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Wikiversity talk:Participants

Archive of discussion up to March 2008

Reconceptualisation of March 2008
In March 2008, I erased the previous "content" (such as it was) and started afresh with a new concept. Hopefully this concept will be useful, at least for an interim period until (hopefully) one day Wikiversity is so busy that it is hopeless keeping track of personalia. --McCormack 11:36, 18 March 2008 (UTC)
 * I moved this part of the discussion to the bottom of the page, as it is common in other discussions (i.e. new discussion entries at the bottom of the page). Small question: What is that * mark near some names? --Gbaor 12:12, 19 March 2008 (UTC)
 * I moved the previous discussion to an archive. We don't want people starting to read at the top of the page and thinking that had anything to do with the current page ;-) --McCormack 12:54, 19 March 2008 (UTC)
 * The star means "new in the list this month". I've added some explanation. --McCormack 12:54, 19 March 2008 (UTC)
 * Way to take a useless page and turn it into something somewhat useful. I'm impressed.  The Jade Knight 11:38, 3 September 2008 (UTC)

Keeping the very active participants list up-to-date
I believe it is possible to get hold of database dumps which list participants in order of edits - see e.g. w:Wikipedia:List of Wikipedians by number of recent edits, but I haven't found out how to do this yet. There are some pages which give the number of active editors, but not their names. So I'm proposing that keeping this page up-to-date should be a manual exercise for the time being. Anyone can add people to the most recent month as time goes by, as names crop up on "recent changes", and it might be nice to have the list more or less complete at the end of the month. A problem with wiki projects is contributor-retention, and identifying new active users would be a crucial pre-condition for encouraging, involving and retaining them in the long term. --McCormack 13:02, 19 March 2008 (UTC)

which namespace
100 contributions to become a very active contributor - meant for the main namespace or also ''discussions, templates. categories, etc.''? --Gbaor 13:21, 19 March 2008 (UTC)

 * Personally, I look at everything. But then I discount people who are only very temporarily here, plus vandals and trolls. --McCormack 04:55, 9 August 2008 (UTC)

title: Wikiversity talk:Participants


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Wikiversity:Mission/Initial development

Refining the mission statement
This is a space in which to develop further a community Wikiversity mission statement. This can (amongst other things) help us to clarify our complex vision and help us to come up with a catchy motto that can be used with our logo on the front page of sister projects.

Current mission statements
Mission statement from Approved Wikiversity project proposal:
 * "Wikiversity is a centre for the creation and use of free learning materials and activities. Its primary priorities and goals are to:
 * - Create and host a range of free-content, multilingual learning materials/resources, for all age groups in all languages
 * - Host scholarly/learning projects and communities that support these materials
 * - Complement and develop existing Wikimedia projects (eg. a project devoted to finding good sources for Wikipedia articles)"

Mission statement from top of front page (as of August 20, 2006):
 * "Wikiversity is a space for the creation and use of free learning materials and activities. Its primary goals are to:
 * - Create and host free content, multimedia learning materials, resources, and curricula for all age groups in all languages
 * - Develop collaborative learning projects and communities around these materials
 * "Wikiversity supports both learning and teaching."

Mission statement/invite from top of front page (as of September 5, 2006):
 * "Wikiversity is a community for the creation and use of free learning materials and activities. Wikiversity supports both learning and teaching. Its primary goals are to:
 * Create and host free content, multimedia learning materials, resources, and curricula for all age groups in all languages
 * Develop collaborative learning projects and communities around these materials
 * "Wikiversity provides various communication media and a wiki website where anyone can edit the pages. Learners and teachers are invited to join the Wikiversity community."

Mission statement/invite from top of front page (as of September 19, 2006):
 * "Wikiversity is a community for the creation and use of free learning materials and activities. Wikiversity is a multidimensional social organization dedicated to learning, teaching, research and service. Its primary goals are to:
 * Create and host free content, multimedia learning materials, resources, and curricula for all age groups in all languages
 * Develop collaborative learning projects and communities around these materials
 * Learners and teachers are invited to join the Wikiversity community as editors of this wiki website where anyone can edit the pages. The community portal lists information about many aspects of Wikiversity."

Refining mission statement(s)
The current mission statement versions are longish; the second sentence of the project proposal mission has a main clause and three subclauses. Perhaps that length is necessary. Perhaps not.

Can we create a more elegant statement for general readers which inspires participation and evokes the depth, breadth and power of the innovative aspects of Wikiversity that are discussed in the proposal, such as issues relating to e-learning and research?

Using a flexible Delphi method (see discussion below) is suggested for generating alternate mission statements and arriving at a synthesis.

Step 1: Develop Mission Statement Alternates
Method tips: If edits are substantial, please create a new alternate. Please feel free to copyedit any of these (except the current statements which are for reference). Please discuss merits of alternates on talk page. Thanks.

Note: I grouped these by a simple emergent category system -- based on length. Other categorizations can and probably should be used in the synthesizing in step 2. Reswik 15:20, 20 August 2006 (UTC)

Shorter mission statements
Short Alternate 1 - Focus on our piece of Wikimedia Foundation's goals.
 * Wikiversity develops free learning materials, processes, and knowledge to help all people access all free human knowledge.
 * Footnote for posterity: People = Sentient

Short Alternate 2 - Focus on key words in a short sentence
 * Wikiversity is a community collaboration based shared learning resource for all.

Short Alternate 3 - Focus on collaborative cyber-campus and sharing learning resources
 * Wikiversity is a collaborative cyber-campus commited to sharing learning resources at all levels with all people. -- Smithgrrl

Short Alternate 4
 * Wikiversity is an open educational environment that facilitates the integration of learners, teachers, and community builders everywhere. -- Aldenis

Short Alternate 5
 * Wikiversity celebrates the love of learning, sharing openly all knowledge everywhere with everyone. -- Anon.

Short Alternate 6
 * To boldly go where no University has gone before. -- Hillgentleman

Short Alternate 7
 * Wikiversity is a place where everybody can find the kind of university he likes most -- Raoul

Longer mission statements
Long Alternate 1 - Focus on collaborative learning
 * Wikiversity will provide the world with quality, multilingual, multimedia learning resources as well as a space for collaborative learning for all education levels to all people.

 * Long Alternate 2 - Focus on community and learning resources
 * Wikiversity is a diverse community of learners, teachers, and researchers. Wikiversity is space for creating and using free content, multimedia learning resources for all ages groups in all languages.

Long Alternate 3 - Focus on university/diversity, learning and scholarship
 * Wikiversity is a free university [alternately, "free diversity"] which creates quality, multilingual, multimedia learning resources and facilitates collaborative scholarship and learning for all education levels to all people. While Wikiversity fosters creating and sharing free knowledge, it does not grant degrees or titles at this time.

Long Alternate 4 - Focus on free space and network, learning and scholarship
 * Wikiversity is a free space and network of scholars for creating quality, multilingual, multimedia learning resources and facilitating collaborative scholarship and learning for all education levels to all people.

Long Alternate 5 - Multiple focus

 * Wikiversity is an open educational environment that facilitates the integration of learners, teachers, and community builders everywhere.

 * We learn by collaborating in the development of free instructional resources.

 * Everyone already involved in any wikimedia project is learning all the time. We are all learning about specific topics, but also about the general nature of collaborative knowledge production within a highly dynamic community. Wikiversity focus on education makes it the best place to explore the larger implications of this model. Our instructional materials should explicitly benefit from the fact that they were born over a network, were raised in a virtual village, and can be used by everyone. This is a new way of doing curriculum development, and we all need to learn it.

 * We teach new ways of implementing the collective use of these resources.

 * All wikimedia projects are based on an innovative model of open collaboration that results in the creation of rather conventional repositories of information. Our encyclopedias, dictionaries, databases, and archives are designed to replace and/or complement their closed, expensive, copyrighted, or plainly useless equivalent. Wikiversity is different. Producing great free content is only part of our mission. We want to deliver instructional resources in ways that promotes collaboration among users of these resources. A network of collective users would be the perfect counterpart of our network of collaborative producers.

 * We build a dynamic interface between virtual communities of free content creators and the pedagogical infrastructure of the physical world.

 * Wikiversity is a hybrid network. We create instructional materials that make use of the wealth of resources generated by all wikimedia projects. We deliver these materials in ways that encourage their collective use. We promote further collaboration by designing educational assignments geared toward the development of all wikimedia projects. Our ultimate goal is to harness the power of existing learning communities, erasing the distinction between producers and consumers of free information worldwide. Deploying wikiversity resources in every brick-and-mortar classroom is one of the best ways to bring new contributors back to wikimedia.

Step 2: Synthesize Mission Statements into New Alternates
When we have a number of alternates above (over five or ten), we can start synthesizing the best features of these into a small number of options. Then, we can discuss them (on talk page). If necessary, we can repeat the synthesis process another time.

Step 2, if repeated, could lead to whole process taking a few weeks or a month or more. Hopefully quality and broad(er) agreement will result.

Step 3: Select Mission Statement(s)
When a group of editors active here have generated what seem to be final synthesized versions then we can call the community for choosing, per some process discussed below.

Statement Development: Delphi method
One way of working with collbaratively evolving and synthesizing differing ideas or theories is known as the Delphi method.

In essence, we can develop "themed" alternates and edit existing alternates. Favored alternates can be synthesized, possibly dropping points that are most problematic or unworkable. Then, hopefully we can arrive at one or a few synthesized choice(s). There is usually a facilitator in this method, but we could just do this all together in these steps:

Step 1. We could develop "themed" alternates and edit existing alternates per the "focus" of the alternates. Step 2. We can synthesize the alternates to generate a separate smaller set of more agreeable and elegant alternates. Step 3. Iterate until we have one or a few polished alternates.

If we arrive at several distinct alternates, we can choose from amongst favored alternates to use. Or, we could have a few mission statements for the time being.

This application of the Delphi method deviates from the "traditional" method in several ways. Group facilitation is suggested, not one facilitator. There is not an explicit mention of using steps of developing a thesis, antithesis, and synthesis (though this can be implicit in developing various alternates). There is not an intention for buy in at each stage of a new synthesis (though we can repeatedly look at and edit versions or generate new versions from different points of view). Hence, this is a flexible or loose version of the Delphi method focusing on generating diverse options and interatively synthesizing and refining those.

(Note that the delphi method might be helpful in some planning contexts in Wikiversity. Perhaps it would be interesting to try working with both a formal version of the Delphi method and with the more flexible method discussed here.)

Source Documents
1. Some key passages from Approved Wikiversity project proposal:
 * "Wikiversity is a centre for the creation and use of free learning materials and activities. Its primary priorities and goals are to:
 * Create and host a range of free-content, multilingual learning materials/resources, for all age groups in all languages
 * Host scholarly/learning projects and communities that support these materials
 * Complement and develop existing Wikimedia projects (eg. a project devoted to finding good sources for Wikipedia articles)"

 * Regarding learning/e-learning:
 * "The Wikiversity e-Learning model. Existing "bricks and mortar" universities began as meeting places for scholarly individuals seeking knowledge and those with mastery of a subject who could act as teachers to guide the learning process. Wikiversity will be a virtual meeting place for masters and scholars, a wiki that hosts and promotes a flexible online learning environment.

 * "Conventional universities evolved to have classrooms, collections of courses, grades, fees for students, pay for teachers, the granting of degrees, the certification of teachers and accreditation of universities. That entire structure grew out of the need to concentrate expensive resources (people and facilities) at a particular location in the physical world. The Wikiversity e-Learning model abandons all aspects of conventional universities that arise from the need to focus people and facilities in one place and time. The Wikiversity e-Learning model grows out of the power of the wiki user environment to liberate learning from conventional constraints of time and place. See Wikiversity:Learning for more.

 * "Learning groups

 * "It is natural for the wiki format to develop "learning groups" (creating and maintaining learning trails; interest portals; project or task artifacts) where all participants can discuss and learn collaboratively."

 * Regarding resources:
 * "Resources will include teaching aids, lesson plans, curricula, links, reading lists, etc. Each subject area (or 'course', 'project'), essentially, each community, creates a web of resources that would form the basis of discussions and activities within that field of Wikiversity..."

 * Regarding research:
 * "In the fulfillment of its mission, other tasks and goals may be initiated and developed by participants to support learning and the creation of new content. In particular, guidelines will be developed during the beta phase of Wikiversity's development on hosting and fostering research based in part on existing resources in Wikiversity and other Wikimedia projects." ...

 * "Finally, research may one day take place based on materials in Wikiversity (eg. materials on sociology prompt a survey of attitudes), and also based on Wikimedia projects. Wikiversity could act as a repository of research carried out by the Wikimedia Research Network or other people involved in wiki-based research, and could also host the proceedings of Wikimania. Guidelines for what would be appropriate research will be developed during the beta phase of the project, and reviewed after six months.

 * Whether or not Wikiversity will ever host original research in addition to secondary research is the subject of debate (see talk page.)"

2. Keep in mind the scope of beta stage of Wikiversity.

[Sudhir, 15th January 2007]: Just a suggestion ... "Free Knowledge for Open Minds (FKOM)". I hope it gels with the mission of "WIKIVERSITY".

Choosing
When this mission statement is well-enough developed...

 * Signing: We, the community, sign the statement as a kind of act of solidarity? It might be nice to have something that we can present to the world at this stage (even if our mission has been worked on on Meta for quite some time :-)) Cormaggio 08:04, 19 August 2006 (UTC)

 * Voting: If there is not one option, we could vote or rest with several statements for awhile.

Related projects

 * Logo contest for Wikiversity on meta.
 * Motto and slogan contest - Please list your suggestions and help select a motto and a slogan.

source: wikimedia

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

title: Wikiversity:Mission/Initial development


text:
uncompensated

Adjective

 * 1) Not compensated; having no compensation.
 * 2) Not paid for one's work.

Translations

 * Finnish: kompensoimaton
 * Greek:

 * Greek:

title: uncompensated


text:
1913–14 Isthmian League

The 1913–14 season was the ninth in the history of the Isthmian League, an English football competition.

New Crusaders were newly admitted to what would be their only season in the Isthmian League. London Caledonians were champions, winning their fifth Isthmian League title.

It was the last season before the league was suspended for the First World War. Shepherd's Bush never returned to the league after the war, while four other clubs missed the short 1919 season.

title: 1913–14 Isthmian League


text:
Talk:Transfering content to a website using commercial packages

FTP Client Software
Just a thought with the list of FTP client software: might be helpful for learners to just have one or two options for each platform - ones that you recommend. We can always link to a separate page with a full list for those interested. Just might overwhelm to have so many options? What things you? Michaelnelson 02:41, 27 January 2007 (UTC)

 * That sounds like a much better idea. I also agree with a statement in the Notes and discrepancies that it is hard to justify the focus on commercial software packages.  We really should focus on ease of use, with a preference for open source softare, or at least free software.  --mikeu talk 22:57, 6 July 2009 (UTC)

FTP Scenario
I'll add the FTP scenario that i use to get students demoing (with the grading options).

 * A note should probably be added that many firewalls do not allow ftp connections. Programs like WinSCP are free and allow the use of FTP/SFTP/SCP as may be needed.  They are also very easy to use.  --mikeu talk 21:48, 6 July 2009 (UTC)


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Introduction to Philosophy/Logic/Modal Logic

Introduction to Philosophy > Logic > Modal Logic

Modality
"Still holding the copy of The Grasshopper Lies Heavy, Robert said, 'What sort of alternate present does this book describe?' Betty, after a moment, said, 'One in which Germany and Japan lost the war.' They were all silent. (Philip K. Dick, The Man in the High Castle)" This is the basic premise of modal logic: some things could have been otherwise. In our everyday reasoning, we distinguish between necessary truths and statements that just happen to be true but could have been false. We say that the latter are contingently true, or that their negation is possible. The concepts of necessary, contingent, possible and impossible are very closely related: something is necessary if it is impossible for it to be false, and something is possible if its falsehood is not necessary. Contingency is the negation of necessity, and impossibility the negation of possibility. Modal logic attempts to include the notions of modality (necessary, contingent, possible and impossible, among others) into the structure of classical logic (propositional logic and predicate calculus) and is therefore an extension of classical logic.

Syntax
Modal logic introduces three new symbols into classical logic: $$\Box$$(necessary),$$\Diamond$$ (possible) and $$\Rightarrow$$ (if, then). Formulae are constructed in the usual way, with the following rules added before the closure clause (see the rules for Well-Formed Formulae in propositional calculus):  If $$\alpha$$ is a well-formed formula, then $$\Box \alpha$$ and $$\Diamond \alpha$$ are also well-formed formulae. If $$\alpha$$ and $$\beta$$ are well-formed formulae, then $$\alpha \Rightarrow \beta$$ is also a well formed formula.  Actually, one can define the modal propositional calculus axiomatically using just $$\Box$$ or $$\Diamond$$. For example, if we wish to define $$\Diamond$$ and $$\Rightarrow$$ in terms of $$\Box$$, $$\Diamond \alpha$$ can be defined simply as a abbreviated notation for $$\neg \Box \neg \alpha$$ and $$\alpha \Rightarrow \beta$$ as another way of writing $$\Box (\alpha \rightarrow \beta)$$.


text:
User:Jeff D

Welcome to Zetetikon

This wikiversity page is devoted to the aim of publishing new work in philosophy that is written, composed or constructed primarily by undergraduates interested in philosophy. The journal includes traditional philosophical essays as well as poetry, comedy, graphic art, photography, and any other medium that might be used to express philosophical ideas. We publish works in all areas of philosophy. The journal is edited by students studying philosophy at Northern Arizona University.

/Zetetikon: volume 2, Spring 2007

Category:Journals Category:Philosophy

title: User:Jeff D


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Ada Programming/Installing

Ada compilers are available from several vendors, on a variety of host and target platforms. The Ada Resource Association maintains a list of available compilers.

Below is an alphabetical list of available compilers with additional comments.

AdaMagic from SofCheck
SofCheck used to produce an Ada 95 front-end that can be plugged into a code generating back-end to produce a full compiler. This front-end is offered for licensing to compiler vendors.

Based on this front-end, SofCheck used to offer:

 * AdaMagic, an Ada-to-C/C++ translator
 * AppletMagic, an Ada-to-Java bytecode compiler

SofCheck has merged with AdaCore under the AdaCore name, leaving no visible trace of AdaMagic offering on AdaCore website.

However, MapuSoft is now licensed to resell AdaMagic. They renamed it to "Ada-to-C/C++ changer". New name sounds like fake. Almost no Ada developer heard of MapuSoft. MapuSoft is never seen making Ada libraries, commercial or FLOSS. They are never seen at Ada conferences. Yet this is a real stuff, a validated Ada compiler that knows lots of tricks required to work on top of C/C++ compilers. E.g. it contains a proven knowledge of handling integer overflow with a special "-1" case.

Thanks to MapuSoft, AdaMagic really became available to developers. Get AppCOE, but not Win64 one, install it. In the MapuSoft/AppCOE_x32/Tools/Ada there will be AdaMagic. AdaMagic is known to support Win64, but AppCOE for Win64 is known to contain no AdaMagic at all.

Using AdaMagic from command line is badly supported in AppCOE, but possible. Set up ADA_MAGIC environment variable, edit Tools/Ada/{linux|windows}/SITE/rts_path to point to real path, edit SITE/config to get rid of unsupported C compiler keys, and compile via e.g.

Commercial; proprietary.

AdaMULTI from Green Hills Software
Green Hills Software sells development environments for multiple languages and multiple targets (including DSPs), primarily to embedded software developers.

GHS claims to make great efforts to ensure that their compilers produce the most efficient code and often cites the EEMBC benchmark results as evidence, since many of the results published by chip manufacturers use GHS compilers to show their silicon in the best light, although these benchmarks are not Ada specific.

GHS has no publicly announced plans to support the two most recent Ada standards (2005 and 2012) but they do continue to actively market and develop their existing Ada products.

DEC Ada from HP
DEC Ada was an Ada 83 compiler for OpenVMS. While “DEC Ada” is probably the name most users know, the compiler has also been called “HP Ada”, "VAX Ada", and "Compaq Ada".

 * Ada for OpenVMS Alpha Installation Guide (PDF)
 * Ada for OpenVMS VAX Installation Guide (PDF)

GNAT, the GNU Ada Compiler from AdaCore and the Free Software Foundation
GNAT is the free GNU Ada compiler, which is part of the GNU Compiler Collection. It is the only Ada compiler that supports all of the optional annexes of the language standard. The original authors formed the company AdaCore to offer professional support, consulting, training and custom development services. It is thus possible to obtain GNAT from many different sources, detailed below.

GNAT is always licensed under the terms of the GNU General Public License.

However, the run-time library uses either the GPL, or the GNAT Modified GPL, depending on where you obtain it.

Several optional add-ons are available from various places:

 * ASIS, the Ada Semantic Interface Specification, is a library that allows Ada programs to examine and manipulate other Ada programs.
 * FLORIST is a library that provides a POSIX programming interface to the operating system.
 * GDB, the GNU Debugger, with Ada extensions.
 * GLADE implements Annex E, the Distributed Systems Annex. With it, one can write distributed programs in Ada, where partitions of the program running on different computers communicate over the network with one another and with shared objects.
 * GPS, the GNAT Programming Studio, is a full-featured integrated development environment, written in Ada. It allows you to code in Ada, C and C++.

Many Free Software libraries are also available.

GNAT GPL (or Community) Edition
As of may 2022, AdaCore no longer supports GNAT GPL. It has been replaced with Alire, a package manager for Ada sources, which also provides toolchains. The following is no longer relevant for post May 2022 users.

This is a source and binary release from AdaCore, intended for use by Free Software developers only. If you want to distribute your binary programs linked with the GPL run-time library, then you must do so under terms compatible with the GNU General Public License.

As of GNAT GPL Edition 2013:

GNAT Modified GPL releases
With these releases of GNAT, you can distribute your programs in binary form under licensing terms of your own choosing; you are not bound by the GPL.

GNAT 3.15p
This is the last public release of GNAT from AdaCore that uses the GNAT Modified General Public License.

GNAT 3.15p has passed the Ada Conformity Assessment Test Suite (ACATS). It was released in October 2002.

The binary distribution from AdaCore also contains an Ada-aware version of the GNU Debugger (GDB), and a graphical front-end to GDB called the GNU Visual Debugger (GVD).

GNAT Pro
GNAT Pro is the professional version of GNAT, offered as a subscription package by AdaCore. The package also includes professional consulting, training and maintenance services. AdaCore can provide custom versions of the compiler for native or cross development. For more information, see http://www.adacore.com/.

GCC
GNAT has been part of the Free Software Foundation's GCC since October 2001. The Free Software Foundation does not distribute binaries, only sources. Its licensing of the run-time library for Ada (and other languages) allows the development of proprietary software without necessarily imposing the terms of the GPL.

Most GNU/Linux distributions and several distributions for other platforms include prebuilt binaries; see below.

For technical reasons, we recommend against using the Ada compilers included in GCC 3.1, 3.2, 3.3 and 4.0. Instead, we recommend using GCC 3.4, 4.1 or later, or one of the releases from AdaCore (3.15p, GPL Edition or Pro).

Since October 2003, AdaCore merge most of their changes from GNAT Pro into GCC during Stage 1; this happens once for each major release. Since GCC 3.4, AdaCore has gradually added support for revised language standards, first Ada 2005 and now Ada 2012.

GCC version 4.4 switched to version 3 of the GNU General Public License and grants a Runtime Library Exception similar in spirit to the GNAT Modified General Public License used in all previous versions. This Runtime Library Exception applies to run-time libraries for all languages, not just Ada.

As of GCC 4.7, released on 2012-03-22:

The GNU Ada Project
The GNU Ada Project provides source and binary packages of various GNAT versions for several operating systems, and, importantly, the scripts used to create the packages. This may be helpful if you plan to port the compiler to another platform or create a cross-compiler; there are instructions for building your own GNAT compiler for GNU/Linux and Mac OS X users.

Both GPL and GMGPL or GCC Runtime Library Exception versions of GNAT are available.

A# (A-Sharp, a.k.a. Ada for .NET)
This compiler is historical as it has now been merged into GNAT GPL Edition and GNAT Pro.

A# is a port of Ada to the |Microsoft .NET Platform. A# was originally developed at the Department of Computer Science at the United States Air Force Academy which distribute A# as a service to the Ada community under the terms of the GNU general public license. A# integrates well with Microsoft Visual Studio 2005, AdaGIDE and the RAPID open-source GUI Design tool. As of 2006-06-06:

GNAT for AVR microcontrollers
Rolf Ebert and others provide a version of GNAT configured as a cross-compiler to various AVR microcontrollers, as well as an experimental Ada run-time library suitable for use on the microcontrollers. As of Version 1.1.0 (2010-02-25):

GNAT for LEON
The Real-Time Research Group of the Technical University of Madrid (UPM, Universidad Politécnica de Madrid) wrote a Ravenscar-compliant real-time kernel for execution on LEON processors and a modified run-time library. They also provide a GNAT cross-compiler. As of version 2.0.1:

GNAT for Macintosh (Mac OS X)
GNAT for Macintosh provides both FSF (GMGPL) and AdaCore (GPL) versions of GNAT with Xcode and Carbon integration and bindings.

Note that this site was last updated for GCC 4.3 and Mac OS X Leopard (both PowerPC and Intel-based). Aside from the work on integration with Apple’s Carbon graphical user interface and with Xcode 3.1 it may be preferable to see above.

There is also support at MacPorts; the last update (at 25 Nov 2011) was for GCC 4.4.2.

Prebuilt packages as part of larger distributions
Many distributions contain prebuilt binaries of GCC or various public releases of GNAT from AdaCore. Quality varies widely between distributions. The list of distributions below is in alphabetical oder. (Please keep it that way.)

AIDE (for Microsoft Windows)
AIDE — Ada Instant Development Environment is a complete one-click, just-works Ada distribution for Windows, consisting of GNAT, comprehensive documentation, tools and libraries. All are precompiled, and source code is also available. The installation procedure is particularly easy (just unzip to default c:\aide and run). AIDE is intended for beginners and teachers, but can also be used by advanced users.

Cygwin (for Microsoft Windows)
Cygwin, the Linux-like environment for Windows, also contains a version of the GNAT compiler. The Cygwin version of GNAT is older than the MinGW version and does not support DLLs and Multi-Threading (as of 11.2004).

Debian (GNU/Linux and GNU/kFreeBSD)
There is a Debian Policy for Ada which tries to make Debian the best Ada development and deployment platform. The development platform includes the compiler and many libraries, pre-packaged and integrated so as to be easy to use in any program. The deployment platform is the renowned stable distribution, which is suitable for mission-critical workloads and enjoys long life cycles, typically 3 to 4 years. Because Debian is a binary distribution, it is possible to deploy non-free, binary-only programs on it while enjoying all the benefits of a stable platform. Compiler choices are conservative for this reason, and the Policy mandates that all Ada programs and libraries be compiled with the same version of GNAT. This makes it possible to use all libraries in the same program. Debian separates run-time libraries from development packages, so that end users do not have to install the development system just to run a program.

The GNU Ada compiler can be installed on a Debian system with this command:

aptitude install gnat

This will also give you a list of related packages, which are likely to be useful for an Ada programmer.

Debian is unique in that it also allows programmers to use some of GNAT's internal components by means of two libraries: Debian packages make use of these libraries.
 * libgnatvsn (licensed under GNAT-Modified GPL) and
 * libgnatprj (the project manager, licensed under pure GPL).

In the table below, the information about the future Debian 8.0 Jessie is accurate as of October 2014 and will change.

The ADT plugin for Eclipse (see section ObjectAda from Aonix) can be used with GNAT as packaged for Debian Etch. Specify "/usr" as the toolchain path.

DJGPP (for MS-DOS)
DJGPP has GNAT as part of their GCC distribution.

DJGPP is a port of a comprehensive collection of GNU utilities to MS-DOS with 32-bit extensions, and is actively supported (as of 1.2005). It includes the whole GCC compiler collection, that now includes Ada. See the DJGPP website for installation instructions.

DJGPP programs run also in a DOS command box in Windows, as well as in native MS-DOS systems.

FreeBSD and DragonFly
FreeBSD's ports collection has an Ada framework with an expanding set of software packages. The Framework is currently built by FSF GCC 6.3.1, although FSF GCC 5.4 can optionally be used instead. The AdaCore GPL compilers are not present. There are several reasons for this, not the least of which is the addition maintenance of multiple compilers is significant. There are no non-GCC based Ada compilers represented in ports either.

While FreeBSD does have a snapshot that goes with each release, the ports are updating in a rolling fashion continuously, and the vast majority of users prefer the "head" of ports which has the latest packages.

There are two ways to install the software. The quickest and easiest way is to install prebuilt binaries using the command "pkg install ". For example, to install the GNAT Programming Studio and all of its dependencies including the GNAT compiler, all you need is one command:

pkg install gps-ide

If a specific package is not available, or the user just prefers to build from source (this can take a long time), then a typical command would be:

cd /usr/ports/devel/gps && make install clean

As with the binary installation, if any dependencies are missing they will be built first, also from source.

Available software as of 8 February 2017

Gentoo GNU/Linux
The GNU Ada compiler can be installed on a Gentoo system using emerge:

emerge dev-lang/gnat

In contrast to Debian, Gentoo is primarily a source distribution, so many packages are available only in source form, and require the user to recompile them (using emerge).

Also in contrast to Debian, Gentoo supports several versions of GNAT in parallel on the same system. Be careful, because not all add-ons and libraries are available with all versions of GNAT.

Mandriva Linux
The GNU Ada compiler can be installed on a Mandriva system with this command:

urpmi gnat

MinGW (for Microsoft Windows)
MinGW — Minimalist GNU for Windows contains a version of the GNAT compiler.

The current version of MinGW (5.1.6) contains gcc-4.5.0. This includes a fully functional GNAT compiler. If the automatic downloader does not work correctly you can download the compiler directly: pick gcc-4.5.0-1 from MinGW/BaseSystem/GCC/Version4/

old instructions
The following list should help you with the installation. (I may have forgotten something — but this is wiki, just add to the list)

 * 1) Install MinGW-3.1.0-1.exe
 * 2) extract binutils-2.15.91-20040904-1.tar.gz
 * 3) extract mingw-runtime-3.5.tar.gz
 * 4) extract gcc-core-3.4.2-20040916-1.tar.gz
 * 5) extract gcc-ada-3.4.2-20040916-1.tar.gz
 * 6) extract gcc-g++-3.4.2-20040916-1.tar.gz (Optional)
 * 7) extract gcc-g77-3.4.2-20040916-1.tar.gz (Optional)
 * 8) extract gcc-java-3.4.2-20040916-1.tar.gz (Optional)
 * 9) extract gcc-objc-3.4.2-20040916-1.tar.gz (Optional)
 * 10) extract w32api-3.1.tar.gz
 * 11) Install mingw32-make-3.80.0-3.exe (Optional)
 * 12) Install gdb-5.2.1-1.exe (Optional)
 * 13) Install MSYS-1.0.10.exe (Optional)
 * 14) Install msysDTK-1.0.1.exe (Optional)
 * 15) extract msys-automake-1.8.2.tar.bz2 (Optional)
 * 16) extract msys-autoconf-2.59.tar.bz2 (Optional)
 * 17) extract msys-libtool-1.5.tar.bz2 (Optional)

I have made good experience in using D:\MinGW as target directory for all installations and extractions.

Also noteworthy is that the Windows version for GNAT from Libre is also based on MinGW.

In gcc-3.4.2-release_notes.txt from MinGW site reads: ''please check that the files in the /lib/gcc/mingw32/3.4.2/adainclude and adalib directories are flagged as read-only. This attribute is necessary to prevent them from being deleted when using gnatclean to clean a project.''

So be sure to do this.

OpenCSW (for Solaris on SPARC and x86)
OpenCSW has binary packages of GCC 3.4.6 and 4.6.2 with Ada support. The package names are gcc3ada and gcc4ada respectively.

pkgsrc: NetBSD, DragonFly, FreeBSD and Solaris
The pkgsrc portable package file system has a small Ada framework. It is based on FSF GCC 5.4 currently and the FSF GCC 6.2 is available as well. The AdaCore GPL versions are not present, nor are non-GCC based compilers.

The pkgsrc system is released in quarterly branches, which are normally recommended. However, a user could also choose the "head" which would the very latest package versions. The pkgsrc system supports 21 platforms, but for Ada this is potentially limited to 5 due to the bootstrap compiler requirement: NetBSD, DragonFly, SunOS (Solaris/Illumos), OpenBSD/MirBSD, and FreeBSD.

There are two ways to install the software. The quickest and easiest way is to install prebuilt binaries using the command "pkg_add ". For example, to install the GNAT Programming Studio and all of its dependencies including the GNAT compiler, all you need is one command:

pkg_add gps

If a specific package is not available, or the user just prefers to build from source (this can take a long time), then a typical command would be:

cd /usr/pkg/devel/gps && bmake install

As with the binary installation, if any dependencies are missing they will be built first, also from source.

Available software as of 14 December 2016

SuSE Linux
All versions of SuSE Linux have a GNAT compiler included. SuSE versions 9.2 and higher also contains ASIS, Florist and GLADE libraries. The following two packages are needed:

gnat gnat-runtime

For SuSE version 12.1, the compiler is in the package gcc46-ada libada46

For 64 bit system you will need the 32 bit compatibility packages as well:

gnat-32bit gnat-runtime-32bit

Ubuntu
Ubuntu (and derivatives like Kubuntu, Xubuntu...) is a Debian-based Linux distribution, thus the installation process described above can be used. Graphical package managers like Synaptic or Adept can also be employed to select the Ada packages.

ICC from Irvine Compiler Corporation
Irvine Compiler Corporation provides native and cross compilers for various platforms. The compiler and run-time system support development of certified, safety-critical software.

Commercial, proprietary. No-cost evaluation is possible on request. Royalty-free redistribution of the run-time system is allowed.

Janus/Ada 83 and 95 from RR Software
RR Software offers native compilers for MS-DOS, Microsoft Windows and various Unix and Unix-like systems, and a library for Windows GUI programming called CLAW. There are academic, personal and professional editions, as well as support options.

Janus/Ada 95 supports subset of Ada 2007 and Ada 2012 features.

Commercial but relatively cheap; proprietary.

MAXAda from Concurrent
Concurrent offers MAXAda, an Ada 95 compiler for Linux/Xeon and PowerPC platforms, and Ada bindings to POSIX and X/Motif.

Commercial, proprietary.

ObjectAda from PTC (formerly Aonix/Atego)
PTC offers ObjectAda native (Windows, some flavors of Unix, and Linux) and cross (PPC, Intel, VxWorks, and ERC32) compilers.

Limited support of Ada 2012 is available.

Commercial, proprietary.

PowerAda from OC Systems
OC Systems offers Ada compilers and bindings to POSIX and X-11:
 * PowerAda, an Ada 95 compiler for Linux and AIX,
 * LegacyAda/390, an Ada 83 compiler for IBM System 370 and 390 mainframes

Commercial, proprietary.

ApexAda from PTC (formerly IBM Rational)
PTC ApexAda for native and embedded development.

Commercial, proprietary.

SCORE from DDC-I
DDC-I offers its SCORE cross-compilers for embedded development. SCORE stands for Safety-Critical, Object-oriented, Real-time Embedded.

Commercial, proprietary.

TADS from Tartan
Tartan offers the Tartan Ada Development System (TADS), with cross-compilers for some digital signal processors.

Commercial, proprietary.

XD Ada from DXC
XD Ada is an Ada 83 cross-compiler for embedded development. Hosts include VAX, Alpha and Integrity Servers running OpenVMS. Targets include Motorola 68000 and MIL-STD-1750A processors.

Commercial, proprietary.

XGC Ada from XGC Software
XGC compilers are GCC with custom run-time libraries suitable for avionics and space applications. The run-time kernels are very small and do not support exception propagation (i.e. you can handle an exception only in the subprogram that raised it).

Commercial but some versions are also offered as free downloads. Free Software.

title: Ada Programming/Installing


text:
Talk:Kaustubh Radkar

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 20:08, 5 September 2020 (UTC)
 * Dr. Kaustubh Radkar at Ironman World Championship race, 2017.jpg

title: Talk:Kaustubh Radkar


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MTV Sound Trippin

MTV Sound Trippin is a youth-based popular music television show on MTV India, part of the channel's strategy to place focus on original music.

Format
The show follows Hindi film music director Sneha Khanwalkar, who travels to ten cities across the country to record unusual sounds and create ten songs, one for each place she visits, that capture the spirit of the places. Many of the artists who record for the show "have never before recorded in a studio".

Reception
The show has been well received. Amitava Sanyal of Hindustan Times called it a "remarkable experiment". Sneha Mahadevan of ''DNA' said that "The shoots, crisp edits, refreshingly new visuals take this show to a new level altogether".

title: MTV Sound Trippin


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Radiation lobectomy

Radiation lobectomy is a form of radiation therapy used in interventional radiology to treat liver cancer. It is performed in patients that would be surgical candidates for resection, but cannot undergo surgery due to insufficient remaining liver tissue. It consists of injecting small radioactive beads loaded with yttrium-90 into the hepatic artery feeding the hepatic lobe in which the tumor is located. This is done with the intent of inducing growth in the contralateral hepatic lobe, not dissimilarly from portal vein embolization (PVE).

Medical uses
RL is performed in people with liver cancer, both primary such as hepatocellular carcinoma and metastatic such as from colon adenocarcinoma. Surgical resection is considered the only curative treatment for liver cancer (other than liver transplantation for hepatocellular carcinoma) but it can only be performed in patients with sufficient remnant liver after resection (amongst other criteria). Both PVE and RL are performed in patients who are not surgical candidates due to insufficient future liver remnant (FLR), which is advised to be between 20-30% and 30-40% of the native liver volume in healthy and cirrhotic livers, respectively.

Results
Radiation lobectomy is a relatively new application of radioembolization and results are mainly reported in the form of retrospective chart review studies and case reports, without any prospective validation. Most authors report a comparable future liver remnant hypertrophy between portal vein embolization and RL, ranging between 10 and 47% with cases reaching up to 119% with RL. The main difference between the two is the time interval necessary for appropriate hypertrophy, greater for RL. PVE requires a shorter time frame to achieve comparable results, ranging between 2–6 weeks, while the hypertrophy kinetics of RL are slower but more constant, without significant plateau (some studies report continued hypertrophy up to 9 months). Some authors have even raised concerns regarding PVE and the potential interval disease progression in the embolized and treatment naive lobes while allowing hypertrophy, which is of less concern with RL due to its added tumoricidal effect. Additionally, RL has been demonstrated to aid surgical resection in some cases by inducing a “vascular shift” of tumor masses via necrosis and contraction away from major vascular pedicles, converting patients to resectable status. One study has shown preliminary 600-day survival in 12 out of 13 patients who received RL and subsequent resection. Ultimately, further studies are needed to prospectively compare survival and recurrence outcomes in patients receiving RL versus PVE.

Side effects
Common side effects include fatigue, abdominal pain, nausea and anorexia, usually self-limiting. Post-radioembolization syndrome occurs in 20-70% of patients that undergo traditional radioembolization, presenting with shakes, chills, fatigue, nausea/vomiting, abdominal pain/discomfort, and/or cachexia and possibly hemodynamic changes, rarely requiring admission. Unfortunately, most data, if not all, is derived from traditional radioembolization outcomes studies and more will be needed to assess the actual incidence and risk of post-radioembolization syndrome in RL.

Complications are abscess formation, biliary complications (biloma, radiation induced cholecystitis and cholangitis, biliary necrosis), gastrointestinal complications (diarrhea, radiation induced gastritis and gastrointestinal ulceration), radiation induced pancreatitis, dermatitis, pneumonitis and lymphopenia.

Procedure
RL is performed by an interventional radiologist in the angiography suite, in a fashion similar to radioembolization. The procedure is composed of two different portions, a planning phase and the actual radiation lobectomy, usually performed in two different sessions:
 * 1) Planning phase:  the patient undergoes planning angiography of the abdominal aorta and its major vessels. The interventional radiologist accesses the femoral artery via Seldinger technique and advances a wire and catheter to the level of the superior mesenteric artery and the celiac axis, injecting contrast in order to delineate the patient's anatomy. Utilizing smaller catheters and wires, he does the same thing evaluating the common hepatic artery, gastroduodenal, proper hepatic, left hepatic, right hepatic and phrenic arteries. The purpose of this planning angiogram is to evaluate for anatomical variants and collaterals that need to be coil embolized, in order to minimize the risk of non-target radioembolization. At this point, once the vascular anatomy has been delineated and necessary vessels have been embolized, the physician will inject 4-5 mCi of tc-99m macroaggregated albumin (MAA) in order to evaluate hepatopulmonary shunting, which serves as a proxy in assessing the risk of developing radiation pneumonitis. The dose of yttrium-90 to be infused is calculated with the manufacturer's formula based on lung shunting, body surface area, liver and tumor volume.
 * 2) Radiation lobectomy: after gaining femoral artery access and advancing a catheter in the right hepatic artery (most often), 90Y microspheres are infused in a lobar fashion, optimizing tumor and parenchymal coverage. Once the procedure has been completed, the patient is usually sent to the nuclear medicine department where a Bremsstrahlung scan will demonstrate the distribution of the radioactive material and assess for non-target embolization. Often, patients are started on proton pump inhibitors (with the addition of ursodeoxycholic acid - based on each center's protocol) for gastro-hepatic protection with or without a low-dose corticosteroid for prevention of post radioembolization syndrome and a fluoroquinolone antibiotic when the gallbladder is present (both per center protocol).

Follow-up
Patients undergo cross-sectional imaging at approximately 30–60 days from the procedure for evaluation of the degree of hypertrophy undergone by the contralateral side (as assessed by future liver remnant) and to assess tumor burden. At this time, the surgeons and/or a multi-specialty tumor board will convene to determine if the patient can/should undergo safe surgical resection.

title: Radiation lobectomy


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sintonia

Etymology
.

Noun

 * 1)  theme music, jingle
 * 2)  syntony
 * 3)  harmony

Etymology
. Compare 🇨🇬 and 🇨🇬.

Noun

 * 1)  tuning of a radio etc.
 * 2)  harmony
 * 1)  harmony

Etymology
. Compare 🇨🇬, 🇨🇬, 🇨🇬.

Noun

 * 1)  tuning
 * 2) simultaneity
 * 3)  mutual agreement, harmony between people or objects

title: sintonia


text:
Talk:Japanoise

Info from Noise music article
There is a lot of information in the "Japan" section of the Noise music article that could probably be moved here, with a more concise synopsis taking its place in the more general article, but I wanted to get this stub created before tearing apart the Noise music article. The section on Japan is actually the best part of that (wildly uneven) article, so I'm not sure where to start and what information to transfer, though I do think Japanoise should have its own article. If someone less intimidated by the prospect wants to take it on, that would be great. MrBook 16:40, 20 March 2006 (UTC)

title: Talk:Japanoise


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User:Dom0803/Sandbox

DO NOT EDIT THIS, THANK YOU

A Locator map is a dynamic map which comprises of an image background as a map, and a foreground image which is a red dot pinpointing the location of the desired town or city on the map. Beside the red dot is the name of the location. To the right you can see the Ireland locator map I have created, showing the location of Belfast, Northern Ireland. Creating a locator map may seem complex when you see the code, but it's quite simple once you understand it. Hopefully by the end of this article you will be a discerned location mapper and will be able to create and use the locator map confidently. The coding for the locator map is not yet 100% completed, and it doesn't handle longitude properly for maps crossing the +/- 180 meridian yet. The locator map was created by Zocky

How the locator map works
For this page I will be using the Ireland locator map as my example. The locator map works on a user defined grid reference. Let's take a look at the string that makes up the Ireland locator map, and the code that makes up the initial template required by wikipedia to use the locator map code on the wikiarticle. The locator map works like a real world three figure grid map. Well, quite similar. Instead of using co-ordinates like NNN, NNN number it uses one co-ords from Multimap, one number to two decimal places; NN.NN NN.NN

The locator map's source-code uses the numbers you have input from multimap to determine where the red dot will be places in reference to your provided co-ords on the source code, that are the most northernly, southernly, westernly, and easternly points visible on the template map image.

I'll use the grid beside to show an example of how the grid system works in relative to Belfast, and the Irish co-ords. Note: The orange grid lines have been drawen on to give an idea of how the template-text uses the defined location co-ord. They are only rough drawings, and the entire grid is not drawen to accurate measurements, but should give you a fair idea. Here's the template text that has been used in this article to display the template map: Text used to impliment map into this article: Text that is in the template map source-code: see Location map

In the image I have used the relative co-ords. Belfast's co-ords as seen in the impliment text is lat=54.59, long=-5.93 (lat-latitude:long-longtitude) and if you look on the map you will see that the orange lines drawen on (for lat) are rounded to .5. As the Belfast lat is 54.59 this is just off the .5 line. Study the example image and you should be able to figure out how it works. To learn further how to work grid references follow this link. Ordnancesurvey.co.uk (.PDF)

 * DELME

Template:Location map Ireland template ireland wiki location map wiki

title: User:Dom0803/Sandbox


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Jobst Kuch

Jobst Kuch (26 October 1902 – 23 May 1963) was a German painter. His work was part of the painting event in the art competition at the 1936 Summer Olympics.

title: Jobst Kuch


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Franklin High School (Franklin, Ohio)

Franklin High School is a public high school in Franklin, Ohio, part of the Franklin City School District. It opened in 1969.

Notable alumni

 * Luke Kennard - professional basketball player
 * Travis Lakins Sr. - professional baseball player

title: Franklin High School (Franklin, Ohio)


text:
Electoral results for the district of Braidwood

Braidwood, an electoral district of the Legislative Assembly in the Australian state of New South Wales was created in 1859 and abolished in 1904.


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Ahmad Said Hamdan

Datuk Seri Panglima Ahmad Said bin Hamdan (Jawi: أحمد سيد بن حمدان; died 22 September 2019) was a Malaysian civil servant who served as the first chief commissioner of the Malaysian Anti-Corruption Commission (MACC) when it was created from the preceding Anti-Corruption Agency (ACA).

Career
Ahmad Said succeeded Zulkipli Mat Noor as director-general of the ACA in mid-May 2007 after the latter's contract was not renewed amidst graft allegations. When the ACA was upgraded into a full commission body known as the MACC, Ahmad Said was in turn, made its first chief commissioner.

On 4 December 2009, the Chief Secretary to the Government of Malaysia, Mohamad Sidek Hassan, announced that Ahmad Said has opted for early retirement at the end of 2009 with his contract due to expire in May 2010. His term officially came to an end on 31 December 2009 instead of 25 May 2010. On the following day, he released a statement denying that his early retirement was due to pressure from outsiders or political parties. He added that his retirement was due to his own personal reasons and after having served in the commission for a long period rather than because of other reasons. Ahmad Said said he retired early to give way to his successor and to spend time with his family after serving with the MACC for 34 years. Then-prime minister, Mohammad Najib Abdul Razak, also reiterated that Ahmad Said retired early because he wanted to spend more time with his family and that it has nothing to do with Teoh Beng Hock's death. The government also did not request him to retire 6 months earlier.

Honours

 * 🇲🇾 Malaysia :
 * Kesatria Mangku Negara.png Officer of the Order of the Defender of the Realm (KMN) (1992)
 * MY Darjah Jasa Negara - Order of Meritorious Service - PJN.svg Commander of the Order of Meritorious Service (PJN) – Datuk (2008)
 * Malacca :
 * MY-MAL Exalted Order of Malacca.svg Knight Commander of the Exalted Order of Malacca (DCSM) – Datuk Wira (2009)
 * Pahang :
 * MY-PAH Order of Sultan Ahmad Shah of Pahang - Grand Knight - SSAP.svg Grand Knight of the Order of Sultan Ahmad Shah of Pahang (SSAP) – Dato' Sri (2008)
 * Penang :
 * MY-PEN_Order_of_the_Defender_of_State_-_Officer_-_DSPN.svg Officer of the Order of the Defender of State (DSPN) – Dato' (1999)
 * MY-PEN Order of the Defender of State - Commander - DGPN.svg Commander of the Order of the Defender of State (DGPN) – Dato' Seri (2008)
 * Perlis :
 * MY-PERL Order of the Crown of Perlis - Knight Commander - DPMP.svg Knight Commander of the Order of the Crown of Perlis (DPMP) – Dato' (2002)
 * Sabah :
 * MY-SAB Order of Kinabalu - PGDK.svg Commander of the Order of Kinabalu (PGDK) – Datuk (2000)
 * MY-SAB Order of Kinabalu - SPDK.svg Grand Commander of the Order of Kinabalu (SPDK) – Datuk Seri Panglima (2007)

Death
Ahmad Said died on the night of 22 September 2019 at his daughter's house in Rawang. He had previously been admitted to the National Heart Institute of Malaysia (IJN) after suffering from stroke.

title: Ahmad Said Hamdan


text:
Halictus lucidipennis

Halictus lucidipennis is a species of bee in the genus Halictus, of the family Halictidae.

title: Halictus lucidipennis


text:
Jimmy Joy

James Monte Maloney (April 20, 1902 – March 7, 1962), known professionally as Jimmy Joy, was an American saxophonist, clarinetist, singer, and big band leader. His claim to fame was his ability to play two clarinets at the same time.

Recordings
His recordings with his orchestra included "The Yale Blues", the Bing Crosby composition "From Monday On", "I Got Worry", "Today is Today", "Can't You Understand", "Harmonica Harry", "If It Wasn't For the Moon", "Chilly Pom-Pom Pee", "Apple Blossoms and Chapel Bells", and "You're the First Thing I think of in the Morning". He reorded for Brunswick Records and Varsity Records.

title: Jimmy Joy


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Order-4 icosahedral honeycomb

In the geometry of hyperbolic 3-space, the order-4 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,4}.

Geometry
It has four icosahedra {3,5} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an order-4 pentagonal tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {3,51,1}, Coxeter diagram,, with alternating types or colors of icosahedral cells. In Coxeter notation the half symmetry is [3,5,4,1+] = [3,51,1].

Related polytopes and honeycombs
It a part of a sequence of regular polychora and honeycombs with icosahedral cells: {3,5,p}

Order-5 icosahedral honeycomb
In the geometry of hyperbolic 3-space, the order-5 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,5}. It has five icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an order-5 pentagonal tiling vertex arrangement.

Order-6 icosahedral honeycomb
In the geometry of hyperbolic 3-space, the order-6 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,6}. It has six icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an order-6 pentagonal tiling vertex arrangement.

Order-7 icosahedral honeycomb
In the geometry of hyperbolic 3-space, the order-7 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,7}. It has seven icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an order-7 pentagonal tiling vertex arrangement.

Order-8 icosahedral honeycomb
In the geometry of hyperbolic 3-space, the order-8 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,8}. It has eight icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an order-8 pentagonal tiling vertex arrangement.

Infinite-order icosahedral honeycomb
In the geometry of hyperbolic 3-space, the infinite-order icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,∞}. It has infinitely many icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing around each vertex in an infinite-order triangular tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {3,(5,∞,5)}, Coxeter diagram, =, with alternating types or colors of icosahedral cells. In Coxeter notation the half symmetry is [3,5,∞,1+] = [3,((5,∞,5))].

title: Order-4 icosahedral honeycomb


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Sir Thomas More and Family

Sir Thomas More and Family is a lost painting by Hans Holbein the Younger, painted circa 1527 and known from a number of surviving copies.

The original was destroyed in 1752 in a fire at Schloss Kremsier (Kroměříž Castle), the Moravian residence of Carl von Liechtenstein, archbishop of Olmutz.

A study by Holbein for the painting survives in the Kunstmuseum Basel (Öffentliche Kunstsammlung Basel, Kupferstichkabinett Inv. 1662.31). The work is also preserved in a number of sixteenth-century versions by Rowland Lockey, including those in Nostell Priory and the National Portrait Gallery (formerly part of the Lenthall pictures).

Strong calls it "arguably the greatest and most innovative work of his English period" and "the earliest portrait conversation piece in English painting, at least a century ahead of its time" and asserts that "its destruction means we lost the greatest single visual artefact to epitomize the aims and ideals of the early Renaissance in England."

NPG version
Sir Thomas More and Family in the National Portrait Gallery is a painting that was once part of the Lenthall pictures.

The picture
Sir Thomas More and Family is one of two near life-size copies by Rowland Lockey of an original by Holbein that was lost in a fire in the 18th century. It is dated 1593; Holbein died in 1543. It is oil on canvas and measures 89.5 in by 120 in. It was probably commissioned by More's grandson, Thomas More II, to commemorate five generations of the family. The National Portrait Gallery lists the sitters as:
 * Elizabeth Dauncey (née More) (1506–1564), Second daughter of Sir Thomas More.
 * Cecily Heron (née More) (born 1507–?), Youngest daughter of Sir Thomas More.
 * Anne More (née Cresacre) (1511–1577), Wife of John More, son of Sir Thomas More.
 * Cresacre More (1572–1649), Great-grandson and biographer of Sir Thomas More.
 * Sir John More (circa 1451–1530), in red robes of office as a Judge of the King's Bench; father of Sir Thomas More.
 * John More (1510–1547), Son of Sir Thomas More.
 * John More (1557–1599?), Eldest son of Thomas More II.
 * Maria More (née Scrope) (1534–1607), Wife of Thomas More II.
 * Sir Thomas More (1478–1535) wearing his official Tudor Collar of Esses. This part reproduces Holbein's famous portrait of More now at the Frick Collection.
 * Thomas More II (1531–1606), Grandson of Sir Thomas More.
 * Margaret Roper (1505–1544), Daughter of Sir Thomas More.

The copy from the Lenthall collection has been described as “the most accomplished extant version”.

The surviving drawing by Holbein confirms the general accuracy of the picture.

The scene contrasts the sombre, berobed More and his father, with the messy and lively surrounding family in various demure but relatively informal poses: women, pets, books, and instruments.

Provenance
The painting had been at Gubbins in Hertfordshire. At some time it came into the possession of the Lenthall family, but how this happened is not known, although it may have been borrowed from the More family and never returned. In the 17th century, John Aubrey viewed it at the Besselsleigh home of Sir John Lenthall, but by 1727 it was at Burford Priory. It was discussed in detail by John Loveday who saw it in 1736. The painting was unsold in a small sale of the Lenthall pictures in 1808 but was offered again and sold in a major sale in 1833. It was subsequently owned by Walter Strickland, CW Dormer, Sir Hugh Lane, Viscount Lee, and EJ Horniman whose widow bequeathed it to the National Portrait Gallery where it remains. It was the centre piece in the exhibition, The King's Good Servant, at the National Portrait Gallery in 1977.

Nostell Priory version
The version at Nostell Priory is described as "the only faithful, same-size representation of the lost original" and is inscribed “Rolandus Lockey/fecit a.d." dated 1592. It includes other members of his household: More's secretary peeking through a door, his "fool" and his pet monkey.

It is unclear who the artist was, who commissioned it or who originally owned it. A radiocarbon dating test was carried out on 1982 which concluded the flax to be no later than 1520. For this reason, it is highly likely that it predates the NPG Roland Lockey version of 1593. Lockey was known as an excellent copyist, but his sitters' faces are lacking subtle character details.

Those of the Nostell version—which includes all the sitters—closely resemble the heads of the original Holbein study now preserved in Windsor Castle. The Holbein head studies were acquired by Lord Arundel when he cleared out Holbein's workshop in 1546. It was Lord Arundel's family who later sold the original lost Holbein in 1654, but how they obtained it is unclear.

The art connoisseur of the period Van Mander records that a life-sized portrait by Holbein of Thomas More and his family was owned by Andries de Loo, an avid Holbein collector. He records also that a member of the More family on de Loos's death purchased this same portrait [1590]. This story is also confirmed by the art historian George Virtue, recorded in 1731, referring to the portrait now identified as the Nostell version.

This makes sense if there were in fact two versions done by Holbein. The book above Judge John More's right shoulder is Boethius’s Consolation of Philosophy in which the story parallels Thomas More's arrest and execution, suggesting that the Nostell version reflects More's execution in 1535. It could just be that Holbein was asked by Thomas Cromwell to make a propaganda piece to go with the Great Bible of 1538, Thomas More representing the old order and Cromwell the new.

Other versions
A cabinet miniature version of this portrait c. 1594 with different details, also likely to be by Lockey, is in the Victoria and Albert Museum.

Two further copies of the Holbein, at old Chelsea Town Hall (formerly one of the Petre Pictures) and Hendred House, East Hendred, may be by Lockey, but are too damaged and over-painted for any certainty to be possible.

Holbein or More sent a small preparatory drawing to Erasmus, which survives.

Cultural influences
The painting is described in Wolf Hall, a historical novel by Hilary Mantel about the rise to power of Thomas Cromwell that won the 2009 Man Booker Prize:

"The favorite, Meg, sits at her father's feet with a book on her knee. Gathered loosely about the Lord Chancellor are his son John; his ward Anne Cresacre, who is John's wife; Margaret Giggs, who is also his ward; his aged father, Sir John More; his daughters Cicely and Elizabeth; Pattinson, with goggle eyes; and his wife, Alice, with lowered head and wearing a cross, at the edge of the picture. Master Holbein has grouped them under his gaze, filed them forever: as long as no moth consumes, no flame or mould or blight."

title: Sir Thomas More and Family


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Cookbook talk:Homemade Peanut Butter

This module uses text adapted from the Wikipedia article Peanut butter. The page history, at the time the text was copied, is included below.

* (cur) (last). . 07:23, 14 Apr 2004. . Darac (Several clarifications/expansions.) * (cur) (last). . 13:36, 4 Apr 2004. . Bkonrad (rephrase a bit) * (cur) (last). . m 13:20, 4 Apr 2004. . Dmn (Earth's rotation) * (cur) (last). . 19:44, 25 Mar 2004. . Bkonrad (I don't think so) * (cur) (last). . m 18:05, 25 Mar 2004. . Dmn * (cur) (last). . m 20:20, 17 Mar 2004. . Modeha (ja:) * (cur) (last). . 08:15, 17 Mar 2004. . Ellywa * (cur) (last). . 11:58, 12 Mar 2004. . Bkonrad (Kellogg and Battle Creek connection) * (cur) (last). . 11:41, 12 Mar 2004. . Bkonrad (Kellogg and Battle Creek connection) * (cur) (last). . m 13:33, 22 Feb 2004. . Minesweeper (Reverted edits by <IP_ADDRESS> to last version by Marj Tiefert) * (cur) (last). . 13:28, 22 Feb 2004. . <IP_ADDRESS>   * (cur) (last). . 11:52, 30 Dec 2003. . Marj Tiefert (mouse bait, too) * (cur) (last). . m 11:29, 30 Dec 2003. . Infrogmation * (cur) (last). . m 11:04, 30 Dec 2003. . Robertb-dc (Not the Charlie Brown kind) * (cur) (last). . 19:02, 8 Dec 2003. . <IP_ADDRESS> (Peanut butter) * (cur) (last). . m 22:05, 4 Oct 2003. . Branddobbe (typo) * (cur) (last). . m 19:39, 11 Aug 2003. . Maximus Rex (aflatoxin) * (cur) (last). . 12:20, 5 Aug 2003. . Xj14y (link fix. again.) * (cur) (last). . 12:18, 5 Aug 2003. . Xj14y * (cur) (last). . m 12:17, 5 Aug 2003. . Wfeidt * (cur) (last). . 12:16, 5 Aug 2003. . Wfeidt (sentences) * (cur) (last). . m 12:15, 5 Aug 2003. . Wfeidt (Peanut Butter => Peanut butter) * (cur) (last). . 12:06, 5 Aug 2003. . Xj14y (surprised I had to add this one.)

title: Cookbook talk:Homemade Peanut Butter


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User:Harborporpoise/be bold

Being bold is important on Wikipedia. I have sandbox writer's block. I can't figure out how to cite the table directly so I will add text below the table then cite that. This text is in reference to the table.

title: User:Harborporpoise/be bold


text:
Talk:Jobaria

External links modified
Hello fellow Wikipedians,

I have just modified one external link on Jobaria. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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Cheers.— InternetArchiveBot  (Report bug) 06:32, 26 November 2017 (UTC)

title: Talk:Jobaria


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R3 (video game)

R3: The Art of Rocketry is a video game written by Bruce Webster for the Amiga released in 1995. It was a playable demo on the coverdisks of Amiga Power (issue 54) in October 1995 and on Amiga Format (issue 89) in September 1996.

The game was initially released as shareware, but the author later released the full game as freeware on Aminet in 2000. The registered version included Tritus from Davin Pearson, a three-player competitive Tetris-inspired game, much in the same manner of the game Super Foul Egg.

Gameplay
R3 is a Thrust clone where the player navigates a flying craft by rotating applying power in that direction. Vertical movement is affected by gravity.

R3 adds the ability to purchase new and better craft, which are organised into five classes. Each craft in the same class has similar characteristics, such as class 3 being large on the cargo space and shields, but low on missiles and low on thrust power. Each class has three craft within it, the weakest having lower everything (engine power, gun range, gun speed, cargo space, shields) but being much cheaper.

title: R3 (video game)


text:
Groot Constantia

Groot Constantia is the oldest wine estate in South Africa and provincial heritage site in the suburb of Constantia in Cape Town, South Africa.

"Groot" in Dutch and Afrikaans translates as "great" (as in large) in English.

History
In 1685, during an annual visit to the Cape, Hendrik Adriaan van Rheede tot Drakenstein granted the grounds of Groot Constantia to Simon van der Stel the VOC Governor of the Cape of Good Hope.

Van der Stel built the house and used the land to produce wine as well as other fruit and vegetables, and for cattle farming. Following Van der Stel's death in 1712 the estate was broken up and sold in three parts: Groot Constantia; Klein Constantia; and Bergvliet.

In 1779 the portion of the estate including Van der Stel's Cape Dutch-style manor house was sold to the Cloete family, who planted extensive vineyards and extended and improved the mansion by commissioning the architect Louis Michel Thibault. The wine cellar was added by Cloete in 1791. The house remained in the possession of the Cloete family until 1885, during which period the estate became famous for its production of Constantia dessert wine.

In 1885 Groot Constantia was purchased by the government of the Cape of Good Hope and was used as an experimental wine and agricultural estate. Following a disastrous fire in 1925 the house was extensively restored.

In the year 1925 the manor house completely burnt down. Funds were raised to reconstruct it to its original Cape Dutch splendour.

In 1969 the manor house became part of the South African Cultural History Museum, and in 1993 the estate passed into the ownership of the Groot Constantia Trust. The exhibition in the house is managed by Iziko South African Museum, and is particularly focused on rural slavery and the life of slaves during the early Cape colonial period.

Today, other estates have joined Groot Constantia to form the scenic Constantia wine route. These estates include Klein Constantia, Buitenverwachting, Constantia Uitsig, Steenberg, Constantia Glen, Eagles Nest and High Constantia.

Wine production
Groot Constantia is noted particularly for its production of high-quality red wines, including Shiraz, Merlot and blended red Gouverneurs Reserve. In 2003 the estate began production of a Constantia dessert wine, called Grand Constance, for the first time since the 1880s.

Popular culture

 * A number of scenes for the 1955 movie Untamed was set at and within Groot Constantia after the protagonist discovers a diamond and returns to Cape Town to live in a stately mansion.

title: Groot Constantia


text:
Choćmirowo railway station

Choćmirowo is a non-operational PKP railway station in Choćmirowo (Pomeranian Voivodeship), Poland.

title: Choćmirowo railway station


text:
Discrete Mathematics/Functions and relations

Introduction
This article examines the concepts of a function and a relation.

A relation is any association or link between elements of one set, called the domain or (less formally) the set of inputs, and another set, called the range or set of outputs. Some people mistakenly refer to the range as the codomain(range), but as we will see, that really means the set of all possible outputs—even values that the relation does not actually use. (Beware: some authors do not use the term codomain(range), and use the term range instead for this purpose. Those authors use the term image for what we are calling range.  So while it is a mistake to refer to the range or image as the codomain(range), it is not necessarily a mistake to refer to codomain as range.)

For example, if the domain is a set Fruits = {apples, oranges, bananas} and the codomain(range) is a set Flavors = {sweetness, tartness, bitterness}, the flavors of these fruits form a relation: we might say that apples are related to (or associated with) both sweetness and tartness, while oranges are related to tartness only and bananas to sweetness only. (We might disagree somewhat, but that is irrelevant to the topic of this book.) Notice that "bitterness", although it is one of the possible Flavors (codomain)(range), is not really used for any of these relationships; so it is not part of the range (or image) {sweetness, tartness}.

Another way of looking at this is to say that a relation is a subset of ordered pairs drawn from the set of all possible ordered pairs (of elements of two other sets, which we normally refer to as the Cartesian product of those sets). Formally, R is a relation if

 * $$R \subseteq X \times Y = \{(x, y) | x \in X, y \in Y\}$$

for the domain X and codomain(range) Y. The inverse relation of R, which is written as R-1, is what we get when we interchange the X and Y values:

 * $$R^{-1} = \{(y, x) | (x, y) \in R\}$$

Using the example above, we can write the relation in set notation: {(apples, sweetness), (apples, tartness), (oranges, tartness), (bananas, sweetness)}. The inverse relation, which we could describe as "fruits of a given flavor", is {(sweetness, apples), (sweetness, bananas), (tartness, apples), (tartness, oranges)}. (Here, as elsewhere, the order of elements in a set has no significance.)

One important kind of relation is the function. A function is a relation that has exactly one output for every possible input in the domain. (The domain does not necessarily have to include all possible objects of a given type. In fact, we sometimes intentionally use a restricted domain in order to satisfy some desirable property.)  The relations discussed above (flavors of fruits and fruits of a given flavor) are not functions: the first has two possible outputs for the input "apples" (sweetness and tartness); and the second has two outputs for both "sweetness" (apples and bananas) and "tartness" (apples and oranges).

The main reason for not allowing multiple outputs with the same input is that it lets us apply the same function to different forms of the same thing without changing their equivalence. That is, if f is a function with a (or b) in its domain, then a = b implies that f(a) = f(b). For example, z - 3 = 5 implies that z = 8 because f(x) = x + 3 is a function unambiguously defined for all numbers x.

The converse, that f(a) = f(b) implies a = b, is not always true. When it is, there is never more than one input x for a certain output y = f(x). This is the same as the definition of function, but with the roles of X and Y interchanged; so it means the inverse relation f-1 must also be a function. In general—regardless of whether or not the original relation was a function—the inverse relation will sometimes be a function, and sometimes not.

When f and f-1 are both functions, they are called one-to-one, injective, or invertible functions. This is one of two very important properties a function f might (or might not) have; the other property is called onto or surjective, which means, for any y ∈ Y (in the codomain), there is some x ∈ X (in the domain) such that f(x) = y. In other words, a surjective function f maps onto every possible output at least once.

A function can be neither one-to-one nor onto, both one-to-one and onto (in which case it is also called bijective or a one-to-one correspondence), or just one and not the other. (As an example which is neither, consider f = {(0,2), (1,2)}. It is a function, since there is only one y value for each x value; but there is more than one input x for the output y = 2; and it clearly does not "map onto" all integers.)

Relations
In the above section dealing with functions and their properties, we noted the important property that all functions must have, namely that if a function does map a value from its domain to its co-domain, it must map this value to only one value in the co-domain.

Writing in set notation, if a is some fixed value:
 * |{f(x)|x=a}| ∈ {0, 1}

The literal reading of this statement is: the cardinality (number of elements) of the set of all values f(x), such that x=a for some fixed value a, is an element of the set {0, 1}. In other words, the number of outputs that a function f may have at any fixed input a is either zero (in which case it is undefined at that input) or one (in which case the output is unique).

However, when we consider the relation, we relax this constriction, and so a relation may map one value to more than one other value. In general, a relation is any subset of the Cartesian product of its domain and co-domain.

All functions, then, can be considered as relations also.

Notations
When we have the property that one value is related to another, we call this relation a binary relation and we write it as
 * x R y

where R is the relation.

For arrow diagrams and set notations, remember for relations we do not have the restriction that functions do and we can draw an arrow to represent the mappings, and for a set diagram, we need only write all the ordered pairs that the relation does take: again, by example
 * f = {(0,0),(1,1),(-1,1),(2,2),(-2,2)}

is a relation and not a function, since both 1 and 2 are mapped to two values, (1 and -1, and 2 and -2 respectively) example let A=2,3,5;B=4,6,9 then A*B=(2,4),(2,6),(2,9),(3,4),(3,6),(3,9),(5,4),(5,6),(5,9) Define a relation R=(2,4),(2,6),(3,6),(3,9) add functions and problems to one another.

Some simple examples
Let us examine some simple relations.

Say f is defined by
 * {(0,0),(1,1),(2,2),(3,3),(1,2),(2,3),(3,1),(2,1),(3,2),(1,3)}

This is a relation (not a function) since we can observe that 1 maps to 2 and 3, for instance.

Less-than, "<", is a relation also. Many numbers can be less than some other fixed number, so it cannot be a function.

Properties
When we are looking at relations, we can observe some special properties different relations can have.

Reflexive
A relation is reflexive if, we observe that for all values a:
 * a R a

In other words, all values are related to themselves.

The relation of equality, "=" is reflexive. Observe that for, say, all numbers a (the domain is R):
 * a = a

so "=" is reflexive.

In a reflexive relation, we have arrows for all values in the domain pointing back to themselves:
 * [[Image:Arrow diagram reflexive.png]]

Note that ≤ is also reflexive (a ≤ a for any a in R). On the other hand, the relation < is not (a < a is false for any a in R).

Symmetric
A relation is symmetric if, we observe that for all values of a and b:
 * a R b implies b R a

The relation of equality again is symmetric. If x=y, we can also write that y=x also.

In a symmetric relation, for each arrow we have also an opposite arrow, i.e. there is either no arrow between x and y, or an arrow points from x to y and an arrow back from y to x:
 * [[Image:Arrow diagram symmetric.png]]

Neither ≤ nor < is symmetric (2 ≤ 3 and 2 < 3 but neither 3 ≤ 2 nor 3 < 2 is true).

Transitive
A relation is transitive if for all values a, b, c:
 * a R b and b R c implies a R c

The relation greater-than ">" is transitive. If x > y, and y > z, then it is true that x > z. This becomes clearer when we write down what is happening into words. x is greater than y and y is greater than z. So x is greater than both y and z.

The relation is-not-equal "≠" is not transitive. If x ≠ y and y ≠ z then we might have x = z or x ≠ z (for example 1 ≠ 2 and 2 ≠ 3 and 1 ≠ 3 but 0 ≠ 1 and 1 ≠ 0 and 0 = 0).

In the arrow diagram, every arrow between two values a and b, and b and c, has an arrow going straight from a to c.
 * [[Image:Arrow diagram transitive.png]]

Antisymmetric
A relation is antisymmetric if we observe that for all values a and b:
 * a R b and b R a implies that a=b

Notice that antisymmetric is not the same as "not symmetric."

Take the relation greater than or equal to, "≥" If x ≥ y, and y ≥ x, then y must be equal to x. a relation is anti-symmetric if and only if a∈A, (a,a)∈R

Trichotomy
A relation satisfies trichotomy if we observe that for all values a and b it holds true that: aRb or bRa

The relation is-greater-or-equal satisfies since, given 2 real numbers a and b, it is true that whether a ≥ b or b ≥ a (both if a = b).

Problem set
Given the above information, determine which relations are reflexive, transitive, symmetric, or antisymmetric on the following - there may be more than one characteristic. (Answers follow.) x R y if
 * 1) x = y
 * 2) x < y
 * 3) x2 = y2
 * 4) x ≤ y

Answers

 * 1) Symmetric, Reflexive, and transitive
 * 2) Transitive, Trichotomy
 * 3) Symmetric, Reflexive, and transitive (x2 = y2 is just a special case of equality, so all properties that apply to x = y also apply to this case)
 * 4) Reflexive, Transitive and Antisymmetric (and satisfying Trichotomy)

Equivalence relations
We have seen that certain common relations such as "=", and congruence (which we will deal with in the next section) obey some of these rules above. The relations we will deal with are very important in discrete mathematics, and are known as equivalence relations. They essentially assert some kind of equality notion, or equivalence, hence the name.

Characteristics of equivalence relations
For a relation R to be an equivalence relation, it must have the following properties, viz. R must be: (A helpful mnemonic, S-T-R)
 * symmetric
 * transitive
 * reflexive

In the previous problem set you have shown equality, "=", to be reflexive, symmetric, and transitive. So "=" is an equivalence relation.

We denote an equivalence relation, in general, by $$x \sim y$$.

Example proof
Say we are asked to prove that "=" is an equivalence relation. We then proceed to prove each property above in turn (Often, the proof of transitivity is the hardest).

 * Reflexive: Clearly, it is true that a = a for all values a. Therefore, = is reflexive.
 * Symmetric: If a = b, it is also true that b = a. Therefore, = is symmetric
 * Transitive: If a = b and b = c, this says that a is the same as b which in turn is the same as c. So a is then the same as c, so a  = c, and thus = is transitive.

Thus = is an equivalence relation.

Partitions and equivalence classes
It is true that when we are dealing with relations, we may find that many values are related to one fixed value.

For example, when we look at the quality of congruence, which is that given some number a, a number congruent to a is one that has the same remainder or modulus when divided by some number n, as a, which we write
 * a ≡ b (mod n)

and is the same as writing
 * b = a+kn for some integer k.

(We will look into congruences in further detail later, but a simple examination or understanding of this idea will be interesting in its application to equivalence relations)

For example, 2 ≡ 0 (mod 2), since the remainder on dividing 2 by 2 is in fact 0, as is the remainder on dividing 0 by 2.

We can show that congruence is an equivalence relation (This is left as an exercise, below Hint use the equivalent form of congruence as described above).

However, what is more interesting is that we can group all numbers that are equivalent to each other.

With the relation congruence modulo 2 (which is using n=2, as above), or more formally:
 * x ~ y if and only if x ≡ y (mod 2)

we can group all numbers that are equivalent to each other. Observe:
 * $$0 \equiv 2 \equiv 4 \equiv \ldots \pmod{2}$$
 * $$1 \equiv 3 \equiv 5 \equiv \ldots \pmod{2}$$

This first equation above tells us all the even numbers are equivalent to each other under ~, and all the odd numbers under ~.

We can write this in set notation. However, we have a special notation. We write:
 * [0]={0,2,4,...}
 * [1]={1,3,5,...}

and we call these two sets equivalence classes.

All elements in an equivalence class by definition are equivalent to each other, and thus note that we do not need to include [2], since 2 ~ 0.

We call the act of doing this 'grouping' with respect to some equivalence relation partitioning (or further and explicitly partitioning a set S into equivalence classes under a relation ~). Above, we have partitioned Z into equivalence classes [0] and [1], under the relation of congruence modulo 2.

Problem set
Given the above, answer the following questions on equivalence relations (Answers follow to even numbered questions) $$ x \sim y\ \mbox{iff}\ x \equiv y \pmod{6}$$
 * 1) Prove that congruence is an equivalence relation as before (See hint above).
 * 2) Partition {x | 1 ≤ x ≤ 9} into equivalence classes under the equivalence relation

Answers
2. [0]={6}, [1]={1,7}, [2]={2,8}, [3]={3,9}, [4]={4}, [5]={5}

Partial orders
We also see that "≥" and "≤" obey some of the rules above. Are these special kinds of relations too, like equivalence relations? Yes, in fact, these relations are specific examples of another special kind of relation which we will describe in this section: the partial order.

As the name suggests, this relation gives some kind of ordering to numbers.

Characteristics of partial orders
For a relation R to be a partial order, it must have the following three properties, viz R must be: (A helpful mnemonic, R-A-T)
 * reflexive
 * antisymmetric
 * transitive

We denote a partial order, in general, by $$x \preceq y$$.

Question:
 * 1) Suppose R is a relation on a set of integers Z then prove that R is a partial order relation on Z iff a=b raise to power r.

Example proof
Say we are asked to prove that "≤" is a partial order. We then proceed to prove each property above in turn (Often, the proof of transitivity is the hardest).

Reflexive
Clearly, it is true that a ≤ a for all values a. So ≤ is reflexive.

Antisymmetric
If a ≤ b, and b ≤ a, then a must be equal to b. So ≤ is antisymmetric

Transitive
If a ≤ b and b ≤ c, this says that a is less than b and c. So a is less than c, so a ≤ c, and thus ≤ is transitive.

Thus ≤ is a partial order.

Problem set
Given the above on partial orders, answer the following questions
 * 1) Prove that divisibility, |, is a partial order (a | b means that a is a factor of b, i.e., on dividing b by a, no remainder results).
 * 2)  Prove the following set is a partial order: (a, b) $$\preceq$$ (c, d) implies ab≤cd for a,b,c,d integers ranging from 0 to 5.

Answers
2. Simple proof; Formalization of the proof is an optional exercise.
 * Reflexivity: (a, b) $$\preceq$$ (a, b) since ab=ab.
 * Antisymmetric: (a, b) $$\preceq$$ (c, d) and (c, d) $$\preceq$$ (a, b) since ab≤cd and cd≤ab imply ab=cd.
 * Transitive: (a, b) $$\preceq$$ (c, d) and (c, d) $$\preceq$$ (e, f) implies (a, b) $$\preceq$$ (e, f) since ab≤cd≤ef and thus ab≤ef

Posets
A partial order imparts some kind of "ordering" amongst elements of a set. For example, we only know that 2 ≥ 1 because of the partial ordering ≥.

We call a set A, ordered under a general partial ordering $$\preceq$$, a partially ordered set, or simply just poset, and write it (A, $$\preceq$$).

Terminology
There is some specific terminology that will help us understand and visualize the partial orders.

When we have a partial order $$\preceq$$, such that a $$\preceq$$ b, we write $$\prec$$ to say that a $$\preceq$$ but a ≠ b. We say in this instance that a precedes b, or a is a predecessor of b.

If (A, $$\preceq$$) is a poset, we say that a is an immediate predecessor of b (or a immediately precedes b) if there is no x in A such that a $$\prec$$ x $$\prec$$ b.

If we have the same poset, and we also have a and b in A, then we say a and b are comparable if a $$\preceq$$ b or b $$\preceq$$ a. Otherwise they are incomparable.

Hasse diagrams
Hasse diagrams are special diagrams that enable us to visualize the structure of a partial ordering. They use some of the concepts in the previous section to draw the diagram.

A Hasse diagram of the poset (A, $$\preceq$$) is constructed by
 * placing elements of A as points
 * if a and b ∈ A, and a is an immediate predecessor of b, we draw a line from a to b
 * if a $$\prec$$ b, put the point for a lower than the point for b
 * not drawing loops from a to a (this is assumed in a partial order because of reflexivity)

Operations on Relations
There are some useful operations one can perform on relations, which allow to express some of the above mentioned properties more briefly.

Inversion
Let R be a relation, then its inversion, R-1 is defined by

R-1 := {(a,b) | (b,a) in R}.

Concatenation
Let R be a relation between the sets A and B, S be a relation between B and C. We can concatenate these relations by defining

R • S := {(a,c) | (a,b) in R and (b,c) in S for some b out of B}

Diagonal of a Set
Let A be a set, then we define the diagonal (D) of A by

D(A) := {(a,a) | a in A}

Shorter Notations
Using above definitions, one can say (lets assume R is a relation between A and B):

R is transitive if and only if R • R is a subset of R.

R is reflexive if and only if D(A) is a subset of R.

R is symmetric if R-1 is a subset of R.

R is antisymmetric if and only if the intersection of R and R-1 is D(A).

R is asymmetric if and only if the intersection of D(A) and R is empty.

R is a function if and only if R-1 • R is a subset of D(B).

In this case it is a function A → B. Let's assume R meets the condition of being a function, then

R is injective if R • R-1 is a subset of D(A).

R is surjective if {b | (a,b) in R} = B.

Functions
A function is a relationship between two sets of numbers. We may think of this as a mapping; a function maps a number in one set to a number in another set. Notice that a function maps values to one and only one value. Two values in one set could map to one value, but one value must never map to two values: that would be a relation, not a function.

For example, if we write (define) a function as:
 * $$f(x)=x^2$$

then we say:
 * 'f of x equals x squared'

and we have
 * $$f(-1)=1$$
 * $$f(1)=1$$
 * $$f(7)=49$$
 * $$f(1/2)=1/4$$
 * $$f(4)=16$$

and so on.

This function f maps numbers to their squares.

Range and codomain
If D is a set, we can say
 * $$f(D) = \{f(x) |\ x \in D\}$$

which forms a née of f is usually a subset of a larger set. This set is known as the codomain of a function. For example, with the function f(x)=cos x, the range of f is [-1,1], but the codomain is the set of real numbers.

Notations
When we have a function f, with domain D and range R, we write:
 * $$f : D \longrightarrow R$$

If we say that, for instance, x is mapped to x2, we also can add
 * $$f : D \longrightarrow R;\ x \longmapsto x^2$$

Notice that we can have a function that maps a point (x,y) to a real number, or some other function of two variables -- we have a set of ordered pairs as the domain. Recall from set theory that this is defined by the Cartesian product - if we wish to represent a set of all real-valued ordered pairs we can take the Cartesian product of the real numbers with itself to obtain
 * $$\mathbb{R}\times\mathbb{R}=\mathbb{R}^2=\{(x,y)|\ x\ \mbox{and}\ y \in\mathbb{R}\}$$.

When we have a set of n-tuples as part of the domain, we say that the function is n-ary (for numbers n=1,2 we say unary, and binary respectively).

Other function notation
Functions can be written as above, but we can also write them in two other ways. One way is to use an arrow diagram to represent the mappings between each element. We write the elements from the domain on one side, and the elements from the range on the other, and we draw arrows to show that an element from the domain is mapped to the range.

For example, for the function f(x)=x3, the arrow diagram for the domain {1,2,3} would be:

Another way is to use set notation. If f(x)=y, we can write the function in terms of its mappings. This idea is best to show in an example.

Let us take the domain D={1,2,3}, and f(x)=x2. Then, the range of f will be R={f(1),f(2),f(3)}={1,4,9}. Taking the Cartesian product of D and R we obtain F={(1,1),(2,4),(3,9)}.

So using set notation, a function can be expressed as the Cartesian product of its domain and range. f(x) This function is called f, and it takes a variable x. We substitute some value for x to get the second value, which is what the function maps x to.

Types of functions
Functions can either be one to one (injective), onto (surjective), or bijective.  INJECTIVE Functions  are functions in which every element in the domain maps into a unique elements in the codomain.

 SURJECTIVE Functions  are functions in which every element in the codomain is mapped by an element in the domain.

 'BIJECTIVE Functions  are functions that are both injective and surjective.

---onto functions   a function f form A to B is onto ,


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Tom Tom Blues

Tom Tom Blues is the title of The 77s' eighth album, released in 1995 on the Brainstorm Artists, Intl label.

Track listing

 * 1) "Rocks In Your Head"
 * 2) "Honesty"
 * 3) "You Still Love Me"
 * 4) "Outskirts"
 * 5) "Flowers In the Sand"
 * 6) "Don't Leave Me Long"
 * 7) "Gravy Train"
 * 8) "Five In the Nave"
 * 9) "Earache"
 * 10) "Deliverance"

Personnel
The band
 * Mike Roe – guitars, lead vocals
 * Mark Harmon – bass guitar, background vocals
 * Bruce Spencer – drums

Additional musicians
 * Carey Avery – percussion

Production notes
 * Gene Eugene – executive producer
 * Ojo Taylor – executive producer
 * Guy Niosi – engineer, mixing
 * John Flanagan – engineer, mixing
 * Rachel Thornton – cover illustration Ashley Sad, Avery Happy – oil on canvas, 1988

title: Tom Tom Blues


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Nike of Paros

The Nike of Paros is an early classical depiction of Nike from the 5th century BC (c. 480 BC). The white marble figure was found before 1885 on the island of Paros. It is currently on display at the Archaeological Museum of Paros.

Description
The female figure, originally winged, was depicted floating in mid-air, in an unbelted peplos which hung open. The wings and this posture identify her as Nike.

The head, left arm, lower right arm, most of the wings and the feet are missing. Even so, it can be recognised that the left leg is slightly further forward, while the right leg seems to have been pulled back. This posture in connection with the forward lean of the figure as a whole is also a characteristic posture in later depictions of Nike like the Nike of Paionios. In the classical period this posture replaced the archaic "kneeling run" as the usual way of depicting Nike. The forward slope of the body's axis, which is created mainly by the straightness of the upper body and the strong incline of the lower body to the left, would have made the whole figure tilt slightly and would have shifted all weight off the left leg. The left arm must be reconstructed as having stretched upwards, when the figure was fixed in place. It is the resulting disregard for the rules of gravity which gave the Nike of Paros the appearance of floating. A transition takes place then in statuary from a sideways to a forward moving figure, as a result of the change in pose.

The original circumstances of this Nike's creation are not clearly known. Either she served as an acroterion or she must have been a victory monument. Although no Parian victory is known to have occurred around 470/60 BC, the fact that it is carved all the way round makes it more likely that it was a victory monument.

title: Nike of Paros


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User:Barrow Clement/citing sources

Diogenes heteropsammicola is a species of hermit crab  that lives within "walking corals" of the genera Heterocyathus and Heteropsammia.

title: User:Barrow Clement/citing sources