text:
IMI

IMI, Imi, may refer to:

Companies and organizations

 * IMI plc, a British engineering company
 * IMI Systems, an Israeli weapons manufacturer
 * Independent Media Institute, founder of AlterNet
 * Indian Music Industry, a trust that represents the recording industry distributors in India
 * Indonesian Motor Association
 * Institute of Mathematics and Informatics (Bulgarian Academy of Sciences)
 * Institute of the Motor Industry, UK
 * Integrated Micro-Electronics, Inc., a semiconductor maker in the Philippines
 * International Hotel Management Institute Switzerland
 * International Maritime Institute, India
 * International Media Investments, United Arab Emirates
 * International Migration Institute, at Oxford University
 * International Mycological Institute, England
 * Irish Management Institute
 * Israel Music Institute

Other

 * IMI Desert Eagle, a semi-automatic handgun
 * Inclusive Mosque Initiative, UK
 * Innovative Medicines Initiative, a partnership of the European Union
 * Internal Market Information System, network that links public bodies in the European Economic Area
 * International Migration Initiative, of the Open Society Foundation
 * Italian military internees, name given by Germany to captured Italian soldiers
 * "iMi", a song from the album I, I by American folk band Bon Iver

 * Imi, Ethiopia
 * Imi, a Babylonian king
 * IMI (Morse code  ), abbreviation for "I say again" in morse code

title: IMI


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Israel Weapon Industries

Israel Weapon Industries (IWI), formerly the Magen division of the Israel Military Industries Ltd. (IMI), is an Israeli firearms manufacturer.

It was founded in 1933. Formerly owned by the State of Israel, the Small Arms Division of IMI was privatized and renamed IWI in 2005.

IWI is one of the world's most famous and bestselling military arms manufacturers. The Magen division rose to international prominence in the 1950s, as the creator of the Uzi, of which over 10 million would be produced, netting billions of dollars for the company. Subsequent well known military exports have included the Jericho 941 semi-automatic pistol, Negev light machine gun, Galil assault rifle, Tavor assault rifle, and the DAN .338 sniper rifle.

IWI develops and manufactures guns used by armies and law enforcement agencies around the world.

Ramat HaSharon
For many decades, IWI and the Magen division of Israeli Military Industries before it, has manufactured its weapons in Ramat HaSharon. The factory has for many years been regarded an important component of the manufacturing sector in Ramat HaSharon. In 2017, IWI announced it is planning to construct a new factory in Kiryat Gat, to which its manufacturing will re-locate when completed in 2020. The new Kiryat Gat factory, whose construction will cost NIS 180 million, will employ 560 full-time production workers and engineers on its assembly lines.

India
IWI owns several factories overseas, for the manufacture of weapons for local markets. In India, IWI is establishing a joint-manufacturing center with Punj Lloyd (with IWI owning 49% of the plant, and Punj Lloyd owning 51% of the plant), which will be India's first privately-owned small-arms manufacturing plant. The factory will manufacture firearms for the Indian army. IWI said in 2017, that it expects tenders with the Indian army in the region of $200–300 million.

USA
IWI also operates a manufacturing facility in Middletown, Pennsylvania USA. They locally manufacture the Zion-15, Tavor and Galil rifles, TS12 15+1 round semi-automatic shotgun as well as the Jericho, Masada and Galil pistols, among others.

Security training
IWI offers anti-terrorism training to Israeli citizens and contracts its services to outside countries requiring security training and anti-terror training to protect assets and high-ranking officials. IWI collaborates with the Metropolitan College of New York (MCNY) in New York City, which offers a classroom-based MA degree in Public Administration, Emergency Management, and Homeland Security.

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

title: Israel Weapon Industries


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Aalborg University

Aalborg University (AAU) is an international public university with campuses in Aalborg, Esbjerg, and Copenhagen, Denmark. Founded in 1974, the university awards bachelor's degrees, master's degrees, and PhD degrees in a wide variety of subjects within humanities, social sciences, information technology, design, engineering, exact sciences, and medicine.

According to the 2024 edition of the QS World University Rankings, Aalborg University is ranked 336th worldwide. The university is especially known for its mechanical engineering study program, ranked eighth worldwide and first in Europe in 2021 according to U.S. News & World Report. The motto of the university in Danish is ad nye veje (on new paths).

History
The idea of a university in the North Jutland Region started in 1961 when the North Jutland Committee for higher education institutions was established. On 19 August 1969 the Aalborg University Association was founded and a planning group was established with Eigil Hastrup as chairman. The same year in December, about 1,000 people from North Jutland demonstrated in front of the Folketinget (the Danish Parliament) for their cause.

In 1970, a law about the establishment of a university centre in Aalborg was passed in the Danish Parliament. In 1972, it was decided that the first rector of the new university center should be the Swedish historian and professor Jörgen Weibull. On 1 September 1974, Aalborg University Center (AUC) was inaugurated by Queen Margrethe II of Denmark. Jørgen Weibull was replaced by Sven Caspersen as rector of Aalborg University Center (AUC) in 1976. At the same time, a new management organization was established under a consistory. The first formal cooperation agreement was signed with the University of Wisconsin–Green Bay in 1980. The North Jutland knowledge park was established in 1989 as a neighbor to Aalborg University Center (AUC).

In 1993, external representatives joined the consistory. In 1994, Aalborg University Center (AUC) changed its name to Aalborg University (AAU). Aalborg University - Esbjerg was established through a merger between the engineering college in Esbjerg and Aalborg University in 1995. In 1998, the NOVI science park was connected to Aalborg University. Aalborg University Copenhagen was formed in collaboration with the engineering college in Copenhagen in 2003. A new university board was formed and joined by its members on 1 February 2004, with Jørgen Østergaard appointed as rector. In 2005, Finn Kjærsdam was hired by the university board as rector. Aalborg University and the Danish Building Research Institute merged in 2007. In 2010, Aalborg University established a faculty of Medicine and created a medical education. Per Michael Johansen was hired as rector by the university board in 2014.

List of rectors
Since Aalborg University's foundation in 1974, the university has had a total of five rectors in office.

Profile
Aalborg University differentiates itself from the older and more traditional Danish universities with its focus on interdisciplinary, inter-faculty studies; an experimental curriculum based on an interdisciplinary basic course with subsequent specialisation; a pedagogical structure based on problem-centred, real-life projects of educational and research relevance – which internationally has become known and recognised as The Aalborg Model. With the problem-based, project-organised model, semesters at AAU are centred around complex real-life problems which students attempt to find answers to in a scientific manner while working together in groups. In February 2007, the foundation of the UICEE Centre for Problem Based Learning (UCPBL) paid recognition to Aalborg University, which subsequently led to the appointment of AAU as UNESCO Chair in problem-based learning.

University rankings
According to U.S. News & World Report's 2021 ranking, Aalborg University (AAU) was ranked the eighth best university in the world and the best in Europe within mechanical engineering.

In a Massachusetts Institute of Technology (MIT) study which analyzed the global state of art in the engineering education, Aalborg University (AAU) was named as the leading university in Europe in engineering education by 50 thought leaders from all over the world.

In 2021, Times Higher Education Impact Rankings ranked Aalborg University number 6 in the world, out of 1,117 universities from 94 countries/regions, according to the United Nations' Sustainable Development Goals. That is the number 1 university in the European Union (EU). In 2022, Times Higher Education Impact Rankings ranked Aalborg University (AAU) as the best university in the world in Sustainable Development Goal 4 (Quality Education) for the third year in a row.

For the academic year 2023, in overall terms, Aalborg University (AAU) has significantly dropped in worldwide university rankings, according to THE and QS. In addition, the Danish university dropped even more drastically in worldwide academic rankings during 2022 according to ARWU. In the 2024 QS top, Aalborg University (AAU) dropped to the 336th position.

Administration and organisation
The university is governed by a board consisting of 11 members as follows:

 * Six members recruited outside the university form the majority of the board;
 * Two members are appointed by the scientific staff;
 * One member is appointed by the administrative staff;
 * Two members are appointed by the university students.

The rector is appointed by the university board. The rector in turn appoints deans, and deans appoint heads of departments. There is no faculty senate and faculty are not involved in the appointment of rector, deans, or department heads. Hence the university has no faculty governance.

Campuses
Aalborg University (AAU) has campuses in Aalborg, Esbjerg, and Copenhagen.

Esbjerg
Aalborg University Esbjerg (AAU-Esbjerg) is an organisational unit (department) under Aalborg University, but is geographically located in Esbjerg. The institute's official name is "Esbjerg Technical Institute", formerly the "Department of Chemistry and Applied Engineering."

AAUE has approximately 500 students and educates mainly engineers, but also offers a number of niche programmes such as fishing technology and a graduate degree in computer science education (Bachelor of Science in software engineering).

Aalborg University Esbjerg was created through a merger of Engineering College Esbjerg and Aalborg University in 1995. Since the merger, the number of applicants for Aalborg University Esbjerg has risen steadily and therefore there have been a need for extensions of the physical environment in several stages.

The university offers programmes in information technology, with a Department of Software and Media Technology.

The student organisation at AAU-Esbjerg is called DSR-SE and the student bar is called "The Loophole" (Smuthullet).

Faculties and departments
Aalborg University has five faculties with a number of departments:

 * Faculty of Humanities
 * Department of Communication and Psychology
 * Department of Culture and Learning
 * Faculty of Social Sciences
 * AAU Business School
 * Department of Law
 * Department of Politics and Society
 * Department of Sociology and Social Work
 * Technical Faculty of IT and Design
 * Department of Electronic Systems
 * Department of Computer Science
 * Department of Architecture, Design, and Media Technology
 * Department of Planning
 * Faculty of Engineering and Science
 * Department of the Built Environment
 * Department of Materials and Production
 * Department of Chemistry and Bioscience
 * Department of Mathematical Sciences
 * Department of AAU Energy
 * Faculty of Medicine
 * Department of Health Science and Technology
 * Department of Clinical Medicine

Library and Press
Aalborg University Library is a public research library for the North Jutland region. The library's primary mission is to support research and education at Aalborg University by providing appropriate information and documentation. The main branch of the University Library is located at Kroghstræde 3 in Aalborg, which is linked to smaller branches located on other campuses in Aalborg, Esbjerg, and Copenhagen.

Aalborg University through Aalborg University Press is a publisher of wide range of journals, and among them four journals are listed in Scopus: International Journal of Sustainable Energy Planning and Management, Journal of Somaesthetics, Journal of China and International Relations and Academic quarter (Journal for humanistic research). Other journals are, for example, Journal of Business Models, Coaching Psychology - The Danish Journal of Coaching Psychology, Journal of Problem Based Learning in Higher Education, Globe: A Journal of Language, Culture and Communication, Music Therapy in Psychiatry Online.

Aalborg University Press was founded in 1978 and it focuses on political science, sociology, media and cultural studies. However, according to Scopus, the journal with highest score and number of citations is International Journal of Sustainable Energy Planning and Management, with focus on Energy System analysis, Economics, Socio economics and Feasibility studies as well as specific feasibility studies and analyses of the transition to sustainable energy systems. All journals are Open Access and most of the journal content is peer-reviewed. Majority of authors are affiliated with Aalborg University (AU), but few of the authors are international scholars, since AU is an international orientated University.

Special action areas and cross-disciplinary research
AAU conducts research within all faculties. Aalborg University is among the leading universities in the world within health technology research, wireless communication, energy, computer science, innovation economics and comparative welfare studies. AAU has established centres for telecommunication at Birla Institute of Technology in India, at Bandung Institute of Technology in Indonesia, and at the University of Rome. Furthermore, AAU has established a research centre for health technology at Xi'an Jiaotong University in China.

AAU has conducted several experiments in the field of CubeSat technology. The first AAU CubeSat was launched on 30 June 2003, the second (called AAUSAT-II) on 28 April 2008 and the third will be launched in Q1, 2013. After launching AAUSAT3 the fourth will begin development.

AAU has always adopted a cross-disciplinary, problem-based approach to research which often requires contributions from a number of scientific disciplines. Aalborg University has five cross-disciplinary action areas:

 * Sustainable energy, the environment and construction;
 * Global production, innovation, knowledge development and coherence;
 * Information technology;
 * Nanotechnology and nanoproduction;
 * Experience technology and design.

Cooperative agreements with other universities and colleges
Aalborg University is a member of the European Consortium of Innovative Universities (ECIU), which was founded in 1997 by 10 European universities. The other 9 European universities are: Dublin City University, Ireland; Linköping University, Sweden; University of Aveiro, Portugal; Autonomous University of Barcelona, Spain; Hamburg University of Technology, Germany; University of Stavanger, Norway; Kaunas University of Technology, Lithuania; Tampere University of Technology, Finland; University of Twente, The Netherlands.

The aim of the ECIU is to create a European network where participating universities can exchange experiences and practices in projects in education, research, and regional development. In 2010, the ECIU consisted of eleven members and three foreign affiliates.

Notable alumni and people associated with Aalborg University

 * Frank Aaen, Danish economist, former member of the Danish Parliament and member of the Red–Green Alliance
 * Gunhild Moltesen Agger, professor in Danish media history
 * Erik Bach, Danish composer and music teacher
 * Louis Becker, Danish architect and lecturer
 * Jens Blauert, German scientist and emeritus professor
 * Frede Blaabjerg, World known Danish researcher within the areas of renewable energy and power electronics
 * Anette Borchorst, Danish Professor
 * Vladimir Bouchler, Uzbek theatre director and pedagogue
 * Ann-Dorte Christensen, Danish Professor
 * Henrik I. Christensen, Danish roboticist and Distinguished Professor
 * Jesper deClaville Christiansen, Danish professor
 * Klaus Dittrich, German computer scientist
 * Jan Fagerberg, Norwegian professor
 * Bent Flyvbjerg, Danish social scientist
 * Mette Frederiksen, Danish politician, leader of the Social Democrats and Prime Minister of Denmark
 * Christopher Freeman, British economist
 * Christian Graugaard, Danish physician, professor, researcher, commentator, critic, poet and writer
 * Lars Graugaard, Danish flutist, composer, music teacher and researcher
 * Carsten Greve, Danish professor
 * Birkir Hólm Guðnason, Icelandic business leader and CEO of Icelandair
 * Dorte Hammershøi, Danish Professor
 * Thomas Blom Hansen, Danish anthropologist
 * Fredric J. Harris, American professor
 * Cathrine Hasse, Danish professor with special responsibilities
 * Christian Geo Heltboe, Danish comedian
 * Peter Hervik, Danish anthropologist and professor
 * Arlie Russell Hochschild, American professor
 * Anders Post Jacobsen, Danish professional football player
 * Frank Jensen, Danish politician, former Lord Mayor of Copenhagen, a member of the Social Democrats and former minister
 * Anja Jørgensen, Danish Professor
 * Per Michael Johansen, Danish rector
 * Rosabeth Moss Kanter, American professor
 * Finn Kjærsdam, Danish former rector at Aalborg University and professor
 * Anette Kolmos, Danish Professor
 * Arnulf Kolstad, Norwegian social psychologist
 * Kim Guldstrand Larsen, Danish scientist and professor
 * Mads Mensah Larsen, Danish handball player
 * Torben Larsen, Danish scientist
 * Karsten Lauritzen, Branch Director of DI, former member of the Danish Parliament and member of Venstre. Served as minister of taxation under Lars Løkke Rasmussen II Cabinet
 * Steffen Lauritzen, Danish professor
 * Henrik Lund, Danish engineer and professor
 * Bengt-Åke Lundvall Danish organizational theorist
 * Brian Vad Mathiesen, Danish engineer and professor
 * Morten Middelfart, Danish entrepreneur, inventor and technologist
 * Søren Hald Møller, Danish official
 * Henrik Frystyk Nielsen, Danish engineer and computer scientist
 * Malene Freudendal-Pedersen, Danish Professor
 * Anne Phillips, British professor
 * Vincent Poor, American dean and professor
 * Zenon J. Pudlowski, Polish engineer and educator
 * Herbert Pundik, Danish Jewish journalist and author
 * Toke Reichstein, Danish economist and professor
 * Mike Sandbothe, German intellectual and philosopher
 * Henrik Scharfe, Danish professor
 * Lene Siel, Danish singer
 * Hege Skjeie, Norwegian political scientist and feminist
 * David Spiegelhalter, British statistician
 * Jakob Stoustrup, Danish professor
 * Emil Wolf, Czech born American physicist
 * Jonas Kærlev, creator of A Hat in Time.

title: Aalborg University


text:
Cofiniteness

In mathematics, a cofinite subset of a set $$X$$ is a subset $$A$$ whose complement in $$X$$ is a finite set. In other words, $$A$$ contains all but finitely many elements of $$X.$$ If the complement is not finite, but is countable, then one says the set is cocountable.

These arise naturally when generalizing structures on finite sets to infinite sets, particularly on infinite products, as in the product topology or direct sum.

This use of the prefix "'" to describe a property possessed by a set's 'mplement is consistent with its use in other terms such as "meagre set".

Boolean algebras
The set of all subsets of $$X$$ that are either finite or cofinite forms a Boolean algebra, which means that it is closed under the operations of union, intersection, and complementation. This Boolean algebra is the  on $$X.$$

In the other direction, a Boolean algebra $$A$$ has a unique non-principal ultrafilter (that is, a maximal filter not generated by a single element of the algebra) if and only if there exists an infinite set $$X$$ such that $$A$$ is isomorphic to the finite–cofinite algebra on $$X.$$ In this case, the non-principal ultrafilter is the set of all cofinite subsets of $$X$$.

Cofinite topology
The cofinite topology (sometimes called the finite complement topology) is a topology that can be defined on every set $$X.$$ It has precisely the empty set and all cofinite subsets of $$X$$ as open sets. As a consequence, in the cofinite topology, the only closed subsets are finite sets, or the whole of $$X.$$ Symbolically, one writes the topology as $$\mathcal{T} = \{A \subseteq X : A = \varnothing \mbox{ or } X \setminus A \mbox{ is finite} \}.$$

This topology occurs naturally in the context of the Zariski topology. Since polynomials in one variable over a field $$K$$ are zero on finite sets, or the whole of $$K,$$ the Zariski topology on $$K$$ (considered as affine line) is the cofinite topology. The same is true for any irreducible algebraic curve; it is not true, for example, for $$XY = 0$$ in the plane.

Properties

 * Subspaces: Every subspace topology of the cofinite topology is also a cofinite topology.
 * Compactness: Since every open set contains all but finitely many points of $$X,$$ the space $$X$$ is compact and sequentially compact.
 * Separation: The cofinite topology is the coarsest topology satisfying the T1 axiom; that is, it is the smallest topology for which every singleton set is closed. In fact, an arbitrary topology on $$X$$ satisfies the T1 axiom if and only if it contains the cofinite topology. If $$X$$ is finite then the cofinite topology is simply the discrete topology. If $$X$$ is not finite then this topology is not Hausdorff (T2), regular or normal because no two nonempty open sets are disjoint (that is, it is hyperconnected).

Double-pointed cofinite topology
The double-pointed cofinite topology is the cofinite topology with every point doubled; that is, it is the topological product of the cofinite topology with the indiscrete topology on a two-element set. It is not T0 or T1, since the points of each doublet are topologically indistinguishable. It is, however, R0 since topologically distinguishable points are separated. The space is compact as the product of two compact spaces; alternatively, it is compact because each nonempty open set contains all but finitely many points.

For an example of the countable double-pointed cofinite topology, the set $$\Z$$ of integers can be given a topology such that every even number $$2n$$ is topologically indistinguishable from the following odd number $$2n+1$$. The closed sets are the unions of finitely many pairs $$2n,2n+1,$$ or the whole set. The open sets are the complements of the closed sets; namely, each open set consists of all but a finite number of pairs $$2n,2n+1,$$ or is the empty set.

Product topology
The product topology on a product of topological spaces $$\prod X_i$$ has basis $$\prod U_i$$ where $$U_i \subseteq X_i$$ is open, and cofinitely many $$U_i = X_i.$$

The analog without requiring that cofinitely many factors are the whole space is the box topology.

Direct sum
The elements of the direct sum of modules $$\bigoplus M_i$$ are sequences $$\alpha_i \in M_i$$ where cofinitely many $$\alpha_i = 0.$$

The analog without requiring that cofinitely many summands are zero is the direct product.

title: Cofiniteness


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User talk:80.255/archive 1

This is an archive page. See User talk:80.255 for current talk.

Newer old talk now in User talk:80.255/archive 2.

Fish names
I'm going through a systematic list of fish types (Bond's book), and you inserted a bunch randomly right in the middle - when I'm done, I'll go back and add yours that are valid but not on my list. Sorry about the silent overwrite, it's more efficient this way. Stan 21:17, 28 Sep 2003 (UTC)

Ant references
Not to be too much of a stickler, but let's be honest -- of all of the characteristics of this peninsula that could be written about, is it really the fact that "the rare formicine ant Formica exsecta (the narrow-headed ant)" can possibly be found there?

I truly don't want to discourage you from working on the Wikipedia, but it really does seem to me that you could contribute a lot of new information about ants, rather than simply adding obscure information on rare ant species to different articles -- especially those which are entries on geographical locations?

Cheers, -- Bcorr 03:04, 29 Sep 2003 (UTC)

 * I consider this reference very relevant; it certainly isn't unreasonable that someone wanting to know about lizard point would find information about rare wildlife there both interesting and relevant. Granted, mentioning HStJKD is going a little overboard, but mention of and link to Formica exsecta (an article on which I have just started) is not.
 * Since I don't know a great deal about the geology of the peninsula, I cannot contribute information on it. Conversly, since I do know alot about its ant-fauna, I can, and will. The fact that it is currently absurdly overbalanced towards what you call "obscure information on rare ant species" is solely because no-one has yet added any more "mainstream" information - when this is present, the balance will be restored, and my ant reference will be a interesting a relevant detail to the whole article.

Plural term redirects
Hi :) Please don't create redirects with plural terms, ie Beetles is unnecessary since you can create the same effect with Beetles and it'll show up as Beetles. Thanks Dysprosia 07:03, 29 Sep 2003 (UTC)

 * Certainly. I'll change the link to Beetless. 80.225

naming conventions
Hi. I just see you two articles Dorylinae and Driver ant. However the consensus is to have articles about animals (same applies for plants and fungi and bacteria of course) placed on their common english name (if it have one), and make the taxonomic name a redirect to this. Any alternative (less common names, obsolete taxonomic names) should be redirects as well, and eventually mentioned in the article. You can find it and its rationale somewhere in the discussion around WikiProject Tree of Life. If you do two articles then one would basically only contain "xxx is yyy" - hence nothing else but a redirect. andy 12:49, 2 Oct 2003 (UTC)

Counties, part I
Hi. I notice you've been going around modifying articles to clarify what county means. This is great, except that the specific way you've been doing this is not neutral. Affording historical counties a capital C, and relegating administrative counties to have the county within scare quotes is clearly judgemental. Could you please use the actual term as defined, which is "administrative county" in future? Put the whole lot in quotes if you must, even that would be better. Thanks, Morwen 22:42, 4 Oct 2003 (UTC)

In regards to your communication, I and many others consider the historical counties just an interesting historical anomaly, and the disclaimer in the legislation merely a sop to tradionalists such as yourself. I would contend they do indeed not have equal status with administrative counties - rather they are inferior. And it is not as if the traditional counties are anything more than government-created boundaries for administrative purposes - just by governments centuries ago. If I were editing the articles in accordance with my prejudices, I would not even mention the historical counties as something presently existing and just mention them as former boundaries. So what I suggestedg, treating them neutrally, with equal status is I hope a reasonable compromise between these positions. I'm not quite sure what you mean with the proper noun thing - can you find any usage of "County" like that in non-polemical works? Hope we can reach a consensus on this. Morwen 18:31, 7 Oct 2003 (UTC)

My proposed wording is ''"xyz town is administered as part of This-and-that, but is in the historic county of Suchandsuch. Prior to the 1998 local government act is was administered as part of the metropolitcan county of Suchandsuch."

The only reason that I can see why wikipedia would want to use quote marks round terms like administrative county or metropolitan county is to express disapproval of them. But I should hope always qualifying county with administrative (or metropolitan or whatever) where it doesn't refer to a traditional county, should satisfy both sides - it takes care of the ambiguity issue which seems to have been your reason for making the changes. In many cases the wording can just be altered to omit the term at all, which may often be the best course - no need to have thousands of pages explaining the difference between the two entities. Though it pains me I'll even offer you county on its own meaning a traditional one, so long as the quote marks round the qualified versions go. ;) Morwen 22:03, 7 Oct 2003 (UTC)

--- I believe we have a deal. Morwen 06:50, 8 Oct 2003 (UTC)

Counties, part II

 * But sadly the Wikipedia is poorer for it. The compromise means we are writing things like "The town is in the County of Kent, but not in the county of Kent." and expecting people to know that this means "The town used to be in Kent nearly 40 years ago, but isn't any more because the Kent boundary changed nearly 40 years ago." Ho hum. Pete 17:46, 11 Oct 2003 (UTC)
 * Pre-emptive response to what 80.255 might say. The alternative "The town is in the County of Kent, but in not in the administrative county of Kent" is also unsatisfactory as it suggests that administrative counties have a lesser status in British geopolitics than historic counties, which, to be frank, is complete rubbish, and obviously so to all but the most obtuse of grumbling traditionalists.

This is patent rubbish, I'm afraid. The compromise means we are writing "The town is in the County of Kent (which is true), and in the administrative county of Greater London (as the case may be)". Both of these satements are true and reasonably unambiguous, although I would still prefer that "administrative county" were put in parentheses. The rest of you post is unfactual nonsense; the boundaries of kent did not change whatsoever in 1974 and the government made this crystal clear. Perhaps you don't care about truth and factual accuracy, but I do! Try googling "Bexley Heath, Kent" (or bexleyheath) and compare with "Bexley heath, London". The people of this town are certainly under no illusions as to which County they are in! The same is echoed in hundreds of places affected administratively only in 1974. As for administrative "counties" having a "lesser status", I have implied no such thing. Administrative "counties" are used for administrative purposes; Geographical (historic) counties are used for normal geographic purposes by most people; ascribing a higher of lower "status" to either is inapplicable since they have different uses. In the same way, if asked where I live I would not reply by stating the electoral ward, but the Town - this is not to say that the ward has a "lower status" - the term is simply inapplicable to matters not relating to its administrative purpose. I'm still removing rubbish about "former counties" which still exist and are absolutely current; wikipedia is very much the better for it as it now reflects correct, factual information, and not what was, to put it franky, complete balderdash. And if you have the strange idea that County boundaries somehow changed in 1974, then you are quite franky utterly wrong, and would be doing wikipedia no favours by entered downright misleading, unfactual and incorrect information. This is simply a matter of correct facts; I take it that you believe in encyclopaedias giving correct information? 80.255 18:09, 11 Oct 2003 (UTC)
 * Yes you've made your position perfectly clear and you know my feelings on it. If I open a road atlas and look at the bit called Kent, is Bexleyheath in it? Pete 23:07, 11 Oct 2003 (UTC)

 * Which part of the simple and unequivocal facts I have stated do you not accept? Road Atlases are completely irrelevant to this matter - they neither create boundaries nor are they concerned with either geographical or administrative divisions of britain - they are concerned with showing the road network! And, for your information, if you open a road atlas it will not show the current administrative boundaries. In short, your mentioning them is nothing short of obfuscation. Sp why are you so determined to pit yourself against simple, unequivocal facts? 80.255 23:18, 11 Oct 2003 (UTC)

 * I would've thought that road atlases, such as the AA atlas in front of me here, which actually print the county boundaries in them(!) are of more relevance and authority than your Google search, the first few pages of which are full of identikit generic hotel pages which exist for every town in the country.

 * P.S. Just noticed that again you are suggesting that county boundaries change very frequently ("as often as the wind changes direction")... I've pointed out before that this an obvious falsehood... how many times has their been a change of boundaries in the last 100 years. Once a decade at the absolute most. Hmm... a real chore keeping with those 'rapid' changes. Please do not lecture me about simple, uniequivocal facts when you are peddling nothing but the sort all over the wikipedia (fake articles about Donisthorpe initially, then getting BNP protected through edit warring, now I see your ever so neutral line on Mugabe...).

 * Whether or not you personaly consider road atlases authorititive is immaterial. You have made a number of utterly false statements implying that post 1970s administrative "counties" somehow caused historic Counties to cease to exist, and you have as yet refused to accept that they are downright wrong. Instead, all you can do is bring up some irrelevant reference to a road atlas which "you have in front of you"! Then, whilst still not accepting your proven inaccuracies, you try to rope in another complete irrelevancy - my other contributions to wikipedia. You are grasping for whatever straws you can find to avoid facing the crux of this issue - perhaps you would make a good politician...
 * There have been many administrative boundary changes in the last decade of entities which are anthing but Counties. There will undoubtably be many more. It is a matter of common sense that an unchanging reference frame is a good thing for any article that provides reference, irrespective of whether or not you consider these changes to be infrequent enough to merit mention; on the contrary, by all means state administrative boundaries (and change them to keep up with the latest beaurocratic reshuffle), but it is quite pontless the base articles around such boundaries when unchanging and better understood boundaries already exist in the form of Counties. My bexleyheath example simply illustrates that the people of bexleyheath are in no doubt that they are in Kent - in other words, they understand the County system. The fact that Hotels and other bussinesses also use the correct County is no supprise, since such establishments will use the terms with which people are most familiar and which they best understand. These real people obviously couldn't care less about the contents of your road atlas, or any other small beaurocratic group which bears little relation to commonly used and commonly understood frames of geographic reference!
 * What exactly are you trying to prove? It can't be that (to take this example) Bexleyheath is no longer in Kent, since this is plainly and unequivocally incorrect. So please explain why exactly you would like to withold correct information from articles where it is relevant, putting in its place facts that are not true! Call me a "traditionalist", but I was under the impression that this was meant to be an encyclopaedia...
 * 80.255 00:19, 12 Oct 2003 (UTC)
 * P.s. I've never written any "fake articles" about Donisthorpe. Perhaps you could provide example of these?
 * Oops sorry I should've checked Vandalism_in_progress before writing that. According to that page, you completely made up a species of stalk, a physicist called Teighnditch and a type of squid and wrote about them. The Donisthorpe pages were just a little esoteric rather than vandalism. My apologies... anyhow now lets resume your rant about how apparently its me who's the inaccurate one.....
 * As I have already said, I am concerned with factual accuracy. The statment is question was "I've never writeen any fake articles about Donisthorpe". You respond to this with a whole lot of irrelevant details and then descibe the Donisthorpe articles as "a little esoteric". Well, "a little esoteric" does not equal "a fake article". But of course you know that very well - you're simply trying to obfuscate the issue yet again and avoid takling my question to you about the matter in hand (i.e. not about irrelevant and unconnected matters that occurded weeks ago)! I have never claimed that when I first discovered this website I didn't make a handfull of joke posts (which were obviously not intended to masquerade as real articles); I do, however, claim that I am correct in this matter. That fact that you continue to nit-pick irrelevant details yet still fail to produce any evidence whatsoever about the fundamental basis of my position leads me to think that perhaps you have already realised that you position is untenable, and are simply tried to keep squabbling about unrelated matters to try and mask this? If this isn't the case, I repeat my earlier question - one which you yet again avoided: what, if anything, are you trying to prove?
 * 80.255 01:51, 12 Oct 2003 (UTC)

Working from memory I got exactly which articles you had made up, I made a mistake, I then fact-checked realized my mistake and I apologized. I hope you will accept that apology. The central point I was making still stands of course. You, in the past, have deliberately tried to vandalize Wikipedia for reasons best know to yourself (there are plenty of places on the internet to make jokes, why try to ruin this place that is trying to be a bit more serious? ) I think this point is relevant when you keep accusing me of being "plainly and unequivocally incorrect", when I am not! The evidence that Bexleyheath is the London Borough of Bexley and not in Kent is utterly plain. Just visit http://www.bexley.gov.uk/ and http://www.kent.gov.uk/ or look at a moderately recent map which has county boundaries on it, or look at the area the Kent and London phone books cover or look where you council tax bill comes from if you live in Bexleyheath! All you've got is a Google search which is pretty bogus because it is full of link farm results that are breaking the Google PageRank algorithm. But yes I am fed up of repeating this because I now know you won't accept anything but your cherished idea that to refer to "Kent" means to refer to the historical county of Kent boundary rather than the new county of Kent. You disagree with all those sources, because you have your own preferred naming convention. I can't shift you off that. I'm not saying your use of terms is inconsistent, I am just saying it is out-dated and irrelevant. The point I have proved is that we shouldn't be listening to you when writing about counties in Wikipedia articles. Pete 09:37, 12 Oct 2003 (UTC)
 * Unfortunately your "plain evidence" simply doesn't exist, and yet you continue to hold up references which I have demonstrated refer to different entities. There is no such thing as the "new county of kent"; there is the County of Kent - which has remained unchanged since time immemorial, and which the government specifically stated did not change in 1974 - and there is the administrative county of kent, which was created in the 19th century, and which has underwent many boundary changes since. The fact that you seem unable to process this straightforward distinction shows that you have little grasp of the subject. What I have stated is fact and not opinion. What you have stated is garbled nonsense, in the most part. I also note that you still have answered none of my questions, and are incessently attempted to bring irrelevant matters into this discussion. You have proved nothing of sort of your last comment, nor have you disproven anything I have consistently maintained. Unless you can do so (which you cannot, since I am correct), I will assume that you have abducated this argument. 80.255 00:15, 25 Oct 2003 (UTC)

Minor edits
Hi, please note that the "This is a minor edit" tick box is for very minor formatting changes, spelling corrections and that sort of thing. More complex changes such as the addition or rewrite of a whole sentence should not be marked as minor, even though they may not appear to be that major in the context of the article as a whole. (I refer in particular to your revert of Bexleyheath. That sort of thing definitely doesn't as minor, as you already know another user is interested in that article and had wanted to write the article in a different way.) Thanks! Pete 07:29, 11 Oct 2003 (UTC)

 * Right ho; Point taken. 80.255 18:11, 11 Oct 2003 (UTC)

Rhodesian terrorists
Calling a Rhodesian faction "terrorist" cannot possibly be NPOV unless the faction calls itself that. If you want to get a point across about Mugabe's evils, cite some evidence, don't just add "terrorist" to every other sentence. Also, the previous government did plenty of bad stuff too, and it's definitely not NPOV to delete that. If a faction is terrorist, a straightforward factual accounting of its actions will get the message across sufficiently. Stan 22:13, 11 Oct 2003 (UTC)

 * The terrorism article states that terrorism is "the calculated use of violence or the threat of violence, against the civilian population, usually for the purpose of obtaining political or religious goals".
 * There is no doubt that this accurately describes the actions of Mugabe's group.
 * The word is also correctly used to descibe Al-Qaeda, the PLO, the Khmer Rouge, and a host of other groups listed at List_of_terrorist_groups. If you consider it so "POV" then you should remove it from every one of those articles. The small number of possibly questionable actions of the Rhodesian government are in no way comparable to Mugabe's atrocities, genocides and oppression. To claim otherwise would be rather like spending an article on the nazis saying how bad the Weimar republic was - a little perspective is required, and it is not POV to use it! There was also several details comprising pro-mugabe POV in the article which are highly contestable but stated as fact, which needed to be addressed. I agree that a straightforward account of actions is what is needed - and that includes using correct terms like terrorism when appropriate. 80.255 22:32, 11 Oct 2003 (UTC)
 * If you read further in terrorism, you also see that there is much dispute over when it can be legimately applied, and it points out that governments frequently accuse insurgents and guerillas of terrorism irrespective of the facts.  I also note that your method of addressing "pro-Mugabe POV" was to delete it entirely, which is not kosher; if you have counter-evidence for a contested claim, add it, don't just delete the stuff you disagree with. Your case will be stronger if you can cite scholarly works. Since you clearly have a strong anti-Mugabe stance (personally I'm mostly indifferent, just doing random policing here), you should realize that a truly NPOV article is likely to be unsatisfying; the pro-Mugabe stuff that such an article must have is always going to be infuriating. Stan 22:54, 11 Oct 2003 (UTC)

 * I don't believe that correctly describing ZANU as "terrorist" is terribly "anti-mugabe", moverover it is simply a correct fact. A NPOV article should simply say what is true; it isn't contestable than ZANU adopted terrorist tactics. "Terrorism" is also a negative word, true, but to describe it as anything less is nothing more than a euphemism - something that has no place in an encyclopaedia. By all means it should be stated (as I have done) that ZANU rejected the "terrorism" label, but it should also be noted that this simply isn't borne out by the facts. That way the facts have been stated in a neutral manner, and various opinions are also stated to maintain NPOV and have been flagged as such. 80.255 23:05, 11 Oct 2003 (UTC)

As you may have noticed, I'm not the only one taking exception to your content, so if you want it to survive the gauntlet of editors, it will have to be worded more judiciously, even if that means using what seem to you like euphemisms. BTW, your Rhodesia additions are semi-redundant with History of Zimbabwe, which ultimately derives from the CIA's factbook - I note that it doesn't use the word "terrorist", so if you're committed to this issue, you'll need to go work on that article too - readers are not going to be impressed by an internally inconsistent encyclopedia! Also, instead of editing out the minority-rule detail of Smith's tenure, you might consider mentioning it, since even though it was not the same thing as apartheid, it was a core issue for the insurgency and for the rest of the world too. Stan 23:26, 11 Oct 2003 (UTC)

 * I will indeed word the changes more judiciously, although I do believe in calling a spade a spade, and I will not compromise the correct and factual description of terrorists as "terrorists". Have you ever seen photographs of the acts perpetrated by ZANU and friends? The babies burt alive? The women and children murdered in their homes? If that is "freedom fighting" or even "armed resistance" then my name's Tony Benn!
 * On the question of of Smith government - there were no constitutional barriers to prevent blacks running for election, and this is a most important fact that should be highlighted. The system was not apartheid, and nor was it terribly unjust as it stood. There were, in fact, several blacks in prominent positions well before ZANU et alii started their violence. Terrorists, of course, could not stand for election and could have no say in the running the country; this being the case, it begs the question: why did ZANU etc. persue a terrorist campaign? The answer is that the "core issue for the insurgency" was not minority rule, as you said, by marxism. ZANU had no interest in representative government - a fact which is borne out to this day by their various persecutions of minority groups, both black and white - their interest was simply imposing a certain political system on the country. This was backed and funded, naturally, by the soviet block, and the "minority rule" excuse they used also provided a handy but false reason for the British, who wanted rid of Rhodesia, to press for "independence" (although this certainly wasn't what the people of rhodesia got!). Isn't it funny how the pro-mugabe position suddenly goes pear-shaped when the real facts are examined? 80.255 03:51, 12 Oct 2003 (UTC)

Hello 80.255. I'll edit the Combat 18 article if I get a chance. To tell you the truth though, I'm bored with the pointless discussions here. I think wikipedia was probably set up by MI5 to keep computer-literate BNP supporters on their computers and off the streets! ;-) The funniest thing about all the anti-Nazi mob is that they're all white, and so are all their family, and so are all their friends etc., whereas I personally have got black, Asian and Jewish friends. One (extremely Westernised) Asian girl I know is even determined to join the BNP! I'd love to see the ANL fanatics trying to work that one out! Anyway, my advice to you, for what it's worth, is to leave the leftist idiots to it. Yes, they'll turn the BNP and related articles into pure ANL propoganda, but then anyone reading it will realise that it's just a load of POV bull***t and ignore it! I'm going to stick to real politics and do things that will actually help the party get more votes come the next elections. That means helping real people, not just tapping away on my keyboard!

Don't forget to vote

Empty redirects
Please don't create empty redirects unless you intend to fill them. Thanks Dysprosia 06:42, 24 Oct 2003 (UTC)
 * I do intend to fill them, which is why they are specific redirects, rather than doing the same for all of them. I only have 10 fingers, however, and their movment is confined to subsonic speeds! The redirects alone provide information (associating a common name with a scientific name - something that most people probably wouldn't know...). However, I certainly have the intention of providing articles for those with redirects, and the redirects will remind me which to do first. 80.255 06:49, 24 Oct 2003 (UTC)
 * No, no, it's okay, just some people tend to create empty redirects, but if you're going to fill them, that's 100% ok :) Dysprosia 06:52, 24 Oct 2003 (UTC)
 * Just be careful, because spot-editors often delete redirects that are empty. Kingturtle 22:25, 24 Oct 2003 (UTC)

You will notice the Formica rufibarbis and Tapinoma erraticum are now started. The rest will follow. 80.255 22:27, 24 Oct 2003 (UTC)

Counties, part III
Will you please stop messing about with the counties. You've been banned for this before and you are clearly upsetting people again with your changes to Bexleyheath, Birmingham, Warwickshire, Harborne etc etc. Angela 00:18, Oct 25, 2003 (UTC)

 * I am not removing correct information. Birmingham is not in Warwickshire. It may have been in the past and you may claim that if you so wish, but you are trying to write that Birmingham is in Warwickshire now which it blatently is not. Are you purposefully trying to make Wikipedia look stupid? Angela 00:28, Oct 25, 2003 (UTC)

 * Birmingham is in the County of warwickshire. It was also formerly (and simultaneously) in the administrative metropolitan county of the West Midllands. It is now a unitary authority area, but remains in the County of Warwickshire. It is also part of the lieutenency area of the West Midlands, although the metropolitan administraive county of the west midlands no longer exists. Administrative counties were created in the 19th century as different entities from historic counties. In 1974 boundary changes took place in administrative counties only, and the government stated unequivocably that historic County coundaries did not change, nor did they "cease to exist". All this is verifiable fact. To say that "Birmingham used to be in Warwickshire" is simply downright wrong. Which part of this do you not understand? 80.255 00:34, 25 Oct 2003 (UTC)

 * There are two things called "Warwickshire" - the historic county and the current adminstrative county. Birmingham is in one but not the other. If you two are going to argue about it, make it clear which one you mean. A link to Traditional counties of England, Scotland and Wales or Counties of England would help Andy G 00:55, 25 Oct 2003 (UTC)

 * The agreement with Morwen consisted of refering to historic counties as "Counties" and to administrative counties as "administrative counties". I think this gives sufficient distinction to the difference, and morwen agreed with the compromise. However, I'm quite happy to modify this to include the links you mention: Counties and administrative counties - if you prefer. I thought this matter was settled after the morwen discussion, but it now seems that some other people want to provide deliberately misleading and flase information. I completely agree that distinction between the two different entities is the main issue. 80.255 01:07, 25 Oct 2003 (UTC)

What have you got against refering to them as "historic counties" and linking them to Traditional counties of England, Scotland and Wales? This would make it much clearer and prevent people thinking the information was simply wrong. Birmingham may be in the historic county of Warwickshire, but it is not in Warwickshire. That is - it is not in what people now refer to as Warwickshire. Angela 01:14, Oct 25, 2003 (UTC)

 * I don't mind refering to them as "historic Counties", as long as administrative counties are consistently refered to as "administrative counties". The trouble comes when people start putting in all sorts of non-terms like "modern counties" or "former counties". To say "birmingham is not in Warwickshire" is very misleading - it is true only in the sense of warickshire as an administrative "county", whereas what most people think of when they see a "shire" is its historic boundaries; if we could agree that "Birmingham is in historic/geographical Warwickshire but not in administrative Warwickshire" then I can live with that. There's a great deal of nonsense using the word "formerly", too - historic Counties didn't change in 1974, nor did they cease to exist. Birmingham is in the historic County of Warwickshire. User:Pigsonthewing, however, keeps reverting to "Birmingham was formerly in the historic County of warwickshire", which is simply wrong - and he refuses to discuss it. The only entity that was formally abolished in the metropolitan county of the "West Midlands", which does no longer exist, so to say "Birmingham is in the Westmidlands" is also wrong. 80.255 01:39, 25 Oct 2003 (UTC)

 * It is not necessary to refer to administrative counties in that way. They are called counties. Counties is the modern term for them. You are just trying to change it to push your own POV about the importance of historical counties. I have no intention of arguing over whether a place is in or was in some historical county or not. Birmingham is in the "area known as the West Midlands" whether you like you it or not. Whether it exists formally as a whatever type of county is irrelevant. No-one is saying BH is in that county; they are saying it is in the WM, whatever that term might mean. Angela 01:47, Oct 25, 2003 (UTC)

 * It is necessary to refer to administrative counties as such to avoid confusion. As you yourself have conceeded, Birmingham is part of two seperate entities - the administrative unitary authority area of Birmingham, and the historic County of Warwickshire. Warwick too lies within two different entities - the administrative county of Warwickshire and the historic County of Warwickshire. They are different, but both are current and both exist; refering to administrative counties as "counties" is simply confusing and potentially misleading - they are technically and officially called "Administrative Counties". "Counties" is not the "modern name" for them; it is simply a term used by people who are too lazy to use the correct term. Furthermore, it is ambiguous and imprecise.
 * Now, you object to "Birmingham is in the County of Warwickshire" because you (correctly) observe that Warwickshire is not the current administrative unit within which Birmingham is governed. So it is reasonable to say that Birmingham is in the historic County of Warwickshire - fine. But you then insist that Birmingham is also in the "West Midlands" - even though the West Midlands is not the current administrative unit in which Birmingham lies in - indeed, the West Midlands does not exist at all as an administrative county! It is a non-entity! This is the inconsistency of your position - you are objecting to something on one criteria, but not accepting an objection on the same criteria for something else.
 * Therefore, I suggest the following: references to administrative counties as "administrative counties"; references to historic Counties as "historic Counties"; references to the West midlands as "the former administrative metropolitan county of the West Midlands". All of these are technically correct, straightfoward and unambiguous. They do exactly what it says on the label, and they are not POV in any way. I hope you can agree to this. 80.255 02:07, 25 Oct 2003 (UTC)

 * No; I'm going with what is normal and common usage. You are going with something that pushes your own ideosyncratic point of view. Angela 02:16, Oct 25, 2003 (UTC)
 * An encyclopaedia should reflect what is accurate and correct, not simply what is "normal". For example, weight is commonly used to mean mass, but the article on weight rightly uses the correct meaning, although mentioning the incorrect one. Similarly, whilst by all means letting it be mentioned that "county" is often used to refer to administrative counties, wikipedia should adopt the correct terminology for articles. I really don't see why you are so opposed to something that is correct and accurate. It would instantly clarify the articles in question, and avoid misunderstnading and subsequent disputes over accuracy in future. 80.255 03:56, 25 Oct 2003 (UTC)

 * "the former administrative metropolitan county of the West Midlands" is superfluous. Why not just say "West Midlands". What else could it mean? This is what it is called. Look it up on a map. Angela 02:16, Oct 25, 2003 (UTC)
 * Three Points: Saying the "United States of America" is superfluous, since simply "America" is often used to refer to this country in common speech. However, America also refers to two continents, so wikipedia rightly uses the "superfluous" term to maintain accuracy and avoid ambiguity.
 * Secondly: Saying "the former metropolitan county of the west midlands" gives vastly more informative information than simply "the west midlands". That is what encyclopaedias should be about - providing information!
 * Lastly: the west midlands has only ever existed as an administrative area, and now it no longer exists. We wouldn't refer to Wessex, Troy or Dacia as current loci in articles, and the west midlands is no different. Contrast this with the reluctance of some people (not necessarily you) to include existant and current historic Counties - that deserves a nobel prize for incoherence...
 * In short, my suggestion alleviates all these problems; apparent superfluousness is necessary to maintain factual accuracy, and neither should this be sacrificed on account of "common references" - both of these points hold for all other articles, so why not here? Why are you so determined to oppose correct and unambigious terminology? 80.255 03:56, 25 Oct 2003 (UTC)

 * Mind if I jump in on this one? In my opinion it is more informative to specify "former West Midlands metropolitan county" as "West Midlands" on its own can refer to the economic region which extends between the "East Midlands" (Derby / Nottingham / Leicester area) to the Welsh border. I'd also identify "North Midlands" as the Stoke-on-Trent area and "South Midlands" as around Oxford. That said, on consideration I view it as totally misleading to baldly claim that places which used to be within a county is still within a county of the same name but not the same boundaries. Wikipedia should be attempting to reflect the current situation - mention the history of the place if you wish, but do not claim what is contrary to the accepted normal usage. This debate has prompted me to take a look at some of the Welsh counties I'm familiar with, and I'm horrified to see that the Wikipedia entries for Denbighshire and Flintshire are completely wrong -- they plainly refer to the pre-1974 counties which bear little commonality with the post-1996 counties - Rhyl, St Asaph, and Rhuddlan are in Denbighshire, Bangor-is-y-Coed is I think in Wrexham (which is now a unitary authority of its own), and there's no detached part of Flintshire any more. I'm going to have to review all the Welsh county articles to see if they make any sense. -- Arwel 10:09, 25 Oct 2003 (UTC)

 * You don't seem to understand the distinctness of the two entities. Both historic Counties and administrative counties are current, that is to say, they both exist at the moment. Post 1996 lieutenency areas are another matter entirely. Let me make this clear: Birmingham has never ceased to be in Warwickshire; in 1974 the historic County of warwickshire did not change, only the administrative county of warwickshire changed, and many a government spokesman has emphasized this. It is therefore misleading and downright false to claim that "Birmingham used to be in the historic County of Warwickshire. It used to be in the administrative county of warwickshire, but this is a different entity.
 * I would suggest moving Flitshire to Flintshire (historic) and creating Flintshire (administrative) to remove any confusion on that matter; in fact, I would suggest doing that for all Counties, it would certainly make things rather easier... 80.255 18:54, 25 Oct 2003 (UTC)

See his article here on wikipedia. -- Cimon Avaro on a pogostick 23:25, Oct 26, 2003 (UTC)

Vandalism (sic.!) in Progress
Perhaps just a misunderstandng, but Birmingham and Harborne_Reserve are not in Warwickshire - please see recent changes); and Warwickshire. Andy Mabbett
 * Now it's looking more like vandalism - can someone please revert Warwickshire to the edit by (18:56, 16 Oct 2003 . . G-Man) Thank you. Andy Mabbett 23:49, 24 Oct 2003 (UTC)
 * see also messages on User talk:Pigsonthewing
 * Wow, I've never heard of a Warwickshire Irredentist before! I see on User talk:80.255 this character was engaged in a long argument about the borders of Kent a few months ago. Don't get too het up at the moment, as it may calm down in a day or two, but if you want to revert an old version yourself, go to "page history", click on the date and time of the version you want, click "edit this page" then save it. -- Arwel 00:18, 25 Oct 2003 (UTC)
 * See further down this page for further evidence when he was editing as User:80.225.73.197. Angela 00:21, Oct 25, 2003 (UTC)
 * See also switching of the order of metric and imperial measurements, on, for example, Warwickshire. Andy Mabbett 21:15, 25 Oct 2003 (UTC)
 * This is because the UK government uses acres, and as per the wikipedia guilines on units, the officially used units should be stated first. 80.255 21:46, 25 Oct 2003 (UTC)
 * Really? In what context? They've been using hectares in agricultural contexts for the better part of 30 years - I know, I used to have to fill in application forms for MAFF and convert our farm map from acres to Hectares! -- Arwel 01:52, 26 Oct 2003 (UTC)
 * I was refering to the boundary comission, who are the relevant authority in this case, not MAFF/DEFRA. 80.255 02:41, 26 Oct 2003 (UTC)
 * The Boundary Commissions are only concerned with electoral constituency boundaries. If you look at their spreadsheet at http://www.statistics.gov.uk/pbc/downloads/2000_Electorates.xls (linked off http://www.statistics.gov.uk/pbc/general_info.asp) you will see that they list counties by their modern boundaries, not this historic county nonsense which you are promoting and which is damaging the reputation of Wikipedia for accuracy. As I think I said elsewhere, it's OK to note the old historic boundaries but it is completely misleading and doing a disservice to the readers to pretend that those boundaries have any contemporary relevance beyond determining the catchment areas of some cricket clubs. -- Arwel 23:23, 26 Oct 2003 (UTC)
 * As I have said many times, historic counties and administrative counties are DIFFERENT ENTITIES. Both exist, both are current. If you do not accept this then you are simply wrong - the government made is clear in 1974, and it continues to make this clear to this day. Historic boundaries are current and relevant boundaries which are quite distinct from administrative boundaries. I really don't see what you difficulty is in grasping this concept - that that town X can be in administrative county Y and historic county Z simultaneuously. Wikipedia should be accurate, of course - and accuracy means stating this fact; it does not mean stating POV rubbish and downright falsehoods about "former counties (sic.!)", "old counties" and "new counties". 80.255 23:46, 26 Oct 2003 (UTC)
 * To call this vandalism is quite ridiculous. I have explained the logic of my changes to User:Pigsonthewing, but he refuses to discuss them, let alone justify his reverts, simply deleting all reference to them. I am therefore unable to discuss this matter with him. I am quite happy to explain the reason for the slight changes in terms to any other, less childish, people, however. I already agreed on the best solution with Morwen, and this discussion took place before. What a pity it is that other people couldn't stick to this compromise, instead of replacing it with information that is misleading at best and downright incorrect at worst. 80.255 01:22, 25 Oct 2003 (UTC)
 * I take his latest on User talk:Pigsonthewing as a threat.Andy Mabbett 01:12, 25 Oct 2003 (UTC)
 * What absurd nonsense, as anyone reading my comments there could tell. I suggested that this matter could be sensibly discussed; User:Pigsonthewing deleted the comment. I then asked User:Pigsonthewing whether he intended to continue childishly deleting comments and refusing to discuss the matter, and suggested that he enter into a sensible discussion rather than childish reversions backed up with no reasoning. Upon his deletion of this I observed that he has obviously chosen the latter option... and now that is a "threat"! I've never heard anything more ridiculous in my life! 80.255 01:22, 25 Oct 2003 (UTC)

Hi :) Take a look at Changing attribution, re User:129.234.4.10 Dysprosia 09:08, 28 Oct 2003 (UTC)

Coventry
Re: Coventry. Technically speaking Coventry (at least the historic walled part of the city) hasn't been a part of Warwickshire since 1451, because king Henry VI granted Coventry a charter which made it a county in it's own right.

A book of mine called "A History of Warwickshire" by local historian Terry Slater, states that:

"In 1345 Edward III granted the town [Coventry] its first Charter of Incorporation, so that henceforth it was governed by a mayor and bailiffs and the influence of the priory came to an end. By the second half of the 15th century the townspeople had freed themselves from both manorial and county jurisdictions and in 1451 this was confirmed when Henry VI granted a Charter which made the city and its environs a county in itself."

I'm not sure whether this is still true or not, but to say that Coventry is a part of historic Warwickshire may not be correct. G-Man 22:21, 30 Oct 2003 (UTC)

 * 1) administrative boundary changes, I expect; however, what do you define as "historic Warwickshire"? Was Coventry subject to being in Warwickshire administratively prior to 1888? I am 100% sure that there is not historic County called coventry! I would imagine what you describe was undone at some point.
 * 2) However, I'll look into the matter and get back to you; by all means put information in the article in the meanwhile.
 * 3) What is considered to be Coventry nowadays certainly spreads beyond the walled portion in any case, and this, whether you are correct or not about the above information, is certainly in Warwickshire. 80.255 01:31, 31 Oct 2003 (UTC)

Eton
... moved to User talk:80.255.

title: User talk:80.255/archive 1


text:
Kouvola

Kouvola is a city in Finland and the administrative capital of Kymenlaakso. It is located in the southeastern interior of the country. The population of Kouvola is approximately 0. It is the most populous municipality in Finland, and the 17th most populous urban area in the country.

Kouvola is located along the Kymijoki River in the region of Kymenlaakso, 62 km kilometers east of Lahti, 87 km west of Lappeenranta and 134 km northeast of the capital, Helsinki. With Kotka, Kouvola is one of the capital centers and is the largest city in the Kymenlaakso region.

The urban area of Kouvola in the city centre itself is home to about 47,000 people. The city covers an area of undefined km2 of which undefined km2 is water. The population density is undefined PD/km2. Kouvola is bordered by the municipalities of Hamina, Heinola, Iitti, Kotka, Lapinjärvi, Loviisa, Luumäki, Miehikkälä, Mäntyharju, Pyhtää and Savitaipale. Kouvola has over 450 lakes and, together with Mäntyharju, the Kouvola area includes the Repovesi National Park.

Kouvola, which had population growth as late as the 1980s, has suffered a loss of migration since the 1990s. Over time, the loss has only deepened, so that at the end of the 2010s Kouvola was Finland's worst migration loss area. Natural demographics have also trended downward; in 2017, more than 450 more people died in the city than new ones were born. The reasons for the emigration are thought to be largely due to job losses in the region.

History
The village of Kouvola has been inhabited since the Middle Ages, and it has belonged alternately to the churches of Hollola, Iitti and Valkeala. However, the actual development did not start until the 1870s when the Riihimäki–Saint Petersburg line was built and Kouvola became a railway junction. Kouvola railroad built Kymin mill founder Axel Wilhelm Wahren railway administration by on application, on the basis of the track engineers decided to recommend the creation of a fifth-end position in a half mile east of the variable alert Otava with acceptance on sandy soil on fabric. In the next decade, the Savonia railway was built from Kouvola to the north and the Kotka line to the south, resulting in Kouvola becoming one of the busiest railway junctions in Finland. Over time, Kouvola developed into an important pulp-producing, paper-milling and printing centre and even had a leading industrial engineering sector.

In 1918, conflict between the Red and White factions raged heavily during the Finnish Civil War. More than 200 people were killed in the area during the fighting.

As a result of the railway, Kouvola was heavily built. In 1922 it was separated from the municipality of Valkeala and gained commercial rights immediately the following year. The city of Kouvola was established in 1960. Kouvola was annexed to Viipuri Province in 1922–1945 but in 1940 and 1944, most of Viipuri County was ceded to the Soviet Union, and the remaining areas were formed into Kymi Province in 1945. Kouvola had also become an administrative center; As the capital of Kymen County, it operated from 1955 until the 1997 county reform.

In January 2009, the six municipalities of Kouvola, Kuusankoski, Elimäki, Anjalankoski, Valkeala and Jaala were consolidated, forming the new municipality of Kouvola. Kouvola has also assumed the slogan Kymijoen kaupunki (the town of Kymijoki) previously used by Anjalankoski.

Culture

 * The name itself derives from Old Finnish kouvo, meaning bear. The arms are Sable, an escarbuncle Or, base wavy Argent.
 * Verla factory, which is a UNESCO World Heritage Site, is located near Kouvola.
 * The newspapers Kouvolan Sanomat and Keskilaakso are published in Kouvola.
 * The third biggest Amusement park in Finland, called Tykkimäki is located in Kouvola.

Province History of Kouvola

 * Viipurin lääni.vaakuna.svg Viipuri Province (1922–1945)
 * Kymen lääni.vaakuna.svg Kymi Province (1945–1997)
 * Etelä-Suomen läänin vaakuna.svg Southern Finland Province (1997–2009)
 * Kymenlaakson maakunnan vaakuna.svg Kymenlaakso (2009–)

Sports
Kouvola is the hometown of the Sudet sports club, which became Finnish champions in bandy six consecutive times, and they have a football team which is playing at the fourth highest level, Kolmonen, despite Sudet being one of the oldest football clubs in Finland. KooKoo is the most successful ice hockey team in Kymenlaakso. It plays in the Finnish top league, SM-liiga. Kouvolan Pallonlyöjät (KPL) is a baseball team based in Kouvola and known for Pesäpallo. KPL was won five Finnish championships and it plays in the Finnish top league, Superpesis. Kouvot is a basketball team based in Kouvola. the team plays in the highest level Korisliiga and has won four Finnish championships.

MyPa is one of the most successful football clubs in Finland and the 1990s was the golden era. MyPa is played 23 seasons in the Finnish top football league Veikkausliiga. MyPa are based in the industrial village of Myllykoski, part of the city of Kouvola. The club became inactive in professional football after having ceased operations in 2015 due to financial difficulties. In 2017, MyPa returned and started again from the fourth highest tier but has quickly risen to the second highest level, Ykkönen, where it is now playing. Kouvola also has a Palomäki Ski Jump Center, very close to the city, where young people and other sports enthusiasts can go to jump on a ski jump.

Climate
Kouvola has humid continental climate (Dfb).The city has four distinct seasons, the amount of precipitation is relatively uniform throughout the year. The driest season is spring. Summers are generally relatively warm as the city is considered to be one of the hottest cities in Finland as it has had the most days with "helle" (temperatures above 25 °C) since 2000. Winters are cold and long, colder than cities located in the coastal areas of Finland because of its location further inland, meaning the marine effect doesn't affect the city as much than those nearer the sea and specially those nearer the southwestern coasts of the Finnish side of Gulf of Finland. This also means that the summers are warmer due to it being further inland as the sea effect is making the summer temperatures slightly cooler in coastal areas. The average annual temperature is 5.4 C. The highest ever recorded temperature in the station was 34.5 C, on July 28, 2010. The lowest ever recorded was -37.3 C. The city has a significant rainfall throughout the year and even in the driest month the precipitation stays over 30 mm a month. The average duration of sunshine per year is 1,658 hours. Kouvola Utti airport weather station has on average somewhat lower average temperatures than in the city.

Population
The city of Kouvola has 0 inhabitants, making it the most populous municipality in Finland. In Kouvola, 5.4% of the population has a foreign background, which is below to the national average.

Languages
Kouvola is a monolingual Finnish-speaking municipality. There are 0 Swedish speakers in Kouvola, or NaN% of the population. As English and Swedish are compulsory school subjects, functional bilingualism or trilingualism acquired through language studies is not uncommon.

At least 40 different languages are spoken in Kouvola. The most commonly spoken foreign languages are Russian (1.9%), Estonian (0.5%), Arabic (0.3%) and Ukrainian (0.2%).

Immigration
, there were 4,221 persons with a migrant background living in Kouvola, or 5.4% of the population. The number of residents who were born abroad was 4,112, or 5.2% of the population. The number of persons with foreign citizenship living in Kouvola was 2,609. Most foreign-born citizens came from the former Soviet Union, Estonia, Russia and Sweden.

The relative share of immigrants in Kouvola's population is below to the national average. However, the city's new residents are increasingly of foreign origin. This will increase the proportion of foreign residents in the coming years.

Religion
In 2023, the Evangelical Lutheran Church was the largest religious group with 69.2% of the population of Kouvola. Other religious groups accounted for 2.0% of the population. 28.8% of the population had no religious affiliation.

Twin towns and sister cities
Kouvola is twinned with:
 * Balatonfüred, Coa Hungary County Veszprém.svg Veszprém County, 🇭🇺 Hungary
 * Vologda, Coat of arms of Vologda oblast.svg Vologda Oblast, 🇷🇺 Russia
 * Mülheim an der Ruhr, Coat of arms of North Rhine-Westfalia.svg North Rhine-Westphalia, 🇩🇪 Germany

Regionalization
Jaala is only one does not form its own regional committee, but is part of the Kuusankoski regional committee.

Notable people

 * Atso Askonen (Former ice hockey player)
 * Arto Bryggare (Former hurdling athlete)
 * Timo Susi (Former ice hockey player)
 * Jarkko A. Immonen (Current ice hockey player)
 * Jari Lindström (Finnish politician)
 * Kaarle Viikate (Finnish musician and metal band Founder of the Viikate)
 * Juhani Aaltonen (Jazz saxophonist and flautist)
 * Roope Tonteri (Finnish snowboarder)
 * Hannu Salama (Finnish author)
 * Ari Koivunen (Heavy metal singer)
 * Ville Nousiainen (cross-country skier)
 * Toni Gardemeister (Professional rally driver)
 * Niilo Halonen (Former ski jumper)
 * Timo Lahti (Speedway rider)
 * Aleksanteri Hakaniemi (singer and YouTuber)

title: Kouvola


text:
Caroline Quentin

Caroline Quentin (born Caroline Amanda Jane Jones; 11 July 1960) is an English actress, broadcaster and television presenter. Quentin became known for her television appearances: portraying Dorothy in Men Behaving Badly (1992–1998), Maddie Magellan in Jonathan Creek (1997–2000), Kate Salinger in Kiss Me Kate and DCI Janine Lewis in Blue Murder (2003–2009).

Early life
Quentin was born in Reigate, Surrey, to Kathleen Jones and her husband Fred, a Royal Air Force pilot. She has three older sisters. She was educated at the independent Arts Educational School, in Tring, Hertfordshire, and appeared locally in the Pendley Open Air Shakespeare Festival.

Television
One of her earliest roles was in the Channel 4 comedy drama Hollywood Hits Chiswick, alongside Derek Newark as W.C. Fields.

Between 1992 and 1998, Quentin appeared as Dorothy in all 42 episodes of the sitcom Men Behaving Badly. From 1997 until 2000, Quentin starred alongside Alan Davies in Jonathan Creek playing investigative journalist Maddie Magellan, who uses Jonathan's mind to solve murder mysteries. In 1998 she starred in the first sitcom that was specifically built around her: Kiss Me Kate; that year she started the major role of Maggie Mee in the drama Life Begins, which returned for a third series in 2006. Quentin appeared in the television film Hot Money (2001), which was based on the true story of the theft of hundreds of thousands of pounds from the Bank of England.

ITV has produced five series of the police drama Blue Murder, in which Quentin plays against type in the main role DCI Janine Lewis. The pilot aired in the UK on 18 May 2003.

Quentin has appeared in Whose Line Is It Anyway?; in a pre-Men Behaving Badly role as a traffic warden in the Mr. Bean episode "The Trouble with Mr. Bean" in 1991; Room 101; Have I Got News for You; and the 2009–10 BBC comedy series Life of Riley, a sitcom about a dysfunctional blended family; and in the BBC Radio 4 improvisational comedy series The Masterson Inheritance, the Radio 4 comedy Any Bloke (starred with Jim Sweeney who was also in The Masterson Inheritance) and the popular BBC Radio 2 sitcom On the Blog. She appeared as Heather Babcock in an episode of Agatha Christie's Miss Marple, The Mirror Crack'd from Side to Side, in 2010. Also in 2010 she started appearing, as a 1970's standard lamp, in Marks & Spencer's revamped food range advertisements.

In March 2011, a documentary entitled Caroline Quentin: A Passage Through India aired on ITV in the UK. The documentary followed Quentin as she traveled from the North of India to the South. Quentin presented Restoration Home on BBC Two. The programme looks into the history and families of the UK's derelict mansion houses which are being restored by their private owners. In 2012, Quentin began working on another documentary series, Cornwall with Caroline Quentin, which shows her travelling across Cornwall, for which she received some criticism due to apparently aiming the show at potential second home owners. She returned to present a second series of the show in 2013. In 2013, she hosted another documentary series, Caroline Quentin’s National Parks for one series. Quentin starred in the Comedy Central series Big Bad World where she played the role of Jan, the mother of the main character Ben (Blake Harrison).

In 2015, she played the role of Angela Sim in an episode of Doc Martin. She played the role of Mrs Bumble in Dickensian (2015–2016). In November 2016, she guest presented an episode of The One Show.

Starting in 2017, Quentin was co-presenter of the BBC Two programme The World's Most Extraordinary Homes with architect Piers Taylor; 12 episodes were completed and aired. Subsequently, the series streamed on Netflix.

In 2020, Quentin participated in the eighteenth series of Strictly Come Dancing. She was partnered with Johannes Radebe. Quentin became the fourth celebrity to be voted off on 22 November 2020. Quentin later commented,"I have had the honour and privilege of working with some of the greatest dancers this country has ever known I mean I really believe it, I think they are absolutely fantastic."

In May 2023 Quentin was featured in the BBC coverage of the Chelsea Flower Show, showing viewers around the garden of her home near Tiverton, Devon.

Theatre
Her early stage work had also included appearing in the chorus of the original English production of the musical Les Misérables in 1985.

In 2019 she played Lady Fancyfull in the Royal Shakespeare Company production of The Provoked Wife. In 2022 she played Mrs Malaprop in the Royal National Theatre's production of Jack Absolute Flies Again, earning her a Laurence Olivier nomination for Best Actress in a Supporting Role.

In 2023 she played elder Emma Hamilton and Mrs Cadogan in Jermyn Street Theatre’s world premier production of Infamous by April de Angelis.

Music
In July 1996, Quentin released a single, a cover of the Exciters' hit "Tell Him", with her Men Behaving Badly co-star Leslie Ash under the name of "Quentin and Ash". The single spent 3 weeks in the UK Singles Chart, reaching number 25.

Recognition
Quentin received an Ian Charleson Award commendation for her Masha in The Seagull at the Oxford Theatre Company in 1991.

At the British Comedy Awards in 2004, Quentin won the "Best Comedy Actress" award for her performance in Von Trapped

Book
In 2023, it was announced that Quentin had written a gardening book, titled "Drawn to the Garden", about her own experience in running a vegetable and flower garden at her home on Devon, which she began sharing on Instagram during the COVID-19 lockdown. Included throughout the book is various watercolours and sketches by Quentin. It will be released 15 February 2024.

Personal life
Quentin was married to comedian Paul Merton from 1990 until their 1998 divorce. Quentin met Sam Farmer in 1998 on the set of Men Behaving Badly, where he was a runner. The couple have two children, Emily Rose and William. Her daughter Rose is also an actress, and has appeared alongside her mother. In 2006, she married Farmer in Tiverton, Devon. They lived briefly in Morebath Manor near the village of Morebath, Devon, close to Tiverton, before moving to a smaller derelict farm nearby, which they renovated. Before moving to Devon, the couple lived at Walberswick, Suffolk.

Quentin has coeliac disease and is the patron of Coeliac UK. She is also president of the charity Campaign for National Parks.

title: Caroline Quentin


text:
User:Davodd

I agree to multi-license all my contributions, with the exception of my user pages, as described below:

title: User:Davodd


text:
Adamstown, Pitcairn Islands

Adamstown is the capital of the Pitcairn Islands, and the only settlement on the Pitcairn Islands, the only British Overseas Territory that is located in the southern Pacific Ocean.

As of January 2020, Adamstown has a population of 47, which is the entire population of the Pitcairn Islands. All the other islands in the group are uninhabited. Adamstown is where most residents live, while they grow food in other areas of the island.

Adamstown is the third smallest capital in the world by population. It has access to television, satellite Internet, and a telephone; however, the main means of communication remains ham radio. The "Hill of Difficulty" connects the island's jetty to the town.

History
The history of the Pitcairn Islands begins with the settlement of the islands by Polynesians in the 11th century. The Polynesians established a culture that flourished for four centuries and then vanished. Pitcairn was settled again in 1790 by a group of British mutineers on HMS Bounty and Tahitians. Adamstown is named for the last surviving mutineer, John Adams.

Geography
The settlement is located on the central-north side of the island of Pitcairn, facing the Pacific Ocean and close to the Bounty Bay, the only seaport of the island.

Climate
Adamstown has a tropical rainforest climate (Af) under the Köppen climate classification system. The hamlet features a wet, very warm climate averaging 60.74 in of rain a year. The wettest month is December and temperatures do not vary significantly throughout the year.

Government
The Present Committee on Geographic Names stated that Auckland, New Zealand is the administrative centre for these islands because the Governor of Pitcairn, the British High Commissioner to New Zealand, is based in Auckland. However the same cited document describes Adamstown as the capital of the BOT on the following page.

Personalities

 * Ned Young (1762–1800)
 * Fletcher Christian (1764–1793)
 * John Adams (1768–1829)
 * Joshua Hill (1773–1844?)
 * Thursday October Christian (1790–1831)
 * Steve Christian (b. 1951)
 * Brenda Christian (b. 1953)
 * Meralda Warren (b. 1959)

Religion

 * Adamstown Church

title: Adamstown, Pitcairn Islands


text:
Baraqiel

Baraqiel (Imperial Aramaic: 𐡁𐡓𐡒𐡀𐡋; Aramaic: ברקאל; Βαρακιήλ, Βαρακήλ), commonly spelt Baraqiel, was the 9th watcher of the 20 leaders of the 200 fallen angels that are mentioned in an ancient work called the Book of Enoch. The name means "lightning of God", which is fitting since it has been said that Baraqiel taught men astrology during the days of Jared or Yered.

It has also been proposed based on a reconstruction by Schniedewind and Zuckerman that Baraqiel was the name of the father of Hazael, mentioned in the 9th century BCE inscription from Tel Dan. The biblical figure, Barak, known from Judges 4 is a shortened version of this longer name.

title: Baraqiel


text:
Birational geometry

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

Rational maps
A rational map from one variety (understood to be irreducible) $$X$$ to another variety $$Y$$, written as a dashed arrow X ⇢Y, is defined as a morphism from a nonempty open subset $$U \subset X$$ to $$Y$$. By definition of the Zariski topology used in algebraic geometry, a nonempty open subset $$U$$ is always dense in $$X$$, in fact the complement of a lower-dimensional subset. Concretely, a rational map can be written in coordinates using rational functions.

Birational maps
A birational map from X to Y is a rational map f : X ⇢ Y such that there is a rational map Y ⇢ X inverse to f. A birational map induces an isomorphism from a nonempty open subset of X to a nonempty open subset of Y, and vice versa: an isomorphism between nonempty open subsets of X, Y by definition gives a birational map f : X ⇢ Y. In this case, X and Y are said to be birational, or birationally equivalent. In algebraic terms, two varieties over a field k are birational if and only if their function fields are isomorphic as extension fields of k.

A special case is a birational morphism f : X → Y, meaning a morphism which is birational. That is, f is defined everywhere, but its inverse may not be. Typically, this happens because a birational morphism contracts some subvarieties of X to points in Y.

Birational equivalence and rationality
A variety X is said to be rational if it is birational to affine space (or equivalently, to projective space) of some dimension. Rationality is a very natural property: it means that X minus some lower-dimensional subset can be identified with affine space minus some lower-dimensional subset.

Birational equivalence of a plane conic
For example, the circle $$X$$ with equation $$x^2 + y^2 - 1 = 0$$ in the affine plane is a rational curve, because there is a rational map f : $\mathbb{A}^1$ ⇢ X given by
 * $$f(t) = \left( \frac{2t}{1+t^2}, \frac{1 - t^2}{1 + t^2}\right),$$

which has a rational inverse g: X ⇢ $$\mathbb{A}^1$$ given by
 * $$g(x,y) = \frac{1-y}{x}.$$

Applying the map f with t a rational number gives a systematic construction of Pythagorean triples.

The rational map $$f$$ is not defined on the locus where $$1 + t^2 = 0$$. So, on the complex affine line $$\mathbb{A}^1_{\Complex}$$, $$f$$ is a morphism on the open subset $$U = \mathbb{A}^1_{\Complex}-\{i, -i\}$$, $$f: U \to X$$. Likewise, the rational map g : X ⇢ $\mathbb{A}^1$ is not defined at the point (0,−1) in $$X$$.

Birational equivalence of smooth quadrics and Pn
More generally, a smooth quadric (degree 2) hypersurface X of any dimension n is rational, by stereographic projection. (For X a quadric over a field k, X must be assumed to have a k-rational point; this is automatic if k is algebraically closed.) To define stereographic projection, let p be a point in X. Then a birational map from X to the projective space $$\mathbb{P}^n$$ of lines through p is given by sending a point q in X to the line through p and q. This is a birational equivalence but not an isomorphism of varieties, because it fails to be defined where q = p (and the inverse map fails to be defined at those lines through p which are contained in X).

Birational equivalence of quadric surface
The Segre embedding gives an embedding $$\mathbb{P}^1\times\mathbb{P}^1 \to \mathbb{P}^3$$ given by
 * $$([x,y],[z,w]) \mapsto [xz,xw,yz,yw].$$

The image is the quadric surface $$x_0x_3=x_1x_2$$ in $$\mathbb{P}^3$$. That gives another proof that this quadric surface is rational, since $$\mathbb{P}^1\times\mathbb{P}^1$$ is obviously rational, having an open subset isomorphic to $$\mathbb{A}^2$$.

Minimal models and resolution of singularities
Every algebraic variety is birational to a projective variety (Chow's lemma). So, for the purposes of birational classification, it is enough to work only with projective varieties, and this is usually the most convenient setting.

Much deeper is Hironaka's 1964 theorem on resolution of singularities: over a field of characteristic 0 (such as the complex numbers), every variety is birational to a smooth projective variety. Given that, it is enough to classify smooth projective varieties up to birational equivalence.

In dimension 1, if two smooth projective curves are birational, then they are isomorphic. But that fails in dimension at least 2, by the blowing up construction. By blowing up, every smooth projective variety of dimension at least 2 is birational to infinitely many "bigger" varieties, for example with bigger Betti numbers.

This leads to the idea of minimal models: is there a unique simplest variety in each birational equivalence class? The modern definition is that a projective variety X is minimal if the canonical line bundle KX has nonnegative degree on every curve in X; in other words, KX is nef. It is easy to check that blown-up varieties are never minimal.

This notion works perfectly for algebraic surfaces (varieties of dimension 2). In modern terms, one central result of the Italian school of algebraic geometry from 1890–1910, part of the classification of surfaces, is that every surface X is birational either to a product $$\mathbb{P}^1\times C$$ for some curve C or to a minimal surface Y. The two cases are mutually exclusive, and Y is unique if it exists. When Y exists, it is called the minimal model of X.

Birational invariants
At first, it is not clear how to show that there are any algebraic varieties which are not rational. In order to prove this, some birational invariants of algebraic varieties are needed. A birational invariant is any kind of number, ring, etc which is the same, or isomorphic, for all varieties that are birationally equivalent.

Plurigenera
One useful set of birational invariants are the plurigenera. The canonical bundle of a smooth variety X of dimension n means the line bundle of n-forms KX = Ωn, which is the nth exterior power of the cotangent bundle of X. For an integer d, the dth tensor power of KX is again a line bundle. For d ≥ 0, the vector space of global sections H0(X, KXd) has the remarkable property that a birational map f : X ⇢ Y between smooth projective varieties induces an isomorphism H0(X, KXd) ≅ H0(Y, KYd).

For d ≥ 0, define the dth plurigenus Pd as the dimension of the vector space H0(X, KXd); then the plurigenera are birational invariants for smooth projective varieties. In particular, if any plurigenus Pd with d > 0 is not zero, then X is not rational.

Kodaira dimension
A fundamental birational invariant is the Kodaira dimension, which measures the growth of the plurigenera Pd as d goes to infinity. The Kodaira dimension divides all varieties of dimension n into n + 2 types, with Kodaira dimension −∞, 0, 1, ..., or n. This is a measure of the complexity of a variety, with projective space having Kodaira dimension −∞. The most complicated varieties are those with Kodaira dimension equal to their dimension n, called varieties of general type.

Summands of ⊗kΩ1 and some Hodge numbers
More generally, for any natural summand

 * $$E(\Omega^1) = \bigotimes^k \Omega^1$$

of the r-th tensor power of the cotangent bundle Ω1 with r ≥ 0, the vector space of global sections H0(X, E(Ω1)) is a birational invariant for smooth projective varieties. In particular, the Hodge numbers

 * $$h^{p,0} = H^0(X,\Omega^p)$$

are birational invariants of X. (Most other Hodge numbers hp,q are not birational invariants, as shown by blowing up.)

Fundamental group of smooth projective varieties
The fundamental group π1(X) is a birational invariant for smooth complex projective varieties.

The "Weak factorization theorem", proved by Abramovich, Karu, Matsuki, and Włodarczyk (2002), says that any birational map between two smooth complex projective varieties can be decomposed into finitely many blow-ups or blow-downs of smooth subvarieties. This is important to know, but it can still be very hard to determine whether two smooth projective varieties are birational.

Minimal models in higher dimensions
A projective variety X is called minimal if the canonical bundle KX is nef. For X of dimension 2, it is enough to consider smooth varieties in this definition. In dimensions at least 3, minimal varieties must be allowed to have certain mild singularities, for which KX is still well-behaved; these are called terminal singularities.

That being said, the minimal model conjecture would imply that every variety X is either covered by rational curves or birational to a minimal variety Y. When it exists, Y is called a minimal model of X.

Minimal models are not unique in dimensions at least 3, but any two minimal varieties which are birational are very close. For example, they are isomorphic outside subsets of codimension at least 2, and more precisely they are related by a sequence of flops. So the minimal model conjecture would give strong information about the birational classification of algebraic varieties.

The conjecture was proved in dimension 3 by Mori. There has been great progress in higher dimensions, although the general problem remains open. In particular, Birkar, Cascini, Hacon, and McKernan (2010) proved that every variety of general type over a field of characteristic zero has a minimal model.

Uniruled varieties
A variety is called uniruled if it is covered by rational curves. A uniruled variety does not have a minimal model, but there is a good substitute: Birkar, Cascini, Hacon, and McKernan showed that every uniruled variety over a field of characteristic zero is birational to a Fano fiber space. This leads to the problem of the birational classification of Fano fiber spaces and (as the most interesting special case) Fano varieties. By definition, a projective variety X is Fano if the anticanonical bundle $$K_X^*$$ is ample. Fano varieties can be considered the algebraic varieties which are most similar to projective space.

In dimension 2, every Fano variety (known as a Del Pezzo surface) over an algebraically closed field is rational. A major discovery in the 1970s was that starting in dimension 3, there are many Fano varieties which are not rational. In particular, smooth cubic 3-folds are not rational by Clemens–Griffiths (1972), and smooth quartic 3-folds are not rational by Iskovskikh–Manin (1971). Nonetheless, the problem of determining exactly which Fano varieties are rational is far from solved. For example, it is not known whether there is any smooth cubic hypersurface in $$\mathbb{P}^{n+1}$$ with n ≥ 4 which is not rational.

Birational automorphism groups
Algebraic varieties differ widely in how many birational automorphisms they have. Every variety of general type is extremely rigid, in the sense that its birational automorphism group is finite. At the other extreme, the birational automorphism group of projective space $$\mathbb{P}^n$$ over a field k, known as the Cremona group Crn(k), is large (in a sense, infinite-dimensional) for n ≥ 2. For n = 2, the complex Cremona group $$Cr_2(\Complex)$$ is generated by the "quadratic transformation"

 * [x,y,z] ↦ [1/x, 1/y, 1/z]

together with the group $$PGL(3,\Complex)$$ of automorphisms of $$\mathbb{P}^2,$$ by Max Noether and Castelnuovo. By contrast, the Cremona group in dimensions n ≥ 3 is very much a mystery: no explicit set of generators is known.

Iskovskikh–Manin (1971) showed that the birational automorphism group of a smooth quartic 3-fold is equal to its automorphism group, which is finite. In this sense, quartic 3-folds are far from being rational, since the birational automorphism group of a rational variety is enormous. This phenomenon of "birational rigidity" has since been discovered in many other Fano fiber spaces.

Applications
Birational geometry has found applications in other areas of geometry, but especially in traditional problems in algebraic geometry.

Famously the minimal model program was used to construct moduli spaces of varieties of general type by János Kollár and Nicholas Shepherd-Barron, now known as KSB moduli spaces.

Birational geometry has recently found important applications in the study of K-stability of Fano varieties through general existence results for Kähler–Einstein metrics, in the development of explicit invariants of Fano varieties to test K-stability by computing on birational models, and in the construction of moduli spaces of Fano varieties. Important results in birational geometry such as Birkar's proof of boundedness of Fano varieties have been used to prove existence results for moduli spaces.

title: Birational geometry