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State park

State parks are parks or other protected areas managed at the sub-national level within those nations which use "state" as a political subdivision. State parks are typically established by a state to preserve a location on account of its natural beauty, historic interest, or recreational potential. There are state parks under the administration of the government of each U.S. state, some of the Mexican states, and in Brazil. The term is also used in the Australian states of Victoria and New South Wales. The equivalent term used in Canada, Argentina, South Africa, and Belgium, is provincial park. Similar systems of local government maintained parks exist in other countries, but the terminology varies.

State parks are thus similar to national parks, but under state rather than federal administration. Similarly, local government entities below state level may maintain parks, e.g., regional parks or county parks. In general, state parks are smaller than national parks, with a few exceptions such as the Anza-Borrego Desert State Park in California, and Wood-Tikchik State Park in Alaska, the largest state park in the United States.

United States
There are 6,792 state park units in the United States, according to the National Association of State Park Directors (NASPD). There are some 813 million annual visits to the country's state parks. The NASPD further counts over 43000 mi of trail, 217,367 campsites, and 8,277 cabins and lodges across U.S. state parks. The largest state park system in the United States is Alaska State Parks, with over 100 sites encompassing 3.3 million acres.

Many states include designations beyond "state park" in their state parks systems. Other designations might be state recreation areas, state beaches, and state nature reserves. Some state park systems include long-distance trails and historic sites. To encourage tourism in rural areas, several states have simple lodges, inns, hotels, or motels (usually with a restaurant) for lodging at some parks. These typically use "Resort" in the name, such as "_____ Resort State Park" in West Virginia state parks and "_____ State Resort Park" in neighboring Kentucky state parks, which has 17 such resort parks, the most of any state. Other states use the Resort name inconsistently (like DeGray Lake Resort State Park, the only one out of three resorts in Arkansas state parks), or have only one such park (South Carolina state parks' Hickory Knob State Resort Park), or do not use the designation at all (such as the lodges of Georgia state parks). The term "lodge" may also refer to a hiking lodge, essentially a large cabin for hikers rather than a large facility with private rooms and a restaurant. Other lodging may include yurts and tipis.

Not all parks owned by a state are necessarily part of its state-park system, such as Stone Mountain Park near Atlanta. Some Texas state parks are a land lease from the U.S. government, while Mackinac National Park was handed down to become the first of the Michigan state parks. As with national parks, facilities at state parks are often leased to concessionaires to operate. Breaks Interstate Park is operated under an interstate compact by Virginia state parks, although it is also one of the Kentucky state parks, straddling both sides of the state line. Other multi-state parks are legally two separate parks with the same name and more informal cooperation between them.

History
The title of oldest state park in the United States is claimed by Niagara Falls State Park in New York, established in 1885. Several public parks previously or currently maintained at the state level pre-date it. Indian Springs State Park has been operated continuously by the state of Georgia as a public park since 1825, although it did not gain the title "State Park" until 1931. In 1864 Yosemite Valley and Mariposa Grove were ceded by the federal government to California until Yosemite National Park was proclaimed in 1890. In 1878 Wisconsin set aside a vast swath of its northern forests as "The State Park" but, needing money, sold most of it to lumber companies within 20 years. Mackinac National Park was established in 1875 as the second U.S. national park before being converted to a state park in 1895. The first state park with the designation of "state park" was Itasca State Park in Minnesota, established in 1891.

Many state park systems date to the 1930s, when around 800 state parks (and several national ones) across the country were developed with assistance from federal job-creation programs like the Civilian Conservation Corps and Works Progress Administration.

title: State park


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Liao Hua

Liao Hua (d. 264 ), courtesy name Yuanjian, originally named Liao Chun, was a Chinese military general and politician of the state of Shu Han during the Three Kingdoms period of China. Like Zhang Yi and Zong Yu, Liao was one of few officials who served the Shu-Han state throughout its entire existence.

Early career as Guan Yu's subordinate
Liao Hua was from Xiangyang, Jing Province. He was a registrar (主簿) under Guan Yu, a general who served under the warlord Liu Bei and guarded Liu Bei's territories in Jing Province. In late 219, while Guan Yu was away at the Battle of Fancheng, Liu Bei's ally, Sun Quan, broke the Sun–Liu alliance by launching an invasion of Jing Province and conquering most of Liu Bei's territories in the province. Guan Yu was captured and executed by Sun Quan's forces. Liao Hua became a prisoner-of-war of Sun Quan, but he constantly thought of returning to Liu Bei's side, so he faked his own death and succeeded in deceiving his captors and escaping. He brought his elderly mother with him and headed west towards Yi Province (covering present-day Sichuan and Chongqing), where Liu Bei's domain was based.

Career in Shu Han
In 221, Liu Bei declared himself emperor and established the state of Shu Han. Later that year, he launched a military campaign against Sun Quan to retake his lands in Jing Province and avenge Guan Yu. Liao Hua and his mother encountered the Shu army at Zigui County. Liu Bei was very pleased to see Liao Hua and he appointed the latter as the Administrator of Yidu Commandery (宜都郡; around present-day Yidu, Hubei). After Liu Bei died in 223, Liao Hua became an army adviser (參軍) under Zhuge Liang, the Imperial Chancellor of Shu. He was later assigned to be in charge of Guangwu Commandery (廣武郡; around present-day Yongdeng County, Gansu) and was subsequently promoted to Right General of Chariots and Cavalry (右車騎將軍). He was also appointed as the Inspector of Bing Province even though Bing Province was not under Shu's jurisdiction, and enfeoffed as a Marquis of a Central District (中鄉侯). He was known for his fiery personality and determination. His position in the Shu military was equivalent to Zhang Yi while higher than Zong Yu.

During September of the year 238, Liao Hua led his troops to attack the encampment where the Inspector of Yong Province (雍州刺史), at the time Guo Huai stationed along with the main Wei army of the region. In response, Guo Huai dispatched his subordinates Wang Yun (王赟) Administrator of Guangwei (廣魏) along with You Yi (游奕) Administrator of Nan'an (南安) to counter this offensive. The Wei commanders wanted to disperse their forces to encircle the Shu army and occupy the strategic points between the mountains to prevent them from escaping, however at the same time this strategy had the Wei army scattered with many of You Yi's camps exposed in a dangerous position. Liao Hua saw through this and quickly seized the opportunity to defeat them while they were still unprepared. You Yi's army was forced to retreat while Wang Yun was killed in battle by an arrow.

Liao Hua was critical of the Shu general Jiang Wei, who continued Zhuge Liang's aggressive foreign policy against Shu's rival state, Cao Wei, by launching a series of eleven campaigns to attack Cao Wei between 240 and 262. He participated in the third and fourth campaigns in 247 and 249 respectively. In 262, when Jiang Wei was about to embark on the eleventh campaign, Liao Hua remarked: "'One who does not refrain from using military force will end up burning himself.' This is Boyue(Jiang Wei)'s current situation. He is inferior to the enemy in terms of intelligence and military power, yet he keeps attacking them. How can he expect to overcome them? The events of today are exactly as described in this line from the Classic of Poetry: 'Why were these things not before me? Or why were they not after me?'"

Life after the fall of Shu
In late 263, Shu's rival state, Cao Wei, launched a campaign to conquer Shu and succeeded in doing so within a year when the Shu emperor Liu Shan surrendered. After the fall of Shu, Liao Hua was ordered to move out of former Shu territory to the Wei capital Luoyang. He died of illness on the journey.

Liao Hua's birth year could not be determined because his age at the time of his death was not recorded in history. However, it could be deduced that he was in his 70s when he died: Around 261, when Zhuge Zhan took charge of affairs in the Shu imperial court, Liao Hua visited Zong Yu, who said: "Both of us are already above the age of 70, ..."

Sao Mi Zhou
The Sao Mi Zhou (掃迷帚; literally The broom sweeping away superstitions), a novel written by a certain Zhuangzhe (壯者; literally "strong man") during the Qing dynasty, contained a saying about Liao Hua: "There is no young reliable commander in Shu, so old generals like Liao Hua still have to be the vanguard." (蜀中無大將，廖化作先鋒)

It can be interpreted as: Shu was so lacking in young talents in its twilight years that elderly Liao Hua (more than 70 years old at that time) had to lead the vanguard of the Shu army in battle. The proverb is to describe a situation that there is a lack of young talents in a group or company and hence, old but experienced people will have to take the responsibilities themselves.

However, it can also be understood to describe a situation in which a person who is seemingly unfit for a job is forced into doing it, but is willing to face what seems to be insurmountable odds against him/her. This interpretation can be criticized as Liao Hua was adept in military affairs and he was one of a few people who experienced the whole ups and downs of the Shu Han regime. He is regarded one of four cornerstones of the late Shu Han regime in the Hanzhong region, together first with Wang Ping and Ju Fu then with Zhang Yi (Bogong) and him.

Romance of the Three Kingdoms
The 14th-century historical novel Romance of the Three Kingdoms has a few stories about Liao Hua which are not found in historical records.

In Chapter 27, Liao Hua, a bandit chief and former Yellow Turban rebel, encountered Guan Yu while the latter was on a quest to reunite with Liu Bei. He was thanked by Guan Yu after rescuing Liu Bei's two kidnapped wives, Lady Gan and Lady Mi, from a fellow bandit named Du Yuan, but refused to accept him as a follower owing to his bandit roots. He would only reappear in Chapter 60, joining Guan Yu as he guarded Jing Province, and as Liu Bei was entering Yi Province.

In Chapter 73, Liao Hua took control of the vanguard during Guan Yu's march on Xiangyang. He successfully lured the enemy generals Cao Ren and Zhai Yuan out of their castle, allowing Guan Yu to seize it. In the subsequent Battle of Fancheng, Liao Hua was stationed at Sizhong where he was in mutual support of Guan Ping's encampment at Yancheng. When the enemy general Xu Huang captured both Sizhong and Yancheng, Liao Hua and Guan Ping fought their way south to join Guan Yu. When Guan Yu received news that Liu Bei's territories in Jing Province had been conquered by Sun Quan's army, he retreated to Maicheng (麥城) and was besieged there by Sun's forces. In Maicheng, Liao Hua volunteered to break out of the siege and seek reinforcements from Liu Feng and Meng Da in Shangyong (上庸). However, Liu Feng and Meng Da refused to help Guan Yu, so Liao Hua had no choice but to travel to Chengdu to report the situation to Liu Bei. By then, Guan Yu had been captured in an ambush and executed by Sun Quan.

In his later life and career, Liao Hua actively participated in the Shu campaigns (Zhuge Liang's Northern Expeditions and Jiang Wei's Northern Expeditions) against Wei. One of his most celebrated moments came in Chapter 103, when Sima Yi was retreating from Shangfang Valley. Liao Hua pursued the fleeing general into a dense forest and, being a proficient horseman, was able to catch up and get close enough to strike him down. However, when Sima Yi swerved around a tree, Liao Hua missed the shot and his sword became lodged into the wood, allowing Sima Yi to escape. During the chase, however, Sima Yi dropped his golden helmet. Liao Hua took the helmet and traveled back to Zhuge Liang who rewarded him with the first grade of merit for his attempt. This event angered Wei Yan who felt Liao Hua was being unfairly praised. Zhuge Liang noticed this but said nothing, leading to a mild distaste for Wei Yan's jealousy. The helmet was henceforth used as a means of mocking and provoking the Wei army. Following Zhuge Liang's death, Liao Hua moved up the ranks under Jiang Wei, eventually receiving the second-in-command military rank of General of Chariots and Cavalry. As Jiang Wei's senior general, Liao Hua was often tasked with the most important of duties, such as leading the vanguard and dueling enemy generals. Despite his steadfast loyalty to Shu, Liao Hua disagreed with Jiang Wei's constant invasions of Wei and his attempts to claim victory through overpowering numbers, believing these tactics to be a drain on resources and morale; he let it be known that he would run the military differently if he were in command, and this led to quarrels between Jiang Wei and himself. When Liu Shan eventually submitted to Wei in Chapter 119, Liao Hua succumbed to grief and died.

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

title: Liao Hua


text:
Talk:Totalitarian religious group

Why isn't this just a redirect to Cult? Morwen 09:12, 27 Nov 2003 (UTC)
 * Dear Morwen, thank you for the question. As I see it, this is a neat helpful article that deserves extra space. It is also because in other countries the term "cult" has not caught on yet but "totalitarian" has everywhere. So why shouldn't the English Wiki take over a good idea from the German one? ;-) ly 17:01, 28 Nov 2003 (UTC)
 * I'm afraid that's not an answer. Morwen
 * Actually, since the article on "Cult" is very long already, it is for practical reasons that such a basic question is dealt with separately, I believe. That is why there is a link at the end of the Cult article. (ly)
 * Ok. But it still doesnt' explain the difference between the two terms anywhere, and I'm not convinced there is any. Except of course Cult can be used in a more specific sense to mean, for example, the cult of [insert saint]. Morwen 07:12, 1 Dec 2003 (UTC)

 * I tend to agree with Morwen. The expression totaliarian religious group was used in German probably because there is no good equivalent for cult in German. 'Sekte' has too many different meanings, just like in Dutch and French ('Secte')Andries 21:32, 13 Feb 2004 (UTC)

Whatever the origins, the subject of this article is the same as the subject of Cult. They should be one article. DJ Clayworth 21:43, 13 Feb 2004 (UTC)

Easily misapplied
This reads almost word-for-word like the kind of "cult warning" propaganda that was directed against the Unification Church in the 1970s and 1980s. Especially the section marked How can I find out whether a group is totalitarian? They just changed the word cult to totalitarian -- as if nobody would notice. Ha!

This article is sheer advocacy and should either be deleted, or re-written so that its points of view are clearly attributed to their proponents. Also, would someone please look up the references? I've seen that checklist somewhere else, but since I'm "on vacation" I must leave it to others to find it. Try googling for "cult characteristics". --Uncle Ed 19:43, 9 Mar 2004 (UTC)

 * Ed, yes, this article should be merged with cults but DO NOT DELETE its contents but instead improve it. I had already listed this article as such wikipedia duplicate articles I have to agree with your removal of the link about bigotry though.Andries 13:19, 10 Mar 2004 (UTC)

Lots of big cuts
I deleted everything that was unattributed POV. With a few minutes of on-line searching, anyone could easily trace which organizations or individuals advocates these points of view. Please do so, then put the info back in properly attributed.

Also this external link is about bigotry, not cults:

 * THE NATURE OF RELIGIOUS BIGOTRY

--Uncle Ed 20:18, 9 Mar 2004 (UTC)

title: Talk:Totalitarian religious group


text:
Talk:John Corigliano

Gay composer
"is he a "gay composer" or a composer who is gay?", any difference between gay composer and a composer who is gay? :O --Yacht 09:19, Nov 27, 2003 (UTC)

 * Is there a difference between a French composer and a composer who is French? Hyacinth 20:41, 31 Aug 2004 (UTC)

I'm confused by the "Duck Season - Rabbit Season" series of edits. Is there a dispute about whether or not Corigliano is gay? MK 06:22, 31 Aug 2004 (UTC)

Was this issue ever resolved? I couldn't find evidence either way...--SingCal 20:06, 8 January 2006 (UTC)

 * Yes, he is, and its fairly well known. Hyacinth (talk) 03:26, 13 January 2008 (UTC)

I notice a banner asking for citations, and since this is the only subject discussed on the talk page, I'm guessing it might have something to do with this. So, Hyacinth: do you have references? More importantly, can you explain why you think (assuming you do) that this has relevance? TheScotch (talk) 12:00, 12 June 2011 (UTC)

 * We have him in gay/LGBT categories, yet there is absolutely nothing in the article that would support those categorisations. It is simply not acceptable to categorise people based on what may be "fairly well known".
 * It has to explicitly stated in the article, or the cats must be removed. --  Jack of Oz   [pleasantries]  12:57, 31 May 2017 (UTC)
 * Jack is correct - still no citation stating this, and I can't find one, either. If you slap the cat on this guy, you need to verify it with a Reliable Source. 104.169.22.138 (talk) 05:37, 9 May 2021 (UTC)

Shotgun?
A friend told me today that Corigliano's Symphony #3 (Circus Maximus) includes a part for shotgun. I trust him, because he has played the piece with the BSO, but I do not see any reference to it here (and I expected something like that must be in the Wikipedia article). Anyone know anything about it? --Yakatz (talk) 00:58, 3 November 2011 (UTC)

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"Jr."?
If the composer has exactly the same name as his violinist father, isn't he technically John Corigliano, Jr.? 173.88.246.138 (talk) 23:42, 28 January 2022 (UTC)
 * Wikipedia doesn't decide these things. Look to the media and follow their consensus. Binksternet (talk) 00:41, 29 January 2022 (UTC)

I believe that Oliver Wendell Holmes Jr. dropped the "Jr." after his father died. I don't know whether that is standard practice.Maurice Magnus (talk) 11:14, 27 April 2022 (UTC)

To consider for inclusion
To consider for inclusion in this article: these allegations. Source: https://www.washingtonpost.com/arts-entertainment/2022/12/18/composers-open-letter-juilliard/ 204.11.186.190 (talk) 15:09, 20 December 2022 (UTC)

title: Talk:John Corigliano


text:
Wei Yan

Wei Yan (died c. October 234 ), courtesy name Wenchang, was a Chinese military general and politician of the state of Shu Han during the Three Kingdoms period of China. Originally a subordinate of the warlord Liu Bei in the late Eastern Han dynasty, Wei Yan rose through the ranks and became a general when Liu Bei seized control of Yi Province (covering present-day Sichuan and Chongqing) in 214. His performance in battle helped him to become a prominent figure in the Shu military in a short period of time. He was later appointed as the Administrator of Hanzhong Commandery and as an Area Commander in 219. Between 228 and 234, he participated actively in the Northern Expeditions led by the Shu regent Zhuge Liang against Shu's rival state, Cao Wei. After Zhuge Liang's death in c. September 234, Wei Yan was killed by another Shu general, Ma Dai, for alleged treason.

Early life
Wei Yan was from Yiyang Commandery (義陽郡), which covered parts of present-day Nanyang in southern Henan and parts of northern Hubei. He started his career as a foot soldier under the warlord Liu Bei, probably sometime between 209 and 211 when Liu Bei was in southern Jing Province (covering present-day Hubei and Hunan). Around 212, he followed Liu Bei into Yi Province (covering present-day Sichuan and Chongqing) and served Liu Bei as a personal retainer in a war against Liu Zhang, the Governor of Yi Province (益州牧). Huang Zhong and Wei Yan scored many military exploits during the capture of Guanghan County. Thus, Wei Yan promoted to full general.

The campaign met early success with the quick death of Gao Pei and Yang Huai and the later occupation of the passes, followed by the defeat of Liu Zhang's reinforcements at Fu County. Pang Tong was killed during the siege of Luo castle and the siege became a prolonged one. One year later, Wei Yan and Liu Bei finally captured Luocheng, then surrounded and occupied Chengdu together with Zhuge Liang, Zhang Fei along with others. Thus, around summer 214, Liu Bei seized control of Yi Province from Liu Zhang. As Wei Yan has made several contributions in the campaign of Yi, Liu Bei promoted him to the rank of General of Ivory Gate (牙門將軍).

Administrator of Hanzhong
In 219, Wei Yan participated in Liu Bei campaign against his rival Cao Cao in the Hanzhong Campaign. After Liu Bei captured Hanzhong, Liu Bei asked his subjects to nominate one of his generals to remain behind and guard Hanzhong. His subjects nominated Zhang Fei, who also strongly believed that he would most likely be chosen. However, much to everyone's surprise, Liu Bei chose Wei Yan instead and appointed him as General Who Guards Distant Lands (鎮遠將軍) and acting Administrator of Hanzhong (漢中太守). When Liu Bei asked Wei Yan in front of everyone how would he perform his duty, the latter confidently replied:

"'If Cao Cao leads all the forces in China to attack Hanzhong, let me assist Your Highness in resisting them. If an enemy general comes with an army of 100,000, let me engulf them for Your Highness.' Liu Bei was very pleased and everyone was impressed with Wei Yan's reply."

During his tenure, Wei Yan explained to Liu Bei that he borrowed a strategy which were called the "double gates" (重门之计). The ancient text I Ching described this strategy as a particularly designed fortification which laid numerous military garrisons surrounding the outskirt and trail exits linking to Hanzhong.

Following the end of the Eastern Han dynasty and the start of the Three Kingdoms period in 220, Liu Bei declared himself emperor in 221 and established the state of Shu Han (or Shu) to challenge the legitimacy of the Cao Wei (or Wei) state established by Cao Cao's successor, Cao Pi, to replace the Eastern Han dynasty. Liu Bei further promoted Wei Yan to General Who Guards the North (鎮北將軍) after his coronation.

Northern Expeditions

After Liu Bei died in 223, his son Liu Shan succeeded him as the emperor of Shu. In the same year, Liu Shan enfeoffed Wei Yan as a Marquis of a Chief Village (都亭侯).

In 227, Zhuge Liang, the Imperial Chancellor of Shu, mobilised the Shu military and gathered troops in Hanzhong Commandery in preparation for a large-scale invasion of Shu's rival state, Cao Wei (or Wei), where he put Wei Yan in charge of the vanguard division and appointed him as acting Major under the Imperial Chancellor (丞相司馬) and acting Inspector of Liang Province (涼州刺史). During this campaign, Wei Yan always requested to lead a separate detachment of 10,000 troops, take a different route and rendezvous with the Shu main army at Tong Pass (潼關; in present-day Tongguan County, Shaanxi).

Wei Yan argued that the valley and the people in it has sufficient food supply which can support the operation at least for a week. However, Zhuge Liang rejected the plan because he thought that it was too risky, which prompted Wei Yan to scold Zhuge Liang as a coward and complained that his talent was not put to good use. When Chen Shou compiled the unofficial works on the history of Shu to write the Sanguozhi, he only mentioned that Wei Yan suggested to Zhuge Liang to split the Shu army into two, and the two forces would take two different routes and rendezvous at Tong Pass.

Later in 230, during the Ziwu Campaign, Wei Yan led some troops towards Yangxi (陽谿; southwest of present-day Wushan County, Gansu) and engaged the Wei forces led by and Guo Huai and Fei Yao, where Wei Yan managed to inflict a heavy defeat to them. Also, during the same year, he assisted another Shu general Wu Yi, both of them were ordered to attack Nan'an Commandery (南安郡; southeast of present-day Longxi County, Gansu) where they scored another victory against Wei's army led by Fei Yao.

During the fourth campaign in 231, Wei Yan was also involved in the Battle of Mount Qi when he together with the Shu generals Gao Xiang and Wu Ban, scored a major victory against the Wei army led by Sima Yi, where they killed 3,000 Wei soldiers and seized 5,000 sets of armour and 3,100 crossbows. Sima Yi was forced to retreat back to his camp. Zhang He, a veteran Wei general was also killed in battle during this conflict. As a reward for his contributions, the Shu government promoted Wei Yan to Vanguard Military Adviser (前軍師) and Senior General Who Attacks the West (征西大將軍), and elevated him from a village marquis to a county marquis under the title "Marquis of Nanzheng" (南鄭侯).

Battle of Wuzhang Plains

In 234, Zhuge Liang launched the fifth Shu invasion of Wei, with Wei Yan leading the Shu vanguard force as one of the commanding officers. Wei Yan reportedly had a dream that a horn grew on top of his head. He asked the dream diviner Zhao Zhi (趙直) the meaning of this. Zhao Zhi lied to him and said:

"'A qilin has horns, but does not use them; this is an auspicious sign that the enemy will destroy themselves without battle'."

After he left, he revealed to someone that the word "horn" (角) is composed of a "knife" (刀) with "use" (用) below it, which meant dreaming of "using a knife" atop one's head should be considered an extremely ominous omen. Later, in the encampment Wei Yan had a quarrel with Yang Yi, Zhuge Liang's chief clerk, as Wei Yan was extremely resentful of Yang Yi. Whenever they got into heated quarrels, Wei Yan often drew his sword and brandished it in front of Yang Yi who sobbed as tears rolled down his cheeks; which prompted Fei Yi then to stepped in to stop them from fighting and managed to keep them under control until Zhuge Liang's death. Zhuge Liang was upset by the lack of harmony between Wei Yan and Yang Yi, but was unwilling to side with either of them because he appreciated the talents of both men.

When Zhuge Liang became critically ill during the invasion, he gave secret orders to Yang Yi, Fei Yi and Jiang Wei to lead the army back to Shu after his death, with Wei Yan in charge of the rearguard and Jiang Wei to follow behind, and if Wei Yan refused to follow the order, they were to retreat without him. When Zhuge Liang died, news of his death were kept secret. Yang Yi sent Fei Yi to meet Wei Yan and assess his intentions. Wei Yan told Fei Yi:

"'Although the Imperial Chancellor is dead, I am still alive. The officials serving in the Imperial Chancellor's Office may bring his body back (to Chengdu) for burial, but I should remain behind to lead the army to attack the enemy. Must we abandon our mission just because of the death of one man? Besides, who am I, Wei Yan, to submit to Yang Yi's command and lead the rearguard?'"

Wei Yan then asked Fei Yi to assist him in making arrangements for part of the Shu army to remain behind and continue with the campaign, while the rest would retreat back to Shu. Fei Yi pretended to write a letter, signed by both of them, and told Wei Yan that he would read out the letter to all the officers about the new arrangements, where he lied by telling Wei Yan that he will go back and explain Wei Yan's answer to Yang Yi.

Death
Wei Yan then let Fei Yi leave, but he immediately regretted his decision and went after Fei Yi, although Wei Yan could not catch up Fei Yi in time. He then sent his subordinate to meet Yang Yi and the others, but was shocked to discover that all units were preparing to retreat in accordance with Zhuge Liang's final orders. Wei Yan wanted to continue the battle even though Zhuge Liang had died, so he became furious when he heard of the retreat. He intended to block the Shu forces from retreating, so he led his force towards the south – ahead of the main army under Yang Yi's command – and sealed the return route by destroying the gallery roads leading back to Shu.

Wei Yan and Yang Yi separately wrote memorials to the Shu imperial court to accuse each other, and both memorials arrived in Chengdu on the same day. The Shu emperor Liu Shan asked the ministers Dong Yun and Jiang Wan for their opinions. Both of them sided with Yang Yi and felt that Wei Yan's actions were suspicious. In the meantime, Yang Yi ordered his men to cut down trees to rebuild the gallery roads, and his troops marched day and night to catch up with Wei Yan. Wei Yan arrived at the southern valley first and ordered his soldiers to attack Yang Yi. Yang Yi sent Wang Ping to resist Wei Yan. Wang Ping shouted at Wei Yan:

"'His Excellency (Zhuge Liang) had just died and his body had yet to turn cold, and now you dare to do something like this!' Wei Yan's men knew that their commander was in the wrong so they deserted."

Wei Yan was left with only his son(s) and a few followers. They fled towards Hanzhong Commandery. Yang Yi ordered Ma Dai to give chase. Ma Dai killed Wei Yan, brought his head back, and threw it in front of Yang Yi. Yang Yi trampled on Wei Yan's severed head and said:

"'You inferior slave! Now, can you still commit evil?'"

Thus, the family members and close relatives of Wei Yan were also executed. Before Wei Yan's death, Jiang Wan had led the imperial guards from Chengdu to deal with what appeared to be a mutiny by Wei Yan. They had travelled for about 10 li (about three miles) when they received news of Wei Yan's death; they then turned back and returned to Chengdu.

Character analysis
Wei Yan was known to treat his soldiers well and for his bravery with valor that surpassed others, although he was also boastful of his talents hence his peers tended to avoid him. Sun Quan, the ruler of Wu and another contemporary figure of three kingdoms era, has remarked that the moment Zhuge Liang passed away, Wei Yan will be proven unreliable. Chen Shou, who wrote Wei Yan's biography in the Sanguozhi, analysed Wei Yan's death as such: "'Wei Yan's initial intention was not to head north to surrender to Cao Wei. Instead, he wanted to retreat back to the south. He desired to kill Yang Yi and the others who disagreed with him. Although the officers held differing opinions, he strongly believed that they would generally agree to him becoming Zhuge Liang's successor. That was his true intention; he was not thinking of rebelling.'" Chen Shou also remarked that Zhuge Liang himself highly valued Wei Yan bravery and caught in dilemma when the latter had conflict with Yang Yi, ration and transportation staff officer which talent in managing his duties Zhuge Liang also valued.

A similar, but somewhat different and more detailed account exists in the historical text Weilüe work by later Wei dynasty historian named Yu Huan stated that Zhuge Liang told Wei Yan to setting up defense, although he also gave further instruction to "not return here". Wei Yan kept this order for himself and did not share with others, thus prompting Wei Yan's rival, Yang Yi, to spread false rumours that Wei Yan has intended to defect to the enemy, which led the incited Shu soldiers to attack Wei Yan and killing him. However, Pei Songzhi, who added the Weilüe account to Wei Yan's biography and annotated the Sanguozhi, doubted the Weilüe account as he remarked:

"'I believe this account (Weilue) was derived from hearsay in the enemy state (Cao Wei) and may not be as reliable as compared to the original account (by Chen Shou).'"

Furthermore, modern era historical analysis stated that Wei Yan's death was explained in political terms in Injustice to Wei Yan (魏延的千古奇冤), a neoteric article by Zhu Ziyan, a history professor from Shanghai University, where Zhu wrote that Zhuge Liang personally appointed Jiang Wan, Fei Yi and Jiang Wei to be his successors, but Wei Yan's appointments and contributions were greater than those of any of them at the time. Zhuge Liang ostracised Wei Yan and cracked down on him because he wanted to eliminate Wei Yan as a possible obstacle to his appointed successors.

Meanwhile, in the Analysis of the Three Kingdoms, Yi Zhongtian commented that Zhuge Liang's last order to forcibly retreat and leave Wei Yan alone was contradicted by what he personally instructed Wei Yan, such contradiction indirectly leading to the tragedy between Wei Yan and Yang Yi. Hence the forcible retreat might be the idea of Yang Yi, not Zhuge Liang, since Zhuge Liang died before devising any withdrawal plan, thus prompted Yi Zhongtian to theorized that there was no evidence of this theory that Yang Yi fabricated the order. Yi Zhongtian also explained another possible hypothesis that Zhuge Liang's final order "leave Wei Yan alone" simply meant "ignore Wei Yan", did not mean "kill Wei Yan". Shu Han's main forces must withdraw to guard the rear area, and if Wei Yan could not be stopped then just let him be. Yi Zhongtian analized and criticize that Wei Yan did not grasp the political-economical reasons behind both of Zhuge Liang's expeditions and his extreme caution. Zhuge Liang launched the expeditions not only to restore the Han dynasty, but also to keep Shu Han in warring conditions and used that to increase his control over the internal affair and suppress the potential dissidents amongst local nobility.

As smallest and weakest amongst the Three Kingdoms, Shu Han would be the first one to be targeted at, hence it had to make pre-emptive attacks to intimidate the opponents, to enlarge its territory and to improve its conditions - the rate of success was not high but it was better than doing nothing. Zhuge Liang's goal of Han restoration was sincere and never changed; however, the powerful Cao Wei could not be defeated quickly in one single blow, hence the expeditions must be done in a careful manner with guaranteed advances rather than daring but risky strikes which could lead to disasters like Xiaoting or Fancheng. Such a complicated situation could not be explained clearly to Wei Yan, and probably it did not need to be, as Zhuge Liang wanted to keep Wei Yan's spirit at its highest.

Ziwu Valley plan analysis
Wei Yan's reasoning for his Ziwu Valley Plan was recorded in the Weilüe, which was then added as an annotation to his biography in the Sanguozhi, where Chen Shou recorded that Wei Yan received intelligence which led him to conclude that the defender of the strategic city of Chang'an, Xiahou Mao, was incompetent. Thus, Wei Yan reasoned, it would be easy for him to take 5,000 troops (and another 5,000 to carry supplies) across the Qin Mountains via the Ziwu Valley (子午谷) and into Chang'an. Wei Yan estimated that he would reach Chang'an in ten days and scare Xiahou Mao into flight, leaving the grain in Chang'an's storehouses for Shu's taking. There, Wei Yan's force can wait for Zhuge Liang's main army to take the safer road out of Xie Valley (斜谷) and rendezvous in Chang'an. In this way, the region west of Xianyang could be conquered in one movement." Weilue argued that the plan might have worked, as although Sima Yi acknowledged the plan, Xiahou Mao did not realize it.

When the Wei government received intelligence about Wei Yan's Ziwu Valley Plan, the Wei emperor Cao Rui immediately removed Xiahou Mao from his military command in Chang'an and reassigned him to be a Master of Writing (尚書) in Luoyang. Yi Zhongtian in his Analysis of the Three Kingdoms commented that both proponents and opponents of Wei Yan's plan have their own good reasons. Cao Wei met the first Northern Expedition with little preparation as they didn't fathom that Shu Han could make such an offensive, hence the combination of Zhuge Liang's and Wei Yan's strikes could result in huge impact. However, Wei Yan's plan was also very risky, as neither the Xiahou Mao's flight nor the timely arrival of Zhuge Liang's main forces was guaranteed, moreover the formidable Guo Huai was also in nearby region and could come to assist Xiahou Mao.

However, recent scholarship of Chinese history criticized the account of Yu Huan in his Weilue work that Yu Huan has exaggerated the alleged conflict between Wei Yan with his superior, Zhuge Liang, regarding the rejection of the latter for the strategy which proposed by Wei Yan. Wen-Chin Wang from Department of Chinese Language and Literature has suspected the bias of Yu Huan personal view which he viewed Yu Huan as Wei supporter, where Wei kingdom during the late Han era were the arch enemy of Shu kingdom.

Military fortification
The "Heavy Gate" (重门之计) bulwark which designed by Wei Yan during his tenure as administrator of Hanzhong particularly came to use twice when used by the successor administrator of Hanzhong. And greatly helped Wang Ping, to defend the province from a massive invasion led by Cao Shuang. Later, Jiang Wei, the grand commandant of Shu kingdom dismantled this "Heavy Gate" fortification which designed by Wei Yan in favor of his own design. However, Jiang Wei's new defense strategy failed to impede the advance of Zhong Hui, general of Wei, while Jiang Wei himself were repelled from Hanzhong effectively causing Hanzhong fall to Wei kingdom.

Wei Yan Shrines
A Wei Yan Shrine (魏延祠) is located in Baique Village, Sanquan Township, Zitong County, Sichuan. In front of the shrine flows a Wei Family River (魏家河). On the plains east of the river, there once stood a Wei Family River Temple (魏家河廟), which had three stone tablets in front of it. One of the stone tablets bore the words "Wei Yan once led soldiers and was stationed here.". According to legend, in 231, during the fourth Shu invasion of Wei, Zhuge Liang ordered Wei Yan to lead a separate force to station south of the Wei Family River where, in memory of the incident, the locals built the Wei Family River Temple beside the river and a small bridge called "General Bridge" (將軍橋). The Wei Yan Shrine was initially demolished by the government but was rebuilt in 1995. A statue of Wei Yan stands in the main hall of the shrine.

There is another temple attributed to Wei Yan in allegedly Wei Yan hometown, in Weijia village Gaobao Township, Qingfeng County, Puyang City, in Henan Province.

In Romance of the Three Kingdoms
Wei Yan appears as a character in the historical novel Romance of the Three Kingdoms by Luo Guanzhong, which romanticises the historical events leading to, and during the Three Kingdoms period, such as Wei Yan participation in the fictional Battle of Changsha. Wei Yan surrendered to Liu Bei after killing his superior, Han Xuan.

During a clash between Liu Bei against Ma Chao forces, Wei Yan defeat Ma Dai after they duelled for several bouts, causing the latter to flee.

During the battle in Hanzhong, Wei Yan and Zhang Fei were unable to overcame Zhang He, causing both to retreat.

According to Zhang Chaoju, Wei Yan was beaten during this campaign by Cao Cao's general, Pang De.

Later, during the battle of Wuzhang plains, Wei Yan lured Sima Yi and his two sons, Sima Shi and Sima Zhao into a fire ambush. However, a sudden, heavy rain caused the fire to extinguish, and the plan failed; prompting the Simas to escape.

Modern era depictions
“Sun Qi Mountain” drama which was written by Wei Ming-Lun, that described the relationship between two important historical figures Zhuge Liang and Wei Yan depicted the latter in positive light as it was not Wei Yan intent to betray Shu, which making him as tragic hero figure.

Wei Yan is featured as a playable character in Koei's Dynasty Warriors and Warriors Orochi video game series. He also appears in Koei's Dynasty Tactics 2.

Primary & secondary sources

 * Chen, Shou (3rd century). Records of the Three Kingdoms (Sanguozhi).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).
 * Pei, Songzhi (5th century). Annotations to Records of the Three Kingdoms (Sanguozhi zhu).

title: Wei Yan


text:
City of London Police

The City of London Police is the territorial police force responsible for law enforcement within the City of London, England, including the Middle and Inner Temples.

The force responsible for law enforcement within the remainder of the London region, outside the city, is the much larger Metropolitan Police, a separate organisation. The City of London, which is now primarily a financial business district with a small resident population but a large commuting workforce, is the historic core of London, and has an administrative history distinct from that of the rest of the metropolis, of which its separate police force is one manifestation.

The City of London area has a resident population of around 8,700, however there is also a daily influx of approximately 513,000 commuters into the city, along with thousands of tourists.

The police authority is the Common Council of the City and, unlike other territorial forces in England and Wales, there is not a police and crime commissioner replacing that police authority by way of the Police Reform and Social Responsibility Act 2011, but like a police and crime commissioner, the Common Council is elected.

, the force had a workforce of 1,355 including 861 full-time police officers and 494 support staff. The force is also supported by much smaller numbers of special constables, police community support officers, and designated officers. The headquarters is located at the Guildhall and there is an additional station at Bishopsgate. The City of London Police is the smallest territorial police force in England and Wales, both in terms of geographic area and head-count. The current commissioner (equivalent to the chief constable in non-London forces), appointed in 2022, is Angela McLaren.

History
Traditionally the responsibility for policing in the city had been divided between day and night City Watch, primarily under the two sheriffs. Their responsibilities were shared with the aldermen's officers – the ward beadles – who are now purely ceremonial. It was these officers' responsibility for ensuring that the Night Watch was maintained. Policing during the day eventually came under the City Patrol, which evolved into the City Day Police, which was modelled on the Metropolitan Police. The London City Police was officially formed in 1832, before becoming the City of London Police with the passing of the City of London Police Act 1839, which gave statutory approval to the force as an independent police body and headed off attempts made to merge it with the Metropolitan Police.

In 1840, the City of London Police moved its headquarters from the corporation's Guildhall to 26 Old Jewry, where it remained until it was relocated to Wood Street in 2001. The force's current headquarters is at the Guildhall. Former stations include Moor Lane (destroyed in the Blitz on 29 December 1940) and Cloak Lane (closed 1965).

Some notable events the force has been involved with include the Jack the Ripper murders, the 1910 Houndsditch murders, and the response to the IRA's bombing campaign during the years of the Troubles. The early 1990s saw the IRA carry out a number of high-profile attacks in the city, such as the 1992 Baltic Exchange bombing and the 1993 Bishopsgate bombing, resulting in huge economic and infrastructural damage. As a result, the Traffic and Environmental Zone, better known as the "ring of steel", was officially established in 1993 by Owen Kelly, the then City of London Police commissioner. Some aspects of the ring of steel were 'stepped down' in the late 1990s following the cessation of IRA hostilities but stepped up again after the September 11 terrorist attacks.

In May 2020, City of London Police officers stopped a vehicle driven by a man who had recently been interviewed by Channel 4 about a prior instance of police harassment, who they incorrectly accused of concealing drugs. After smashing his car window, officers strip-searched him, detained him for 21 hours and impounded his car. Following an investigation, City of London Police acknowledged failings in their treatment of the man, including returning the vehicle to him without first removing the broken glass, but declined to apologise and said his arrest had been lawful. In March 2021 the Independent Office for Police Conduct ordered City of London Police to conduct a new investigation into the incident, which resulted in the City of London Police having to apologise to the driver and identified 'organisational and individual learning'.

List of commissioners

 * Daniel Whittle Harvey (1839–1863)
 * Colonel Sir James Fraser (1863–1890)
 * Lieutenant-Colonel Sir Henry Smith (1890–1902)
 * Captain Sir William Nott-Bower (1902–1925)
 * Lieutenant-Colonel Sir Hugh Turnbull (1925–1950)
 * Colonel Sir Arthur Young (1950–1971)
 * James Page (1971–1977)
 * Peter Marshall (1977–1985)
 * Owen Kelly (1985–1994)
 * William Taylor (1994–1998)
 * Perry Nove (1998–2002)
 * James Hart (2002–2006)
 * Mike Bowron (2006–2011)
 * Adrian Leppard (2011–2015)
 * Ian Dyson (2016–2022)
 * Angela McLaren (2022–present)

Officers killed in the line of duty
According to the Police Roll of Honour Trust, 32 City of London Police staff have died in the line of duty, the first in 1857 and the most recent in 2002. Line-of-duty deaths include three officers who were fatally shot in 1910 prior to the Siege of Sidney Street; several killed in Nazi German air raids over London in 1941 and 1942; and the 1993 death of Commander Hugh Moore (who suffered a heart failure following a violent arrest).

Organisation
The City Police is organised into five directorates:
 * Economic Crime Directorate
 * Crime Directorate
 * Uniformed Policing Directorate
 * Information and Intelligence Directorate
 * Business Support Directorate

Because of the City's role as a world financial centre, the City of London Police has developed a great deal of expertise in dealing with fraud and "is the acknowledged lead force within the UK for economic crime investigation." The Economic Crime Directorate includes:
 * Dedicated Card and Payment Crime Unit (DCPCU)
 * Insurance Fraud Department (IFED)
 * National Fraud Intelligence Bureau (NFIB) and Action Fraud
 * Police Intellectual Property Crime Unit (PIPCU)
 * Economic Crime Academy (ECA) responsible for delivering counter fraud and economic crime training both nationally and internationally
 * The Directorate also formerly had an Overseas Anti-Corruption Unit (OACU), however this unit (along with the Metropolitan Police's Proceeds of Corruption Unit) was transferred to the NCA in 2015 and renamed the International Corruption Unit (ICU).

Leadership structure

 * Commissioner – Angela McLaren
 * Assistant Commissioner (Operational Policing) – Paul Betts
 * Assistant Commissioner (Fraud and Cyber Crime) – Peter O'Doherty
 * Chief Operating Officer - Mari Ladu
 * Commander (Operations and Security) – Umer Khan
 * Commander (National Coordinator for Economic and Cyber Crime) – Nik Adams

Uniform

Whereas the majority of British police forces have white metal cap badges and buttons, those of the City Police are brass. The force also have red and white chequered sleeve and cap bands (red and white being the colours of the City of London), which in most other British police forces are black and white. In formal uniform, female officers wear a red and white cravat.

Their helmet (worn by male constables and sergeants) has altered little since its introduction in 1865 and has a crest instead of the white metal boss worn on the Metropolitan Police helmet. The "helmet plate" or badge is the City of London coat of arms; this is unusual for a police force in England and Wales in that it does not include St Edward's Crown, neither does it have the Brunswick Star, which is used on most other police helmets in England and Wales.

On state and ceremonial occasions, the commissioner and assistant commissioners wear a special court dress uniform with a gold aiguillette and a cocked hat adorned with white swan's feathers; other than on these occasions, they wear standard uniform.

Equipment and vehicles
City of London police officers carry warrant cards. Like most other police forces in Great Britain, City of London police officers are not routinely armed, but some officers have received firearms training and are authorised firearms officers. City of London police equipment includes PAVA irritant spray, batons, and handcuffs. Many officers are also equipped with the Taser electroshock weapon; according to the police force's reported figures, Tasers have been deployed (including drawing or "red-dotting") about seven times per month. In the September 2018 to September 2020 period, the City of London Police recorded 11 incidents of police officers firing Tasers on suspects.

The City of London Police maintains a fleet of police vehicles, including SUVs, compact cars, motorcycle, and vans, as well as one horsebox. All of the force's response vehicles, including armed response vehicles (ARVs) carry a defibrillator and first aid supplies, for use in the event of an emergency.

Mounted unit
The City of London Police maintains a mounted police unit. In addition to regular duties, the horses of the mounted unit have been used to trample wildflower seeds at the Barbican Wildlife Garden at the request of the community wildlife gardeners. The horses' ceremonial duties include participation in Trooping the Colour and the Lord Mayor's Show; the City of London Police mounted unit also escorted the exhumed remains of King Richard III through the city of Leicester from St Nicholas Church to Leicester Cathedral, en route to their reburial.

Ranks
The ranks from constable to chief superintendent are the same as all other British police forces. The three senior ranks are similar to those used by the Metropolitan Police.

Insignia
Constables and sergeants display collar numbers on their rank badges (in the range 1 to 150 for sergeants and 151 to 999 for constables). Officers between the ranks of inspector and chief superintendent (who do not have collar numbers) display their warrant numbers instead. All officers also wear name badges with their rank and surname (e.g. Police Constable John Smith would wear a badge displaying "Constable Smith").

The City of London police also has a special constabulary with seven ranks of officers. As with regular officers, constables and sergeants display collar numbers on their rank badges (in the range 1001 to 1099 for sergeants and 1101 to 1299 for constables) and officers between the ranks of inspector and chief superintendent display their warrant numbers, in all cases followed by the letters "SC". The rank badge for a special commander is identical to that for a regular commander. Name badges are identical to those worn by regular officers (e.g. Special Sergeant Mary Jones would wear a badge displaying "Sergeant Jones").

As well as a PCSO rank

Workforce
The following is the current released workforce data. The "chief officer" category includes the commissioner, assistant commissioner and commanders, and the "special constable" category includes all special constable ranks.

History
The City of London Police have had special constables since at least 1911, when 1,648 were called for duty during docks strikes. There was one day in 1918, when the only warranted officer within the city of London was a special constable

Current status
It consists of 62 special constables, the majority of whom are attached to the Uniformed Policing Directorate (led by a special superintendent, who forms part of that directorate's management team, assisted by a special chief inspector and a number of special inspectors and special sergeants), and undertake duties during evenings and nights in support of the regular force in dealing with issues arising from the busy night-time economy of the city. However, other officers perform more specialist roles in the force's other directorates, including fraud investigation in the Economic Crime Directorate and control room operation in the Intelligence and Information Directorate. Many officers have specialist training and perform duties as response drivers, "Level 2" public order officers and cycle officers.

As in all forces, special constables are expected to commit to a minimum of 200 hours' duty each year, and in return receive out-of-pocket expenses and free travel on the Transport for London network. They receive no pay.

Uniform and equipment is identical to that of regular (full-time) police officers. Officers of the Honourable Artillery Company Detachment of Special Constabulary (which forms part of the CLSC) wear the title "HAC" when in formal uniform. Special Constables have four-digit collar numbers beginning 11 or 12, and Special Sergeants have four-digit collar numbers beginning 10.

The CLSC were awarded the Ferrers Trophy in 2006 for the efforts of their officers after the 7 July 2005 London bombings. The award is given annually to police volunteers, for exceptional dedication and innovation. It was the first time in the award's history that an entire special constabulary received the trophy.

Honourable Artillery Company Detachment
In 1919, following a decision to increase the strength of the Metropolitan Police Reserve Force, the Home Secretary approached the Honourable Artillery Company to form a division of special constabulary. Some 150 members, mostly Great War veterans, rallied to the call and joined the division, forming the HAC Detachment. At the outbreak of the Second World War, the detachment was integrated into G Division of the Metropolitan Police and then later with Islington Division. Following reorganisation, the detachment is now part of the City of London Police Special Constabulary, its administrative base is Armoury House.

In 2010, the Ferrers Trophy was awarded to Special Constable Patrick Rarden of the detachment for using his banking skills and experience to help train colleagues and provide invaluable assistance to solve fraud cases.

Olympics

Teams of the City of London Police have participated in the Olympic games three times in the tug of war tournament. At the 1908 Summer Olympics they won the gold medal, beating a team of the Liverpool Police in the final. In 1912 the team was beaten in the final by one of the Stockholm Police. At the 1920 Summer Olympics the team regained its title, beating the Netherlands. This was the last time tug of war was an Olympic sport, which means the City of London Police is still the reigning Olympic champion.

Museum
The City of London Police Museum is dedicated to the police force and its story of policing. Exhibits include uniforms, Victorian-era police equipment and artefacts, communication devices, World War II displays, and exhibits about Jack the Ripper and other famous murder cases.

The museum relocated in November 2016 to the space formerly used by the Clockmakers' Museum, next to the Guildhall Library. The new museum was funded by a £90,000 Heritage Lottery Fund grant. It was closed to become a COVID testing centre during the COVID-19 pandemic and as of May 2022 had not yet reopened.

Other corporation policing bodies
The Corporation of London, the local authority for the city, also operates further limited policing bodies. These bodies are not part of the City of London Police:
 * City of London market constabularies
 * Hampstead Heath Constabulary,
 * Epping Forest Keepers

title: City of London Police


text:
Bishopsgate

Bishopsgate was one of the eastern gates in London's former defensive wall. The gate's name is traditionally attributed to Earconwald, who was Bishop of London in the 7th century. It was first built in Roman times and marked the beginning of Ermine Street, the ancient road running from London to York (Eboracum). The gate was rebuilt twice in the 15th and 18th centuries, but was permanently demolished in 1760.

Bishopsgate gave its name to the Bishopsgate Ward of the City of London. The ward is traditionally divided into Bishopsgate Within, inside the line of the former wall, and Bishopsgate Without beyond it. Bishopsgate Without is described as part of London's East End. The ancient boundaries of the City wards were reviewed in 1994 and 2013, so that the wards no longer correspond very closely to their historic extents. Bishopsgate Without gained a significant part of Shoreditch from the London Borough of Hackney, while nearly all of Bishopsgate Within was transferred to other wards.

Bishopsgate is also the name of the street, being the part of the originally Roman Ermine Street (now the A10) within the traditional extent of the Ward.

The gate
The gate was first built in the Roman era, probably at the time the wall was first built. The road though the gate, Ermine Street (known at this point as Bishopsgate) was in place long before the wall and the gate.

The gate is traditionally held to be named after Earconwald, a 7th-century Bishop of London (Bishop of the East Saxons). One of the ward's ancient churches, St Ethelburga-the-Virgin within Bishopsgate, is dedicated to Eorconwald's sister, St Ethelburga of Barking, the first Abbess of Barking Abbey.

In 1471, during the Wars of the Roses, the Yorkist-turned supporter of the House of Lancaster Bastard Fauconberg attacked London, trying to force his way across London Bridge and also attacking the eastern gates with a further five thousand men and artillery. Bishopsgate was set on fire and the attackers came close to capturing nearby Aldgate and with it the city. The attackers were repulsed from both gates with heavy losses, before being chased back to Bow Bridge and Blackwall.

The Bishop's Gate was rebuilt by the Hansa merchants in 1471 in exchange for steelyard privileges. Its final form was erected in 1735 by the City authorities, but demolished in 1760. This gate often displayed the heads of criminals on spikes. London Wall (which is no longer extant in this sector) divided the ward and road into an intramural portion called Bishopsgate Within and an extramural portion called Bishopsgate Without.

The site of this former gate is marked by a stone bishop's mitre, fixed high upon a building located near Bishopsgate's junction with Wormwood Street, by the gardens there and facing the Heron Tower.

Ward
The ward is notable for its skyscrapers, and is home to the main London offices of several major banks, including National Westminster Bank and the European Bank for Reconstruction and Development. Although tens of thousands of people commute to and work in the ward, it has a resident population of only 222 (2011).

The ward is divided into two parts by the line of the former London Wall and gate which lay just north of Wormwood and Camomile Streets.

Bishopsgate Without
Bishopsgate Without corresponds to the parish of St Botolph-without-Bishopsgate. The church is located immediately north of the site of the original Gate on the west side of the road. The church was one of four in medieval London dedicated to Saint Botolph or Botwulf, a 7th-century East Anglian saint; three of these were outside city gates, with a fourth near London Bridge and the riverside wharves. The locations result from Botolph being regarded as the patron saint of boundaries, and by extension of trade and travel.

The eastern boundary of Bishopsgate Without is formed by Middlesex Street (better known as Petticoat Lane), with Blomfield Street on the western boundary. Blomfield Street was built on part of the historic course of the former River Walbrook, known at this point as Deepditch. Beyond Deepditch was the Moorfields (in Coleman Street Ward). The Blomfield Street section of the river was the focal point of the Walbrook Skulls; the result of the deposit of large quantities of decapitated Roman-era human skulls into the water. These are still often uncovered during building work.

Bishopsgate Without was, from 1247 to 1633, the first home of the Bethlem Royal Hospital (also known as Bedlam). This psychiatric hospital lay immediately north of St Botolph's church.

Around 1597, the merchant Sir Paul Pindar, purchased several existing properties, and built himself a new home on the site (incorporating part of one or more of the old properties). The house had a fairly narrow frontage but extended a long way back. Bishopsgate Street had recently been paved, making the site convenient for Pindar's business activities in East Anglia. The house had views over the open space in nearby Moorfields and Finsbury Fields, west of the Walbrook. The house was soon prestigious enough to be used as a base by several foreigh ambassadors, including the Venetian ambassador Pietro Contarini in 1617–18.

The district was then on the edge of London, something Contarini had mixed feelings about, describing Bishopsgate Without as "…an airy and fashionable area…a little too much in the country"

In the 1600s, Bishopsgate Without, together with neighbouring Bethnal Green and Spitalfields was home to many Huguenot refugees, many of them weavers. In the late 1600s wealthy residents began to migrate to the newly developed areas of West End of London and the character of the area began to change, partly due to the more prosperous parts of the community leaving, and partly to the densification of the area and rapid urbanisation of the neighbouring rural areas.

In time, the East and West Ends of London became more strikingly different in character, writing of the period around 1800, Rev. Richardson commented:

"The inhabitants of the extreme east of London knew nothing of the western localities and vice-versa. There was little communication or sympathy between the two ends of London. …and thus the householders of Westminster were as distinct from householders of Bishopsgate Without, Shoreditch and all those localities which stretch towards the Essex side of the city, as they are from the inhabitants of Holland or Belgium."

Bishopsgate Without was a very densely populated neighbourhood, prior to the opening (1874) and later expansion (1891) of Liverpool Street station, which now dominates the area. The initial opening of the station saw 3,000 residents of Bishopsgate Without evicted and their homes demolished. Around 7,000 people in neighbouring Shoreditch also lost their homes to the railway tracks feeding into the station.

Notable buildings include:
 * Broadgate Tower
 * Heron Tower
 * Liverpool Street station
 * Great Eastern Hotel
 * Bishopsgate Institute
 * Broadgate Estate
 * Dirty Dick's (a 200 year old pub)
 * Bishopsgate Victorian Bath House

Bishopsgate Within
Bishopsgate Within was originally divided into many parishes, each with its own parish church: St Andrew Undershaft, St Ethelburga Bishopsgate, St Martin Outwich, St Mary Axe and St Helen's Bishopsgate, now all amalgamated under the last of these. St Helen's is a historic medieval church and former monastic establishment with many ancient funerary monuments and a stained glass window commemorating William Shakespeare, a local parishioner in the early to mid-1590s. The area was well located for Shakespeare, being close to the theatres in Shoreditch where he worked; The Theatre and the Curtain Theatre.

Notable buildings include:
 * 99 Bishopsgate
 * 100 Bishopsgate
 * Tower 42
 * 22 Bishopsgate

Ward boundary changes
The 1994 (city), 2003 and 2013 (ward) boundary revisions made fundamental changes to the ancient boundaries of the ward. The 1994 changes saw Bishopsgate Without (and with it the City of London) gain a large area from the Shoreditch area of the London Borough of Hackney,

The changes made in 2003 and 2013 shifted land between wards of the city. The effect of this was to transfer nearly all of Bishopsgate Within (except for a small area surrounding the Leathersellers' livery hall) to other wards. The ward previously extended much further south, along the Bishopsgate road and Gracechurch Street. At this time Bishopsgate Without lost a small block of buildings east Blomfield Street to the Broad Street ward.

There were no changes to Bishopsgate's ward boundaries in the 2013 boundary changes.

The revised ward borders the London Borough of Hackney to the north, it neighbours The Portsoken and the borough of Tower Hamlets in the east. The other neighbours are Aldgate (southeast), Coleman Street (west), Cornhill (south-west), Broad Street and Lime Street (south).

Politics
Bishopsgate is one of 25 wards in the City of London, each electing an Alderman to the Court of Aldermen, and Commoners (the City equivalent of a councillor) to the Court of Common Council of the City of London Corporation. Only electors who are Freemen of the City of London are eligible to stand. On 15 September 2022 the ward elected Kawsar Zaman as its Alderman. He is only the third non-white Alderman in the city's hundreds of years of history, the first British-Bangladeshi ever to hold the office, and the youngest ever elected to the Court of Alderman.

Street
The street called Bishopsgate (formerly Bishopsgate Street), which takes its name from the Gate, is the main thoroughfare of the Ward. It is a stretch of the originally Roman Ermine Street (now the A10) between Gracechurch Street and Norton Folgate, taking the name Bishopsgate only within the historical area of the ward.

Although it takes its name from the gate, the road pre-dates the building of the London Wall which was built in the late second or early third centuries. Ermine Street (sometimes called the Old North Road) connected London to Cambridge, Lincoln, York and other towns and cities.

Early history
In the Roman period it was illegal to bury the dead within the city, so cemeteries were established outside the city gates. There were large burial grounds outside Bishopsgate, on both side of Ermine Street.

The wards of London appear to have taken shape in the 11th century, before the Norman Conquest. Their administrative, judicial and military purpose made them equivalent to hundreds in the countryside. The primary purpose of wards like Bishopsgate, which included a gate, appears to be the defence of the gate, as gates were the weakest points in any fortification.

The earliest origins of the wards reach back further than the 11th century but their emergence and evolution is uncertain and any narrative conjectural. The ward may have developed from the Soke of Bishopsgate, a set of rights, and possibly land, held by the Bishop of London over an area to the east of the River Walbrook. The Bishop may have been granted the land and rights in order to promote growth in the under-developed part of the city east of the Walbrook. Outside the wall the Walbrook formed the boundary between the Soke of Bishopsgate to the east and the Soke of Cripplegate on the other side of the brook.

Bishopsgate may have originally included the area that subsequently became known as Lime Street Ward.

The Domesday Survey of 1086 did not cover London, but a landholding called Bishopsgate is recorded nearby; this may have been the property later known as Norton Folgate.

Coaching inns
Bishopsgate had many coaching inns which accommodated passengers setting out on the originally Roman Ermine Street, that issued from the gate. Although they survived the Great Fire of London, they have now all been demolished. These included the Angel, the Black Bull, the Dolphin, the Flower Pot, the Green Dragon, the Magpie and Punchbowl, the White Hart and the Wrestlers. The Black Bull was a venue for the Queen's Men theatrical troupe in the 16th century. The English politician Anthony Bacon moved nearby with his mother in May 1594 and she complained about the plays and interludes at the Bull which might "corrupt his servants".

An inn called the Catherine Wheel (demolished 1911) is commemorated by Catherine Wheel Alley which leads off Bishopsgate to the east. The 17th century façade of Sir Paul Pindar's House on Bishopsgate, demolished, with many other old buildings, for the expansion of Liverpool Street railway station in 1890, was also preserved and can now be seen in the Victoria and Albert Museum. In the 18th century this grand residence became a tavern called Sir Paul Pindar's Head; another notable venue was the London Tavern (1768–1876). Also demolished (but then re-erected in Chelsea in 1910) was the old Crosby Hall, at one time the residence of Richard III and Thomas More.

Bishopsgate Mutiny
In 1649, during the Wars of the Three Kingdoms, Colonel Whalley's Regiment, a parliamentary unit, was stationed in Bishopsgate Ward, helping to protect London from Royalists. The Bishopsgate mutiny occurred when soldiers of the regiment, mutinied against parliament - partly due to their radical Leveller sympathies. A surrender was eventually negotiated, but Robert Lockyer a parishioner of Bishopsgate Without as well as a soldier in the regiment, was executed as a ringleader.

Communist Manifesto
The Communist Manifesto was first printed, anonymously and in German, by the Workers Educational Association at 46 Liverpool Street in Bishopsgate Without in 1848.

Terrorist attack
On 24 April 1993, it was the site of an IRA truck bombing which killed journalist Ed Henty, injured over 40 people and caused £1 billion worth of damage, including the destruction of St Ethelburga's church and damage to the NatWest Tower and Liverpool Street station. Police had received a coded warning, but were still evacuating the area at the time of the explosion. The area had already suffered damage from the Baltic Exchange bombing one year before.

St Ethelburga's was rebuilt, functioning not just as a church but also as home to the St Ethelburga's Centre for Reconciliation and Peace charity.

title: Bishopsgate


text:
SMAD

SMAD may refer to:
 * Soviet Military Administration in Germany, government of the Soviet occupation zone of Germany from May 1945 to October 1949
 * Solvated metal atom dispersion, a method of producing nanoparticles
 * SMAD (protein), proteins involved in cell signaling
 * I-SMAD, inhibitory SMAD proteins
 * R-SMAD, receptor regulated SMAD proteins
 * Smad, Syria, a village in southern Syria

title: SMAD


text:
House of Milan

House of Milan (HOM) was a successful publisher of bondage magazines and BDSM videos, that was mostly run by fetish photographer and producer Barbara Behr. HOM was considered one of the three big houses during the period known as the Golden Age of Bondage productions, along with Harmony Communications (later renamed to Harmony Concepts) and California Star (Calstar) from approximately the mid-1970s to the late 1990s.

House of Milan was sold to Lyndon Distributors, which occasionally reprinted and reissueed some of the House of Milan magazines.

Some of HOM's longest-running titles have included:
 * Bondage Classics (1972 - 1991)
 * Bondage in the Buff (1982 - 1999)
 * Bondage Photographer (1982 - 2000)
 * Bound to Please (1972 - 1999)
 * Captured  (1975 - 1999)
 * Hogtie (1972 - 1992)
 * Hogtied (1993 - 1999)
 * Hush  (1993 - 1999)
 * Kidnaped! (1975 - 1992)
 * Knotty (1971 - 2002)
 * Latent Image (1972 - 1995)
 * Leashed (1983 - 2002)
 * Now, Darling (1983 - 1992)
 * Punished  (1978 - 2001)
 * Slave Auction (1985 - 1992)
 * Strict  (1982 - 1997)
 * Men in Bondage  (1980 - 1985)
 * Suspended  (1982 - 1992)
 * Tied & Tickled (1981 - 1993)
 * Ties That Bind (1985 - 1999)
 * Tight Ropes (1980 - 2001)

title: House of Milan


text:
River Ravensbourne

The River Ravensbourne is a tributary of the River Thames in south London, England. It flows into the tidal River Thames at Deptford, where its tidal reach is known as Deptford Creek.

Geography
The Ravensbourne is 11 miles (17 km) in length with a total catchment area of 180 km2. It flows through the London Boroughs of Bromley, Lewisham and Greenwich.

The Ravensbourne rises at Caesar's Well, Keston, four miles south of Bromley town centre, and flows initially in a northerly direction. For the initial third of its length, the river flows across common land (including Hayes Common and Bromley Common) until it reaches the southern outskirts of Bromley town. There it is joined by the Ravensbourne South Branch and the Ravensbourne East Branch, which substantially increase the flow. The Ravensbourne then flows northwards alongside the A21, passing below Bromley town centre through Church Gardens and Glassmill Reservoir, then on into Beckenham Place Park, the last semi-natural reach of the river. Further north, it passes through Ladywell Fields, where considerable restoration work has been taking place since 2007/08, with the removal of a long stretch of 1980's concrete channeling, re-routing to more closely match its natural course, and the introduction of terraces and submerged aquatic vegetation (SAV) to provide animal habitat and improve flood control.

North of Ladywell Fields, passing to the east of Ladywell station, it continues under Lewisham, passing west of the Lewisham Shopping Centre and forming the boundary of the Cornmill Gardens playground. It flows to the east of Lewisham station, and then flows north into Deptford, forming the northeastern border of Brookmill Park. The Docklands Light Railway closely follows this stretch from Lewisham to Greenwich, as the river is crossed by the A2 and then widens north of Deptford Bridge station into its tidal reach, where it is named Deptford Creek.

Its confluence with the Thames is in Greenwich Reach, north-east of Deptford town centre and west of Greenwich.

Tributaries
South of Bellingham, the small Spring Brook joins the Ravensbourne after flowing only about one mile (1.6 km) from the east through Plaistow and Downham; it crosses the borough boundary from Bromley to Lewisham and follows a narrow strip of parkland named Shaftesbury Park Recreation Ground and Downham Playing Fields along its short course.

Just above Catford the Ravensbourne is joined by the River Pool. The Ravensbourne is also joined by the River Quaggy (known upstream of Sundridge Park as Kyd Brook, and 3.5 miles (5.6 km) in length). This rises near Princess Royal University Hospital at Locksbottom then flows north through Petts Wood to Sundridge Park in Bromley where its name changes to the River Quaggy. It then flows northwards through the Mottingham area to Kidbrooke where it then turns westwards through Manor Park in Lee, before joining the Ravensbourne at Loampit Vale in Lewisham.

Numerous other small streams and surface water outfalls join the main river between its source and confluence. Until the 19th century one such stream flowed from Brockley Cross crossing Tanners Hill before joining at Deptford Creek.

History
The earliest documented name is Randesbourne 1360, then Rendesburne 1372, Randysborne 1516 and Ravensburn 1575. The later spelling of Ravensbourne is thus due to folk etymology, and the likely meaning is 'boundary stream', from Old English rand and burna. In its ten-mile course, the Ravensbourne forms the boundary between several sets of parishes.

The Domesday Book recorded eleven corn mills on the Ravensbourne in the 11th century. The 17th century London diarist John Evelyn bought one of these mills – Brookmills – in 1668 for "grinding colour" from the Beecher family. It was later used by the Kent Waterworks company. It was finally demolished in the 1850s.

The bridge over Deptford Creek was the site of the Battle of Deptford Bridge, 17 June 1497, the last battle of the Cornish Rebellion of 1497.

From the 16th century onwards until its closure in the 19th century, the proximity of Deptford Dockyard, a Royal Dockyard created by Henry VIII, gave employment to many small shipbuilders on the creek. Queen Elizabeth I knighted Francis Drake on board the Golden Hind in Deptford Creek on Drake's return from his circumnavigation of the globe in 1580. The Golden Hind remained moored in the creek until it broke up.

Deptford Creek was also host to a large power station, now dismantled, as well as other heavy industries. Now regeneration of the area is under way. For much of the lower reach between Lewisham and the Thames, the Ravensbourne (and Deptford Creek) is joined by the Docklands Light Railway. Indeed, the channel was diverted in Brookmill Park so that the DLR could run along the route of the river. A new bend in the river was constructed that gave more natural banks and created a better habitat for flora and fauna. Just south of the DLR's final northern crossing of the river, on the eastern bank, is Deptford pumping station, constructed in the 1860s as part of the London sewerage system. There are also a number of new developments, including the Laban Dance Centre and apartment blocks at the mouth of the creek alongside the Thames, approximately 0.5 km west of Greenwich town centre.

Between 1974 and 1997, the name of the river was used for the Ravensbourne Parliament constituency within the London Borough of Bromley. It also gives its name to a railway station. Every year on 1 May at 5.32am, the Ravensbourne Morris Men dance up the Beltaine Sunrise at Caesars Well, the source of the Ravensbourne River.

title: River Ravensbourne


text:
Metropolitan Borough of Westminster

The Metropolitan Borough of Westminster was a metropolitan borough in the County of London, England, from 1900 to 1965.

City status
By royal charter dated 29 October 1900, the borough was granted the title City of Westminster. Westminster had originally been created a city and seat of the short-lived Diocese of Westminster in 1541. The diocese was suppressed in 1550, but the area was still known as a "city", although without official sanction.

Arms and motto
The arms of Westminster represent two monarchs, closely associated with the City. Edward the Confessor, who rebuilt the church of St Peter (Westminster Abbey), and Henry VII, who added a chapel, within the Abbey. The portcullis and rose emblems are derived from the Tudor dynasty, from which Westminster first achieved its status; and they appear throughout many public and religious buildings in Westminster, and the portcullis was adopted by the House of Commons. The supporting lions are adopted from the Cecil family, who have had a long association with the borough. The arms were first granted in 1601.

The motto Custodi Civitatem Domine, is translated as O Lord, watch over the City.

The arms can still be seen on the Portland stone parapet of the former Westminster City Hall in St Martin's Place (built in 1890–91 by Robert Walker, replacing an earlier vestry hall). It can also be seen on the entrance to the car park beneath 10 Spring Gardens (home of the British Council) and on Chelsea and Hammersmith Bridges.

Formation and boundaries
It consisted of the area that is now part of the City of Westminster and south of Oxford Street and Bayswater Road. It included Soho, Mayfair, St. James's, The Strand, Westminster, Pimlico, Belgravia, and Hyde Park.

The borough was formed from eleven civil parishes and extra-parochial places: Close of the Collegiate Church of St Peter, Liberty of the Rolls, Precinct of the Savoy, St Anne Soho, St Clement Danes, St George Hanover Square, St James Piccadilly, St Martin in the Fields, St Mary-le-Strand, St Paul Covent Garden and Westminster St Margaret and St John. These eleven were combined into a single civil parish called City of Westminster, which was conterminous with the metropolitan borough, in 1922.

Previous to the borough's formation it had been administered by five separate local bodies: the Vestry of St George Hanover Square, the Vestry of St Martin in the Fields, Strand District Board of Works, Westminster District Board of Works and the Vestry of Westminster St James. The Close of the Collegiate Church of St Peter had not been under the control of any local authority prior to 1900.

Population and area
The borough covered 2503 acre. The population recorded in the Census was:

Constituent parishes 1801–1899 Metropolitan Borough 1900–1961

Politics
The borough was divided into fourteen wards for elections: Charing Cross, Conduit, Covent Garden, Great Marlborough, Grosvenor, Hamlet of Knightsbridge, Knightsbridge St George's, Pall Mall, Regent, St Anne, St John, St Margaret, Strand and Victoria.

Parliament constituency
For elections to Parliament, the borough was divided into three constituencies: In 1918 the borough's representation was reduced to two seats: In 1950 the borough's representation was reduced to half a seat, when it was merged with the City of London:
 * St George's, Hanover Square
 * Strand
 * Westminster
 * Westminster Abbey
 * Westminster St George's
 * Cities of London and Westminster

Poor law
The parishes which made up the borough were within the St George's, Strand and Westminster unions. The unions were amalgamated in 1913 to form the City of Westminster Union. The parishes and unions were then abolished in 1922 and replaced with a single City of Westminster parish for poor law purposes. The parish continued to exist until 1965, but ceased to have any role in the administration of the poor law in 1930 when responsibility transferred to the London County Council.

Replacement
It was abolished in 1965 and its area became part of the City of Westminster along with the Metropolitan Borough of Paddington and the Metropolitan Borough of St Marylebone.

title: Metropolitan Borough of Westminster


text:
Walsh function

In mathematics, more specifically in harmonic analysis, Walsh functions form a complete orthogonal set of functions that can be used to represent any discrete function—just like trigonometric functions can be used to represent any continuous function in Fourier analysis. They can thus be viewed as a discrete, digital counterpart of the continuous, analog system of trigonometric functions on the unit interval. But unlike the sine and cosine functions, which are continuous, Walsh functions are piecewise constant. They take the values −1 and +1 only, on sub-intervals defined by dyadic fractions.

The system of Walsh functions is known as the Walsh system. It is an extension of the Rademacher system of orthogonal functions.

Walsh functions, the Walsh system, the Walsh series, and the fast Walsh–Hadamard transform are all named after the American mathematician Joseph L. Walsh. They find various applications in physics and engineering when analyzing digital signals.

Historically, various numerations of Walsh functions have been used; none of them is particularly superior to another. This articles uses the Walsh–Paley numeration.

Definition
We define the sequence of Walsh functions $$W_k : [0,1] \rightarrow \{-1,1\}$$, $$k\in\mathbb{N}$$ as follows.

For any natural number k, and real number $$x \in [0,1]$$, let

 * $$k_j$$ be the jth bit in the binary representation of k, starting with $$k_0$$ as the least significant bit, and

 * $$x_j$$ be the jth bit in the fractional binary representation of $$x$$, starting with $$x_1$$ as the most significant fractional bit.

Then, by definition

 * $$W_k(x) = (-1)^{\sum_{j=0}^\infty k_jx_{j+1}}$$

In particular, $$W_0(x) = 1$$ everywhere on the interval, since all bits of k are zero.

Notice that $$W_{2^m}$$ is precisely the Rademacher function rm. Thus, the Rademacher system is a subsystem of the Walsh system. Moreover, every Walsh function is a product of Rademacher functions:

 * $$W_k(x) = \prod_{j=0}^\infty r_j(x)^{k_j}$$

Comparison between Walsh functions and trigonometric functions
Walsh functions and trigonometric functions are both systems that form a complete, orthonormal set of functions, an orthonormal basis in the Hilbert space $$L^2[0,1]$$ of the square-integrable functions on the unit interval. Both are systems of bounded functions, unlike, say, the Haar system or the Franklin system.

Both trigonometric and Walsh systems admit natural extension by periodicity from the unit interval to the real line. Furthermore, both Fourier analysis on the unit interval (Fourier series) and on the real line (Fourier transform) have their digital counterparts defined via Walsh system, the Walsh series analogous to the Fourier series, and the Hadamard transform analogous to the Fourier transform.

Properties
The Walsh system $$\{W_k\}, k \in \mathbb{N}_0$$ is an abelian multiplicative discrete group isomorphic to $$\coprod_{n=0}^\infty \mathbb{Z}/2\mathbb{Z}$$, the Pontryagin dual of the Cantor group $$\prod_{n=0}^\infty \mathbb{Z}/2\mathbb{Z}$$. Its identity is $$W_0$$, and every element is of order two (that is, self-inverse).

The Walsh system is an orthonormal basis of the Hilbert space $$L^2[0,1]$$. Orthonormality means

 * $$\int_0^1 W_k(x)W_l(x) dx = \delta_{kl}$$,

and being a basis means that if, for every $$f \in L^2[0,1]$$, we set $$f_k = \int_0^1 f(x)W_k(x)dx$$ then

 * $$\int_0^1 ( f(x) - \sum_{k=0}^N f_k W_k(x) )^2 dx \;\ \xrightarrow[N\rightarrow\infty]{}\;\ 0$$

It turns out that for every $$f \in L^2[0,1]$$, the series $$\sum_{k=0}^\infty f_k W_k(x)$$ converges to $$f(x)$$ for almost every $$x \in [0,1]$$.

The Walsh system (in Walsh-Paley numeration) forms a Schauder basis in $$L^p[0,1]$$,  $$1 < p < \infty$$. Note that, unlike the Haar system, and like the trigonometric system, this basis is not unconditional, nor is the system a Schauder basis in $$L^1[0,1]$$.

Walsh-Ferleger systems
Let $$\mathbb{D} = \prod_{n=1}^\infty \mathbb{Z}/2\mathbb{Z}$$ be the compact Cantor group endowed with Haar measure and let $$ \hat {\mathbb D} = \coprod_{n=1}^\infty \mathbb Z / 2\mathbb Z $$ be its discrete group of characters. Elements of $$ \hat {\mathbb D} $$ are readily identified with Walsh functions. Of course, the characters are defined on $$ \mathbb D $$ while Walsh functions are defined on the unit interval, but since there exists a modulo zero isomorphism between these measure spaces, measurable functions on them are identified via isometry.

Then basic representation theory suggests the following broad generalization of the concept of Walsh system.

For an arbitrary Banach space $$(X, ||\cdot||)$$ let $$\{ R_t \}_{t \in \mathbb D} \subset \operatorname{Aut}X$$ be a strongly continuous, uniformly bounded faithful action of $$\mathbb D$$ on X. For every $$\gamma \in \hat{\mathbb D}$$, consider its eigenspace $$ X_\gamma = \{x \in X : R_t x = \gamma(t)x \}$$. Then X is the closed linear span of the eigenspaces: $$X = \overline{\operatorname{Span}}(X_\gamma, \gamma \in \hat {\mathbb D})$$. Assume that every eigenspace is one-dimensional and pick an element $$w_\gamma \in X_\gamma$$ such that $$\|w_\gamma\| = 1$$. Then the system $$\{w_\gamma\}_{\gamma \in \hat {\mathbb D}}$$, or the same system in the Walsh-Paley numeration of the characters $$\{w_k\}_{k \in {\mathbb N}_0}$$ is called generalized Walsh system associated with action $$\{ R_t \}_{t \in \mathbb D}$$. Classical Walsh system becomes a special case, namely, for

 * $$R_t: x = \sum_{j=1}^\infty x_j2^{-j} \mapsto \sum_{j=1}^\infty (x_j \oplus t_j)2^{-j}$$

where $$\oplus$$ is addition modulo 2.

In the early 1990s, Serge Ferleger and Fyodor Sukochev showed that in a broad class of Banach spaces (so called UMD spaces ) generalized Walsh systems have many properties similar to the classical one: they form a Schauder basis and a uniform finite-dimensional decomposition in the space, have property of random unconditional convergence. One important example of generalized Walsh system is Fermion Walsh system in non-commutative Lp spaces associated with hyperfinite type II factor.

Fermion Walsh system
The Fermion Walsh system is a non-commutative, or "quantum" analog of the classical Walsh system. Unlike the latter, it consists of operators, not functions. Nevertheless, both systems share many important properties, e.g., both form an orthonormal basis in corresponding Hilbert space, or Schauder basis in corresponding symmetric spaces. Elements of the Fermion Walsh system are called Walsh operators.

The term Fermion in the name of the system is explained by the fact that the enveloping operator space, the so-called hyperfinite type II factor $$ \mathcal R$$, may be viewed as the space of observables of the system of countably infinite number of distinct spin $$1/2$$ fermions. Each Rademacher operator acts on one particular fermion coordinate only, and there it is a Pauli matrix. It may be identified with the observable measuring spin component of that fermion along one of the axes $$ \{x,y,z\}$$ in spin space. Thus, a Walsh operator measures the spin of a subset of fermions, each along its own axis.

Vilenkin system
Fix a sequence $$\alpha = (\alpha_1,\alpha_2,...)$$ of integers with $$\alpha_k \geq 2, k=1,2,\dots$$ and let $$\mathbb{G} = \mathbb{G}_\alpha = \prod_{n=1}^\infty \mathbb{Z}/\alpha_k\mathbb{Z}$$ endowed with the product topology and the normalized Haar measure. Define $$A_0 = 1$$ and $$A_k = \alpha_1 \alpha_2 \dots \alpha_{k-1}$$. Each $$x \in \mathbb G$$ can be associated with the real number

 * $$ \left|x\right| = \sum_{k=1}^{\infty} \frac{x_k}{A_{k}} \in \left[0,1\right].$$

This correspondence is a module zero isomorphism between $$\mathbb G$$ and the unit interval. It also defines a norm which generates the topology of $$\mathbb G$$. For $$k=1,2,\dots$$, let $$\rho_k: \mathbb{G}\to\mathbb{C}$$ where

 * $$\rho_k(x) = \exp\left(i\frac{2 \pi x_k}{\alpha_k}\right) = \cos\left(\frac{2 \pi x_k}{\alpha_k}\right) + i \sin\left(\frac{2 \pi x_k}{\alpha_k}\right).$$

The set $$\{\rho_k\}$$ is called generalized Rademacher system. The Vilenkin system is the group $$\hat{\mathbb G} = \coprod_{n=1}^\infty \mathbb{Z}/\alpha_k\mathbb{Z}$$ of (complex-valued) characters of $$\mathbb G$$, which are all finite products of $$\{\rho_k\}$$. For each non-negative integer $$n$$ there is a unique sequence $$n_0, n_1, \dots$$ such that $$0 \leq n_k < \alpha_{k+1}, k=0,1,2,\dots$$ and

 * $$n = \sum_{k=0}^{\infty} n_k A_k.$$

Then $$\hat{\mathbb G} = {\chi_n | n=0,1,\dots}$$ where

 * $$\chi_n = \sum_{k=0}^{\infty} \rho_{k+1}^{n_k}.$$

In particular, if $$\alpha_k = 2, k=1,2...$$, then $$\mathbb G$$ is the Cantor group and $$\hat{\mathbb G} = \left\{\chi_n | n=0,1,\dots\right\}$$ is the (real-valued) Walsh-Paley system.

The Vilenkin system is a complete orthonormal system on $$ \mathbb G $$ and forms a Schauder basis in $$L^p(\mathbb{G}, \mathbb{C})$$, $$1 < p < \infty$$.

Nonlinear Phase Extensions
Nonlinear phase extensions of discrete Walsh-Hadamard transform were developed. It was shown that the nonlinear phase basis functions with improved cross-correlation properties significantly outperform the traditional Walsh codes in code division multiple access (CDMA) communications.

Applications
Applications of the Walsh functions can be found wherever digit representations are used, including speech recognition, medical and biological image processing, and digital holography.

For example, the fast Walsh–Hadamard transform (FWHT) may be used in the analysis of digital quasi-Monte Carlo methods. In radio astronomy, Walsh functions can help reduce the effects of electrical crosstalk between antenna signals. They are also used in passive LCD panels as X and Y binary driving waveforms where the autocorrelation between X and Y can be made minimal for pixels that are off.

title: Walsh function