherd of Hermas The 2nd-century work Shepherd of Hermas may also have taught that Jesus was a virtuous man filled with the Holy Spirit and adopted as the Son. While the Shepherd of Hermas was popular and sometimes bound with the canonical scriptures, it didn't retain canonical status, if it ever had it.	wikipedia
wiki_44_chunk_9	Adoptionism	Theodotus of Byzantium Theodotus of Byzantium (fl. late 2nd century), a Valentinian Gnostic, was the most prominent exponent of adoptionism. According to Hippolytus of Rome (Philosophumena, VII, xxiii) Theodotus taught that Jesus was a man born of a virgin, according to the Council of Jerusalem, that he lived like other men, and was most pious. At his baptism in the Jordan the "Christ" came down upon the man Jesus, in the likeness of a dove (Philosophumena, VII, xxiii), but Jesus was not himself God until after his resurrection.	wikipedia
wiki_44_chunk_10	Adoptionism	Adoptionism was declared heresy at the end of the 3rd century and was rejected by the Synods of Antioch and the First Council of Nicaea, which defined the orthodox doctrine of the Trinity and identified the man Jesus with the eternally begotten Son or Word of God in the Nicene Creed. The belief was also declared heretical by Pope Victor I. Ebionites Adoptionism was also adhered to by the Jewish Christians known as Ebionites, who, according to Epiphanius in the 4th century, believed that Jesus was chosen on account of his sinless devotion to the will of God.	wikipedia
wiki_44_chunk_11	Adoptionism	The Ebionites were a Jewish Christian movement that existed during the early centuries of the Christian Era. They show strong similarities with the earliest form of Jewish Christianity, and their specific theology may have been a "reaction to the law-free Gentile mission." They regarded Jesus as the Messiah while rejecting his divinity and his virgin birth, and insisted on the necessity of following Jewish law and rites. They used the Gospel of the Ebionites, one of the Jewish–Christian gospels; the Hebrew Book of Matthew starting at chapter 3; revered James the brother of Jesus (James the Just); and rejected Paul the Apostle as an apostate from the Law. Their name ( Ebionaioi, derived from Hebrew ebyonim, ebionim, meaning "the poor" or "poor ones") suggests that they placed a special value on voluntary poverty.	wikipedia
wiki_44_chunk_12	Adoptionism	Distinctive features of the Gospel of the Ebionites include the absence of the virgin birth and of the genealogy of Jesus; an Adoptionist Christology, in which Jesus is chosen to be God's Son at the time of his Baptism; the abolition of the Jewish sacrifices by Jesus; and an advocacy of vegetarianism. Spanish Adoptionism	wikipedia
wiki_44_chunk_13	Adoptionism	Spanish Adoptionism was a theological position which was articulated in Umayyad and Christian-held regions of the Iberian peninsula in the 8th and 9th centuries. The issue seems to have begun with the claim of archbishop Elipandus of Toledo that – in respect to his human nature – Christ was adoptive Son of God. Another leading advocate of this Christology was Felix of Urgel. In Spain, adoptionism was opposed by Beatus of Liebana, and in the Carolingian territories, the Adoptionist position was condemned by Pope Hadrian I, Alcuin of York, Agobard, and officially in Carolingian territory by the Council of Frankfurt (794).	wikipedia
wiki_44_chunk_14	Adoptionism	Despite the shared name of "adoptionism" the Spanish Adoptionist Christology appears to have differed sharply from the adoptionism of early Christianity. Spanish advocates predicated the term adoptivus of Christ only in respect to his humanity; once the divine Son "emptied himself" of divinity and "took the form of a servant" (Philippians 2:7), Christ's human nature was "adopted" as divine.	wikipedia
wiki_44_chunk_15	Adoptionism	Historically, many scholars have followed the Adoptionists' Carolingian opponents in labeling Spanish Adoptionism as a minor revival of “Nestorian” Christology. John C. Cavadini has challenged this notion by attempting to take the Spanish Christology in its own Spanish/North African context in his study, The Last Christology of the West: Adoptionism in Spain and Gaul, 785–820.	wikipedia
wiki_44_chunk_16	Adoptionism	Scholastic Neo-adoptionism A third wave was the revived form ("Neo-adoptionism") of Peter Abelard in the 12th century. Later, various modified and qualified Adoptionist tenets emerged from some theologians in the 14th century. Duns Scotus (1300) and Durandus of Saint-Pourçain (1320) admit the term Filius adoptivus in a qualified sense. In more recent times the Jesuit Gabriel Vásquez, and the Lutheran divines Georgius Calixtus and Johann Ernst Immanuel Walch, have defended adoptionism as essentially orthodox.	wikipedia
wiki_44_chunk_17	Adoptionism	Modern adoptionist groups A form of adoptionism surfaced in Unitarianism during the 18th century as denial of the virgin birth became increasingly common, led by the views of Joseph Priestley and others.	wikipedia
wiki_44_chunk_18	Adoptionism	A similar form of adoptionism was expressed in the writings of James Strang, a Latter Day Saint leader who founded the Church of Jesus Christ of Latter Day Saints (Strangite) after the death of Joseph Smith in 1844. In his Book of the Law of the Lord, a purported work of ancient scripture found and translated by Strang, he offers an essay entitled "Note on the Sacrifice of Christ" in which he explains his unique (for Mormonism as a whole) doctrines on the subject. Jesus Christ, said Strang, was the natural-born son of Mary and Joseph, who was chosen from before all time to be the Savior of mankind, but who had to be born as an ordinary mortal of two human parents (rather than being begotten by the Father or the Holy Spirit) to be able to truly fulfill his Messianic role. Strang claimed that the earthly Christ was in essence "adopted" as God's son at birth, and fully revealed as such during the Transfiguration. After proving himself to God by living a perfectly sinless life, he was enabled to provide an acceptable sacrifice for the sins of men, prior to his resurrection and ascension.	wikipedia
wiki_44_chunk_19	Adoptionism	See also Adoptivi Arianism Binitarianism Notes References Sources Printed sources Philip Schaff History of the Christian Church, Volume IV, 1882. (6th German edition, translated by George Ogg) Web sources External links Adoptionism in Catholic Encyclopedia Adoptionism in Christian Cyclopedia Chapter XI. Doctrinal Controversies, from Philip Schaff's History of the Christian Church Nontrinitarianism Christian terminology Christology Heresy in ancient Christianity Adoption and religion	wikipedia
wiki_45_chunk_0	Algebraic closure	In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma or the weaker ultrafilter lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.	wikipedia
wiki_45_chunk_1	Algebraic closure	The algebraic closure of a field K can be thought of as the largest algebraic extension of K. To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K. The algebraic closure of K is also the smallest algebraically closed field containing K, because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.	wikipedia
wiki_45_chunk_2	Algebraic closure	The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.	wikipedia
wiki_45_chunk_3	Algebraic closure	Examples The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers. The algebraic closure of the field of rational numbers is the field of algebraic numbers. There are many countable algebraically closed fields within the complex numbers, and strictly containing the field of algebraic numbers; these are the algebraic closures of transcendental extensions of the rational numbers, e.g. the algebraic closure of Q(π). For a finite field of prime power order q, the algebraic closure is a countably infinite field that contains a copy of the field of order qn for each positive integer n (and is in fact the union of these copies).	wikipedia
wiki_45_chunk_4	Algebraic closure	Existence of an algebraic closure and splitting fields Let be the set of all monic irreducible polynomials in K[x]. For each , introduce new variables where . Let R be the polynomial ring over K generated by for all and all . Write	wikipedia
wiki_45_chunk_5	Algebraic closure	with . Let I be the ideal in R generated by the . Since I is strictly smaller than R, Zorn's lemma implies that there exists a maximal ideal M in R that contains I. The field K1=R/M has the property that every polynomial with coefficients in K splits as the product of and hence has all roots in K1. In the same way, an extension K2 of K1 can be constructed, etc. The union of all these extensions is the algebraic closure of K, because any polynomial with coefficients in this new field has its coefficients in some Kn with sufficiently large n, and then its roots are in Kn+1, and hence in the union itself.	wikipedia
wiki_45_chunk_6	Algebraic closure	It can be shown along the same lines that for any subset S of K[x], there exists a splitting field of S over K.	wikipedia
wiki_45_chunk_7	Algebraic closure	Separable closure An algebraic closure Kalg of K contains a unique separable extension Ksep of K containing all (algebraic) separable extensions of K within Kalg. This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of Ksep, of degree > 1. Saying this another way, K is contained in a separably-closed algebraic extension field. It is unique (up to isomorphism).	wikipedia
wiki_45_chunk_8	Algebraic closure	The separable closure is the full algebraic closure if and only if K is a perfect field. For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension. In general, the absolute Galois group of K is the Galois group of Ksep over K. See also Algebraically closed field Algebraic extension Puiseux expansion Complete field References Field extensions	wikipedia
wiki_46_chunk_0	Advanced Power Management	Advanced power management (APM) is an API developed by Intel and Microsoft and released in 1992 which enables an operating system running an IBM-compatible personal computer to work with the BIOS (part of the computer's firmware) to achieve power management. Revision 1.2 was the last version of the APM specification, released in 1996. ACPI is the successor to APM. Microsoft dropped support for APM in Windows Vista. The Linux kernel still mostly supports APM, though support for APM CPU idle was dropped in version 3.0. Overview	wikipedia
wiki_46_chunk_1	Advanced Power Management	APM uses a layered approach to manage devices. APM-aware applications (which include device drivers) talk to an OS-specific APM driver. This driver communicates to the APM-aware BIOS, which controls the hardware. There is the ability to opt out of APM control on a device-by-device basis, which can be used if a driver wants to communicate directly with a hardware device.	wikipedia
wiki_46_chunk_2	Advanced Power Management	Communication occurs both ways; power management events are sent from the BIOS to the APM driver, and the APM driver sends information and requests to the BIOS via function calls. In this way the APM driver is an intermediary between the BIOS and the operating system. Power management happens in two ways; through the above-mentioned function calls from the APM driver to the BIOS requesting power state changes, and automatically based on device activity.	wikipedia
wiki_46_chunk_3	Advanced Power Management	In APM 1.0 and APM 1.1, power management is almost fully controlled by the BIOS. In APM 1.2, the operating system can control PM time (e.g. suspend timeout). Power management events There are 12 power events (such as standby, suspend and resume requests, and low battery notifications), plus OEM-defined events, that can be sent from the APM BIOS to the operating system. The APM driver regularly polls for event change notifications. Power Management Events:	wikipedia
wiki_46_chunk_4	Advanced Power Management	APM functions There are 21 APM function calls defined that the APM driver can use to query power management statuses, or request power state transitions. Example function calls include letting the BIOS know about current CPU usage (the BIOS may respond to such a call by placing the CPU in a low-power state, or returning it to its full-power state), retrieving the current power state of a device, or requesting a power state change. Power states The APM specification defines system power states and device power states.	wikipedia
wiki_46_chunk_5	Advanced Power Management	System power states APM defines five power states for the computer system: Full On: The computer is powered on, and no devices are in a power saving mode. APM Enabled: The computer is powered on, and APM is controlling device power management as needed. APM Standby: Most devices are in their low-power state, the CPU is slowed or stopped, and the system state is saved. The computer can be returned to its former state quickly (in response to activity such as the user pressing a key on the keyboard). APM Suspend: Most devices are powered off, but the system state is saved. The computer can be returned to its former state, but takes a relatively long time. (Hibernation is a special form of the APM Suspend state). Off: The computer is turned off.	wikipedia
wiki_46_chunk_6	Advanced Power Management	Device power states APM also defines power states that APM-aware hardware can implement. There is no requirement that an APM-aware device implement all states. The four states are: Device On: The device is in full power mode. Device Power Managed: The device is still powered on, but some functions may not be available, or may have reduced performance. Device Low Power: The device is not working. Power is maintained so that the device may be 'woken up'. Device Off: The device is powered off.	wikipedia
wiki_46_chunk_7	Advanced Power Management	CPU The CPU core (defined in APM as the CPU clock, cache, system bus and system timers) is treated specially in APM, as it is the last device to be powered down, and the first device to be powered back up. The CPU core is always controlled through the APM BIOS (there is no option to control it through a driver). Drivers can use APM function calls to notify the BIOS about CPU usage, but it is up to the BIOS to act on this information; a driver cannot directly tell the CPU to go into a power saving state.	wikipedia
wiki_46_chunk_8	Advanced Power Management	In ATA drives The ATA specification defines APM provisions for hard drives via the subcommand , which specifies a trade-off between spin-down frequency and always-on performance. Unlike the BIOS-side APM, the ATA APM has never been deprecated. Aggressive spin-down frequencies may reduce drive lifespan by unnecessarily accumulating load cycles; most modern drives are specified to sustain 300,000 cycles and usually last at least 600,000. On the other hand, not spinning down the drive will cause extra power draw and heat generation; high temperatures also reduce the lifespan of hard drives.	wikipedia
wiki_46_chunk_9	Advanced Power Management	See also Active State Power Management - hardware power management protocol for PCI Express Advanced Configuration and Power Interface (ACPI) - successor to APM Green computing Power management BatteryMAX (idle detection) References External links APM V1.2 Specification (RTF file). BIOS	wikipedia
wiki_47_chunk_0	Alternative algebra	In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have for all x and y in the algebra. Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions. The associator	wikipedia
wiki_47_chunk_1	Alternative algebra	Alternative algebras are so named because they are the algebras for which the associator is alternating. The associator is a trilinear map given by . By definition, a multilinear map is alternating if it vanishes whenever two of its arguments are equal. The left and right alternative identities for an algebra are equivalent to Both of these identities together imply that the associator is totally skew-symmetric. That is, for any permutation σ. It follows that for all x and y. This is equivalent to the flexible identity	wikipedia

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AIM (software)

Chat robots AOL and various other companies supplied robots (bots) on AIM that could receive messages and send a response based on the bot's purpose. For example, bots could help with studying, like StudyBuddy. Some were made to relate to children and teenagers, like Spleak.

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Others gave advice. The more useful chat bots had features like the ability to play games, get sport scores, weather forecasts or financial stock information. Users were able to talk to automated chat bots that could respond to natural human language. They were primarily put into place as a marketing strategy and for unique advertising options. It was used by advertisers to market products or build better consumer relations.

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Before the inclusions of such bots, the other bots DoorManBot and AIMOffline provided features that were provided by AOL for those who needed it. ZolaOnAOL and ZoeOnAOL were short-lived bots that ultimately retired their features in favor of SmarterChild.

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AIM (software)

URI scheme AOL Instant Messenger's installation process automatically installed an extra URI scheme ("protocol") handler into some Web browsers, so URIs beginning "aim:" could open a new AIM window with specified parameters. This was similar in function to the mailto: URI scheme, which created a new e-mail message using the system's default mail program. For instance, a webpage might have included a link like the following in its HTML source to open a window for sending a message to the AIM user notarealuser: <a href="aim:goim?screenname=notarealuser">Send Message</a>

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To specify a message body, the message parameter was used, so the link location would have looked like this: aim:goim?screenname=notarealuser&message=This+is+my+message To specify an away message, the message parameter was used, so the link location would have looked like this: aim:goaway?message=Hello,+my+name+is+Bill When placing this inside a URL link, an AIM user could click on the URL link and the away message "Hello, my name is Bill" would instantly become their away message.

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To add a buddy, the addbuddy message was used, with the "screenname" parameter aim:addbuddy?screenname=notarealuser This type of link was commonly found on forum profiles to easily add contacts.

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Vulnerabilities AIM had security weaknesses that have enabled exploits to be created that used third-party software to perform malicious acts on users' computers. Although most were relatively harmless, such as being kicked off the AIM service, others performed potentially dangerous actions, such as sending viruses. Some of these exploits relied on social engineering to spread by automatically sending instant messages that contained a Uniform Resource Locator (URL) accompanied by text suggesting the receiving user click on it, an action which leads to infection, i.e., a trojan horse. These messages could easily be mistaken as coming from a friend and contain a link to a Web address that installed software on the user's computer to restart the cycle.

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Users also have reported sudden additions of toolbars and advertisements from third parties in the newer version of AIM. Multiple complaints about the lack of control of third party involvement have caused many users to stop using the service. Extra features

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iPhone application On March 6, 2008, during Apple Inc.'s iPhone SDK event, AOL announced that they would be releasing an AIM application for iPhone and iPod Touch users. The application was available for free from the App Store, but the company also provides a paid version, which displays no advertisements. Both were available from the App Store. The AIM client for iPhone and iPod Touch supported standard AIM accounts, as well as MobileMe accounts. There was also an express version of AIM accessible through the Safari browser on the iPhone and iPod Touch.

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In 2011, AOL launched an overhaul of their Instant Messaging service. Included in the update was a brand new iOS application for iPhone and iPod Touch that incorporated all the latest features. A brand new icon was used for the application, featuring the new cursive logo for AIM. The user-interface was entirely redone for the features including: a new buddy list, group messaging, in-line photos and videos, as well as improved file-sharing.

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Version 5.0.5, updated in March 2012, it supported more social stream features, much like Facebook and Twitter, as well as the ability to send voice messages up to 60 seconds long. iPad application On April 3, 2010, Apple released the first generation iPad. Along with this newly released device AOL released the AIM application for iPad. It was built entirely from scratch for the new version iOS with a specialized user-interface for the device. It supports geo location, Facebook status updates and chat, Myspace, Twitter, YouTube, Foursquare and many social networking platforms.

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AIM (software)

AIM Express AIM Express ran in a pop-up browser window. It was intended for use by people who are unwilling or unable to install a standalone application or those at computers that lack the AIM application. AIM Express supported many of the standard features included in the stand-alone client, but did not provide advanced features like file transfer, audio chat, video conferencing, or buddy info. It was implemented in Adobe Flash. It was an upgrade to the prior AOL Quick Buddy, which was later available for older systems that cannot handle Express before being discontinued. Express and Quick Buddy were similar to MSN Web Messenger and Yahoo! Web Messenger. This web version evolved into AIM.com's web-based messenger.

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AIM (software)

AIM Pages AIM Pages was a free website released in May 2006 by AOL in replacement of AIMSpace. Anyone who had an AIM user name and was at least 16 years of age could create their own web page (to display an online, dynamic profile) and share it with buddies from their AIM Buddy list.

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Layout AIM Pages included links to the email and Instant Message of the owner, along with a section listing the owners "buddies", which included AIM user names. It was possible to create modules in a Module T microformat. Video hosting sites like Netflix and YouTube could be added to ones AIM Page, as well as other sites like Amazon.com. It was also possible to insert HTML code. The main focus of AIM Pages was the integration of external modules, like those listed above, into the AOL Instant Messenger experience.

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Discontinuation By late 2007, AIM Pages had been discontinued. After AIM Pages shutdown, links to AIM Pages were redirected to AOL Lifestream, AOL's new site aimed at collecting external modules in one place, independent of AIM buddies. AOL Lifestream was shut down February 24, 2017.

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AIM for Mac AOL released an all-new AIM for the Macintosh on September 29, 2008 and the final build on December 15, 2008. The redesigned AIM for Mac is a full universal binary Cocoa API application that supports both Tiger and Leopard — Mac OS X 10.4.8 (and above) or Mac OS X 10.5.3 (and above). On October 1, 2009, AOL released AIM 2.0 for Mac.

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AIM (software)

AIM real-time IM This feature is available for AIM 7 and allows for a user to see what the other is typing as it is being done. It was developed and built with assistance from Trace Research and Development Centre at University of Wisconsin–Madison and Gallaudet University. The application provides visually impaired users the ability to convert messages from text (words) to speech. For the application to work users must have AIM 6.8 or higher, as it is not compatible with older versions of AIM software, AIM for Mac or iChat.

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AIM to mobile (messaging to phone numbers) This feature allows text messaging to a phone number (text messaging is less functional than instant messaging). Discontinued features

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AIM Phoneline AIM Phoneline was a Voice over IP PC-PC, PC-Phone and Phone-to-PC service provided via the AIM application. It was also known to work with Apple's iChat Client. The service was officially closed to its customers on January 13, 2009. The closing of the free service caused the number associated with the service to be disabled and not transferable for a different service. AIM Phoneline website was recommending users switch to a new service named AIM Call Out, also discontinued now.

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Launched on May 16, 2006, AIM Phoneline provided users the ability to have several local numbers, allowing AIM users to receive free incoming calls. The service allowed users to make calls to landlines and mobile devices through the use of a computer. The service, however, was only free for receiving and AOL charged users $14.95 a month for an unlimited calling plan. In order to use AIM Phoneline users had to install the latest free version of AIM Triton software and needed a good set of headphones with a boom microphone. It could take several days after a user signed up before it started working.

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AIM (software)

AIM Call Out AIM Call Out is a discontinued Voice over IP PC-PC, PC-Phone and Phone-to-PC service provided by AOL via its AIM application that replaced the defunct AIM Phoneline service in November 2007. It did not depend on the AIM client and could be used with only an AIM screenname via the WebConnect feature or a dedicated SIP device. The AIM Call Out service was shut down on March 25, 2009.

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Security On November 4, 2014, AIM scored one out of seven points on the Electronic Frontier Foundation's secure messaging scorecard. AIM received a point for encryption during transit, but lost points because communications are not encrypted with a key to which the provider has no access, i.e., the communications are not end-to-end encrypted, users can't verify contacts' identities, past messages are not secure if the encryption keys are stolen, (i.e., the service does not provide forward secrecy), the code is not open to independent review, i.e., the code is not open-source), the security design is not properly documented, and there has not been a recent independent security audit. BlackBerry Messenger, Ebuddy XMS, Hushmail, Kik Messenger, Skype, Viber, and Yahoo! Messenger also scored one out of seven points.

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See also Comparison of cross-platform instant messaging clients List of defunct instant messaging platforms References External links 1997 software Android (operating system) software Instant Messenger BlackBerry software Classic Mac OS instant messaging clients Computer-related introductions in 1997 Cross-platform software Defunct instant messaging clients Instant messaging clients Internet properties disestablished in 2017 IOS software MacOS instant messaging clients Online chat Symbian software Unix instant messaging clients Videotelephony Windows instant messaging clients

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Ackermann function

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive. All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive. After Ackermann's publication of his function (which had three nonnegative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function" may refer to any of numerous variants of the original function. One common version, the two-argument Ackermann-Péter function is defined as follows for nonnegative integers m and n:

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Its value grows rapidly, even for small inputs. For example, is an integer of 19,729 decimal digits (equivalent to 265536−3, or 22222−3).

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History In the late 1920s, the mathematicians Gabriel Sudan and Wilhelm Ackermann, students of David Hilbert, were studying the foundations of computation. Both Sudan and Ackermann are credited with discovering total computable functions (termed simply "recursive" in some references) that are not primitive recursive. Sudan published the lesser-known Sudan function, then shortly afterwards and independently, in 1928, Ackermann published his function (the Greek letter phi). Ackermann's three-argument function, , is defined such that for , it reproduces the basic operations of addition, multiplication, and exponentiation as

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and for p > 2 it extends these basic operations in a way that can be compared to the hyperoperations: (Aside from its historic role as a total-computable-but-not-primitive-recursive function, Ackermann's original function is seen to extend the basic arithmetic operations beyond exponentiation, although not as seamlessly as do variants of Ackermann's function that are specifically designed for that purpose—such as Goodstein's hyperoperation sequence.)

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Ackermann function

In On the Infinite, David Hilbert hypothesized that the Ackermann function was not primitive recursive, but it was Ackermann, Hilbert's personal secretary and former student, who actually proved the hypothesis in his paper On Hilbert's Construction of the Real Numbers. Rózsa Péter and Raphael Robinson later developed a two-variable version of the Ackermann function that became preferred by almost all authors. The generalized hyperoperation sequence, e.g. , is a version of Ackermann function as well.

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Ackermann function

In 1963 R.C. Buck based an intuitive two-variable variant on the hyperoperation sequence: Compared to most other versions Buck's function has no unessential offsets: Many other versions of Ackermann function have been investigated. Definition Definition: as m-ary function Ackermann's original three-argument function is defined recursively as follows for nonnegative integers and : Of the various two-argument versions, the one developed by Péter and Robinson (called "the" Ackermann function by most authors) is defined for nonnegative integers and as follows:

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The Ackermann function has also been expressed in relation to the hyperoperation sequence: or, written in Knuth's up-arrow notation (extended to integer indices ): or, equivalently, in terms of Buck's function F: Definition: as iterated 1-ary function Define as the n-th iterate of : Iteration is the process of composing a function with itself a certain number of times. Function composition is an associative operation, so . Conceiving the Ackermann function as a sequence of unary functions, one can set .

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The function then becomes a sequence of unary functions, defined from iteration: As function composition is associative, the last line can as well be Computation The recursive definition of the Ackermann function can naturally be transposed to a term rewriting system (TRS). TRS, based on 2-ary function The definition of the 2-ary Ackermann function leads to the obvious reduction rules Example Compute The reduction sequence is To compute one can use a stack, which initially contains the elements . Then repeatedly the two top elements are replaced according to the rules Schematically, starting from :

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WHILE stackLength <> 1 { POP 2 elements; PUSH 1 or 2 or 3 elements, applying the rules r1, r2, r3 } The pseudocode is published in . For example, on input , Remarks The leftmost-innermost strategy is implemented in 225 computer languages on Rosetta Code. For all the computation of takes no more than steps. pointed out that in the computation of the maximum length of the stack is , as long as . Their own algorithm, inherently iterative, computes within time and within space.

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TRS, based on iterated 1-ary function The definition of the iterated 1-ary Ackermann functions leads to different reduction rules As function composition is associative, instead of rule r6 one can define Like in the previous section the computation of can be implemented with a stack. Initially the stack contains the three elements . Then repeatedly the three top elements are replaced according to the rules Schematically, starting from : WHILE stackLength <> 1 { POP 3 elements; PUSH 1 or 3 or 5 elements, applying the rules r4, r5, r6; } Example

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On input the successive stack configurations are The corresponding equalities are When reduction rule r7 is used instead of rule r6, the replacements in the stack will follow The successive stack configurations will then be The corresponding equalities are

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Remarks On any given input the TRSs presented so far converge in the same number of steps. They also use the same reduction rules (in this comparison the rules r1, r2, r3 are considered "the same as" the rules r4, r5, r6/r7 respectively). For example, the reduction of converges in 14 steps: 6 × r1, 3 × r2, 5 × r3. The reduction of converges in the same 14 steps: 6 × r4, 3 × r5, 5 × r6/r7. The TRSs differ in the order in which the reduction rules are applied. When is computed following the rules {r4, r5, r6}, the maximum length of the stack stays below . When reduction rule r7 is used instead of rule r6, the maximum length of the stack is only . The length of the stack reflects the recursion depth. As the reduction according to the rules {r4, r5, r7} involves a smaller maximum depth of recursion, this computation is more efficient in that respect.

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TRS, based on hyperoperators As — or — showed explicitly, the Ackermann function can be expressed in terms of the hyperoperation sequence: or, after removal of the constant 2 from the parameter list, in terms of Buck's function Buck's function , a variant of Ackermann function by itself, can be computed with the following reduction rules: Instead of rule b6 one can define the rule To compute the Ackermann function it suffices to add three reduction rules

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These rules take care of the base case A(0,n), the alignment (n+3) and the fudge (-3). Example Compute The matching equalities are when the TRS with the reduction rule is applied: when the TRS with the reduction rule is applied:

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Remarks The computation of according to the rules {b1 - b5, b6, r8 - r10} is deeply recursive. The maximum depth of nested s is . The culprit is the order in which iteration is executed: . The first disappears only after the whole sequence is unfolded. The computation according to the rules {b1 - b5, b7, r8 - r10} is more efficient in that respect. The iteration simulates the repeated loop over a block of code. The nesting is limited to , one recursion level per iterated function. showed this correspondence. These considerations concern the recursion depth only. Either way of iterating leads to the same number of reduction steps, involving the same rules (when the rules b6 and b7 are considered "the same"). The reduction of for instance converges in 35 steps: 12 × b1, 4 × b2, 1 × b3, 4 × b5, 12 × b6/b7, 1 × r9, 1 × r10. The modus iterandi only affects the order in which the reduction rules are applied. A real gain of execution time can only be achieved by not recalculating subresults over and over again. Memoization is an optimization technique where the results of function calls are cached and returned when the same inputs occur again. See for instance . published a cunning algorithm which computes within time and within space.

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Huge numbers To demonstrate how the computation of results in many steps and in a large number: Table of values Computing the Ackermann function can be restated in terms of an infinite table. First, place the natural numbers along the top row. To determine a number in the table, take the number immediately to the left. Then use that number to look up the required number in the column given by that number and one row up. If there is no number to its left, simply look at the column headed "1" in the previous row. Here is a small upper-left portion of the table:

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The numbers here which are only expressed with recursive exponentiation or Knuth arrows are very large and would take up too much space to notate in plain decimal digits. Despite the large values occurring in this early section of the table, some even larger numbers have been defined, such as Graham's number, which cannot be written with any small number of Knuth arrows. This number is constructed with a technique similar to applying the Ackermann function to itself recursively. This is a repeat of the above table, but with the values replaced by the relevant expression from the function definition to show the pattern clearly: Properties

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General remarks It may not be immediately obvious that the evaluation of always terminates. However, the recursion is bounded because in each recursive application either decreases, or remains the same and decreases. Each time that reaches zero, decreases, so eventually reaches zero as well. (Expressed more technically, in each case the pair decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of single non-negative integers; this means one cannot go down in the ordering infinitely many times in succession.) However, when decreases there is no upper bound on how much can increase — and it will often increase greatly. For small values of m like 1, 2, or 3, the Ackermann function grows relatively slowly with respect to n (at most exponentially). For , however, it grows much more quickly; even is about 2, and the decimal expansion of is very large by any typical measure. An interesting aspect is that the only arithmetic operation it ever uses is addition of 1. Its fast growing power is based solely on nested recursion. This also implies that its running time is at least proportional to its output, and so is also extremely huge. In actuality, for most cases the running time is far larger than the output; see above. A single-argument version that increases both and at the same time dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi- and superfactorial functions, and even functions defined using Knuth's up-arrow notation (except when the indexed up-arrow is used). It can be seen that is roughly comparable to in the fast-growing hierarchy. This extreme growth can be exploited to show that which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

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Not primitive recursive The Ackermann function grows faster than any primitive recursive function and therefore is not itself primitive recursive. Specifically, one shows that to every primitive recursive function there exists a non-negative integer such that for all non-negative integers , Once this is established, it follows that itself is not primitive recursive, since otherwise putting would lead to the contradiction The proof proceeds as follows: define the class of all functions that grow slower than the Ackermann function

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and show that contains all primitive recursive functions. The latter is achieved by showing that contains the constant functions, the successor function, the projection functions and that it is closed under the operations of function composition and primitive recursion. Inverse Since the function considered above grows very rapidly, its inverse function, f, grows very slowly. This inverse Ackermann function f−1 is usually denoted by α. In fact, α(n) is less than 5 for any practical input size n, since is on the order of .

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This inverse appears in the time complexity of some algorithms, such as the disjoint-set data structure and Chazelle's algorithm for minimum spanning trees. Sometimes Ackermann's original function or other variations are used in these settings, but they all grow at similarly high rates. In particular, some modified functions simplify the expression by eliminating the −3 and similar terms. A two-parameter variation of the inverse Ackermann function can be defined as follows, where is the floor function:

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This function arises in more precise analyses of the algorithms mentioned above, and gives a more refined time bound. In the disjoint-set data structure, m represents the number of operations while n represents the number of elements; in the minimum spanning tree algorithm, m represents the number of edges while n represents the number of vertices. Several slightly different definitions of exist; for example, is sometimes replaced by n, and the floor function is sometimes replaced by a ceiling. Other studies might define an inverse function of one where m is set to a constant, such that the inverse applies to a particular row.

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The inverse of the Ackermann function is primitive recursive. Use as benchmark The Ackermann function, due to its definition in terms of extremely deep recursion, can be used as a benchmark of a compiler's ability to optimize recursion. The first published use of Ackermann's function in this way was in 1970 by Dragoș Vaida and, almost simultaneously, in 1971, by Yngve Sundblad.

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Sundblad's seminal paper was taken up by Brian Wichmann (co-author of the Whetstone benchmark) in a trilogy of papers written between 1975 and 1982. See also Computability theory Double recursion Fast-growing hierarchy Goodstein function Primitive recursive function Recursion (computer science) Notes References Bibliography

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External links An animated Ackermann function calculator Ackerman function implemented using a for loop Scott Aaronson, Who can name the biggest number? (1999) Ackermann functions. Includes a table of some values. Hyper-operations: Ackermann's Function and New Arithmetical Operation Robert Munafo's Large Numbers describes several variations on the definition of A. Gabriel Nivasch, Inverse Ackermann without pain on the inverse Ackermann function. Raimund Seidel, Understanding the inverse Ackermann function (PDF presentation). The Ackermann function written in different programming languages, (on Rosetta Code) Ackermann's Function (Archived 2009-10-24)—Some study and programming by Harry J. Smith.

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Arithmetic Large integers Special functions Theory of computation Computability theory

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AMOS (programming language)

AMOS BASIC is a dialect of the BASIC programming language implemented on the Amiga computer. AMOS BASIC was published by Europress Software and originally written by François Lionet with Constantin Sotiropoulos in the year 1990. AMOS was considered to be a fast language. It also had 3D capabilities. History AMOS is a descendant of STOS BASIC for the Atari ST. AMOS BASIC was first produced in 1990.

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AMOS competed on the Amiga platform with Acid Software's Blitz BASIC. Both BASICs differed from other dialects on different platforms, in that they allowed the easy creation of fairly demanding multimedia software, with full structured code and many high-level functions to load images, animations, sounds and display them in various ways.

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AMOS (programming language)

The original AMOS was a BASIC interpreter which, whilst working fine, suffered the same disadvantages of any language being run interpretively. By all accounts, AMOS was extremely fast among interpreted languages, being speedy enough that an extension called AMOS 3D could produce playable 3D games even on plain 7 MHz 68000 Amigas. Later, an AMOS compiler was developed that further increased speed. AMOS could also run MC68000 machine code, loaded into a program's memory banks.

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To simplify animation of sprites, AMOS included the AMOS Animation Language (AMAL), a compiled sprite scripting language which runs independently of the main AMOS BASIC program. It was also possible to control screen and "rainbow" effects using AMAL scripts. AMAL scripts in effect created CopperLists, small routines executed by the Amiga's Agnus chip.

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After the original version of AMOS, Europress released a compiler (AMOS Compiler), and two other versions of the language: Easy AMOS, a simpler version for beginners, and AMOS Professional, a more advanced version with added features, such as a better IDE, ARexx support, a new UI API and new flow control constructs. Neither of these new versions was significantly more popular than the original AMOS. AMOS was used mostly to make multimedia software, video games (platformers and graphical adventures) and educational software. The language was mildly successful within the Amiga community. Its ease of use made it especially attractive to beginners.

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Perhaps AMOS BASIC's biggest disadvantage, stemming from its Atari ST lineage, was its incompatibility with the Amiga's operating system functions and interfaces. Instead, AMOS BASIC controlled the computer directly, which caused programs written in it to have a non-standard user interface, and also caused compatibility problems with newer versions of hardware. Today, the language has declined in popularity along with the Amiga computer for which it was written. Despite this, a small community of enthusiasts are still using it. The source code to AMOS was released around 2001 under a BSD style license by Clickteam, a company that includes the original programmer.

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On the 4 April 2019, François Lionet announced the release of AMOS2 on his website amos2.org. AMOS2 replaces STOS and AMOS together, using JavaScript as its code interpreter, making the new development system independent and generally deployed in internet browsers. Amos 2 is now called AOZ Studio. Its website is at https://www.aoz.studio/. Software Software written using AMOS BASIC includes:

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Miggybyte Scorched Tanks Games by Vulcan Software, amongst which was the Valhalla trilogy Amiga version of Ultimate Domain (called Genesia) by Microïds Flight of the Amazon Queen, by Interactive Binary Illusions Extreme Violence, included on an Amiga Power cover disk Jetstrike, a commercial game by Rasputin Software References

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External links Source code for AMOS Professional 68000 ASM from pianetaamiga.it (archived, ZIP) Source code for AMOS and STOS 68000 ASM from clickteam.com (archived, ZIP) The AMOS Factory (an AMOS support/community site) Amigacoding website (contains in-depth info and references for AMOS) History of STOS and AMOS: how they came to be published in the UK Amos Professional group on Facebook (one of the members is AMOS' original developer François Lionet)

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BASIC programming language family Video game development software Amiga development software Software using the BSD license Programming languages created in 1990

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Adoptionism

Adoptionism, also called dynamic monarchianism, is an early Christian nontrinitarian theological doctrine, which holds that Jesus was adopted as the Son of God at his baptism, his resurrection, or his ascension.

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Definition Adoptionism is one of two main forms of monarchianism (the other is modalism which considers God to be one while working through the different "modes" or "manifestations" of God the Father, God the Son, and God the Holy Spirit, without limiting his modes or manifestations). Adoptionism denies the eternal pre-existence of Christ, and although it explicitly affirms his deity subsequent to events in his life, many classical trinitarians claim that the doctrine implicitly denies it by denying the constant hypostatic union of the eternal Logos to the human nature of Jesus. Under adoptionism Jesus is currently divine and has been since his adoption, although he is not equal to the Father, per "my Father is greater than I" and as such is a kind of subordinationism. Adoptionism is sometimes, but not always, related to denial of the virgin birth of Jesus.

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History Early Christianity Adoptionism and High Christology

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Bart Ehrman holds that the New Testament writings contain two different Christologies, namely a "low" or adoptionist Christology, and a "high" or "incarnation Christology." The "low Christology" or "adoptionist Christology" is the belief "that God exalted Jesus to be his Son by raising him from the dead," thereby raising him to "divine status." The other early Christology is "high Christology," which is "the view that Jesus was a pre-existent divine being who became a human, did the Father’s will on earth, and then was taken back up into heaven whence he had originally come," and from where he appeared on earth. The chronology of the development of these early Christologies is a matter of debate within contemporary scholarship.

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According to the "evolutionary model" c.q. "evolutionary theories," as proposed by Bousset, followed by Brown, the Christological understanding of Christ developed over time, from a low Christology to a high Christology, as witnessed in the Gospels. According to the evolutionary model, the earliest Christians believed that Jesus was a human who was exalted, c.q. adopted as God's Son, when he was resurrected, signaling the nearness of the Kingdom of God, when all dead would be resurrected and the righteous exalted. Adoptionist concepts can be found in the Gospel of Mark. As Daniel Johansson notes, a majority consensus holds Mark's Jesus as "an exalted, but merely human figure", especially when read in the apparent context of Jewish beliefs. Later beliefs shifted the exaltation to his baptism, birth, and subsequently to the idea of his eternal existence, as witnessed in the Gospel of John. Mark shifted the moment of when Jesus became the son to the baptism of Jesus, and later still Matthew and Luke shifted it to the moment of the divine conception, and finally John declared that Jesus had been with God from the beginning: "In the beginning was the Word".

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Since the 1970s, the late datings for the development of a "high Christology" have been contested, and a majority of scholars argue that this "High Christology" existed already before the writings of Paul. This "incarnation Christology" or "high Christology" did not evolve over a longer time, but was a "big bang" of ideas which were already present at the start of Christianity, and took further shape in the first few decades of the church, as witnessed in the writings of Paul.

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According to Ehrman, these two Christologies existed alongside each other, calling the "low Christology" an "adoptionist Christology, and "the "high Christology" an "incarnation Christology."

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New Testamental epistles Adoptionist theology may also be reflected in canonical epistles, the earliest of which pre-date the writing of the gospels. The letters of Paul the Apostle, for example, do not mention a virgin birth of Christ. Paul describes Jesus as "born of a woman, born under the law" and "as to his human nature was a descendant of David" in the Epistle to the Galatians and the Epistle to the Romans. Many interpreters, however, take his statements in Philippians 2 to imply that Paul believed Jesus to have existed as equal to God before his incarnation.

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The Book of Hebrews, a contemporary sermon by an unknown author, describes God as saying "You are my son; today I have begotten you." Shepherd of Hermas The 2nd-century work Shepherd of Hermas may also have taught that Jesus was a virtuous man filled with the Holy Spirit and adopted as the Son. While the Shepherd of Hermas was popular and sometimes bound with the canonical scriptures, it didn't retain canonical status, if it ever had it.

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Theodotus of Byzantium Theodotus of Byzantium (fl. late 2nd century), a Valentinian Gnostic, was the most prominent exponent of adoptionism. According to Hippolytus of Rome (Philosophumena, VII, xxiii) Theodotus taught that Jesus was a man born of a virgin, according to the Council of Jerusalem, that he lived like other men, and was most pious. At his baptism in the Jordan the "Christ" came down upon the man Jesus, in the likeness of a dove (Philosophumena, VII, xxiii), but Jesus was not himself God until after his resurrection.

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Adoptionism was declared heresy at the end of the 3rd century and was rejected by the Synods of Antioch and the First Council of Nicaea, which defined the orthodox doctrine of the Trinity and identified the man Jesus with the eternally begotten Son or Word of God in the Nicene Creed. The belief was also declared heretical by Pope Victor I. Ebionites Adoptionism was also adhered to by the Jewish Christians known as Ebionites, who, according to Epiphanius in the 4th century, believed that Jesus was chosen on account of his sinless devotion to the will of God.

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The Ebionites were a Jewish Christian movement that existed during the early centuries of the Christian Era. They show strong similarities with the earliest form of Jewish Christianity, and their specific theology may have been a "reaction to the law-free Gentile mission." They regarded Jesus as the Messiah while rejecting his divinity and his virgin birth, and insisted on the necessity of following Jewish law and rites. They used the Gospel of the Ebionites, one of the Jewish–Christian gospels; the Hebrew Book of Matthew starting at chapter 3; revered James the brother of Jesus (James the Just); and rejected Paul the Apostle as an apostate from the Law. Their name ( Ebionaioi, derived from Hebrew ebyonim, ebionim, meaning "the poor" or "poor ones") suggests that they placed a special value on voluntary poverty.

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Distinctive features of the Gospel of the Ebionites include the absence of the virgin birth and of the genealogy of Jesus; an Adoptionist Christology, in which Jesus is chosen to be God's Son at the time of his Baptism; the abolition of the Jewish sacrifices by Jesus; and an advocacy of vegetarianism. Spanish Adoptionism

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Spanish Adoptionism was a theological position which was articulated in Umayyad and Christian-held regions of the Iberian peninsula in the 8th and 9th centuries. The issue seems to have begun with the claim of archbishop Elipandus of Toledo that – in respect to his human nature – Christ was adoptive Son of God. Another leading advocate of this Christology was Felix of Urgel. In Spain, adoptionism was opposed by Beatus of Liebana, and in the Carolingian territories, the Adoptionist position was condemned by Pope Hadrian I, Alcuin of York, Agobard, and officially in Carolingian territory by the Council of Frankfurt (794).

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Despite the shared name of "adoptionism" the Spanish Adoptionist Christology appears to have differed sharply from the adoptionism of early Christianity. Spanish advocates predicated the term adoptivus of Christ only in respect to his humanity; once the divine Son "emptied himself" of divinity and "took the form of a servant" (Philippians 2:7), Christ's human nature was "adopted" as divine.

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Historically, many scholars have followed the Adoptionists' Carolingian opponents in labeling Spanish Adoptionism as a minor revival of “Nestorian” Christology. John C. Cavadini has challenged this notion by attempting to take the Spanish Christology in its own Spanish/North African context in his study, The Last Christology of the West: Adoptionism in Spain and Gaul, 785–820.

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Scholastic Neo-adoptionism A third wave was the revived form ("Neo-adoptionism") of Peter Abelard in the 12th century. Later, various modified and qualified Adoptionist tenets emerged from some theologians in the 14th century. Duns Scotus (1300) and Durandus of Saint-Pourçain (1320) admit the term Filius adoptivus in a qualified sense. In more recent times the Jesuit Gabriel Vásquez, and the Lutheran divines Georgius Calixtus and Johann Ernst Immanuel Walch, have defended adoptionism as essentially orthodox.

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Modern adoptionist groups A form of adoptionism surfaced in Unitarianism during the 18th century as denial of the virgin birth became increasingly common, led by the views of Joseph Priestley and others.

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A similar form of adoptionism was expressed in the writings of James Strang, a Latter Day Saint leader who founded the Church of Jesus Christ of Latter Day Saints (Strangite) after the death of Joseph Smith in 1844. In his Book of the Law of the Lord, a purported work of ancient scripture found and translated by Strang, he offers an essay entitled "Note on the Sacrifice of Christ" in which he explains his unique (for Mormonism as a whole) doctrines on the subject. Jesus Christ, said Strang, was the natural-born son of Mary and Joseph, who was chosen from before all time to be the Savior of mankind, but who had to be born as an ordinary mortal of two human parents (rather than being begotten by the Father or the Holy Spirit) to be able to truly fulfill his Messianic role. Strang claimed that the earthly Christ was in essence "adopted" as God's son at birth, and fully revealed as such during the Transfiguration. After proving himself to God by living a perfectly sinless life, he was enabled to provide an acceptable sacrifice for the sins of men, prior to his resurrection and ascension.

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See also Adoptivi Arianism Binitarianism Notes References Sources Printed sources Philip Schaff History of the Christian Church, Volume IV, 1882. (6th German edition, translated by George Ogg) Web sources External links Adoptionism in Catholic Encyclopedia Adoptionism in Christian Cyclopedia Chapter XI. Doctrinal Controversies, from Philip Schaff's History of the Christian Church Nontrinitarianism Christian terminology Christology Heresy in ancient Christianity Adoption and religion

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Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma or the weaker ultrafilter lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

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Algebraic closure

The algebraic closure of a field K can be thought of as the largest algebraic extension of K. To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K. The algebraic closure of K is also the smallest algebraically closed field containing K, because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.

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Algebraic closure

The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.

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Examples The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers. The algebraic closure of the field of rational numbers is the field of algebraic numbers. There are many countable algebraically closed fields within the complex numbers, and strictly containing the field of algebraic numbers; these are the algebraic closures of transcendental extensions of the rational numbers, e.g. the algebraic closure of Q(π). For a finite field of prime power order q, the algebraic closure is a countably infinite field that contains a copy of the field of order qn for each positive integer n (and is in fact the union of these copies).

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Algebraic closure

Existence of an algebraic closure and splitting fields Let be the set of all monic irreducible polynomials in K[x]. For each , introduce new variables where . Let R be the polynomial ring over K generated by for all and all . Write

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with . Let I be the ideal in R generated by the . Since I is strictly smaller than R, Zorn's lemma implies that there exists a maximal ideal M in R that contains I. The field K1=R/M has the property that every polynomial with coefficients in K splits as the product of and hence has all roots in K1. In the same way, an extension K2 of K1 can be constructed, etc. The union of all these extensions is the algebraic closure of K, because any polynomial with coefficients in this new field has its coefficients in some Kn with sufficiently large n, and then its roots are in Kn+1, and hence in the union itself.

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It can be shown along the same lines that for any subset S of K[x], there exists a splitting field of S over K.

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Separable closure An algebraic closure Kalg of K contains a unique separable extension Ksep of K containing all (algebraic) separable extensions of K within Kalg. This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of Ksep, of degree > 1. Saying this another way, K is contained in a separably-closed algebraic extension field. It is unique (up to isomorphism).

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The separable closure is the full algebraic closure if and only if K is a perfect field. For example, if K is a field of characteristic p and if X is transcendental over K, is a non-separable algebraic field extension. In general, the absolute Galois group of K is the Galois group of Ksep over K. See also Algebraically closed field Algebraic extension Puiseux expansion Complete field References Field extensions

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Advanced Power Management

Advanced power management (APM) is an API developed by Intel and Microsoft and released in 1992 which enables an operating system running an IBM-compatible personal computer to work with the BIOS (part of the computer's firmware) to achieve power management. Revision 1.2 was the last version of the APM specification, released in 1996. ACPI is the successor to APM. Microsoft dropped support for APM in Windows Vista. The Linux kernel still mostly supports APM, though support for APM CPU idle was dropped in version 3.0. Overview

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Advanced Power Management

APM uses a layered approach to manage devices. APM-aware applications (which include device drivers) talk to an OS-specific APM driver. This driver communicates to the APM-aware BIOS, which controls the hardware. There is the ability to opt out of APM control on a device-by-device basis, which can be used if a driver wants to communicate directly with a hardware device.

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Advanced Power Management

Communication occurs both ways; power management events are sent from the BIOS to the APM driver, and the APM driver sends information and requests to the BIOS via function calls. In this way the APM driver is an intermediary between the BIOS and the operating system. Power management happens in two ways; through the above-mentioned function calls from the APM driver to the BIOS requesting power state changes, and automatically based on device activity.

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Advanced Power Management

In APM 1.0 and APM 1.1, power management is almost fully controlled by the BIOS. In APM 1.2, the operating system can control PM time (e.g. suspend timeout). Power management events There are 12 power events (such as standby, suspend and resume requests, and low battery notifications), plus OEM-defined events, that can be sent from the APM BIOS to the operating system. The APM driver regularly polls for event change notifications. Power Management Events:

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Advanced Power Management

APM functions There are 21 APM function calls defined that the APM driver can use to query power management statuses, or request power state transitions. Example function calls include letting the BIOS know about current CPU usage (the BIOS may respond to such a call by placing the CPU in a low-power state, or returning it to its full-power state), retrieving the current power state of a device, or requesting a power state change. Power states The APM specification defines system power states and device power states.

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Advanced Power Management

System power states APM defines five power states for the computer system: Full On: The computer is powered on, and no devices are in a power saving mode. APM Enabled: The computer is powered on, and APM is controlling device power management as needed. APM Standby: Most devices are in their low-power state, the CPU is slowed or stopped, and the system state is saved. The computer can be returned to its former state quickly (in response to activity such as the user pressing a key on the keyboard). APM Suspend: Most devices are powered off, but the system state is saved. The computer can be returned to its former state, but takes a relatively long time. (Hibernation is a special form of the APM Suspend state). Off: The computer is turned off.

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Advanced Power Management

Device power states APM also defines power states that APM-aware hardware can implement. There is no requirement that an APM-aware device implement all states. The four states are: Device On: The device is in full power mode. Device Power Managed: The device is still powered on, but some functions may not be available, or may have reduced performance. Device Low Power: The device is not working. Power is maintained so that the device may be 'woken up'. Device Off: The device is powered off.

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Advanced Power Management

CPU The CPU core (defined in APM as the CPU clock, cache, system bus and system timers) is treated specially in APM, as it is the last device to be powered down, and the first device to be powered back up. The CPU core is always controlled through the APM BIOS (there is no option to control it through a driver). Drivers can use APM function calls to notify the BIOS about CPU usage, but it is up to the BIOS to act on this information; a driver cannot directly tell the CPU to go into a power saving state.

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Advanced Power Management

In ATA drives The ATA specification defines APM provisions for hard drives via the subcommand , which specifies a trade-off between spin-down frequency and always-on performance. Unlike the BIOS-side APM, the ATA APM has never been deprecated. Aggressive spin-down frequencies may reduce drive lifespan by unnecessarily accumulating load cycles; most modern drives are specified to sustain 300,000 cycles and usually last at least 600,000. On the other hand, not spinning down the drive will cause extra power draw and heat generation; high temperatures also reduce the lifespan of hard drives.

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Advanced Power Management

See also Active State Power Management - hardware power management protocol for PCI Express Advanced Configuration and Power Interface (ACPI) - successor to APM Green computing Power management BatteryMAX (idle detection) References External links APM V1.2 Specification (RTF file). BIOS

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Alternative algebra

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have for all x and y in the algebra. Every associative algebra is obviously alternative, but so too are some strictly non-associative algebras such as the octonions. The associator

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Alternative algebra

Alternative algebras are so named because they are the algebras for which the associator is alternating. The associator is a trilinear map given by . By definition, a multilinear map is alternating if it vanishes whenever two of its arguments are equal. The left and right alternative identities for an algebra are equivalent to Both of these identities together imply that the associator is totally skew-symmetric. That is, for any permutation σ. It follows that for all x and y. This is equivalent to the flexible identity

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