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Talk:Overview of gun laws by nation

RfC for last sentence in lead
Should the last sentence in the lead ", appended to the lead in July 2019 stay in the lead? or in the article at all anywhere? (this is currently the only place in the article where that information is mentioned) --- Avatar317 (talk) 05:42, 28 September 2019 (UTC) 21:48, 3 September 2019 (UTC)

Please read the lead before answering.

 * No - As I said on my previous edits and multiple other editors have also stated, it is not relevant to THIS article. (It IS relevent to the Gun control article and is already present in that article.) --- Avatar317 (talk) 21:48, 3 September 2019 (UTC)
 * No - I don't think we should go down that rabbit hole in this article. Frankly, the lede itself could use some heavy trimming as it continues to stick one foot into the gun control article. May His Shadow Fall Upon You     Talk  18:20, 4 September 2019 (UTC)
 * No - let's keep the politics out of this article. People are likely to come here seeking information. Let them have it without the clutter. Adoring nanny (talk) 23:10, 8 September 2019 (UTC)
 * Yes Definitely. This is a discussion about the effects of these laws. Doc James  (talk · contribs · email) 12:31, 10 September 2019 (UTC)
 * THIS article is not a discussion of the effects of the laws, nor does it provide justification(s) for the laws; it is merely a listing and description of what laws exist. --- Avatar317 (talk) 23:11, 10 September 2019 (UTC)
 * And this is one sentence on the effects of these laws based on recent reviews of the topic in major journals. It is within topic. Should it also be in other places? Maybe. Doc James  (talk · contribs · email) 23:25, 10 September 2019 (UTC)
 * So what you are saying is that we should BROADEN THE SCOPE of this article to also include the EFFECTS of gun laws? (which this article did not include until you added this disputed sentence)  Should we also include the ~50 studies listed in the Gun control article in this one, and thereby duplicate ~60% of that article into this one? --- Avatar317 (talk) 03:56, 12 September 2019 (UTC)
 * A one sentence overview of the effects of gun laws based on the best avaliable sources is perfectly appropriate. Doc James  (talk · contribs · email) 04:38, 14 September 2019 (UTC)

 * yes agree w/ Doc James--Ozzie10aaaa (talk) 12:55, 10 September 2019 (UTC)
 * Yes (coming over from WT:MED) it seems that the coverage is WP:DUE based on sources cited, but the tone should clearly represent reliable sources for the statement made. Bears directly on the article topic. Just because a topic is politically charged doesn't mean it's off-limits, we just need to care for NPOV. — soupvector (talk) 14:49, 10 September 2019 (UTC)
 * Yes Central to the topic obviously. Roxy, the dog . wooF 14:55, 10 September 2019 (UTC)
 * Yes In an article examining the differences in gun control laws by nation, a fact related to the difference in effect of those gun laws in different nations is surely on-topic. As long as the fact is reliably sourced, WP:NPOV requires "representing fairly, proportionately, and, as far as possible, without editorial bias, all of the significant views that have been published". I'm not sure it's in quite the right place, but it surely belongs in the overview (which is what the lead serves as in these sort of articles). --RexxS (talk) 23:08, 10 September 2019 (UTC)
 * Yes, per Doc James and the other WP:Med editors. Flyer22 Reborn (talk) 02:58, 11 September 2019 (UTC)
 * No I thought this was so self-evident that I deleted just now - without first checking here - opps. My thoughts are in line with User:Avatar317. This is an article on what the laws are, none of the content refers to the effect of these, nor should it. It is reasonable to make some general note of the intent of the laws, but any comment on the effect should go as a WL to a fuller article. -Snori (talk) 07:24, 11 September 2019 (UTC)
 * I though it was so self-evidently relevant to the topic that I restored it. This article is an overview and discusses divers aspects of gun laws by nation, such as their effects on the levels of gun ownership from one jurisdiction to another and the procedures that have to be followed to obtain a gun licence in different countries. An examination of the correlation of gun laws with homicide rates is just as relevant to any overview. --RexxS (talk) 12:31, 11 September 2019 (UTC)
 * Comment: Is it really only 10 countries?--Jack Upland (talk) 08:06, 11 September 2019 (UTC)
 * The content of our article covers many more, but of the two research papers on the effects, the second covers just 10 countries - and the first is US-only. - Snori (talk) 20:59, 11 September 2019 (UTC)
 * When research is done, it is quite usual to take a sample of a population for which data is available. Statistical techniques are then used to estimate the accuracy of the conclusions drawn from the sample when extrapolated to the population as a whole. There are 195 counties in the world and it is not surprising that not all of them would be covered by research. It's worth noting that the systematic review 26905895 states its methodology clearly: it found 5,039 studies of which 130 studies, representing 10 countries, eventually met its inclusion and exclusion criteria. This is a high quality review with unimpeachable methodology, and there's no point in Wikipedia editors trying to offer amateur criticism of it. If you wish to challenge its conclusions or its applicability, you need to be bringing to the table equally respectable sources that reach an opposing conclusion or that offer meaningful criticism of the methodology. So far I've seen no evidence of either. --RexxS (talk) 22:24, 11 September 2019 (UTC)
 * I have no criticism of either study, just clarifying. -Snori (talk) 22:31, 11 September 2019 (UTC)
 * Well, I'm sorry, but I have a problem with presenting a worldwide view based on a survey of only 10 countries. The countries are: the US, Canada, Australia, New Zealand, South Africa, Switzerland, Austria, Norway, Brazil, and Colombia. This sample is heavily weighted to English-speaking countries, and includes no Asian countries.--Jack Upland (talk) 23:42, 14 September 2019 (UTC)
 * I'm sorry you have a problem, but it should come as no surprise that the English Wikipedia relies heavily on sources in English. The solution is to find other review articles that survey the languages and countries you're interested in. In the meantime, your objection to a source based only your personal view of its methodology carries no weight. --RexxS (talk) 01:16, 15 September 2019 (UTC)
 * No: In a article taking a global view of a topic, a survey of only 10 countries is not significant.--Jack Upland (talk) 23:26, 14 September 2019 (UTC)
 * Ah they did a systematic review meaning that they found all the studies that were present... Doc James  (talk · contribs · email) 06:36, 19 September 2019 (UTC)
 * OK, but so what? There's not enough evidence to make a global statement. Whereof you do not know, thereof you must be silent.--Jack Upland (talk) 09:00, 19 September 2019 (UTC)
 * Nonsense. We report what the sources say, not make amateur analyses of them. The quality of the source is more than good enough to support the conclusion that "stronger laws regulating firearms are associated with decreased firearm homicide rates". Find equally good sources that reach a different conclusion if you want to argue the issue. --RexxS (talk) 18:07, 19 September 2019 (UTC)
 * In most areas we present a world view based on evidence from one or two country. That fact that we have evidence from 10 countries is fairly impressive. Doc James  (talk · contribs · email) 23:59, 19 September 2019 (UTC)
 * Per study: "Laws restricting the purchase of (e.g., background checks) and access to (e.g., safer storage) firearms are also associated with lower rates of intimate partner homicides and firearm unintentional deaths in children, respectively." Keyword: INTIMATE. It does not find a lower rate of firearm homicides in general but only a specific subset of those deaths. It is wrongly generalized to lower firearm homicides in general. Abatementyogin (talk) 22:47, 25 September 2019 (UTC)
 * Did you miss what the study said in the previous sentence? The study, viewable at 26905895 clearly states "... the simultaneous implementation of laws targeting multiple firearms restrictions is associated with reductions in firearm deaths". That is a lower rate of firearms deaths in general. The specific restriction on purchasing is the one associated with lower rates of intimate partner homicides. Legislating safer storage of firearms is associated with lower rates of firearm unintentional deaths in children. Your misreading of the source leads to your incorrect conclusions. --RexxS (talk) 23:47, 25 September 2019 (UTC)
 * For the last time, the vast majority of firearm deaths are suicides, not homicides. The study found a reduction in firearm suicides which constitute the vast majority of gun deaths. Hence why there there was a decline for overall gun deaths. The only category for firearm homicide that declined were intimate partner homicides which are a small subset of homicides. The vast majority of homicide victims are male and are not domestic-related.Abatementyogin (talk) 21:39, 29 November 2019 (UTC)

 * Comment: If the statement is kept in this article, it needs to be modified because it is not properly supported by the sources.
 * The 2017 Lee et al study studied the US only to find an association with stricter laws and reduced firearm homicides.
 * The 2016 Santaella-Tenorio et al study covered 10 countries, but found no correlation with *overall* firearm homicide reduction, only reduction of deaths, and reduction of firearm homicides for the special class of intimate partner homicides. It is misleading and false to lump these two studies together to attempt to support the statement as it stands now. --- Avatar317 (talk) 02:48, 27 September 2019 (UTC)
 * Then perhaps you think it should read "A 2016 systematic review of 130 studies in 10 countries found that stronger laws regulating firearms are associated with reductions in firearm-related deaths, including suicides,(Santaella-Tenorio) and a 2017 systematic review found that in the US stronger firearm laws are associated with reductions in firearm homicide rates.(Lee)" It would not be difficult to write a more detailed summary of the sources after the conclusion of this RfC. --RexxS (talk) 12:54, 27 September 2019 (UTC)
 * If the RfC decides that it is relevant, yes, I would be happy with your statement; it fairly and accurately summarizes the sources. --- Avatar317 (talk) 22:50, 27 September 2019 (UTC)
 * Then perhaps you think it should read "A 2016 systematic review of 130 studies in 10 countries found that stronger laws regulating firearms are associated with reductions in firearm-related deaths, including suicides,(Santaella-Tenorio) and a 2017 systematic review found that in the US stronger firearm laws are associated with reductions in firearm homicide rates.(Lee)" It would not be difficult to write a more detailed summary of the sources after the conclusion of this RfC. --RexxS (talk) 12:54, 27 September 2019 (UTC)
 * If the RfC decides that it is relevant, yes, I would be happy with your statement; it fairly and accurately summarizes the sources. --- Avatar317 (talk) 22:50, 27 September 2019 (UTC)
 * If the RfC decides that it is relevant, yes, I would be happy with your statement; it fairly and accurately summarizes the sources. --- Avatar317 (talk) 22:50, 27 September 2019 (UTC)

 * No This article is clearly simply a summary of gun control laws in different nations, not an article about the effects of said laws. And even if it was, the statement in question wouldn't belong just tacked onto the end of the lede. Tchouppy (talk) 17:25, 14 October 2019 (UTC)

 * Just curious, as a relative newbie, about this RFC closure - does it fit the recommended pattern? This seemed somewhat contentious, and the closing editor was involved. Also, I didn't think that the basis of resolution was counting !votes. Not stirring the pot, just trying to learn. — soupvector (talk) 05:18, 30 October 2019 (UTC)
 * I understand that consensus is not a vote; but most closures I've seen note the number of opinions on each side. Do you disagree with my closing statement?  Or think it is not correct or accurate?

 * I closed it because it seemed that we were not getting any new comments after two rounds on the bot that invites uninvolved editors in. Do you think it should remain permanently open? The discussion seemed to have reached a natural (and impasseble) end.  --- Avatar317 (talk) 21:41, 30 October 2019 (UTC)

Uruguay
The cited source, "Decreto N° 377/016", was abolished by the new "Decreto N° 345/020" in accordance with article 53 (https://www.impo.com.uy/bases/decretos/345-2020). Also, I feel that the table should display the following clarifications

1 under "Semi-automatic rifles" column: limited to .22 caliber. 2 under "Handguns" column: limited to 9mm caliber in pistols and .45 caliber in revolvers.

Unfortunately, it seems I'm not able to change the sheet myself.

Maryland following "Moore"?
In the "Comparison" section, South Sudan, Yemen, and 39 states are shown in blue—meaning that they require a permit to purchase a handgun.

Recently, though. The 4th Circuit Court of Appeals ruled in Maryland Shall Issue v. Moore that the state's permit to purchase law is unconstitutional. (Although her 7-day waiting period and state-police, background check laws remain in effect.)

Ought Maryland to be changed from green to blue on the bottom map? 00:57, 22 November 2023 (UTC) Pine (talk) 00:57, 22 November 2023 (UTC)

GunPolicy.org Sources
As of January 6, 2024, the GunPolicy.org website is no longer active. Going to it now redirects to a login page with the message, "This site has closed due to a lack of funding." Therefore, all of the citations linking to pages on that site should be re-edited to include Internet Archive and/or ghostarchive links. 73.222.50.208 (talk) 22:09, 6 January 2024 (UTC)

Table discrepancies
Hi,

Just noticed some inconsistencies in the colouring and the language of the comparison table, namely:

Az, Ar, Cr, Kz, Kg, Tj, Uk, Uy should be light green in the "good reason" column as they don't require a good reason for some guns, but not others (similar to how New Zealand is labeled now).

Also, in the "Personal Protection" column, the difference between "justification" and "proof of threat to life" is minimal, shouldn't it be a note under "justification"?

The Philippines' colouring scheme is out of whack in "Personal Protection", "long guns", and "hand guns", it should be yellow for "may issue".

For the USA, shouldn't the constitutionally protected sections ("Good Reason", "Personal Protection", and "Concealed Carry") be blue? As well, shouldn't "Open Carry" be blue as most states are permitless? "Fully Automatic" is also shall-issue as far as I'm aware, it just requires a tax-stamp and registration, however there is still the import ban.

Another things, maybe for the max-penalty column, dark red boxes should have white text for visibility?

Thanks. 2A02:2488:321B:A900:2B84:8705:3395:790D (talk) 08:46, 5 May 2024 (UTC)

Expand Israel Category
There has been a push to loosen gun control in Israel following the 7 October attack. I am unsure of the specific details, but if legislation was passed regarding gun control in Israel following 7 October, this article should be updated to reflect that. Thank you JohnR1Roberts (talk) 00:55, 27 May 2024 (UTC)

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

title: Talk:Overview of gun laws by nation


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Shock site

A shock site is a website that is intended to be offensive or disturbing to its viewers, though it can also contain elements of humor or evoke (in some viewers) sexual arousal. Shock-oriented websites generally contain material that is pornographic, scatological, racist, antisemitic, sexist, graphically violent, insulting, vulgar, profane, or otherwise of some other provocative nature. Websites that are primarily fixated on real death and graphic violence are particularly referred to as gore sites. Some shock sites display a single picture, animation, video clip or small gallery, and are circulated via email or disguised in posts to discussion sites as a prank. Steven Jones distinguishes these sites from those that collect galleries where users search for shocking content, such as Rotten.com. Gallery sites can contain beheadings, execution, electrocution, suicide, murder, stoning, torching, police brutality, hangings, terrorism, cartel violence, drowning, vehicular accidents, war victims, rape, necrophilia, genital mutilation and other sexual crimes.

Some shock sites have also gained their own subcultures and have become internet memes on their own. Goatse.cx featured a page devoted to fan-submitted artwork and tributes to the site's, and a parody of the image was unwittingly shown by a BBC newscast as an alternative for the then-recently unveiled logo for the 2012 Summer Olympics. A 2007 shock video known as 2 Girls 1 Cup also quickly became an Internet phenomenon, with videos of reactions, homages, and parodies widely posted on video sharing sites such as YouTube.

History
There have been several shock galleries that have launched and shut down. Rotten.com hosted murder videos and images of deceased people, and brandished the motto "Pure Evil Since 1996". During their operation, the owners of Rotten.com launched several new sites, one of which was Shockumentary.com in 2006. Shockumentary.com was created to sell mondo films like Traces of Death (1993). Ogrish.com, which was established in 2000, hosted "mutilated corpses, car accidents, burn victims, congenital malformations and other grotesqueries". Ogrish.com's reputation rested on its publication of gore media from terrorists and war. In 2006, Ogrish.com was rebranded as Liveleak.com. Bestgore.com, established in 2008 by Mark Marek, was notorious for its extremely graphic content, such as photos and videos of murders, suicides and violent accidents with an estimated 15–20 million monthly visits during its operation. Marek pleaded guilty and was given a six-month conditional sentence for his role in a case where he was accused of corrupting public morals in Alberta, Canada. Some shock galleries, however, established more specific niches. In the early 2000s, the site Necrobabes hosted images of women pretending to be dead, while the sites Cannibal Café and Gourmet tailored themselves to would-be cannibals. The latter sites gained attention in 2003 when Armin Meiwes, an aspiring cannibal, used the sites to connect with Jürgen Brandes, a man who desired to be eaten. Additionally, Graham Coutts visited Necrobabes, Rapepassion, Violentpleasure, and Hangingbitches frequently before strangling teacher Jane Longhurst.

There have also been several individual videos that received viral attention. Goatse was one of the earliest and best-known shock sites, featuring an image of a man stretching his anus with his hands. The site featured a page devoted to fan-submitted artwork and tributes to the site. The site was shut down in 2004; however, various mirror sites featuring the image still exist. In 2012, it was resurrected as an e-mail service. In 2008, the Dnepropetrovsk maniacs posted the graphic murder video "3 Guys 1 Hammer". This was followed years later by Eric Clinton Kirk Newman's (known now as Luka Rocco Magnotta) video "1 Lunatic 1 Icepick" in 2012—a video of Newman murdering Chinese student Jun Lin that contained dismemberment, cannibalism, and necrophilia, and was posted on Bestgore.com. Newman also shared a video one year prior of him using a vacuum and plastic bag to suffocate two kittens to the song "Happy Xmas (War is Over)" by John Lennon to several gore sites. Meatspin is a shock site containing a looping video (set playing to "You Spin Me Round (Like a Record)" by Dead or Alive) of two people engaging in anal sex, while the penis of the receiving partner spins endlessly. Although frequently reported to be gay pornography, it has been mentioned that the clip was derived from a transgender pornography film. A counter keeps track of how many "spins" the viewer has watched. In 2013, a student at Florida State University hacked the wireless network of his campus and redirected all traffic to Meatspin. In 2015, consternation followed when a family restaurant played the website in front of young children. In 2016, the website was played on a public digital billboard in Sweden, resulting in international media attention. The site first went live on March 10, 2005. , the domain is now meatspin.cc. John-Michael Bond of The Daily Dot stated that to an extent, "casual homophobia" of the 2000s helped popularize Meatspin.

Legality
Currently, there is no federal or state legislation in the United States that outlaws possessing or viewing videos or images that depict the death of a human being. In 2000, a bill was introduced in the California State Legislature to outlaw these films, but after the American Civil Liberties Union (ACLU) raised protest over First Amendment concerns, the bill failed to pass. No other bill has passed since. In the case of Miller v. California, the Supreme Court of the United States established a test to determine whether content falls under the category of unprotected obscenity. The Miller test requires that content "appeals to the prurient interest" to be obscene, meaning content must have a sexual component.

That test was modified by United States v. Richards, which ruled that animal crush videos (videos that involve the killing of animals) can be obscene and therefore, are not protected by the First Amendment even though they do not clearly appeal to sexual interests. The court ruled animal crush videos to be unprotected obscenity for two reasons. First, animal crush videos can appeal to a "specific sexual fetish," which fits the sexual conduct requirement of the Miller test. Second, United States v. Richards modified the Miller test by ruling that obscenity "can also cover unusual deviant acts" even if they are not directly sexual. Child pornography also falls under the category of unprotected obscenity by these tests. Due to the combination of murder and pornography depicted on shock sites that contain murder videos like gore2gasm.com, legal scholars have argued that murder videos also appeal to specific sexual interests and are thus unprotected under United States v. Richards.

In terms of liability, unless death videos are illegal, third party providers like shock sites that host death videos are protected by the Communications Decency Act of 1996 (CDA). However, websites that require users to upload illegal content or actively encourage users to create and share illegal content can be held liable. Additionally, courts have granted increasing privacy rights to families over the publication and distribution of images of deceased relatives. The owners of Rotten.com were successfully sued by families for hosting photos of dead people and videos of their deaths on the site.

In the United Kingdom, Parliament passed the Criminal Justice and Immigration Act 2008, which included a section outlawing extreme pornography (that which is intended to sexually arouse viewers that threatens a person's life, is likely to seriously harm a person's anus, breasts, or genitals, or involves a human corpse or an animal). This has resulted in shock sites, as well as American pornographers including Max Hardcore and Extreme Associates, being convicted of obscenity in the United Kingdom.

During the Christchurch mosque shootings in New Zealand, the shooter broadcast the killings live on Facebook. The video was shared on Facebook and uploaded to YouTube shortly after. Footage of the mass killings were hosted on 4chan, 8chan, LiveLeak, Voat, Zero Hedge, and KiwiFarms. Rather than the Australian government trying to ban this specific instance of murder video, internet service providers in Australia chose to place temporary blocks on any sites that hosted the footage until all the footage was believed to be removed.

Ethics
Several ethical concerns have been raised on the topic of shock sites and murder videos. One concern is that the popularity of shock sites will encourage an increase in violent murders, which can result in more extreme and violent videos that will likely generate more views on shock sites. Murder videos can inspire copycats to replicate the snuff films. After one of the Dnepropetrovsk Maniacs' videos leaked on the internet as "3 Guys 1 Hammer" in 2007, Luka Magnotta murdered Lin Jun, a Chinese student, and uploaded the video (including scenes of dismemberment, cannibalism, and necrophilia) under the similar title of "1 Lunatic 1 Icepick" in 2012.

Another concern is the right of a victim and the victim's family to privacy after death. This is the issue of whether Lin Jun's parents have a right to remove the video of their son's murder from the internet. Murder victims cannot consent to the footage of their deaths being used and uploaded, and several court cases have agreed that parents and loved ones should have a right to prevent the widespread viewership of a personal tragedy and stop the video from being published.

Finally, while shock value is not sufficient to justify banning content legally (as was determined by Cohen v. California), there are still ethical concerns about the emotional damages caused by the jarring nature and content of shock sites. Viewing violent content such as murder videos on social media can cause or trigger post-traumatic stress disorder (PTSD) and cause other emotional distress.

Media
As more people upload and view murder videos on shock sites, some believe that this practice is being mirrored in the horror movie genre. The presence of CCTV in Saw and the online torture auctions in Hostel Part II raise questions on the nefarious use of monitoring systems and the widespread access to videos of Al-Qaeda beheadings, executions in American prisons, and other real depictions of violence and murder on the internet. In examples like Saw, the contemporary horror genre reflects real horror on the internet.

Additionally, a parody of Goatse was shown by a BBC newscast as an alternative for the then recently unveiled logo for the 2012 Summer Olympics.

title: Shock site


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Geography of Albania

Albania is a country in southeastern Europe that lies along the Adriatic and Ionian Seas, with a coastline spanning approximately 476 km. Situated on the Balkan Peninsula, it is one of the most mountainous countries in Europe. It is bounded by Montenegro to the northwest, Kosovo to the northeast, North Macedonia to the east and Greece to the southeast and south.

Most of Albania rises into mountains and hills, tending to run the length of the country from north to south, as for instance the Albanian Alps in the north, the Sharr Mountains in the northeast, the Skanderbeg Mountains in the center, the Korab Mountains in the east, the Pindus Mountains in the southeast, and the Ceraunian Mountains in the southwest. Plains and plateaus extend in the west along the Albanian Adriatic and Ionian Sea Coast.

Some of the most considerable and oldest bodies of freshwater of Europe can be found in Albania. The second largest lake of Southern Europe, the Lake of Shkodër, is located in the northwest surrounded by the Albanian Alps and the Adriatic Sea. And one of the oldest continuously existing lakes in the world, the Lake of Ohrid, lies in the southeast, while the highest tectonic lakes of the Balkan Peninsula, the Large and Small Lake of Prespa, are well hidden among high mountains in the southeast.

Rivers originate in the east of Albania and loop towards the west into the sea. They are encompassed by the drainage basins of the Adriatic, Aegean and Black Sea. The longest river in the country, measured from its mouth to its source, is the Drin that starts at the confluence of its two headwaters, the Black and White Drin, though also notable is the Vjosë, one of the last intact large river systems in Europe.

For a small country, Albania is characterized for its biological diversity and abundance of contrasting ecosystems and habitats, defined in an area of 28,748 square kilometres. This great diversity derives from Albania's geographic location on the Mediterranean Sea, with typical climatic conditions, varied topography, as well as the wealth of terrestrial and marine ecosystems providing a variety of habitats, each with its own typical flora and fauna.

There are 799 Albanian protected areas covering a surface of 5,216.96 square kilometres. These include two strict nature reserves, 14 national parks, one marine park, eight archaeological parks, 750 natural monuments, 22 habitat/species management areas, five protected landscapes, 4 protected landscapes, four managed resources areas and four ramsar wetlands. The national parks cover a surface area of 210668.48 hectare or roughly 13.65% of the overall territory.

Borders
A total surface area of 28.748 square kilometres (11,100 sq mi), the country is located in the southeastern part of the Adriatic and the northeastern part of the Ionian Sea, both located within the Mediterranean Sea. It has a length of borders of about 1094 km, 657 km of which are taken by terrestrial borders, 316 km of shore borders, 48 km river borders and 73 km of lake borders. Inland water surface is 1350 km², composed by natural lakes 325 km², coastal lagoons 130 km², artificial lakes 174 km² and rivers 721 km.

The countries of Montenegro (173 km) and Kosovo (114 km) border the country in the north and northeast, respectively. A significant portion of this border connects high points and follows mountain ridges through the largely inaccessible Albanian Alps. The eastern border is shared with North Macedonia, which stretches 151 km. This border is located at the tripoint between Albania, Kosovo, and North Macedonia passing through the Sharr and Korab Mountains and continues until it reaches Lake Ohrid and Lake Prespa. The southern and southeastern border with Greece is 282 km long. The border is located at the tripoint border between Albania, North Macedonia, and Greece running across the Large and Small Lake Prespa until it reaches the Ionian Sea at the Strait of Corfu.

Topography
The most significant feature of Albania is possibly its relief, with numerous successive mountain ranges and its average altitude, more than 700 metres above sea level. Much of the mountains lie to the north, east and south of the western lowlands in the northern, eastern and southern mountain ranges.

The Albanian Alps extend over 90 kilometres through the north of Albania, traversing an area of 2,000 square kilometres. These mountains represent an extension of the Dinaric Alps and no wider than 40 kilometres. They are deeply fragmented and often inaccessible. It holds the Maja Jezercë, which is the highest point of the Dinarides and simultaneously the second highest point of Albania.

The Korab Mountains dominate the east of the country and expand 40 kilometres along the eastern border of the country, where peaks can clearly reach 2,500 metres. The mountains offer the country's most prominent peak at Mount Korab, which is fragmented by many deep structural depressions. Another distinguishing feature remains the evidence of the last ice age in form of glacial lakes at relatively low altitudes.

One of the most remarkable features about the south of Albania is the presence of the Ceraunian Mountains that cut across the landscape for nearly 100 kilometres. Thousand meter high mountains fall vertically into the Mediterranean Sea constituting at least the first barrier to communication between the sea and the country's southern inland.

Hydrography
The country has a dense network of rivers and streams characterized by a high flow rate. They belong to the drainage basins of the Adriatic, Aegean and Black Sea. They mostly rise in the mountainous eastern half of the country and have their mouths in the west along the coasts. They are sustained from snowmelt of the snow-capped mountains or from the abundant precipitation that falls at loftier elevations.

Eight notable rivers, along with their numerous tributaries, make up the river system of the country. The longest river is the Drin, which flows for 285 km within the country. Its catchment area is one of the most biodiverse places in Europe and encompasses the lakes of Shkodër, Ohrid and Prespa. Of particular concern represent the river of Vjosa as it is considered as the last remaining wild river in Europe. The country's other rivers are Fan, Ishëm, Erzen, Mat, Seman and Shkumbin.

With more than 250 lakes, the country is home to two of the largest lakes in Southern Europe and one of the oldest in the World. The lakes of the country are predominantly of karstic or glacial origin. The largest lake in Southern Europe is the Lake of Shkodër geographically located in the north, shared with Montenegro. One of the ancientest lakes in the world is the Lake of Ohrid located in the southeast, shared with North Macedonia. The highest positioned lakes in Southern Europe are the Large and Small Lake of Prespa in the southeast, shared with North Macedonia and Greece.

The country is also home to many lagoons of varied shape, size and structure. They are primarily positioned along the coast in the west of the country and also in the southeast. They contribute to the overall productivity of the coastal waters by supporting a variety of habitats and ecosystems. The largest lagoon in the country is the Lagoon of Karavasta located between the mouth of Shkumbin and Seman. Another significant lagoons are the lagoons of Patoku, Narta, Kunë-Vain and Butrint.

Biodiversity
The proximity to the Mediterranean Sea and the convergence of exceptional climatic, geological and hydrological conditions, have contributed for the development of a diverse biodiversity, making Albania one of the biodiversity hotspots of Europe.

In terms of phytogeography, the land area of Albania extends within the Boreal Kingdom, specifically within the Illyrian province of the Circumboreal Region. Its territory can be subdivided into four terrestrial ecoregions of the Palearctic realm – the Illyrian, Balkan, Pindus and Dinaric forests.

Forests and woodlands are the most widespread terrestrial ecosystem in Albania. That of the northern edge of the country has an affinity for those of Continental Europe, while those of the southern edge refer to the affinity with that of the Mediterranean Basin. They are substantial because they provide shelter for a vast array of rare and endangered species of animals, among others the brown bear, Balkan lynx, grey wolf, golden jackal, Egyptian vulture and golden eagle. Albania had a 2018 Forest Landscape Integrity Index mean score of 6.77/10, ranking it 64th globally out of 172 countries.

The Mediterranean monk seal, short-beaked common dolphin and common bottlenose dolphin can frequently be seen in the coastal waters of the country. Outstanding is the presence of the Dalmatian pelican, the rarest pelican in the world. The biodiversity of Albania is conserved in its protected areas, which provide protection to hundreds of threatened and endangered species.

Protected areas

Numerous parts of Albania are protected in accordance with a number of national and international designations due to their natural, historical or cultural value. Protected areas belong to the most principal instruments of conservation which in turn contributes effectively to the maintenance of species, habitats and ecosystems.

The country has currently fifteen designated national parks, whereby one is specified as a marine park. Ranging from the Adriatic Sea and the Ionian Sea to the Albanian Alps and the Ceraunian Mountains, they possess outstanding landscapes constituting habitats to thousands of plant and animal species. Butrint, Divjakë-Karavasta, Karaburun-Sazan, Llogara, Prespa, Shebenik-Jabllanicë, Theth and Valbonë are among the most spectacular national parks of the country.

Climate

Albania has a combination of a mediterranean climate and a continental climate, with four distinct seasons. The climatic conditions are highly variable and modified locally by altitude and latitude. Its climate is strongly influenced by the Mediterranean Sea in the west, and the mountains that raise in every corner around the country.

Its diverse regions have a remarkable range of microclimates, with the weather system on the coasts contrasting with that prevailing in the interior. Moreover, the weather varies from the north and towards the south and the west to the east. Albania occupies the climate ranges from temperate climate on the coasts to continental climate in the interior. The warmest areas of the country are at the coasts, which are characterized by a Mediterranean climate (Csa, Csb and Cfa) as defined by the Köppen climate classification. The highlands experiences an Oceanic climate. Winters in Albania are characteristically mild and wet while summers are warm and dry. The northern areas of country such as the Albanian Alps experiences a subarctic climate with frequently very cold winters, and short, mild summers.

The lowlands of Albania have mild winters, averaging about 7 °C. The summer temperatures average 32 °C, however, humidity is low. In the southern lowlands, specifically the areas on the Ionian sea, temperatures average about 5 °C in the winter and 30 °C during the summer.

Physiographic regions
The country is divided into four physiographic regions, the Northern Mountain Range, Central Mountain Range, Southern Mountain Range and Western Lowlands with two subdivisions corresponding roughly to the Albanian Adriatic and Ionian Sea Coast.

Western Lowlands

Except for its sea coast in the west, the western lowlands are ringed by a great arc-shaped line of mountains spreading in the north, east and south. The predominantly flat and regular landscape is morphologically characterized by the sea and rivers, in terms of topography and soil, and also in its climate and biodiversity. The region experiences mild and short winters, with low rainfalls, and long hot and dry summers. It is mostly dominated by the extensive Myzeqe plain, a large alluvial plain traversed by three main rivers, the Shkumbin, Seman and Vjosë.

The Albanian Adriatic Sea Coast stretches from the mouth of the river Buna near the Lake of Shkodër in the north, across the Gulf of Drin, to the Bay of Vlorë in the south. The two largest coastal cities Durrës and Vlorë are located in the northern and the southern part of the region, respectively. The total length of the coastline is approximately 274 km, mostly of which are taken up by sandy beaches, wetlands and alluvial deposits, occurred by quaternary sediments of the main rivers of the country.

The coastline is lined with different habitats and ecosystems, providing optimal conditions for a rich biodiversity. Of particular importance is the presence of numerous lagoons and ponds, representing one of the wealthiest scenery of the country, in terms of biology. Likely, the lagoons of Karavasta and Narta, in the immediate proximity to the sea, are among the most important ones in the Mediterranean Sea.

While the Adriatic coast is relatively low, the Ionian coast is, with few exceptions, rugged and mountainous. The Albanian Ionian Sea Coast stretches from the Peninsula of Karaburun in the north, through the Albanian Riviera, to the Straits of Corfu in the south. The largest coastal city Sarandë is located in the southern part of the region, while smaller villages include Borsh, Dhermi, Himara, Qeparo, Piqeras, and Lukovë. The total length of the coastline is approximately 172 km.

The most characteristic features of the coastline are the Ceraunian Mountains, which extend nearly 100 km along the Albanian Riviera roughly in a southeast–northwest direction. The region is particular fertile and known for its citrus fruits and viticulture, that has a long and special tradition in the region. The coastline is abundant in dolomite from the triassic period, the carbonate rocks follows with limestone from the jurassic period and bituminous schists, cretaceous porcelain and phosphate limestone.

Northern Mountain Range

The northern mountain range is the most mountainous region in the country and its physical geography and shape is distinguished by the convergence of two distinct geological regions, the Albanian Alps and Mirdita Highlands. A dominant feature of the region's landscape is the presence of several u-shaped valleys, such as the Valley of Valbonë, formed by the process of glaciation.

The Albanian Alps are the southernmost extension of the Dinaric Alps and simultaneously the highest and most imposing mountains of the country. Despite the fact that the ice ages had relatively little geological influence on the alps, the southernmost glaciers of Europe were recently discovered on the alps.

The Albanian Alps are home to many important rivers of Western Balkans. The main drainage basins of the Alps are those of the Drin and Danube Rivers. Rivers on the Alps fall roughly into two categories, those that flow into the Lim and those that enter the White Drin and meet the Black Drin downstream at the Drin confluence. However, Drin dominates, draining most of the Alps with its tributaries and when measured from the source of the White Drin to the mouth of the Drin near Lezhë. But not all of the Drin flows near or parallel to the Alps. One Drin tributary is the Valbona River, which drains into the Adriatic Sea, and its eastern tributary the Gashi River.

Central Mountain Range

The terrain of the central mountain range is predominantly mountainous and extremely fragmented carved into its present shape by the glaciers of the last ice age. The region is dominated by three mountain ranges, each running from north-northeast to south-southwest, roughly parallel to the eastern border of Albania.

The Korab Mountains are certainly the most striking feature of the physical geography of the region. They offer simultaneously the highest mountain of the country, the Mount Korab. The mountains extends over 40 kilometres and covers an area of 560 square kilometres. Between the valleys of Shkumbin and Devoll rise the mountains that constitute to the Valamara Mountains, while farther north stretches the connected mountain massifs of Shebenik and Jabllanicë.

The vast majority of the region's natural lakes are located in the southern half of the region and most of them are the product of a long contiguous history. The Lake of Ohrid lie adjacent to the border shared with North Macedonia. It is one of the oldest continuously existing lakes in the world with a unique biodiversity. Further south, well hidden among high mountains, extend the Lake of Prespa that is linked by a small channel with a sluice that separates the two lakes.

Southern Mountain Range
The Ceraunian Mountains, a coastal mountain range in southwestern Albania, stretches about 100 km besides the Ionian Sea from Sarandë in south-east-northwest direction along the Albanian Riviera to Orikum. The relief is varied, with many mountain passes, canyons, gorges, hills and other landforms. The mountains are characterized by housing Black pines, Bulgarian firs, Bosnian pines and Ash trees. The mountain chain is home to many large mammals, including brown bears, grey wolves, lynx, golden eagles and others. The highest point on the chain is Maja e Çikës, that rises to an elevation of 2045 m above the Adriatic. From the peak, there is a view of the Albanian Riviera, the northern Ionian Islands as well as the Italian coast of Apulia and Otranto. The section has wide and long beaches, with a number of bays and headlands.

Stretching until the Llogara Pass at 1027 m, the mountain chain gets separated into the Ceraunians in the west and the Akroceraunians (or Reza e Kanalit) in the east within the Karaburun Peninsula. The villages of Palasë, Dhërmi, Vuno, Himarë, Qeparo, Borsh, Pilur, Kudhës and Ilias are located on the Ceraunian range. The Llogara National Park covers an area of 10100 m².

The Karaburun Peninsula is situated at the eastern side of Strait of Otranto, where the Adriatic Sea meets the Ionian Sea. Its area is 62 km², having a length of 16 km, and a width of only 5 km. The Mesokanali is the narrow channel, that separates the peninsula from the Sazan Island. Geologically, it is made up of carbonic limestone, dating back to the Mesozoic period, while in the northwestern it is composed of terrigenous sediment. Furthermore, these formations have been continuously under the effect of Karst and are exploited as marble. The relief of the peninsula comprises a number of hills with an average altitude of about 800 m above the Adriatic. The highest summits are Maja e Ilqës 733 m, Maja e Flamurit 826 m and Maja Çadëri 839 m.

The coastal landscape is characterized by a rough relief, that dips vertically into the Ionian Sea, it features several solitary peaks, large canyons, bays, caves and gulfs. Examples of typical landforms include Gjipe Canyon, Gjiri i Arushës, Gjiri i Dafinës, Gjiri i Gramës and so on. The geological evolution has formed also capes such as Haxhi Aliu, Galloveci and Kepi i Gjuhëzës, and other of 20 caves along the entire shoreline. The climate is Mediterranean, having hot summers and generally warm to cool, dry winters. Due to its climatic, hydrological and geological conditions, the area is characterized by its unique flora and fauna. Most of the territory consists of forests and is relatively well preserved, it includes many types of trees, such as Mediterranean oak, Manna ash, Kermes oak, and Field maple.

title: Geography of Albania


text:
Gimp

Gimp or GIMP may refer to:

Clothing

 * Bondage suit, also called a gimp suit, a type of suit used in BDSM
 * Bondage mask, also called a gimp mask, often worn in conjunction with a gimp suit

Embroidery and crafts

 * Gimp (thread), an ornamental trim used in sewing and embroidery
 * Gimp thread (scoubidou), plastic thread used in crafts such as lanyards

Arts and entertainment

 * Gimp (album), by Psylons
 * The GIMP Project, a New York dance company
 * "The Gimp", a character wearing a bondage suit in the film Pulp Fiction
 * "The Gimp (Sometimes)", a song by British experimental band Coil off their 2004 album Black Antlers
 * Gimp (gaming), a weak game character

Science and technology

 * GIMP (GNU Image Manipulation Program), an open-source image editor
 * Great Internet Mersenne Prime Search (GIMPS)

title: Gimp


text:
Gymnosphaerid

The gymnosphaerids (or Gymnosphaerida) are a small group of heliozoan protists found in marine environments. They tend to be roughly spherical with radially directed axopods, supported by microtubules in a triangular-hexagonal array arising from an amorphous central granule.

Genera
There are only three genera, each with a single species: Gymnosphaera albida, Hedraiophrys hovassei, and Actinocoryne contractilis.

 * Gymnosphaera albida is free-living, usually benthic in shallow water. The cells are round and naked, around 70-100 μm in diameter, and resemble the unrelated Actinosphaerium.  The outer cytoplasm, or ectoplasm, forms a distinct layer containing large vesicles.
 * Hedraiophrys hovassei is larger and lives attached to algae and other objects. The cells have a conical base, and are covered with long siliceous spicules.  The ectoplasm is distinct and frothy, and typically contains bacterial and algal endosymbionts.
 * Actinocoryne contractilis is benthic. When feeding, it has a multinucleate base and a contractile stalk up to 150 μm in length, supporting a relatively small uninucleate head, where the central granule and axopods are located.  In order to move, it collapses the stalk and head into an amoeboid form which is capable of migration. Reproduction is either by budding off the head or fragmentation of the headless form, producing small free-living cells similar to Gymnosphaera, which then attach themselves and regrow the stalk and base.

Classification
Gymnosphaerids were originally considered centrohelids, which also have microtubules in a triangular-hexagonal array, but are set apart from the others by the structure of the central granule and the mitochondria, which have tubular cristae. The two groups have been treated as separate orders (Axoplasthelida and Centroplasthelida) in a common class, but this has lost support. Instead the gymnosphaerids may be allied with the desmothoracids, and on account of this have been placed in the Cercozoa, but this is somewhat tentative.

 * Order Gymnosphaerida Poche 1913 emend. Mikrjukov 2000
 * Family Gymnosphaeridae Poche 1913
 * Genus ?Actinolophus Schultze 1874
 * Species Actinolophus pedunculatus Schulze 1874
 * Genus ?Wagnerella Mereschkowsky 1878
 * Species Wagnerella borealis Mereschkowsky 1878
 * Genus Gymnosphaera Sassaki 1894 non BIume 1828
 * Species Gymnosphaera albida Sassaki 1894
 * Genus Hedraiophrys Febvre-Chevalier & Febvre 2005
 * Species Hedraiophrys hovassei Febvre-Chevalier & Febvre 2005
 * Genus Actinocoryne Febvre-Chevalier 1980
 * Species Actinocoryne contractilis Febvre-Chevalier 1980

title: Gymnosphaerid


text:
Group representation

In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication.

In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.

Representations of groups allow many group-theoretic problems to be reduced to problems in linear algebra. In physics, they describe how the symmetry group of a physical system affects the solutions of equations describing that system.

The term representation of a group is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical object. More formally, a "representation" means a homomorphism from the group to the automorphism group of an object. If the object is a vector space we have a linear representation. Some people use realization for the general notion and reserve the term representation for the special case of linear representations. The bulk of this article describes linear representation theory; see the last section for generalizations.

Branches of group representation theory
The representation theory of groups divides into subtheories depending on the kind of group being represented. The various theories are quite different in detail, though some basic definitions and concepts are similar. The most important divisions are:

 * Finite groups — Group representations are a very important tool in the study of finite groups. They also arise in the applications of finite group theory to crystallography and to geometry. If the field of scalars of the vector space has characteristic p, and if p divides the order of the group, then this is called modular representation theory; this special case has very different properties. See Representation theory of finite groups.
 * Compact groups or locally compact groups — Many of the results of finite group representation theory are proved by averaging over the group. These proofs can be carried over to infinite groups by replacement of the average with an integral, provided that an acceptable notion of integral can be defined. This can be done for locally compact groups, using the Haar measure. The resulting theory is a central part of harmonic analysis. The Pontryagin duality describes the theory for commutative groups, as a generalised Fourier transform. See also: Peter–Weyl theorem.
 * Lie groups — Many important Lie groups are compact, so the results of compact representation theory apply to them. Other techniques specific to Lie groups are used as well. Most of the groups important in physics and chemistry are Lie groups, and their representation theory is crucial to the application of group theory in those fields. See Representations of Lie groups and Representations of Lie algebras.
 * Linear algebraic groups (or more generally affine group schemes) — These are the analogues of Lie groups, but over more general fields than just R or C. Although  linear algebraic groups have a classification that is very similar to that of Lie groups, and give rise to the same families of Lie algebras, their representations are rather different (and much less well understood). The analytic techniques used for studying Lie groups must be replaced by techniques from algebraic geometry, where the relatively weak Zariski topology causes many technical complications.
 * Non-compact topological groups — The class of non-compact groups is too broad to construct any general representation theory, but specific special cases have been studied, sometimes using ad hoc techniques. The semisimple Lie groups have a deep theory, building on the compact case. The complementary solvable Lie groups cannot be classified in the same way. The general theory for Lie groups deals with semidirect products of the two types, by means of general results called Mackey theory, which is a generalization of Wigner's classification methods.

Representation theory also depends heavily on the type of vector space on which the group acts. One distinguishes between finite-dimensional representations and infinite-dimensional ones. In the infinite-dimensional case, additional structures are important (e.g. whether or not the space is a Hilbert space, Banach space, etc.).

One must also consider the type of field over which the vector space is defined. The most important case is the field of complex numbers. The other important cases are the field of real numbers, finite fields, and fields of p-adic numbers. In general, algebraically closed fields are easier to handle than non-algebraically closed ones. The characteristic of the field is also significant; many theorems for finite groups depend on the characteristic of the field not dividing the order of the group.

Definitions
A representation of a group G on a vector space V over a field K is a group homomorphism from G to GL(V), the general linear group on V. That is, a representation is a map
 * $$\rho \colon G \to \mathrm{GL}\left(V \right)$$

such that
 * $$\rho(g_1 g_2) = \rho(g_1) \rho(g_2), \qquad \text{for all }g_1,g_2 \in G.$$

Here V is called the representation space and the dimension of V is called the dimension or degree of the representation. It is common practice to refer to V itself as the representation when the homomorphism is clear from the context.

In the case where V is of finite dimension n it is common to choose a basis for V and identify GL(V) with GL(n, K), the group of $$n \times n$$ invertible matrices on the field K.

 * If G is a topological group and V is a topological vector space, a continuous representation of G on V is a representation ρ such that the application Φ : G × V → V defined by Φ(g, v) = ρ(g)(v) is continuous.
 * The kernel of a representation ρ of a group G is defined as the normal subgroup of G whose image under ρ is the identity transformation:
 * $$\ker \rho = \left\{g \in G \mid \rho(g) = \mathrm{id}\right\}.$$

 * A faithful representation is one in which the homomorphism G → GL(V) is injective; in other words, one whose kernel is the trivial subgroup {e} consisting only of the group's identity element.

 * Given two K vector spaces V and W, two representations ρ : G → GL(V) and π : G → GL(W) are said to be equivalent or isomorphic if there exists a vector space isomorphism α : V → W so that for all g in G,
 * $$\alpha \circ \rho(g) \circ \alpha^{-1} = \pi(g).$$

Examples
Consider the complex number u = e2πi / 3 which has the property u3 = 1. The set C3 = {1, u, u2} forms a cyclic group under multiplication. This group has a representation ρ on $$\mathbb{C}^2$$ given by:

\rho \left( 1 \right) = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \qquad \rho \left( u \right) = \begin{bmatrix} 1 & 0 \\ 0 & u \\ \end{bmatrix} \qquad \rho \left( u^2 \right) = \begin{bmatrix} 1 & 0 \\ 0 & u^2 \\ \end{bmatrix}. $$

This representation is faithful because ρ is a one-to-one map.

Another representation for C3 on $$\mathbb{C}^2$$, isomorphic to the previous one, is σ given by:

\sigma \left( 1 \right) = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \qquad \sigma \left( u \right) = \begin{bmatrix} u & 0 \\ 0 & 1 \\ \end{bmatrix} \qquad \sigma \left( u^2 \right) = \begin{bmatrix} u^2 & 0 \\ 0 & 1 \\ \end{bmatrix}. $$

The group C3 may also be faithfully represented on $$\mathbb{R}^2$$ by τ given by:

\tau \left( 1 \right) = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix} \qquad \tau \left( u \right) = \begin{bmatrix} a & -b \\ b & a \\ \end{bmatrix} \qquad \tau \left( u^2 \right) = \begin{bmatrix} a & b \\ -b & a \\ \end{bmatrix} $$

where

 * $$a=\text{Re}(u)=-\tfrac{1}{2}, \qquad b=\text{Im}(u)=\tfrac{\sqrt{3}}{2}.$$

Another example:

Let $$V$$ be the space of homogeneous degree-3 polynomials over the complex numbers in variables $$x_1, x_2, x_3. $$

Then $$S_3$$ acts on $$V$$ by permutation of the three variables.

For instance, $$(12)$$ sends $$x_{1}^3$$ to $$x_{2}^3$$.

Reducibility
A subspace W of V that is invariant under the group action is called a subrepresentation. If V has exactly two subrepresentations, namely the zero-dimensional subspace and V itself, then the representation is said to be irreducible; if it has a proper subrepresentation of nonzero dimension, the representation is said to be reducible. The representation of dimension zero is considered to be neither reducible nor irreducible, just as the number 1 is considered to be neither composite nor prime.

Under the assumption that the characteristic of the field K does not divide the size of the group, representations of finite groups can be decomposed into a direct sum of irreducible subrepresentations (see Maschke's theorem). This holds in particular for any representation of a finite group over the complex numbers, since the characteristic of the complex numbers is zero, which never divides the size of a group.

In the example above, the first two representations given (ρ and σ) are both decomposable into two 1-dimensional subrepresentations (given by span{(1,0)} and span{(0,1)}), while the third representation (τ) is irreducible.

Set-theoretical representations
A set-theoretic representation (also known as a group action or permutation representation) of a group G on a set X is given by a function ρ : G → XX, the set of functions from X to X, such that for all g1, g2 in G and all x in X:

 * $$\rho(1)[x] = x$$
 * $$\rho(g_1 g_2)[x]=\rho(g_1)[\rho(g_2)[x]],$$

where $$1$$ is the identity element of G. This condition and the axioms for a group imply that ρ(g) is a bijection (or permutation) for all g in G. Thus we may equivalently define a permutation representation to be a group homomorphism from G to the symmetric group SX of X.

For more information on this topic see the article on group action.

Representations in other categories
Every group G can be viewed as a category with a single object; morphisms in this category are just the elements of G. Given an arbitrary category C, a representation of G in C is a functor from G to C. Such a functor selects an object X in C and a group homomorphism from G to Aut(X), the automorphism group of X.

In the case where C is VectK, the category of vector spaces over a field K, this definition is equivalent to a linear representation. Likewise, a set-theoretic representation is just a representation of G in the category of sets.

When C is Ab, the category of abelian groups, the objects obtained are called G-modules.

For another example consider the category of topological spaces, Top. Representations in Top are homomorphisms from G to the homeomorphism group of a topological space X.

Two types of representations closely related to linear representations are:
 * projective representations: in the category of projective spaces. These can be described as "linear representations up to scalar transformations".
 * affine representations: in the category of affine spaces. For example, the Euclidean group acts affinely upon Euclidean space.

title: Group representation


text:
GRE Physics Test

The GRE physics test is an examination administered by the Educational Testing Service (ETS). The test attempts to determine the extent of the examinees' understanding of fundamental principles of physics and their ability to apply them to problem solving. Many graduate schools require applicants to take the exam and base admission decisions in part on the results.

The scope of the test is largely that of the first three years of a standard United States undergraduate physics curriculum, since many students who plan to continue to graduate school apply during the first half of the fourth year. It consists of 70 five-option multiple-choice questions covering subject areas including classical mechanics, electromagnetism, wave phenomena and optics, thermal physics, relativity, atomic and nuclear physics, quantum mechanics, laboratory techniques, and mathematical methods. The table below indicates the relative weights, as asserted by ETS, and detailed contents of the major topics.

1. Classical mechanics (20%)

 * kinematics
 * Newton's laws of motion
 * work and energy
 * rotational motion about a fixed axis
 * dynamics of systems of particles
 * central forces and celestial mechanics
 * three-dimensional particle dynamics
 * Lagrangian and Hamiltonian formalism
 * noninertial reference frames
 * elementary topics in fluid mechanics

2. Electromagnetism (18%)

 * electrostatics
 * currents and DC circuits
 * magnetic fields in free space
 * Lorentz force
 * Induction
 * Maxwell's equations and their applications
 * electromagnetic waves (electromagnetic radiation)
 * AC circuits
 * magnetic and electric fields in matter

3. Optics and wave phenomena (9%)

 * wave properties
 * superposition
 * interference
 * diffraction
 * geometrical optics
 * light polarization
 * Doppler effect

4. Thermodynamics and statistical mechanics (10%)

 * laws of thermodynamics
 * thermodynamic processes
 * equations of state
 * ideal gases
 * Kinetic theory of gases
 * ensembles
 * statistical concepts and calculation of thermodynamic quantities
 * thermal expansion and heat transfer

5. Quantum mechanics (12%)

 * fundamental concepts
 * solutions of the Schrödinger wave equation
 * square wells (Particle in a box)
 * harmonic oscillators
 * hydrogenic atoms
 * spin
 * angular momentum
 * wave function symmetry
 * elementary perturbation theory

6. Atomic physics (10%)

 * properties of electrons
 * Bohr model
 * energy quantization
 * atomic structure
 * atomic spectra
 * selection rules
 * black-body radiation
 * x-rays
 * atoms in electric and magnetic fields

7. Special relativity (6%)

 * introductory concepts of special relativity
 * time dilation
 * length contraction
 * simultaneity
 * energy and momentum
 * four-vectors and Lorentz transformation

8. Laboratory methods (6%)

 * data and error analysis
 * electronics
 * instrumentation
 * radiation detection
 * counting statistics
 * interaction of charged particles with matter
 * laser and optical interferometers
 * dimensional analysis
 * fundamental applications of probability and statistics

9. Specialized topics (9%)

 * particle and nuclear physics
 * nuclear properties
 * radioactive decay
 * fission and fusion
 * reactions
 * fundamental properties of elementary particles
 * condensed matter
 * crystal structure
 * x-ray diffraction
 * thermal properties
 * electron theory of metals
 * semiconductors
 * superconductors
 * mathematical methods
 * single and multivariate calculus
 * coordinate systems (rectangular, cylindrical, spherical)
 * vector algebra and vector differential operators
 * Fourier series
 * partial differential equations
 * boundary value problems
 * matrices and determinants
 * functions of complex variables
 * miscellaneous
 * astrophysics
 * computer applications

title: GRE Physics Test


text:
Gardnerian Wicca

Gardnerian Wicca, or Gardnerian witchcraft, is a

tradition in the neopagan religion of Wicca, whose members can trace initiatory descent from Gerald Gardner. The tradition is itself named after Gardner (1884–1964), a British civil servant and amateur scholar of magic. The term "Gardnerian" was probably coined by the founder of Cochranian Witchcraft, Robert Cochrane in the 1950s or 60s, who himself left that tradition to found his own.

Gardner claimed to have learned the beliefs and practices that would later become known as Gardnerian Wicca from the New Forest coven, who allegedly initiated him into their ranks in 1939. For this reason, Gardnerian Wicca is usually considered to be the earliest created tradition of Wicca, from which most subsequent Wiccan traditions are derived.

From the supposed New Forest coven, Gardner formed his own Bricket Wood coven, and in turn initiated many Witches, including a series of High Priestesses, founding further covens and continuing the initiation of more Wiccans into the tradition. In the UK, Europe and most Commonwealth countries someone self-defined as Wiccan is usually understood to be claiming initiatory descent from Gardner, either through Gardnerian Wicca, or through a derived branch such as Alexandrian Wicca. Elsewhere, these original lineaged traditions are termed "British Traditional Wicca".

Covens and initiatory lines
Gardnerian Wiccans organize into covens, that traditionally, though not always, are limited to thirteen members. Covens are led by a High Priestess and the High Priest of her choice, and celebrate both a Goddess and a God.

Gardnerian Wicca and other forms of British Traditional Wicca operate as an initiatory mystery cult; membership is gained only through initiation by a Wiccan High Priestess or High Priest. Any valid line of initiatory descent can be traced all the way back to Gerald Gardner, and through him back to the New Forest coven.

Rituals and coven practices are kept secret from non-initiates, and many Wiccans maintain secrecy regarding their membership in the religion. Whether any individual Wiccan chooses secrecy or openness often depends on their location, career, and life circumstances. In all cases, Gardnerian Wicca absolutely forbids any member to share the name, personal information, fact of membership, and so on without advanced individual consent of that member for that specific instance of sharing.

In Gardnerian Wicca, there are three grades of initiation. Ronald Hutton suggests that "the outlines of the first two [initiation] rituals are very clearly Masonic."

Theology
In Gardnerian Wicca, the two principal deities are the Horned God and the Mother Goddess. Gardnerians use specific names for the God and the Goddess in their rituals. Doreen Valiente, a Gardnerian High Priestess, revealed that there were more than one.

Ethics and morality
The Gardnerian tradition teaches a core ethical guideline, often referred to as "The Rede" or "The Wiccan Rede". In the archaic language often retained in some Gardnerian lore, the Rede states, "An it harm none, do as thou wilt."

"Witches [...] are inclined to the morality of the legendary Good King Pausol, 'Do what you like so long as you harm no one'. But they believe a certain law to be important, 'You must not use magic for anything which will cause harm to anyone, and if, to prevent a greater wrong being done, you must discommode someone, you must do it only in a way which will abate the harm.'"

A second ethical guideline is often called the Law of Return, sometimes the Rule of Three. Like the Rede, this guideline teaches Gardnerians that whatever energy or intention one puts out into the world, whether magical or not, will return to that person multiplied by three. This law is controversial, as discussed by John Coughlin, author of The Pagan Resource Guide, in an essay, "The Three-Fold Law."

The religion tends to be non-dogmatic, allowing each initiate to find for themselves what the ritual experience means by using the basic language of the shared ritual tradition, to be discovered through the Mysteries. The tradition is often characterized as an orthopraxy (correct practice) rather than an orthodoxy (correct thinking), with adherents placing greater emphasis on a shared body of practices as opposed to faith.

Gardner and the New Forest coven
In the early 20th century, Margaret Murray promoted the theory that persecuted witches had actually been followers of a surviving pagan religion, but this theory is now rejected by academia. Nevertheless, it was an influence on some neo-pagans. On retirement from the British Colonial Service, Gerald Gardner moved to London but then before World War II moved to Highcliffe, east of Bournemouth and near the New Forest on the south coast of England. After attending a performance staged by the Rosicrucian Order Crotona Fellowship, he reports meeting a group of people who had preserved their historic occult practices. They recognised him as being "one of them" and convinced him to be initiated. It was only halfway through the initiation, he says, that it dawned on him what kind of group it was, and that witchcraft was still being practised in England.

The group into which Gardner was initiated, known as the New Forest coven, was small and utterly secret as the Witchcraft Act 1735 (9 Geo. 2. c. 5) made it illegal to claim to predict the future, conjure spirits, or cast spells; it likewise made an accusation of witchcraft a criminal offence. Gardner's enthusiasm for the coven led him to wish to document it, but both the witchcraft laws and the coven's secrecy forbade that, despite his excitement. After World War II, Gardner's High Priestess and coven leader relented sufficiently to allow a fictional treatment that did not expose them to prosecution, "High Magic's Aid":

"Anyhow, I soon found myself in the circle and took the usual oaths of secrecy which bound me not to reveal any secrets of the cult. But, as it is a dying cult, I thought it was a pity that all the knowledge should be lost, so in the end I was permitted to write, as fiction, something of what a witch believes in the novel High Magic's Aid."

After the witchcraft laws were repealed in 1951, and replaced by the Fraudulent Mediums Act, Gerald Gardner went public, publishing his first non-fiction book, "Witchcraft Today", in 1954. Gardner continued, as the text often iterates, to respect his oaths and the wishes of his High Priestess in his writing. Gardner said that the "Witchcraft" religion was dying out, and he pursued publicity and welcomed new initiates during the last years of his life. Gardner even courted the attentions of the tabloid press, to the consternation of some more conservative members of the tradition. In Gardner's own words, "Witchcraft doesn't pay for broken windows!"

Gardner knew many famous occultists. Ross Nichols was a friend and fellow Druid (until 1964 member of the Druid Order, when he left to found his own Druidic Order of Bards, Ovates, and Druids). Nichols edited Gardner's "Witchcraft Today" and is mentioned extensively in Gardner's "The Meaning of Witchcraft". Near the end of Aleister Crowley's life, Gardner met with him for the first time on 1 May 1947 and visited him twice more before Crowley's death that autumn; at some point, Crowley gave Gardner an Ordo Templi Orientis (OTO) charter and the 4th OTO degree—the lowest degree authorising use of the charter.

Doreen Valiente, one of Gardner's priestesses, identified the woman who initiated Gardner as Dorothy Clutterbuck, referenced in "A Witches' Bible" by Janet and Stewart Farrar. Valiente's identification was based on references Gardner made to a woman he called "Old Dorothy" whom Valiente remembered. Biographer Philip Heselton corrects Valiente, clarifying that Clutterbuck (Dorothy St. Quintin-Fordham, née Clutterbuck), a Pagan-minded woman, owned the Mill House, where the New Forest coven performed Gardner's initiation ritual. Scholar Ronald Hutton argues in his Triumph of the Moon that Gardner's tradition was largely the inspiration of members of the Rosicrucian Order Crotona Fellowship and especially that of a woman known by the magical name of "Dafo". Dr. Leo Ruickbie, in his Witchcraft Out of the Shadows, analysed the documented evidence and concluded that Aleister Crowley played a crucial role in inspiring Gardner to establish a new pagan religion. Ruickbie, Hutton, and others further argue that much of what has been published of Gardnerian Wicca, as Gardner's practice came to be known, was written by Blake, Yeats, Valiente and Crowley and contains borrowings from other identifiable sources.

The witches Gardner was originally introduced to were originally referred to by him as "the Wica" and he would often use the term "Witch Cult" to describe the religion. Other terms used, included "Witchcraft" or "the Old Religion." Later publications standardised the spelling to "Wicca" and it came to be used as the term for the Craft, rather than its followers. "Gardnerian" was originally a pejorative term used by Gardner's contemporary Roy Bowers (also known as Robert Cochrane), a British cunning man, who nonetheless was initiated into Gardnerian Wicca a couple of years following Gardner's death.

Reconstruction of the Wiccan rituals
Gardner stated that the rituals of the existing group were fragmentary at best, and he set about fleshing them out, drawing on his library and knowledge as an occultist and amateur folklorist. Gardner borrowed and wove together appropriate material from other artists and occultists, most notably Charles Godfrey Leland's Aradia, or the Gospel of the Witches, the Key of Solomon as published by S.L. MacGregor Mathers, Masonic ritual, Crowley, and Rudyard Kipling. Doreen Valiente wrote much of the best-known poetry, including the much-quoted Charge of the Goddess.

Bricket Wood coven
In 1948–1949, Gardner and Dafo were running a coven separate from the original New Forest coven at a naturist club near Bricket Wood to the north of London. By 1952 Dafo's health had begun to decline, and she was increasingly wary of Gardner's publicity-seeking. In 1953 Gardner met Doreen Valiente who was to become his High Priestess in succession to Dafo. The question of publicity led to Doreen and others formulating thirteen proposed 'Rules for the Craft', which included restrictions on contact with the press. Gardner responded with the sudden production of the Wiccan Laws which led to some of his members, including Valiente, leaving the coven.

Gardner reported that witches were taught that the power of the human body can be released, for use in a coven's circle, by various means, and released more easily without clothing. A simple method was dancing round the circle singing or chanting; another method was the traditional "binding and scourging." In addition to raising power, "binding and scourging" can heighten the initiates' sensitivity and spiritual experience.

Following the time Gardner spent on the Isle of Man, the coven began to experiment with circle dancing as an alternative. It was also about this time that the lesser 4 of the 8 Sabbats were given greater prominence. Bricket Wood coven members liked the Sabbat celebrations so much, they decided that there was no reason to keep them confined to the closest full moon meeting, and made them festivities in their own right. As Gardner had no objection to this change suggested by the Bricket Wood coven, this collective decision resulted in what is now the standard eight festivities in the Wiccan Wheel of the year.

The split with Valiente led to the Bricket Wood coven being led by Jack Bracelin and a new High Priestess, Dayonis. This was the first of a number of disputes between individuals and groups, but the increased publicity only seems to have allowed Gardnerian Wicca to grow much more rapidly. Certain others also helped fuel this publicity, such as Alex Sanders (real name Orrell Alexander Carter) and Raymond Buckland. Sanders started his own separate tradition, together with his wife Maxine, known as Alexandrian Wicca and frequently were covered by the press. Buckland, who authored dozens of books on the subject, brought the Gardnerian tradition to the United States in 1964, later to start his own tradition known as Seax Wicca.

Controversy Over Transgender Individuals and Male/Female Polarity
On July 18, 2022, an open letter titled “A Declaration of the Traditional Gardnerian Wica” was electronically published by 47 Third-degree and autonomous Second-degree Gardnerian initiates, representing coven leaders and Gardnerian Elders, who identified themselves as practicing Gardnerian Wicca within the framework of male/female polarity. The letter’s signatories claimed that biological gender essentialism was fundamental to Gardnerian practice, and that initiates who disagreed with this view of gender had effectively left the Gardnerian tradition. These claims were met with accusations of transphobia from six members of the Gardnerian community. Pagan blog site The Wild Hunt noted that because of Gardnerian Wicca’s decentralized structure and emphasis on coven autonomy, “the proclamation effectively only applies to covens that are led by or hive from the documents’ signers.”

title: Gardnerian Wicca


text:
Greenwich Mean Time

Greenwich Mean Time (GMT) is the local mean time at the Royal Observatory in Greenwich, London, counted from midnight. At different times in the past, it has been calculated in different ways, including being calculated from noon; as a consequence, it cannot be used to specify a particular time unless a context is given. The term "GMT" is also used as one of the names for the time zone UTC+00:00 and, in UK law, is the basis for civil time in the United Kingdom.

Because of Earth's uneven angular velocity in its elliptical orbit and its axial tilt, noon (12:00:00) GMT is rarely the exact moment the Sun crosses the Greenwich Meridian and reaches its highest point in the sky there. This event may occur up to 16 minutes before or after noon GMT, a discrepancy described by the equation of time. Noon GMT is the annual average (the arithmetic mean) moment of this event, which accounts for the word "mean" in "Greenwich Mean Time".

Originally, astronomers considered a GMT day to start at noon, while for almost everyone else it started at midnight. To avoid confusion, the name Universal Time was introduced in 1928 to denote GMT as counted from midnight. Today, Universal Time usually refers to Coordinated Universal Time (UTC) or UT1; English speakers often use GMT as a synonym for UTC. For navigation, it is considered equivalent to UT1 (the modern form of mean solar time at 0° longitude); but this meaning can differ from UTC by up to 0.9s. The term "GMT" should thus not be used for purposes that require precision.

The term "GMT" is especially used by United Kingdom bodies, such as the BBC World Service, the Royal Navy, and the Met Office; and others particularly in Arab countries, such as the Middle East Broadcasting Centre and OSN.

History

As the United Kingdom developed into an advanced maritime nation, British mariners kept at least one chronometer on GMT to calculate their longitude from the Greenwich meridian, which was considered to have longitude zero degrees, by a convention adopted in the International Meridian Conference of 1884. Synchronisation of the chronometer on GMT did not affect shipboard time, which was still solar time. But this practice, combined with mariners from other nations drawing from Nevil Maskelyne's method of lunar distances based on observations at Greenwich, led to GMT being used worldwide as a standard time independent of location. Most time zones were based upon GMT, as an offset of a number of hours (and occasionally half or quarter hours) "ahead of GMT" or "behind GMT".

Greenwich Mean Time was adopted across the island of Great Britain by the Railway Clearing House in 1847 and by almost all railway companies by the following year, from which the term railway time is derived. It was gradually adopted for other purposes, but a legal case in 1858 held "local mean time" to be the official time. On 14 May 1880, a letter signed by "Clerk to Justices" appeared in The Times, stating that "Greenwich time is now kept almost throughout England, but it appears that Greenwich time is not legal time. For example, our polling booths were opened, say, at 8 13 and closed at 4 13 p.m." This was changed later in 1880, when Greenwich Mean Time was legally adopted throughout the island of Great Britain. GMT was adopted in the Isle of Man in 1883, in Jersey in 1898 and in Guernsey in 1913. Ireland adopted GMT in 1916, supplanting Dublin Mean Time. Hourly time signals from Greenwich Observatory were first broadcast by shortwave radio on 5 February 1924 at 17:30:00 UTC, rendering the time ball at the observatory redundant.

The daily rotation of the Earth is irregular (see ΔT) and has a slowing trend; therefore atomic clocks constitute a much more stable timebase. On 1 January 1972, GMT as the international civil time standard was superseded by Coordinated Universal Time (UTC), maintained by an ensemble of atomic clocks around the world. Universal Time (UT), a term introduced in 1928, initially represented mean time at Greenwich determined in the traditional way to accord with the originally defined universal day; from 1 January 1956 (as decided by the International Astronomical Union in Dublin in 1955, at the initiative of William Markowitz) this "raw" form of UT was re-labelled UT0 and effectively superseded by refined forms UT1 (UT0 equalised for the effects of polar wandering) and UT2 (UT1 further equalised for annual seasonal variations in Earth rotation rate).

"Indeed, even the Greenwich meridian itself is not quite what it used to be—defined by 'the centre of the transit instrument at the Observatory at Greenwich'. Although that instrument still survives in working order, it is no longer in use and now the meridian of origin of the world's longitude and time is not strictly defined in material form but from a statistical solution resulting from observations of all time-determination stations which the BIPM takes into account when co-ordinating the world's time signals. Nevertheless, the line in the old observatory's courtyard today differs no more than a few metres from that imaginary line which is now the prime meridian of the world."

Ambiguity in the definition of GMT
Historically, GMT has been used with two different conventions for numbering hours. The long-standing astronomical convention, dating from the work of Ptolemy, was to refer to noon as zero hours (see Julian day). This contrasted with the civil convention of referring to midnight as zero hours dating from the Roman Empire. The latter convention was adopted on and after 1 January 1925 for astronomical purposes, resulting in a discontinuity of 12 hours, or half a day. The instant that was designated as "December 31.5 GMT" in 1924 almanacs became "January 1.0 GMT" in 1925 almanacs. The term Greenwich Mean Astronomical Time (GMAT) was introduced to unambiguously refer to the previous noon-based astronomical convention for GMT. The more specific terms UT and UTC do not share this ambiguity, always referring to midnight as zero hours.

United Kingdom
Legally, the civil time used in the UK is called "Greenwich mean time" (without capitalisation), with an exception made for those periods when the Summer Time Act 1972 orders an hour's shift for daylight saving. The Interpretation Act 1978, section 9, provides that whenever an expression of time occurs in any Act, the time referred to shall (unless otherwise specifically stated) be held to be Greenwich mean time. Under subsection 23, the same rule applies to deeds and other instruments.

During the experiment of 1968 to 1971, when the British Isles did not revert to Greenwich Mean Time during the winter, the all-year British Summer Time was called British Standard Time (BST).

In the UK, UTC+00:00 is disseminated to the general public in winter and UTC+01:00 in summer.

BBC radio stations broadcast the "six pips" of the Greenwich Time Signal. It is named from its original generation at the Royal Greenwich Observatory. If announced (such as near the start of summer time or of winter time), announcers on domestic channels declare the time as GMT or BST as appropriate. As the BBC World Service is broadcast to all time zones, the announcers use the term "Greenwich Mean Time" consistently throughout the year.

Other countries
Several countries define their local time by reference to Greenwich Mean Time. Some examples are:
 * Belgium: Decrees of 1946 and 1947 set legal time as one hour ahead of GMT.
 * Ireland: "Standard Time" (Am Caighdeánach) is defined as being one hour in advance of GMT. "Winter Time" (Am Geimhridh) is defined as being the same as GMT.
 * Canada: Interpretation Act, R.S.C. 1985, c. I-21, section 35(1). This refers to "standard time" for the several provinces, defining each in relation to "Greenwich time", but does not use the expression "Greenwich mean time". Several provinces, such as Nova Scotia (Time Definition Act. R.S., c. 469, s. 1), have their own legislation which specifically mentions either "Greenwich Mean Time" or "Greenwich mean solar time".
 * Philippines: The term GMT is still in use when it comes to electronics such as cellular phones. Android phones use "UTC" but keypad phones use "GMT" to define any time zone around the world.

Time zone
Greenwich Mean Time is defined in law as standard time in the following countries and areas, which also advance their clocks one hour (GMT+1) in summer. Greenwich Mean Time is used as standard time all year round in the following countries and areas:
 * United Kingdom, where the summer time is called British Summer Time (BST)
 * Ireland, where it is called Winter Time, changing to Standard Time in summer.
 * Portugal (with the exception of the Azores)
 * Canary Islands
 * Faroe Islands
 * Burkina Faso
 * The Gambia
 * Ghana
 * Guinea
 * Guinea-Bissau
 * Iceland
 * Ivory Coast
 * Liberia
 * Mali
 * Mauritania
 * Sahrawi Arab Democratic Republic (disputed)
 * Saint Helena, Ascension and Tristan da Cunha
 * Senegal
 * Sierra Leone
 * Togo

title: Greenwich Mean Time