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# Book of Zechariah
## Composition
The return from exile is the theological premise of the prophet\'s visions in chapters 1--6. Chapters 7--8 address the quality of life God wants his renewed people to enjoy, containing many encouraging promises to them. Chapters 9--14 comprise two \"oracles\" of the future.
### Chapters 1 to 6 {#chapters_1_to_6}
The book begins with a preface in verses 1:1-6, which recalls the role of the \"former prophets\" in calling Israel in times past to repentance. Then follows a series of eight visions succeeding one another in one night, which may be regarded as a symbolical history of Israel, intended to furnish consolation to the returned exiles and to stir up hope in their minds. These visions include seeing four horses, four horns and four craftsmen, a man with a measuring line, Joshua the High Priest, a gold lampstand and two olive trees, a flying scroll and a woman in a basket, and four chariots. The symbolic action, the crowning of Joshua, describes how the kingdoms of the world become the kingdom of God\'s Messiah.
The German commentators Carl Friedrich Keil and Franz Delitzsch enumerate seven visions, arguing that the visions conventionally numbered as the sixth and the seventh are better treated as a single vision.
### Chapters 7 and 8 {#chapters_7_and_8}
Two years after the initial visions, chapters 7 and 8 are delivered. They are an answer to the question whether the days of mourning for the destruction of the city should be kept any longer. The answer is addressed to the entire people, assuring them of God\'s presence and blessing.
### Chapters 9 to 14 {#chapters_9_to_14}
This section consists of two \"oracles\" or \"burdens\": the opening words of both chapter 9 and chapter 12 (and also the first chapter of Malachi) announce \"The burden of the word of the Lord\".
- The first oracle (Zechariah 9--11) gives an outline of the course of God\'s providential dealings with his people down to the time of the coming of the Messiah, although the opening \"burden\" is addressed to the foreign nations.
- The second oracle (Zechariah 12--14) points out the glories that await Israel in \"the latter day\", the final conflict and triumph of God\'s kingdom. The \"burden\" in Zechariah 12:1 stands against Israel.
Katrina Larkin argues that there is a unity across these six chapters established by a series of short \"linking passages\" at 9:9-10, 10:1-2, 11:1-3, 11:17 and 13:7-9\". She refers to these passages as compact and metrical, addressed directly to their audience, which contain material linking with both the previous and the subsequent text.
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# Book of Zechariah
## Themes
The purpose of this book is not strictly historical but theological and pastoral. The main emphasis is that God is at work, and all his good deeds, including the construction of the Second Temple, are accomplished \"not by might nor by power, but by \[his\] Spirit\". Ultimately, YHWH plans to live again with his people in Jerusalem. He will save them from their enemies and cleanse them from sin. However, God requires repentance, a turning away from sin towards faith in him.
Zechariah\'s concern for purity is apparent in the temple, priesthood, and all areas of life as the prophecy gradually eliminates the governor\'s influence in favour of the high priest, and the sanctuary becomes ever more clearly the centre of messianic fulfillment. The prominence of prophecy is quite apparent in Zechariah, but it is also true that Zechariah (along with Haggai) allows prophecy to yield to the priesthood; this is particularly apparent in comparing Zechariah to Third Isaiah (chapters 55--66 of the Book of Isaiah), whose author was active sometime after the first return from exile.
Most Christian commentators read the series of predictions in chapters 7 to 14 as Messianic prophecies, either directly or indirectly. These chapters helped the writers of the Gospels understand Jesus\'s suffering, death, and resurrection, which they quoted as they wrote of Jesus\'s final days. Much of the Book of Revelation, which narrates the denouement of history, is also colored by images in Zechariah.
### Apocalyptic literature {#apocalyptic_literature}
Chapters 9--14 of the Book of Zechariah are an early example of apocalyptic literature. Although not as fully developed as the apocalyptic visions described in the Book of Daniel, the \"oracles\", as they are titled in these chapters, contain apocalyptic elements. One theme these oracles contain is descriptions of the Day of the Lord, when \"the Lord will go forth and fight against those nations as when he fights on a day of battle\". These chapters also contain \"pessimism about the present, but optimism for the future based on the expectation of an ultimate divine victory and the subsequent transformation of the cosmos\".
The final portion in Zechariah states that on the Day of the Lord, \"there shall be no more the Canaanite in the house of the `{{LORD}}`{=mediawiki}\", proclaiming the need for purity in the Temple, which would come when God judged at the end of time. The Hebrew word *כְנַעֲנִי*, often translated as \"Canaanite\", is alternatively translated as \"trader\" or \"trafficker\", as in other translations
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# Book of Zephaniah
250px \|thumb\|The Leningrad Codex (AD. 1008) contains the complete text of the Book of Zephaniah in Hebrew. The **Book of Zephaniah** `{{IPAc-en|ˌ|z|ɛ|f|ə|ˈ|n|aɪ|.|ə}}`{=mediawiki} (*צְפַנְיָה*, *Ṣəfanyā*; sometimes Latinized as *Sophonias*) is the ninth of the Twelve Minor Prophets of the Old Testament and Tanakh, preceded in all traditions by the Book of Habakkuk and followed by the Book of Haggai. The book has three chapters. Zephaniah is a male given name which is usually interpreted to mean \"Yahweh has hidden/protected\", or \"Yahweh hides\". The church father Jerome of Stridon interpreted Zephaniah\'s name to mean \"the watchman of the Lord\". The original text of the prophecy was written in Biblical Hebrew.
Scholars propose various dates of composition; some scholars argue that the book was probably composed during the reign of Josiah (late-seventh century BCE), while others hold that an original core of oracles was expanded and edited in exilic or later times.
## Authorship and date {#authorship_and_date}
thumb\|upright=1.1\|A 13th-century Latin Bible, possibly from Toulouse, with part of the Book of Zephaniah (Latin *Sophonias*) The book\'s superscription attributes its authorship to \"Zephaniah son of Cushi son of Gedaliah son of Amariah son of Hezekiah, in the days of King Josiah son of Amon of Judah\". All that is known of Zephaniah comes from within the text.
The name \"Cushi,\" Zephaniah\'s father, means \"Cushite\" or \"Ethiopian\", and the text of Zephaniah mentions the sin and restoration of *Cushim*. While some have concluded from this that Zephaniah was dark-skinned or African, Ehud Ben Zvi maintains that, based on the context, \"Cushi\" must be understood as a personal name rather than an indicator of nationality. Abraham ibn Ezra interpreted the name Hezekiah in the superscription as King Hezekiah of Judah, though that is not a claim advanced in the text of Zephaniah.
As with many of the other prophets, there is no external evidence to directly associate composition of the book with a prophet by the name of Zephaniah. Some scholars, such as Kent Harold Richards and Jason DeRouchie, consider the words in Zephaniah to reflect a time early in the reign of King Josiah (640--609 BC) before his reforms of 622 BC took full effect, in which case the prophet may have been born during the reign of Manasseh (698/687--642 BC). Others argue that some portion of the book is postmonarchic, that is, dating to later than 586 BC when the Kingdom of Judah fell in the Siege of Jerusalem. Some who consider the book to have largely been written by a historical Zephaniah have suggested that he may have been a disciple of the prophet Isaiah, because of the two books\' similar focus on rampant corruption and injustice in Judah. The Jerusalem Bible links Zephaniah 2:11 and 3:9-10 with the Book of Consolation (Isaiah 40-55).
## Purpose
If Zephaniah was largely composed during the monarchic period, then its composition was occasioned by Judah\'s refusal to obey its covenant obligations toward Yahweh despite having seen northern Israel\'s exile a generation or two previously, an exile which the Judahite literary tradition attributed to Yahweh\'s anger aroused by Israel\'s disobedience to the covenant. In this historical context, Zephaniah urges Judah to obedience to Yahweh, saying that \"perhaps\" he will forgive them if they do.
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# Book of Zephaniah
## Themes
thumb\|upright=1.15\|Illustration depicting Zephaniah addressing the people, from a French 16th-century Bible *The HarperCollins Study Bible* supplies headings for sections within the book as follows:
Verse (NRSV) Heading 1:1 (Superscription) 1:2--13 The Coming Judgment on Judah 1:14--18 The Great Day of the Lord 2:1--15 Judgment on Israel\'s Enemies 3:1--7 The Wickedness of Jerusalem 3:8--13 Punishment and Conversion of the Nations 3:14--20 Song of Joy
-------------- --------- ----- ------------------ --------- ------------------------------ ---------- --------------------------- --------- ------------------------------- -------- ----------------------------- --------- ------------------------------------------ ---------- -------------
: Verse and chapter headings in the HCSB
More consistently than any other prophetic book, Zephaniah focuses on \"the day of the Lord\", developing this tradition from its first appearance in Amos. The day of the Lord tradition also appears in Isaiah, Ezekiel, Obadiah, Joel, and Malachi.
The book begins by describing Yahweh\'s judgement. With a triple repetition of \"I will sweep away\" in Zephaniah 1:2--3, Zephaniah emphasizes the totality of the destruction, as the number three often signifies perfection in the Bible. The order of creatures in Zephaniah 1:2 (\"humans and animals \... the birds \... the fish\") is the opposite of the creation order in Genesis 1:1--28, signifying an undoing of creation. This is also signified by the way that \"from the face of the earth\" forms an *inclusio* around Zephaniah 1:2-3, hearkening back to how the phrase is used in the Genesis flood narrative in Genesis 6:7, Genesis 7:4, and Genesis 8:8, where it also connotes an undoing of creation.
As is common in prophetic literature in the Bible, a \"remnant\" survives Yahweh\'s judgement, by humbly seeking refuge in Yahweh. The book concludes with an announcement of hope and joy, as Yahweh \"bursts forth in joyful divine celebration\" over his people.
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# Book of Zephaniah
## Later influence {#later_influence}
Because of its hopeful tone of the gathering and restoration of exiles, `{{Bibleverse|Zephaniah|3:20|NRSV}}`{=mediawiki} has been included in Jewish liturgy.
Zephaniah served as a major inspiration for the medieval Catholic hymn \"Dies Irae,\" whose title and opening words are from the Vulgate translation of `{{Bibleverse|Zephaniah|1:15–16|NRSV}}`{=mediawiki}.
## Surviving early manuscripts {#surviving_early_manuscripts}
The original manuscript of this book has been lost. Some early manuscripts containing the text of this book in Hebrew are of the Masoretic Text tradition, which includes the Codex Cairensis (895), the Petersburg Codex of the Prophets (916), Aleppo Codex (10th century), Codex Leningradensis (1008). Fragments containing parts of this book in Hebrew were found among the Dead Sea Scrolls, including 4Q77 (4QXII^b^; 150--125 BCE), 4Q78 (4QXII^c^; 75--50 BCE), and Wadi Murabba\'at Minor Prophets (Mur88; MurXIIProph; 75-100 CE).
There is also a translation into Koine Greek known as the Septuagint, made in the last few centuries BC. Extant ancient manuscripts of the Septuagint version include Codex Vaticanus (4th century), Codex Sinaiticus (4th century), Codex Alexandrinus (5th century) and Codex Marchalianus (6th century). Some fragments containing parts of the Septuagint version of this book were found among the Dead Sea Scrolls, i.e., Naḥal Ḥever (1st century CE)
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# Book of Habakkuk
The **Book of Habakkuk** is the eighth book of the Twelve Minor Prophets of the Hebrew Bible. The book has three chapters. It is attributed to the prophet Habakkuk. Most scholars agree that the book was probably composed in the period during Jehoiakim\'s reign as king of Judah (609--597 BC). It is an important text in Judaism, and passages from the book are quoted by authors of the New Testament, and its message has inspired modern Christian hymn writers.
Of the three chapters in the book, the first two are a dialogue between Yahweh and the prophet. Verse 4 in chapter 2, stating that \"the just shall live by his faith\", plays an important role in Christian thought. It is used in the Epistle to the Romans, Epistle to the Galatians, and the Epistle to the Hebrews as the starting point of the concept of faith. A copy of these two chapters is included in the Habakkuk Commentary, found among the Dead Sea Scrolls. Chapter 3 is now recognized as a liturgical piece. It is debated whether chapter 3 and the first two chapters were written by the same author.
## Background
The prophet Habakkuk is generally believed to have written his book in the mid-to-late 7th century BC. It was likely written shortly after the Battle of Nineveh (612 BC) established the Neo-Babylonian Empire but before the Babylonian Siege of Jerusalem (587 BC) and subsequent Babylonian captivity.
### Author
In the opening verse, Habakkuk identifies himself as a prophet. Due to the liturgical nature of Habakkuk\'s book, some scholars think that the author may have been a temple prophet. Temple prophets are described in 1 Chronicles 25:1 as using lyres, harps and cymbals. Some feel that this is echoed in Habakkuk 3:19b, and that Habakkuk may have been a Levite and cantor in Solomon\'s Temple.
There is no biographical information on the prophet Habakkuk. The only canonical information that exists comes from the book that is named for him. His name comes either from the Hebrew word חבק (*ḥavaq*) meaning \"embrace\", or else from an Akkadian word *hambakuku*, for a kind of plant.
Although his name does not appear in any other part of the Bible, Rabbinic tradition holds Habakkuk to be the Shunammite woman\'s son, who was restored to life by Elisha in 2 Kings 4:16. The prophet Habakkuk is also mentioned in the narrative of Bel and the Dragon, part of the deuterocanonical additions to Daniel in a late section of that book. In the superscription of the Old Greek version, Habakkuk is called the son of Joshua of the tribe of Levi. In this book, Habakkuk is lifted by an angel to Babylon to provide Daniel with food while he is in the lion\'s den.
### Historical context {#historical_context}
It is unknown when Habakkuk lived and preached, but the reference to the rise and advance of the Neo-Babylonian Empire in 1:6--11 places him in the middle to last quarter of the 7th century BC. One possible period might be during the reign of Jehoiakim, from 609 to 598 BC. The Neo-Babylonian Empire was growing in power in this period. The Babylonians marched against Jerusalem in 598 BC. Jehoiakim died while the Babylonians marched towards Jerusalem, and Jehoiakim\'s eighteen-year-old son Jeconiah assumed the throne. Upon the Babylonians\' arrival, Jehoiachin and his advisors quickly surrendered Jerusalem and Zedekiah was appointed as a puppet king. With the transition of rulers and the young age and inexperience of Jehoiachin, they could not stand against the Babylonian forces. There is a sense of an intimate knowledge of the Babylonian brutality in 1:12--17.
## Overview
The book of Habakkuk is a book of the Hebrew Bible and stands eighth in a section known as the Twelve Minor Prophets in the Masoretic Text (𝕸) and the Septuagint. In 𝕸, it follows Nahum and precedes Zephaniah, who are considered to be his contemporaries.
The book consists of three chapters and it is neatly divided into three different genres:
- A discussion between God and Habakkuk
- An oracle of woe
- A psalm, \"Habakkuk\'s song\".
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# Book of Habakkuk
## Themes
The major theme of Habakkuk is trying to grow from a faith of perplexity and doubt to the height of absolute trust in God. Habakkuk addresses his concerns over the fact that God will use the Babylonian empire to execute judgment on Judah for their sins.
Habakkuk openly questions the wisdom of God. In the first part of the first chapter, the Prophet sees the injustice among his people and asks why God does not take action. \"Yahweh, how long will I cry, and you will not hear? I cry out to you "Violence!" and will you not save?\" -- (Habakkuk 1:2)
In the middle part of Chapter 1, God explains that he will send the Chaldeans (also known as the Babylonians) to punish his people. In 1:5: \"Look among the nations, watch, and wonder marvelously; for I am working a work in your days, which you will not believe though it is told you.\" In 1:6: \"For, behold, I raise up the Chaldeans, that bitter and hasty nation, that march through the breadth of the earth, to possess dwelling places that are not theirs.\"
One of the \"Eighteen Emendations to the Hebrew Scriptures\" appears at 1:12. According to the professional Jewish scribes, the Sopherim, the text of 1:12 was changed from \"You \[God\] do not die\" to \"We shall not die\". The Sopherim considered it disrespectful to say to God, \"*You* do not die.\"
In the final part of the first chapter, the prophet expresses shock at God\'s choice of instrument for judgment, in 1:13: \"You who have purer eyes than to see evil, and who cannot look on perversity, why do you tolerate those who deal treacherously, and keep silent when the wicked swallows up the man who is more righteous than he\[\...\]?\"`{{better source needed|date=September 2024}}`{=mediawiki}
In Chapter 2, he awaits God\'s response to his challenge. God explains that He will also judge the Chaldeans, and much more harshly. \"Because you have plundered many nations, all the remnant of the peoples will plunder you, because of men's blood, and for the violence done to the land, to the city and to all who dwell in it. Woe to him who gets an evil gain for his house.\" (Habakkuk 2:8-9)
Finally, in Chapter 3, Habakkuk expresses his ultimate faith in God, even if he does not fully understand: \"For though the fig tree doesn't flourish, nor fruit be in the vines; the labor of the olive fails, the fields yield no food; the flocks are cut off from the fold, and there is no herd in the stalls: 3:18 yet I will rejoice in Yahweh. I will be joyful in the God of my salvation!\" Some scholars suggest that the final chapter may be a later independent addition to the book, in part because it is not included among the Dead Sea Scrolls.
## Surviving early manuscripts {#surviving_early_manuscripts}
Some early manuscripts containing the text of this book in Hebrew language are found among the Dead Sea Scrolls, i.e., **1QpHab**, known as the \"Habakkuk Commentary\" (later half of the 1st century BC), and of the Masoretic Text tradition, which includes Codex Cairensis (895 CE), the Petersburg Codex of the Prophets (916), Aleppo Codex (10th century), Codex Leningradensis (1008). Fragments containing parts of this book in Hebrew were found among the Dead Sea Scrolls, including 4Q82 (4QXII^g^; 25 BCE) with extant verses 4?; and Wadi Murabba\'at Minor Prophets (Mur88; MurXIIProph; 75-100 CE) with extant verses 1:3--13, 1:15, 2:2--3, 2:5--11, 2:18--20, and 3:1--19.
There is also a translation into Koine Greek known as the Septuagint, made in the last few centuries BC. Extant ancient manuscripts of the Septuagint version include Codex Vaticanus (**B**; $\mathfrak{G}$^B^; 4th century), Codex Sinaiticus (**S**; BHK: $\mathfrak{G}$^S^; 4th century), Codex Alexandrinus (**A**; $\mathfrak{G}$^A^; 5th century) and Codex Marchalianus (**Q**; $\mathfrak{G}$^Q^; 6th century). Fragments containing parts of this book in Greek were also found among the Dead Sea Scrolls, that is, Naḥal Ḥever 8Ḥev1 (8ḤevXII^gr^); (late 1st century BCE) with extant verses 1:5--11, 1:14--17, 2:1--8, 2:13--20, and 3:8--15.
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# Book of Habakkuk
## Importance
The Book of Habakkuk is accepted as canonical by adherents of the Jewish and Christian faiths.
### Judaism
The Book of Habakkuk is the eighth book of the Twelve Prophets of the Hebrew Bible, and this collection appears in all copies of texts of the Septuagint, the Ancient Greek translation of the Hebrew Bible completed by 132 BC. Likewise, the book of Sirach (or Ecclesiasticus), also written in the 2nd century BC, mentions \"The Twelve Prophets\".
A partial copy of Habakkuk itself is included in the Habakkuk Commentary, a *pesher* found among the original seven Dead Sea Scrolls discovered in 1947. The Commentary contains a copy of the first two chapters of Habakkuk, but not of the third chapter. The writer of the *pesher* draws a comparison between the Babylonian invasion of the original text and the Roman threat of the writer\'s own period. What is even more significant than the commentary in the *pesher* is the quoted text of Habakkuk itself. The divergences between the Hebrew text of the scroll and the standard Masoretic Text are startlingly minimal. The biggest differences are word order, small grammatical variations, addition or omission of conjunctions, and spelling variations, but these are small enough not to damage the meaning of the text.
Some scholars suggest that Chapter 3 may be a later independent addition to the book, in part because it is not included among the Dead Sea Scrolls. However, this chapter does appear in all copies of the Septuagint, as well as in texts from as early as the 3rd century BC. This final chapter is a poetic praise of God, and has some similarities with Exodus 19, and with texts found in the Book of Daniel. However, the fact that the third chapter is written in a different style, as a liturgical piece, does not necessarily mean that Habakkuk was not also its author.
### Qumran community {#qumran_community}
A commentary on the first two chapters of the book was found among the Dead Sea Scrolls at Qumran. The omission of chapter 3 from the version within the Dead Sea Scrolls has been attributed to incompatibilities with the theology of the Qumran sect.
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# Book of Habakkuk
## Habakkuk 2:4 {#habakkuk_24}
The Talmud (Makkot 24a) mentions that various Biblical figures grouped the 613 commandments into categories that encapsulated all of the 613. At the end of this discussion, the Talmud concludes, \"Habakkuk came and established \[the 613 mitzvoth\] upon one, as it is stated: \'But the righteous person shall live by his faith\' (Habakkuk 2:4)\".
Habakkuk 2:4 is well known in Christianity. In the New International Version of the bible it reads:
: *See, the enemy is puffed up; his desires are not upright*
: *but the righteous person will live by his faithfulness.*
Although the second half of this passage is only three words in the original Hebrew,`{{refn|group=lower-alpha|The [[s:he:חבקוק ניקוד|Hebrew text]] is {{Script/Hebrew|וְצַדִּיק בֶּאֱמוּנָתוֹ יִחְיֶה}}}}`{=mediawiki} it is quoted three times in the New Testament. Paul the Apostle quotes it once in his Epistle to the Romans, and again in his Epistle to the Galatians; its third use is in the Epistle to the Hebrews. It became one of the most important of the verses that were used as foundations of the doctrines of the Protestant reformation.
There is controversy about the translation of the verse: the word \"emunah\" is most often translated as \"faithfulness\", though the word in this verse has been traditionally translated as \"faith\".
The word \"emunah\" is not translated as \"belief\" other than in Habakkuk 2:4, Clendenen, E. Ray defended the translation of the word as \"faith\" on the basis of the context of the verse, arguing that it refers to *Genesis 15:6*, which used the word \"*he'ĕmin\"* \'believed\' of which \"*'ĕmȗnāh*\" is derived from, he also argued that the Essenes in the Qumran community likely understood the verse as referring to faith in the Teacher of Righteousness instead of faithfulness.
Martin Luther believed that Habakkuk 2:4 taught the doctrine of faith alone, commenting on the verse \"For this is a general saying applicable to all of God\'s words. These must be believed, whether spoken at the beginning, middle, or end of the world\".
Rashi interpreted the verse to be about Jeconiah.
The Targum interpreted the verse as \"The wicked think that all these things are not so, but the righteous live by the truth of them\".
Pseudo-Ignatius understood the verse to be about faith.
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# Book of Habakkuk
## Habakkuk 2:6-20: the taunting riddle {#habakkuk_26_20_the_taunting_riddle}
The melitzah ḥidah, or the taunting riddle, is the oracle revealed to Habakkuk the prophet. It is a mashal, which is a proverb and a parable. It is also known as a witty satire, a mocking and an enigma. The riddle is 15 verses long, from verse 6 to verse 20, and is divided into five woes which consist of three verses each.
### Hebrew Text {#hebrew_text}
The following table shows the Hebrew text of Habakkuk 2:6-20 with vowels alongside an English translation based upon the JPS 1917 translation (now in the public domain).
Verse Hebrew text English translation (JPS 1917)
------- ------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
6 Shall not all these take up a parable against him, And a taunting riddle against him, And say: 'Woe to him that increaseth that which is not his! How long? and that ladeth himself with many pledges!
7 Shall they not rise up suddenly that shall exact interest of thee, And awake that shall violently shake thee, And thou shalt be for booties unto them?
8 } Because thou hast spoiled many nations, All the remnant of the peoples shall spoil thee; Because of men\'s blood, and for the violence done to the land, To the city and to all that dwell therein.
9 Woe to him that gaineth evil gains for his house, That he may set his nest on high, That he may be delivered from the power of evil!
10 Thou hast devised shame to thy house, By cutting off many peoples, And hast forfeited thy life.
11 } For the stone shall cry out of the wall, And the beam out of the timber shall answer it.
12 Woe to him that buildeth a town with blood, And establisheth a city by iniquity!
13 Behold, is it not of the LORD of hosts That the peoples labour for the fire, And the nations weary themselves for vanity?
14 } For the earth shall be filled With the knowledge of the glory of the LORD, As the waters cover the sea.
15 Woe unto him that giveth his neighbour drink, That puttest thy venom thereto, and makest him drunken also, That thou mayest look on their nakedness!
16 Thou art filled with shame instead of glory, Drink thou also, and be uncovered; The cup of the LORD'S right hand shall be turned unto thee, And filthiness shall be upon thy glory.
17 For the violence done to Lebanon shall cover thee, And the destruction of the beasts, which made them afraid; Because of men\'s blood, and for the violence done to the land, To the city and to all that dwell therein.
18 } What profiteth the graven image, That the maker thereof hath graven it, Even the molten image, and the teacher of lies; That the maker of his work trusteth therein, To make dumb idols?
19 Woe unto him that saith to the wood: 'Awake', To the dumb stone: 'Arise! ' Can this teach? Behold, it is overlaid with gold and silver, And there is no breath at all in the midst of it.
20 } But the LORD is in His holy temple; Let all the earth keep silence before Him.
## Habakkuk 3:1 {#habakkuk_31}
: *A prayer of Habakkuk the prophet, according to Shigionoth.*
This verse is a heading for the final chapter. The exact meaning of \"Shigionoth\" is not known. The New Living Translation treats the word as an addition in the Hebrew text which \"probably\" indicates the prayer\'s musical setting, and the Jerusalem Bible suggests that the prayer adopts \"the tone as for dirges\".
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# Book of Habakkuk
## Musical uses {#musical_uses}
Modern Christian hymns have been inspired by the words of the prophet Habakkuk:
- the Christian hymn \"The Lord is in His Holy Temple\", written in 1900 by William J. Kirkpatrick, is based on Habakkuk 2:20.
- the fourth verse of William Cowper\'s hymn \"Sometimes a Light Surprises\", written in 1779, quotes Habakkuk 3:17--18:
Irish composer Charles Villiers Stanford set slightly revised portions of text from the first and second chapters of Habakkuk in his choral composition for choir, soprano and tenor soloist and organ, \"For Lo, I Raise Up\"
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# B (programming language)
**B** is a programming language developed at Bell Labs circa 1969 by Ken Thompson and Dennis Ritchie.
B was derived from BCPL, and its name may possibly be a contraction of BCPL. Thompson\'s coworker Dennis Ritchie speculated that the name might be based on Bon, an earlier, but unrelated, programming language that Thompson designed for use on Multics.`{{refn|group=note|"Its name most probably represents a contraction of BCPL, though an alternate theory holds that it derives from Bon [Thompson 69], an unrelated language created by Thompson during the Multics days. Bon in turn was named either after his wife Bonnie or (according to an encyclopedia quotation in its manual), after [[Bon|a religion]] whose rituals involve the murmuring of magic formulas."<ref name="chist">{{cite journal| first = Dennis M.| last = Ritchie| author-link = Dennis Ritchie| title = The Development of the C Language| date=March 1993 | journal = ACM SIGPLAN Notices| volume = 28 | issue = 3| pages = 201–208| url = http://www.bell-labs.com/usr/dmr/www/chist.html| doi = 10.1145/155360.155580|doi-access = free}}</ref>}}`{=mediawiki}
B was designed for recursive, non-numeric, machine-independent applications, such as system and language software. It was a typeless language, with the only data type being the underlying machine\'s natural memory word format, whatever that might be. Depending on the context, the word was treated either as an integer or a memory address.
As machines with ASCII processing became common, notably the DEC PDP-11 that arrived at Bell Labs, support for character data stuffed in memory words became important. The typeless nature of the language was seen as a disadvantage, which led Thompson and Ritchie to develop an expanded version of the language supporting new internal and user-defined types, which became the ubiquitous C programming language.
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# B (programming language)
## History
Circa 1969, Ken Thompson and later Dennis Ritchie developed B basing it mainly on the BCPL language Thompson used in the Multics project. B was essentially the BCPL system stripped of any component Thompson felt he could do without in order to make it fit within the memory capacity of the minicomputers of the time. The BCPL to B transition also included changes made to suit Thompson\'s preferences (mostly along the lines of reducing the number of non-whitespace characters in a typical program). Much of the typical ALGOL-like syntax of BCPL was rather heavily changed in this process. The assignment operator `:=` reverted to the `=` of Rutishauser\'s Superplan, and the equality operator `=` was replaced by `==`.
Thompson added \"two-address assignment operators\" using `x =+ y` syntax to add y to x (in C the operator is written `+=`). This syntax came from Douglas McIlroy\'s implementation of TMG, in which B\'s compiler was first implemented (and it came to TMG from ALGOL 68\'s `x +:= y` syntax). Thompson went further by inventing the increment and decrement operators (`++` and `--`). Their prefix or postfix position determines whether the value is taken before or after alteration of the operand. This innovation was not in the earliest versions of B. According to Dennis Ritchie, people often assumed that they were created for the auto-increment and auto-decrement address modes of the DEC PDP-11, but this is historically impossible as the machine didn\'t exist when B was first developed.
The semicolon version of the for loop was borrowed by Ken Thompson from the work of Stephen Johnson.
B is typeless, or more precisely has one data type: the computer word. Most operators (e.g. `+`, `-`, `*`, `/`) treated this as an integer, but others treated it as a memory address to be dereferenced. In many other ways it looked a lot like an early version of C. There are a few library functions, including some that vaguely resemble functions from the standard I/O library in C. In Thompson\'s words: \"B and the old old C were very very similar languages except for all the types \[in C\]\".
Early implementations were for the DEC PDP-7 and PDP-11 minicomputers using early Unix, and Honeywell `{{nowrap|[[GE-600 series|GE 645]]}}`{=mediawiki} 36-bit mainframes running the operating system GCOS. The earliest PDP-7 implementations compiled to threaded code, and Ritchie wrote a compiler using TMG which produced machine code. In 1970 a PDP-11 was acquired and threaded code was used for the port; an assembler, `{{samp|[[dc (Unix)|dc]]}}`{=mediawiki}, and the B language itself were written in B to bootstrap the computer. An early version of yacc was produced with this PDP-11 configuration. Ritchie took over maintenance during this period.`{{r|reader}}`{=mediawiki}
The typeless nature of B made sense on the Honeywell, PDP-7 and many older computers, but was a problem on the PDP-11 because it was difficult to elegantly access the character data type that the PDP-11 and most modern computers fully support. Starting in 1971 Ritchie made changes to the language while converting its compiler to produce machine code, most notably adding data typing for variables. During 1971 and 1972 B evolved into \"New B\" (NB) and then C.
B is almost extinct, having been superseded by the C language. However, it continues to see use on GCOS mainframes (`{{as of|2014|lc=y}}`{=mediawiki}) and on certain embedded systems (`{{as of|2000|lc=y}}`{=mediawiki}) for a variety of reasons: limited hardware in small systems, extensive libraries, tooling, licensing cost issues, and simply being good enough for the job. The highly influential AberMUD was originally written in B.
## Examples
The following examples are from the *Users\' Reference to B* by Ken Thompson:
``` c
/* The following function will print a non-negative number, n, to
the base b, where 2<=b<=10. This routine uses the fact that
in the ASCII character set, the digits 0 to 9 have sequential
code values. */
printn(n,b) {
extrn putchar;
auto a;
/* Wikipedia note: the auto keyword declares a variable with
automatic storage (lifetime is function scope), not
"automatic typing" as in C++11. */
if(a=n/b) /* assignment, not test for equality */
printn(a, b); /* recursive */
putchar(n%b + '0');
}
```
``` c
/* The following program will calculate the constant e-2 to about
4000 decimal digits, and print it 50 characters to the line in
groups of 5 characters. The method is simple output conver-
sion of the expansion
1/2! + 1/3! + ... = .111...
where the bases of the digits are 2, 3, 4, ..
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# Beer–Lambert law
The **Beer--Bouguer--Lambert (BBL) extinction law** is an empirical relationship describing the attenuation in intensity of a radiation beam passing through a macroscopically homogenous medium with which it interacts. Formally, it states that the intensity of radiation decays exponentially in the absorbance of the medium, and that said absorbance is proportional to the length of beam passing through the medium, the concentration of interacting matter along that path, and a constant representing said matter\'s propensity to interact.
The extinction law\'s primary application is in chemical analysis, where it underlies the **Beer--Lambert law**, commonly called **Beer\'s law**. Beer\'s law states that a beam of visible light passing through a chemical solution of fixed geometry experiences absorption proportional to the solute concentration. Other applications appear in physical optics, where it quantifies astronomical extinction and the absorption of photons, neutrons, or rarefied gases.
Forms of the BBL law date back to the mid-eighteenth century, but it only took its modern form during the early twentieth.
## History
The first work towards the BBL law began with astronomical observations Pierre Bouguer performed in the early eighteenth century and published in 1729. Bouguer needed to compensate for the refraction of light by the earth\'s atmosphere, and found it necessary to measure the local height of the atmosphere. The latter, he sought to obtain through variations in the observed intensity of known stars. When calibrating this effect, Bouguer discovered that light intensity had an exponential dependence on length traveled through the atmosphere (in Bouguer\'s terms, a geometric progression).
Bouguer\'s work was then popularized in Johann Heinrich Lambert\'s *Photometria* in 1760. Lambert expressed the law, which states that the loss of light intensity when it propagates in a medium is directly proportional to intensity and path length, in a mathematical form quite similar to that used in modern physics. Lambert began by assuming that the intensity `{{mvar|I}}`{=mediawiki} of light traveling into an absorbing body would be given by the differential equation $-\mathrm{d}I=\mu I \mathrm{d}x,$ which is compatible with Bouguer\'s observations. The constant of proportionality `{{math|μ}}`{=mediawiki} was often termed the \"optical density\" of the body. As long as `{{math|μ}}`{=mediawiki} is constant along a distance `{{mvar|d}}`{=mediawiki}, the exponential attenuation law, $I=I_0 e^{-\mu d}$ follows from integration.
In 1852, August Beer noticed that colored solutions also appeared to exhibit a similar attenuation relation. In his analysis, Beer does not discuss Bouguer and Lambert\'s prior work, writing in his introduction that \"Concerning the absolute magnitude of the absorption that a particular ray of light suffers during its propagation through an absorbing medium, there is no information available.\" Beer may have omitted reference to Bouguer\'s work because there is a subtle physical difference between color absorption in solutions and astronomical contexts.`{{Original research inline|date=October 2024}}`{=mediawiki} Solutions are homogeneous and do not scatter light at common analytical wavelengths (ultraviolet, visible, or infrared), except at entry and exit. Thus light within a solution is reasonably approximated as due to absorption alone. In Bouguer\'s context, atmospheric dust or other inhomogeneities could also scatter light away from the detector. Modern texts combine the two laws because scattering and absorption have the same effect. Thus a scattering coefficient `{{math|μ<sub>s</sub>}}`{=mediawiki} and an absorption coefficient `{{math|μ<sub>a</sub>}}`{=mediawiki} can be combined into a total extinction coefficient `{{math|μ {{=}}`{=mediawiki} μ~s~ + μ~a~}}.
Importantly, Beer also seems to have conceptualized his result in terms of a given thickness\' opacity, writing \"If `{{math|λ}}`{=mediawiki} is the coefficient (fraction) of diminution, then this coefficient (fraction) will have the value `{{math|λ<sup>2</sup>}}`{=mediawiki} for double this thickness.\" Although this geometric progression is mathematically equivalent to the modern law, modern treatments instead emphasize the logarithm of `{{math|λ}}`{=mediawiki}, which clarifies that concentration and path length have equivalent effects on the absorption. An early, possibly the first, modern formulation was given by Robert Luther and Andreas Nikolopulos in 1913.
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# Beer–Lambert law
## Mathematical formulations {#mathematical_formulations}
There are several equivalent formulations of the BBL law, depending on the precise choice of measured quantities. All of them state that, provided that the physical state is held constant, the extinction process is linear in the intensity of radiation and amount of radiatively-active matter, a fact sometimes called the **fundamental law of extinction**. Many of them then connect the quantity of radiatively-active matter to a length traveled `{{mvar|ℓ}}`{=mediawiki} and a concentration `{{mvar|c}}`{=mediawiki} or number density `{{Mvar|n}}`{=mediawiki}. For concentrations expressed as moles per volume, the latter two are related by Avogadro\'s number: `{{Math|''n'' {{=}}`{=mediawiki} *N*~A~*c*}}.
A collimated beam (directed radiation) with cross-sectional area `{{Mvar|S}}`{=mediawiki} will encounter `{{Math|''Sℓn''}}`{=mediawiki} particles (on average) during its travel. However, not all of these particles interact with the beam. Propensity to interact is a material-dependent property, typically summarized in absorptivity `{{Math|ϵ}}`{=mediawiki} or scattering cross-section `{{Math|σ}}`{=mediawiki}. These almost exhibit another Avogadro-type relationship: `{{Math|ln(10)ε {{=}}`{=mediawiki} *N*~A~σ}}. The factor of `{{math|ln(10)}}`{=mediawiki} appears because physicists tend to use natural logarithms and chemists decadal logarithms.
Beam intensity can also be described in terms of multiple variables: the intensity `{{Mvar|I}}`{=mediawiki} or radiant flux `{{Math|Φ}}`{=mediawiki}. In the case of a collimated beam, these are related by `{{Math|Φ {{=}}`{=mediawiki} *IS*}}, but `{{Math|Φ}}`{=mediawiki} is often used in non-collimated contexts. The ratio of intensity (or flux) in to out is sometimes summarized as a transmittance coefficient `{{Math|''T'' {{=}}`{=mediawiki} `{{frac|''I''|''I''<sub>0</sub>}}`{=mediawiki}}}.
When considering an extinction law, dimensional analysis can verify the consistency of the variables, as logarithms (being nonlinear) must always be dimensionless.
### Formulation
The simplest formulation of Beer\'s relates the optical attenuation of a physical material containing a single attenuating species of uniform concentration to the optical path length through the sample and absorptivity of the species. This expression is$$\log_{10} (I_0/I)=A=\varepsilon \ell c$$The quantities so equated are defined to be the absorbance `{{Mvar|A}}`{=mediawiki}, which depends on the logarithm base. The Naperian absorbance `{{Math|τ}}`{=mediawiki} is then given by `{{Math|τ {{=}}`{=mediawiki} ln(10)*A*}} and satisfies $\ln(I_0/I)=\tau=\sigma\ell n.$
If multiple species in the material interact with the radiation, then their absorbances add. Thus a slightly more general formulation is that $\begin{align}
\tau &= \ell\sum_i \sigma_i n_i, \\[4pt]
A &= \ell\sum_i \varepsilon_i c_i,
\end{align}$where the sum is over all possible radiation-interacting (\"translucent\") species, and `{{mvar|i}}`{=mediawiki} indexes those species.
In situations where length may vary significantly, absorbance is sometimes summarized in terms of an attenuation coefficient $\begin{alignat}{3}
\mu_{10}&=\frac{A}{l}&&=\epsilon c \\
\mu&=\frac{\tau}{l}&&=\sigma n.
\end{alignat}$
In atmospheric science and radiation shielding applications, the attenuation coefficient may vary significantly through an inhomogenous material. In those situations, the most general form of the Beer--Lambert law states that the total attenuation can be obtained by integrating the attenuation coefficient over small slices `{{math|''dz''}}`{=mediawiki} of the beamline: $\begin{alignat}{3}
A&=\int{\mu_{10}(z)\,dz}&&=\int{\sum_i{\epsilon_i(z)c_i(z)}\,dz}, \\
\tau&=\int{\mu(z)\,dz}&&=\int{\sum_i{\sigma_i(z)n_i(z)}\,dz}.
\end{alignat}$These formulations then reduce to the simpler versions when there is only one active species and the attenuation coefficients are constant.
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# Beer–Lambert law
## Derivation
There are two factors that determine the degree to which a medium containing particles will attenuate a light beam: the number of particles encountered by the light beam, and the degree to which each particle extinguishes the light.
Assume that a beam of light enters a material sample. Define `{{mvar|z}}`{=mediawiki} as an axis parallel to the direction of the beam. Divide the material sample into thin slices, perpendicular to the beam of light, with thickness `{{math|d''z''}}`{=mediawiki} sufficiently small that one particle in a slice cannot obscure another particle in the same slice when viewed along the `{{mvar|z}}`{=mediawiki} direction. The radiant flux of the light that emerges from a slice is reduced, compared to that of the light that entered, by $\mathrm{d\Phi_e}(z) = -\mu(z)\Phi_\mathrm{e}(z) \mathrm{d}z,$ where `{{mvar|μ}}`{=mediawiki} is the (Napierian) attenuation coefficient, which yields the following first-order linear, ordinary differential equation$$\frac{\mathrm{d}\Phi_\mathrm{e}(z)}{\mathrm{d}z} = -\mu(z)\Phi_\mathrm{e}(z).$$ The attenuation is caused by the photons that did not make it to the other side of the slice because of scattering or absorption. The solution to this differential equation is obtained by multiplying the integrating factor$\exp\left(\int_0^z \mu(z')\mathrm{d}z' \right)$throughout to obtain$\frac{\mathrm{d}\Phi_\mathrm{e}(z)}{\mathrm{d}z}\, \exp\left(\int_0^z \mu(z')\mathrm{d}z' \right) + \mu(z)\Phi_\mathrm{e}(z)\, \exp\left(\int_0^z \mu(z')\mathrm{d}z' \right) = 0,$which simplifies due to the product rule (applied backwards) to$\frac{\mathrm{d}}{\mathrm{d}z}\left[\Phi_\mathrm{e}(z) \exp\left(\int_0^z \mu(z')\mathrm{d}z' \right)\right] = 0.$
Integrating both sides and solving for `{{math|Φ<sub>e</sub>}}`{=mediawiki} for a material of real thickness `{{mvar|ℓ}}`{=mediawiki}, with the incident radiant flux upon the slice $\mathrm{\Phi_e^i} = \mathrm{\Phi_e}(0)$ and the transmitted radiant flux $\mathrm{\Phi_e^t} = \mathrm{\Phi_e}(\ell)$ gives$\mathrm{\Phi_e^t} = \mathrm{\Phi_e^i} \exp\left(-\int_0^\ell \mu(z)\mathrm{d}z \right),$and finally$T = \mathrm{\frac{\Phi_e^t}{\Phi_e^i}} = \exp\left(-\int_0^\ell \mu(z)\mathrm{d}z \right).$
Since the decadic attenuation coefficient `{{math|''μ''<sub>10</sub>}}`{=mediawiki} is related to the (Napierian) attenuation coefficient by $\mu_{10} = \tfrac{\mu}{\ln 10},$ we also have$\begin{align}
T &= \exp\left(-\int_0^\ell \ln(10)\,\mu_{10}(z)\mathrm{d}z \right) \\[4pt]
&= 10^{\;\!\wedge} \!\! \left( -\int_0^\ell \mu_{10}(z)\mathrm{d}z \right).
\end{align}$
To describe the attenuation coefficient in a way independent of the number densities `{{mvar|n<sub>i</sub>}}`{=mediawiki} of the `{{mvar|N}}`{=mediawiki} attenuating species of the material sample, one introduces the attenuation cross section $\sigma_i = \tfrac{\mu_i(z)}{n_i(z)}.$ `{{mvar|σ<sub>i</sub>}}`{=mediawiki} has the dimension of an area; it expresses the likelihood of interaction between the particles of the beam and the particles of the species `{{mvar|i}}`{=mediawiki} in the material sample$$T = \exp\left(-\sum_{i = 1}^N \sigma_i \int_0^\ell n_i(z)\mathrm{d}z \right).$$
One can also use the molar attenuation coefficients $\varepsilon_i = \tfrac{\mathrm{N_A}}{\ln 10}\sigma_i,$ where `{{math|N<sub>A</sub>}}`{=mediawiki} is the Avogadro constant, to describe the attenuation coefficient in a way independent of the amount concentrations $c_i(z) = n_i \tfrac{z}{\mathrm{N_A}}$ of the attenuating species of the material sample$$\begin{align}
T &= \exp\left(-\sum_{i = 1}^N \frac{\ln(10)}{\mathrm{N_A}}\varepsilon_i \int_0^\ell n_i(z)\mathrm{d}z \right) \\[4pt]
&= \exp\left(-\sum_{i = 1}^N \varepsilon_i \int_0^\ell \frac{n_i(z)}{\mathrm{N_A}}\mathrm{d}z\right)^{\ln(10)} \\[4pt]
&= 10^{\;\!\wedge} \!\! \left(-\sum_{i = 1}^N \varepsilon_i \int_0^\ell c_i(z)\mathrm{d}z \right).
\end{align}$$
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# Beer–Lambert law
## Derivation
### Validity
Under certain conditions the Beer--Lambert law fails to maintain a linear relationship between attenuation and concentration of analyte. These deviations are classified into three categories:
1. Real---fundamental deviations due to the limitations of the law itself.
2. Chemical---deviations observed due to specific chemical species of the sample which is being analyzed.
3. Instrument---deviations which occur due to how the attenuation measurements are made.
There are at least six conditions that need to be fulfilled in order for the Beer--Lambert law to be valid. These are:
1. The attenuators must act independently of each other.
2. The attenuating medium must be homogeneous in the interaction volume.
3. The attenuating medium must not scatter the radiation---no turbidity---unless this is accounted for as in DOAS.
4. The incident radiation must consist of parallel rays, each traversing the same length in the absorbing medium.
5. The incident radiation should preferably be monochromatic, or have at least a width that is narrower than that of the attenuating transition. Otherwise a spectrometer as detector for the power is needed instead of a photodiode which cannot discriminate between wavelengths.
6. The incident flux must not influence the atoms or molecules; it should only act as a non-invasive probe of the species under study. In particular, this implies that the light should not cause optical saturation or optical pumping, since such effects will deplete the lower level and possibly give rise to stimulated emission.
If any of these conditions are not fulfilled, there will be deviations from the Beer--Lambert law.
The law tends to break down at very high concentrations, especially if the material is highly scattering. Absorbance within range of 0.2 to 0.5 is ideal to maintain linearity in the Beer--Lambert law. If the radiation is especially intense, nonlinear optical processes can also cause variances. The main reason, however, is that the concentration dependence is in general non-linear and Beer\'s law is valid only under certain conditions as shown by derivation below. For strong oscillators and at high concentrations the deviations are stronger. If the molecules are closer to each other interactions can set in. These interactions can be roughly divided into physical and chemical interactions. Physical interaction do not alter the polarizability of the molecules as long as the interaction is not so strong that light and molecular quantum state intermix (strong coupling), but cause the attenuation cross sections to be non-additive via electromagnetic coupling. Chemical interactions in contrast change the polarizability and thus absorption.
In solids, attenuation is usually an addition of absorption coefficient $\alpha$ (creation of electron-hole pairs) or scattering (for example Rayleigh scattering if the scattering centers are much smaller than the incident wavelength). Also note that for some systems we can put $1/\lambda$ (1 over inelastic mean free path) in place of `{{nowrap|<math>\mu</math>.}}`{=mediawiki}
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# Beer–Lambert law
## Applications
### In plasma physics {#in_plasma_physics}
The BBL extinction law also arises as a solution to the BGK equation.
### Chemical analysis by spectrophotometry {#chemical_analysis_by_spectrophotometry}
The Beer--Lambert law can be applied to the analysis of a mixture by spectrophotometry, without the need for extensive pre-processing of the sample. An example is the determination of bilirubin in blood plasma samples. The spectrum of pure bilirubin is known, so the molar attenuation coefficient `{{mvar|ε}}`{=mediawiki} is known. Measurements of decadic attenuation coefficient `{{math|''μ''<sub>10</sub>}}`{=mediawiki} are made at one wavelength `{{mvar|λ}}`{=mediawiki} that is nearly unique for bilirubin and at a second wavelength in order to correct for possible interferences. The amount concentration `{{mvar|c}}`{=mediawiki} is then given by $c = \frac{\mu_{10}(\lambda)}{\varepsilon(\lambda)}.$
For a more complicated example, consider a mixture in solution containing two species at amount concentrations `{{math|''c''<sub>1</sub>}}`{=mediawiki} and `{{math|''c''<sub>2</sub>}}`{=mediawiki}. The decadic attenuation coefficient at any wavelength `{{mvar|λ}}`{=mediawiki} is, given by $\mu_{10}(\lambda) = \varepsilon_1(\lambda) c_1 + \varepsilon_2(\lambda) c_2.$
Therefore, measurements at two wavelengths yields two equations in two unknowns and will suffice to determine the amount concentrations `{{math|''c''<sub>1</sub>}}`{=mediawiki} and `{{math|''c''<sub>2</sub>}}`{=mediawiki} as long as the molar attenuation coefficients of the two components, `{{math|''ε''<sub>1</sub>}}`{=mediawiki} and `{{math|''ε''<sub>2</sub>}}`{=mediawiki} are known at both wavelengths. This two system equation can be solved using Cramer\'s rule. In practice it is better to use linear least squares to determine the two amount concentrations from measurements made at more than two wavelengths.
Mixtures containing more than two components can be analyzed in the same way, using a minimum of `{{mvar|m}}`{=mediawiki} wavelengths for a mixture containing `{{mvar|n}}`{=mediawiki} components. So, in general:
$A_{\lambda_i} = \sum_{j=1}^{n} \epsilon_{j, \lambda_i} c_j l$
where $A_{\lambda_i}$is the absorbance at wavelength $\lambda_i$, $\epsilon_{j, \lambda_i}$ is the molar absorptivity of component $j$ at $\lambda_i$, $c_j$ is the concentration of component $j$, and $l$ is the path length.
The law is used widely in infra-red spectroscopy and near-infrared spectroscopy for analysis of polymer degradation and oxidation (also in biological tissue) as well as to measure the concentration of various compounds in different food samples. The carbonyl group attenuation at about 6 micrometres can be detected quite easily, and degree of oxidation of the polymer calculated.
### In-atmosphere astronomy {#in_atmosphere_astronomy}
The Bouguer--Lambert law may be applied to describe the attenuation of solar or stellar radiation as it travels through the atmosphere. In this case, there is scattering of radiation as well as absorption. The optical depth for a slant path is `{{math|1=''{{prime|τ}}'' = ''mτ''}}`{=mediawiki}, where `{{mvar|τ}}`{=mediawiki} refers to a vertical path, `{{mvar|m}}`{=mediawiki} is called the relative airmass, and for a plane-parallel atmosphere it is determined as `{{math|1=''m'' = sec ''θ''}}`{=mediawiki} where `{{mvar|θ}}`{=mediawiki} is the zenith angle corresponding to the given path. The Bouguer-Lambert law for the atmosphere is usually written $T = \exp \big( -m(\tau_\mathrm{a} + \tau_\mathrm{g} + \tau_\mathrm{RS} + \tau_\mathrm{NO_2} + \tau_\mathrm{w} + \tau_\mathrm{O_3} + \tau_\mathrm{r} + \cdots) \bigr),$ where each `{{mvar|τ<sub>x</sub>}}`{=mediawiki} is the optical depth whose subscript identifies the source of the absorption or scattering it describes:
- refers to aerosols (that absorb and scatter);
- are uniformly mixed gases (mainly carbon dioxide (CO~2~) and molecular oxygen (O~2~) which only absorb);
- is nitrogen dioxide, mainly due to urban pollution (absorption only);
- are effects due to Raman scattering in the atmosphere;
- is water vapour absorption;
- is ozone (absorption only);
- is Rayleigh scattering from molecular oxygen (`{{chem2|O2}}`{=mediawiki}) and nitrogen (`{{chem2|N2}}`{=mediawiki}) (responsible for the blue color of the sky);
- the selection of the attenuators which have to be considered depends on the wavelength range and can include various other compounds. This can include tetraoxygen, HONO, formaldehyde, glyoxal, a series of halogen radicals and others.
is the *optical mass* or *airmass factor*, a term approximately equal (for small and moderate values of `{{mvar|θ}}`{=mediawiki}) to `{{tmath|\tfrac{1}{\cos \theta},}}`{=mediawiki} where `{{mvar|θ}}`{=mediawiki} is the observed object\'s zenith angle (the angle measured from the direction perpendicular to the Earth\'s surface at the observation site). This equation can be used to retrieve `{{math|''τ''<sub>a</sub>}}`{=mediawiki}, the aerosol optical thickness, which is necessary for the correction of satellite images and also important in accounting for the role of aerosols in climate
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# British thermal unit
The **British thermal unit** (**Btu**) is a measure of heat, which is a form of energy. It was originally defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit. It is also part of the United States customary units. The SI unit for energy is the joule (J); one Btu equals about 1,055 J (varying within the range of 1,054--1,060 J depending on the specific definition of Btu; see below).
While units of heat are often supplanted by energy units in scientific work, they are still used in some fields. For example, in the United States the price of natural gas is quoted in dollars per the amount of natural gas that would give 1 million Btu (1 \"MMBtu\") of heat energy if burned.
## Definitions
A Btu was originally defined as the amount of heat required to raise the temperature of one pound of liquid water by one degree Fahrenheit at a constant pressure of one atmospheric unit. There are several different definitions of the Btu that differ slightly. This reflects the fact that the temperature change of a mass of water due to the addition of a specific amount of heat (calculated in energy units, usually joules) depends slightly upon the water\'s initial temperature. As seen in the table below, definitions of the Btu based on different water temperatures vary by up to 0.5%.
Variant Energy (J) Notes
---------------- ----------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Thermochemical ≈1,054.35 Originally, the thermochemical Btu was defined as the heat required to raise the temperature of one pound of water from its freezing point to its boiling point, divided by 180 (the temperature change being 180 °F). The basis for its modern definition in terms of SI units is the conceptually similar *thermochemical calorie*, originally defined as the heat required to raise the temperature of one gram of water from freezing to boiling divided by 100 (the temperature change being 100 °C). The thermochemical calorie is exactly 4.184 J by definition of the International Organization for Standardization (ISO). The thermochemical Btu is calculated by converting from grams to pounds and from Celsius to Fahrenheit.
≈1,054.80 Used for American natural gas pricing.
≈1,054.68 {{cite book title=Renewable Energy Focus e-Mega Handbook
≈1,059.67 Uses the calorie value of water at its maximum density (4 °C).
IT ≈1,055.06 An early effort to define heat units directly in terms of energy units, and hence to remove the direct association with the properties of water, was made by the International Steam Table Conferences. These conferences originally adopted the simplified definition that 860 \"IT\" calories corresponded to exactly 1 international watt-hour (not the same as a modern watt-hour). This definition ultimately became the statement that 1 IT calorie is exactly 4.1868 J. {{cite book
### Prefixes
Units of kBtu are used in building energy use tracking and heating system sizing. Energy Use Index (EUI) represents kBtu per square foot of conditioned floor area. \"k\" stands for 1,000.
The unit **MBtu** is used in natural gas and other industries to indicate 1,000 Btu. However, there is an ambiguity in that the metric system (SI) uses the prefix \"M\" to indicate \'Mega-\', one million (1,000,000). Even so, \"MMBtu\" is often used to indicate one million Btu particularly in the oil and gas industry.
Energy analysts accustomed to the metric \"k\" (\'kilo-\') for 1,000 are more likely to use MBtu to represent one million, especially in documents where M represents one million in other energy or cost units, such as MW, MWh and \$.
The unit \'therm\' is used to represent 100,000 Btu. A decatherm is 10 therms or one million Btu. The unit *quad* is commonly used to represent one quadrillion (10^15^) Btu.
## Conversions
One Btu is approximately:
- (kilojoules)
- (watt hours)
- (calories)
- (kilocalories)
- 25,031 to 25,160 ft⋅pdl (foot-poundal)
- (foot-pounds-force)
- 5.40395 (lbf/in^2^)⋅ft^3^
A Btu can be approximated as the heat produced by burning a single wooden kitchen match or as the amount of energy it takes to lift a 1 lb weight 778 ft.
### For natural gas {#for_natural_gas}
- In natural gas pricing, the Canadian definition is that `{{val|1000000|u=Btu|fmt=commas}}`{=mediawiki} ≡ `{{val|1.054615|u=GJ}}`{=mediawiki}.
- The energy content (high or low heating value) of a volume of natural gas varies with the composition of the natural gas, which means there is no universal conversion factor for energy to volume. 1 ft3 of average natural gas yields ≈ 1,030 Btu (between 1,010 Btu and 1,070 Btu, depending on quality, when burned)
- As a coarse approximation, 1000 ft3 of natural gas yields ≈ `{{val|1000000|u=Btu|fmt=commas}}`{=mediawiki} ≈ `{{val|1|u=GJ}}`{=mediawiki}.
- For natural gas price conversion `{{val|1000|u=m3|fmt=commas}}`{=mediawiki} ≈ 36.9 million Btu and `{{val|1000000|u=Btu|fmt=commas}}`{=mediawiki} ≈ `{{val|27.1|u=m3}}`{=mediawiki}
### Btu/h
The SI unit of power for heating and cooling systems is the watt. Btu *per hour* (Btu/h) is sometimes used in North America and the United Kingdom - the latter for air conditioning mainly, though \"Btu/h\" is sometimes abbreviated to just \"Btu\". *MBH*---thousands of Btu per hour---is also common.
- 1 W is approximately 1 W
- 1,000 Btu/h is approximately 1000 Btu/h
- 1 hp is approximately 1 hp
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# British thermal unit
## Associated units {#associated_units}
- 1 *ton of cooling*, a common unit in North American refrigeration and air conditioning applications, is 12,000 Btu/h. It is the rate of heat transfer needed to freeze 1 ST of water into ice in 24 hours.
- In the United States and Canada, the R-value that describes the performance of thermal insulation is typically quoted in square foot degree Fahrenheit hours per British thermal unit (ft^2^⋅°F⋅h/Btu). For one square foot of the insulation, one Btu per hour of heat flows across the insulator for each degree of temperature difference across it.
- 1 *therm* is defined in the United States as 100,000 Btu using the `{{not a typo|Btu<sub>59 °F</sub>}}`{=mediawiki} definition. In the EU it was listed in 1979 with the BTU~IT~ definition and planned to be discarded as a legal unit of trade by 1994. United Kingdom regulations were amended to replace therms with joules with effect from 1 January 2000. `{{As of|2013}}`{=mediawiki} the therm was still used in natural gas pricing in the United Kingdom.
- 1 *quad* (short for quadrillion Btu) is 10^15^ Btu, which is about 1 exajoule (`{{val|1.055|e=18|u=J}}`{=mediawiki}). Quads are used in the United States for representing the annual energy consumption of large economies: for example, the U.S. economy used 99.75 quads in 2005. One quad/year is about 33.43 gigawatts.
The Btu should not be confused with the Board of Trade Unit (BTU), an obsolete UK synonym for kilowatt hour (1 kW.h).
The Btu is often used to express the conversion-efficiency of heat into electrical energy in power plants. Figures are quoted in terms of the quantity of heat in Btu required to generate 1 kW⋅h of electrical energy. A typical coal-fired power plant works at 10500 Btu/kWh, an efficiency of 32--33%.
The centigrade heat unit (CHU) is the amount of heat required to raise the temperature of 1 lb of water by one Celsius degree. It is equal to 1.8 Btu or 1,899 joules. In 1974, this unit was \"still sometimes used\" in the United Kingdom as an alternative to Btu.
Another legacy unit for energy in the metric system is the calorie, which is defined as the amount of heat required to raise the temperature of one gram of water by one degree Celsius
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# Body substance isolation
**Body substance isolation** is a practice of isolating all body substances (blood, urine, feces, tears, etc.) of individuals undergoing medical treatment, particularly emergency medical treatment of those who might be infected with illnesses such as HIV, or hepatitis so as to reduce as much as possible the chances of transmitting these illnesses. BSI is similar in nature to universal precautions, but goes further in isolating workers from pathogens, including substances now known to carry HIV.
## Place of body substance isolation practice in history {#place_of_body_substance_isolation_practice_in_history}
Practice of Universal precautions was introduced in 1985--88. In 1987, the practice of Universal precautions was adjusted by a set of rules known as body substance isolation. In 1996, both practices were replaced by the latest approach known as standard precautions (health care). Nowadays and in isolation, practice of body substance isolation has just historical significance.
Body substance isolation went further than universal precautions in isolating workers from pathogens, including substances now currently known to carry HIV. These pathogens fall into two broad categories, bloodborne (carried in the body fluids) and airborne. The practice of BSI was common in Pre-Hospital care and emergency medical services due to the often unknown nature of the patient and his/her disease or medical conditions. It was a part of the National Standards Curriculum for Prehospital Providers and Firefighters.Types of body substance isolation included:
- Hospital gowns
- Medical gloves
- Shoe covers
- Surgical mask or N95 Respirator
- Safety Glasses
It was postulated that BSI precautions should be practiced in environment where treaters were exposed to bodily fluids, such as:
- blood, semen, preseminal fluid, vaginal secretions, synovial fluid, amniotic fluid, cerebrospinal fluid, pleural fluid, peritoneal fluid, marrow, pericardial fluid, feces, nasal secretions, urine, vomitus, sputum, mucus, cervical mucus, phlegm, saliva, breastmilk, colostrum, and secretions and blood from the umbilical cord
Such infection control techniques that were recommended following the AIDS outbreak in the 1980s. Every patient was treated as if infected and therefore precautions were taken to minimize risk. Other conditions which called for minimizing risks with BSI:
- Diseases with air-borne transmission (e.g., tuberculosis)
- Diseases with droplet transmission (e.g., mumps, rubella, influenza, pertussis)
- Transmission by direct or indirect contact with dried skin (e.g., colonisation with MRSA) or contaminated surfaces
- Prion diseases (e.g., Creutzfeldt--Jakob disease)
or any combination of the above
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# Burroughs Corporation
The **Burroughs Corporation** was a major American manufacturer of business equipment. The company was founded in 1886 as the American Arithmometer Company by William Seward Burroughs. The company\'s history paralleled many of the major developments in computing. At its start, it produced mechanical adding machines, and later moved into programmable ledgers and then computers. It was one of the largest producers of mainframe computers in the world, also producing related equipment including typewriters and printers.
In the 1960s, the company introduced a range of mainframe computers that were well regarded for their performance running high level languages. These formed the core of the company\'s business into the 1970s. At that time the emergence of superminicomputers and the dominance of the IBM System/360 and 370 at the high end led to shrinking markets, and in 1986 the company purchased former competitor Sperry UNIVAC and merged their operations to form Unisys.
## Early history {#early_history}
In 1886, the American Arithmometer Company was established in St. Louis, Missouri, to produce and sell an adding machine invented by William Seward Burroughs (grandfather of Beat Generation author William S. Burroughs). In 1904, six years after Burroughs\' death, the company moved to Detroit and changed its name to the Burroughs Adding Machine Company. It was soon the biggest adding machine company in America.
## Evolving product lines {#evolving_product_lines}
The adding machine range began with the basic, hand-cranked Class 1 which was only capable of adding. The design included some revolutionary features, foremost of which was the dashpot which governed the speed at which the operating lever could be pulled so allowing the mechanism to operate consistently correctly. The machine also had a full-keyboard with a separate column of keys 1 to 9 for each decade where the keys latch when pressed, with interlocking which prevented more than one key in any decade from being latched. The latching allowed the operator to quickly check that the correct number had been entered before pulling the operating lever. The numbers entered and the final total were printed on a roll of paper at the rear, so there was no danger of the operator writing down the wrong answer and there was a copy of the calculation which could be checked later if necessary.
The Class 2 machine, called the \"duplex\" and built in the same basic style, provided a means of keeping two separate totals. The Class 6 machine was built for bookkeeping work and provided the ability for direct subtraction.
Burroughs released the Class 3 and Class 4 adding machines which were built after the purchase of the Pike Adding Machine Company around 1910. These machines provided a significant improvement over the older models because operators could view the printing on the paper tape. The machines were called \"the visible\" for this improvement.
In 1925 Burroughs released a much smaller machine called \"the portable\". Two models were released, the Class 8 (without subtraction) and the Class 9 with subtraction capability. Later models continued to be released with the P600 and top-of-the-range P612 offered some limited programmability based upon the position of the movable carriage. The range was further extended by the inclusion of the Series J ten-key machines which provided a single finger calculation facility, and the Class 5 (later called Series C) key-driven calculators in both manual and electrical assisted comptometers.
In the late 1960s, the Burroughs sponsored \"nixi-tube\" provided an electronic display calculator. Burroughs developed a range of adding machines with different capabilities, gradually increasing in their capabilities. A revolutionary adding machine was the *Sensimatic*, which was able to perform many business functions semi-automatically. It had a moving programmable carriage to maintain ledgers. It could store 9, 18 or 27 balances during the ledger posting operations and worked with a mechanical adder named a Crossfooter. The Sensimatic developed into the *Sensitronic* which could store balances on a magnetic stripe which was part of the ledger card. This balance was read into the accumulator when the card was inserted into the carriage. The Sensitronic was followed by the E1000, E2000, E3000, E4000, E6000 and the E8000, which were computer systems supporting card reader/punches and a line printer.
Later, Burroughs was selling more than adding machines, including typewriters.
## Move into computers {#move_into_computers}
The biggest shift in company history came in 1953: the Burroughs Adding Machine Company was renamed the Burroughs Corporation and began moving into digital computer products, initially for banking institutions. This move began with Burroughs\' purchase in June 1956, of the ElectroData Corporation in Pasadena, California, a spinoff of the Consolidated Engineering Corporation which had designed test instruments and had a cooperative relationship with Caltech in Pasadena. ElectroData had built the Datatron 205 and was working on the Datatron 220. The first major computer product that came from this marriage was the B205 tube computer. In 1968 the L and TC series range was produced (e.g. the TC500---Terminal Computer 500) which had a golf ball printer and in the beginning a 1K (64 bit) disk memory. These were popular as branch terminals to the B5500/6500/6700 systems, and sold well in the banking sector, where they were often connected to non-Burroughs mainframes. In conjunction with these products, Burroughs also manufactured an extensive range of cheque processing equipment, normally attached as terminals to a medium systems such as B200/B300 and larger systems such as a B2700 or B1700.
In the 1950s, Burroughs worked with the Federal Reserve Bank on the development and computer processing of magnetic ink character recognition (MICR) especially for the processing of bank cheques. Burroughs made special MICR/OCR sorter/readers which attached to their medium systems line of computers (2700/3700/4700) and B200/B300 systems and this entrenched the company in the computer side of the banking industry.
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# Burroughs Corporation
## A force in the computing industry {#a_force_in_the_computing_industry}
Burroughs was one of the nine major United States computer companies in the 1960s, with IBM the largest, Honeywell, NCR Corporation, Control Data Corporation (CDC), General Electric (GE), Digital Equipment Corporation (DEC), RCA and Sperry Rand (UNIVAC line). In terms of sales, Burroughs was always a distant second to IBM. In fact, IBM\'s market share was so much larger than all of the others that this group was often referred to as \"IBM and the Seven Dwarves.\" By 1972 when GE and RCA were no longer in the mainframe business, the remaining five companies behind IBM became known as the BUNCH, an acronym based on their initials.
At the same time, Burroughs was very much a competitor. Like IBM, Burroughs tried to supply a complete line of products for its customers, including Burroughs-designed printers, disk drives, tape drives, computer printing paper and typewriter ribbons.
### Developments and innovations {#developments_and_innovations}
The Burroughs Corporation developed three highly innovative architectures, based on the design philosophy of \"language-directed design\". Their machine instruction sets favored one or many high level programming languages, such as ALGOL, COBOL or FORTRAN. All three architectures were considered mainframe class machines:
- The Burroughs Large Systems machines started with the B5000 in 1961. The B5500 came a few years later when large rotating disks replaced drums as the main external memory media. These B5000 Series systems used the world\'s first virtual memory multi-programming operating system. They were followed by the B6500/B6700 in the later 1960s, the B7700 in the mid-1970s, and the A series in the 1980s. The underlying architecture of these machines is similar and continues today as the Unisys ClearPath MCP line of computers: stack machines designed to be programmed in an extended Algol 60. Their operating systems, called MCP (Master Control Program---the name later borrowed by the screenwriters for *Tron*), were programmed in ESPOL (Executive Systems Programming Oriented Language, a minor extension of ALGOL) and DCALGOL (Data Communications ALGOL) and later in NEWP (with further extensions to ALGOL) almost a decade before Unix. The command interface developed into a compiled structured language with declarations, statements and procedures called WFL (Work Flow Language).
Many computer scientists`{{who|date=June 2024}}`{=mediawiki} consider these series of computers to be technologically groundbreaking. Stack oriented processors, with 48 bit word length where each word was defined as data or program contributed significantly to a secure operating environment, long before spyware and viruses affected computing. The modularity of these large systems was unique: multiple CPUs, multiple memory modules and multiple I/O and Data Comm processors permitted incremental and cost effective growth of system performance and reliability.
In industries like banking, where continuous operations was mandatory, Burroughs Large Systems penetrated nearly every large bank, including the Federal Reserve Bank. Burroughs built the backbone switching systems for Society for Worldwide Interbank Financial Telecommunication (SWIFT) which sent its first message in 1977. Unisys is still the provider to SWIFT today.
- Burroughs produced the B2500 or \"medium systems\" computers aimed primarily at the business world. The machines were designed to execute COBOL efficiently. This included a BCD (Binary Coded Decimal) based arithmetic unit, storing and addressing the main memory using base 10 numbering instead of binary. The designation for these systems was Burroughs B2500 through B49xx, followed by Unisys V-Series V340 through V560.
- Burroughs produced the B1700 or \"small systems\" computers that were designed to be microprogrammed, with each process potentially getting its own virtual machine designed to be the best match to the programming language chosen for the program being run.
- The smallest general-purpose computers were the B700 \"microprocessors\" which were used both as stand-alone systems and as special-purpose data-communications or disk-subsystem controllers.
- Burroughs manufactured an extensive range of accounting machines including stand-alone systems such as the Sensimatic, L500 and B80 and dedicated terminals including the TC500 and specialised check processing equipment.
- In 1982, Burroughs began producing personal computers, the B20 and B25 lines with the Intel 8086/8088 family of 16-bit chips as the processor. These ran the BTOS operating system, which Burroughs licensed from Convergent Technologies. These machines implemented an early local area network to share a hard disk between workgroup users. These microcomputers were later manufactured in Kunming, China for use in China under agreement with Burroughs.
- Burroughs collaborated with University of Illinois on a multiprocessor architecture developing the ILLIAC IV computer in the early 1960s. The ILLIAC had up to 128 parallel processors while the B6700 & B7700 only accommodated a total of 7 CPUs and/or I/O units (the 8th unit was the memory tester).
- Burroughs made military computers, such as the D825 (the \"D\" prefix signifying it was for defense industrial use), in its Great Valley Laboratory in Paoli, Pennsylvania. The D825 was, according to some scholars, the first true multiprocessor computer. Paoli was also home to the Defense and Space Group Marketing Division.
- In 1964 Burroughs had completed the D830 which was another variation of the D825 designed specifically for real-time applications, such as airline reservations. Burroughs designated the B8300 after Trans World Airlines (TWA) ordered one in September 1965. A system with three instruction processors was installed at TWA\'s reservations center in Rockleigh, New Jersey in 1968. The system, which was called George, with an application programmed in JOVIAL, was intended to support some 4000 terminals, but the system experienced repeated crashes due to a filing system disk allocation error when operating under a large load. A fourth processor was added but did nothing to resolve the problem. The problem was resolved in late 1970 and the system became stable. The decision to cancel the project was being made at the very time that the problem was resolved. TWA cancelled the project and acquired one IBM System/360 Model 75, two IBM System/360 model 65s, and IBM\'s PARS software for its reservations system. TWA sued Burroughs for non-fulfillment of the contract, but Burroughs counter-sued, stating that the basic system did work and that the problems were in TWA\'s applications software. The two companies reached an out-of-court settlement.
- Burroughs developed a half-size version of the D825 called the D82, cutting the word size from 48 to 24 bits and simplifying the computer\'s instruction set. The D82 could have up to 32,768 words of core memory and continued the use of separate instruction and I/O processors. Burroughs sold a D82 to Air Canada to handle reservations for trips originating in Montreal and Quebec. This design was further refined and made much more compact as the D84 machine which was completed in 1965. A D84 processor/memory unit with 4096 words of memory occupied just 1.4 cuft. This system was used successfully in two military projects: field test systems used to check the electronics of the Air Force General Dynamics F-111 Aardvark fighter plane and systems used to control the countdown and launch of the Army\'s Pershing 1 and 1a missile systems.
## Merger with Sperry {#merger_with_sperry}
In September 1986, Burroughs Corporation merged with Sperry Corporation to form Unisys. For a time, the combined company retained the Burroughs processors as the A- and V-systems lines. As the market for large systems shifted from proprietary architectures to common servers, the company eventually dropped the V-Series line, although customers continued to use V-series systems `{{as of | 2010 | lc =on}}`{=mediawiki}. `{{As of | 2017}}`{=mediawiki} Unisys continues to develop and market the A-Series, now known as ClearPath.
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# Burroughs Corporation
## Burroughs Payment Systems `{{anchor|Reemergence of the Burroughs name}}`{=mediawiki} {#burroughs_payment_systems}
In 2010, Unisys sold off its Payment Systems Division to Marlin Equity Partners, a California-based private investment firm, which incorporated it as **Burroughs Payment Systems, Inc.** (later just **Burroughs, Inc.**), based in Plymouth, Michigan
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# Burnt-in timecode
**Burnt-in timecode** (often abbreviated to **BITC** by analogy to VITC) is a human-readable on-screen version of the timecode information for a piece of material superimposed on a video image. BITC is sometimes used in conjunction with \"real\" machine-readable timecode but more often used in copies of original material onto a nonbroadcast format such as VHS so that the VHS copies can be traced back to their master tape and the original timecodes easily located.
Many professional VTRs can \"burn\" (overlay) the tape timecode onto one of their outputs. This output (which usually also displays the setup menu or on-screen display) is known as the *super out* or *monitor out*. The *character* switch or menu item turns this behaviour on or off. The *character* function also displays the timecode on the preview monitors in linear editing suites.
Videotapes that are recorded with timecode numbers overlaid on the video are referred to as *window dubs*, named after the \"window\" that displays the burnt-in timecode on-screen.
When editing was done using magnetic tapes that were subject to damage from excessive wear, it was common to use a window dub as a working copy for the majority of the editing process. Editing decisions would be made using a window dub, and no specialized equipment was needed to write down an edit decision list, which would then be replicated from the high-quality masters.
Timecode can also be superimposed on video using a dedicated overlay device, often called a \"window dub inserter\". This inputs a video signal and its separate timecode audio signal, reads the timecode, superimposes the timecode display over the video, and outputs the combined display (usually via composite), all in real time. Stand-alone timecode generators/readers often have the window dub function built in.
Some consumer cameras, in particular DV cameras, can \"burn\" (overlay) the tape timecode onto the composite output. This output is typically semitransparent and may include other tape information. It is usually activated by turning on the \"display\" info in one of the camera\'s submenus. While not as \"professional\" as an overlay created by a professional VCR, it is a cheap alternative that is just as accurate.
Timecode is stored in the metadata areas of captured DV AVI files, and some software is able to \"burn\" (overlay) this into the video frames. For example, DVMP Pro is able to \"burn\" timecode or other items of DV metadata (such as date and time, iris, shutter speed, gain, white balance mode, etc.) into DV AVI files.
OCR techniques can be used to read BITC in situations where other forms of timecode are not available
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# Bra–ket notation
**Bra--ket notation**, also called **Dirac notation**, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics. Its use in quantum mechanics is quite widespread.
Bra--ket notation was created by Paul Dirac in his 1939 publication *A New Notation for Quantum Mechanics*. The notation was introduced as an easier way to write quantum mechanical expressions. The name comes from the English word \"bracket\".
## Quantum mechanics {#quantum_mechanics}
In quantum mechanics and quantum computing, bra--ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, `{{char|<math>\langle</math>}}`{=mediawiki} and `{{char|<math>\rangle</math>}}`{=mediawiki}, and a vertical bar `{{char|<math>|</math>}}`{=mediawiki}, to construct \"bras\" and \"kets\".
A **ket** is of the form $|v \rangle$. Mathematically it denotes a vector, $\boldsymbol v$, in an abstract (complex) vector space $V$, and physically it represents a state of some quantum system.
A **bra** is of the form $\langle f|$. Mathematically it denotes a linear form $f:V \to \Complex$, i.e. a linear map that maps each vector in $V$ to a number in the complex plane $\Complex$. Letting the linear functional $\langle f|$ act on a vector $|v\rangle$ is written as $\langle f | v\rangle \in \Complex$.
Assume that on $V$ there exists an inner product $(\cdot,\cdot)$ with antilinear first argument, which makes $V$ an inner product space. Then with this inner product each vector $\boldsymbol \phi \equiv |\phi\rangle$ can be identified with a corresponding linear form, by placing the vector in the anti-linear first slot of the inner product: $(\boldsymbol\phi,\cdot) \equiv \langle\phi|$. The correspondence between these notations is then $(\boldsymbol\phi, \boldsymbol\psi) \equiv \langle\phi|\psi\rangle$. The linear form $\langle\phi|$ is a covector to $|\phi\rangle$, and the set of all covectors forms a subspace of the dual vector space $V^\vee$, to the initial vector space $V$. The purpose of this linear form $\langle\phi|$ can now be understood in terms of making projections onto the state $\boldsymbol \phi,$ to find how linearly dependent two states are, etc.
For the vector space $\Complex^n$, kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplication. If $\Complex^n$ has the standard Hermitian inner product $(\boldsymbol v, \boldsymbol w) = v^\dagger w$, under this identification, the identification of kets and bras and vice versa provided by the inner product is taking the Hermitian conjugate (denoted $\dagger$).
It is common to suppress the vector or linear form from the bra--ket notation and only use a label inside the typography for the bra or ket. For example, the spin operator $\hat \sigma_z$ on a two-dimensional space $\Delta$ of spinors has eigenvalues $\pm \frac{1}{2}$ with eigenspinors $\boldsymbol \psi_+,\boldsymbol \psi_- \in \Delta$. In bra--ket notation, this is typically denoted as $\boldsymbol \psi_+ = |+\rangle$, and $\boldsymbol \psi_- = |-\rangle$. As above, kets and bras with the same label are interpreted as kets and bras corresponding to each other using the inner product. In particular, when also identified with row and column vectors, kets and bras with the same label are identified with Hermitian conjugate column and row vectors.
Bra--ket notation was effectively established in 1939 by Paul Dirac; it is thus also known as Dirac notation, despite the notation having a precursor in Hermann Grassmann\'s use of $[\phi{\mid}\psi]$ for inner products nearly 100 years earlier.
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# Bra–ket notation
## Vector spaces {#vector_spaces}
### Vectors vs kets {#vectors_vs_kets}
In mathematics, the term \"vector\" is used for an element of any vector space. In physics, however, the term \"vector\" tends to refer almost exclusively to quantities like displacement or velocity, which have components that relate directly to the three dimensions of space, or relativistically, to the four of spacetime. Such vectors are typically denoted with over arrows ($\vec r$), boldface ($\mathbf{p}$) or indices ($v^\mu$).
In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number) or some more abstract Hilbert space constructed more algebraically. To distinguish this type of vector from those described above, it is common and useful in physics to denote an element $\phi$ of an abstract complex vector space as a ket $|\phi\rangle$, to refer to it as a \"ket\" rather than as a vector, and to pronounce it \"ket-$\phi$\" or \"ket-A\" for `{{math|{{ket|''A''}}}}`{=mediawiki}.
Symbols, letters, numbers, or even words---whatever serves as a convenient label---can be used as the label inside a ket, with the $|\ \rangle$ making clear that the label indicates a vector in vector space. In other words, the symbol \"`{{math|{{ket|''A''}}}}`{=mediawiki}\" has a recognizable mathematical meaning as to the kind of variable being represented, while just the \"`{{math|''A''}}`{=mediawiki}\" by itself does not. For example, `{{math|{{ket|1}} + {{ket|2}}}}`{=mediawiki} is not necessarily equal to `{{math|{{ket|3}}}}`{=mediawiki}. Nevertheless, for convenience, there is usually some logical scheme behind the labels inside kets, such as the common practice of labeling energy eigenkets in quantum mechanics through a listing of their quantum numbers. At its simplest, the label inside the ket is the eigenvalue of a physical operator, such as $\hat x$, $\hat p$, $\hat L_z$, etc.
### Notation
Since kets are just vectors in a Hermitian vector space, they can be manipulated using the usual rules of linear algebra. For example:
$$\begin{align}
|A \rangle &= |B\rangle + |C\rangle \\
|C \rangle &= (-1+2i)|D \rangle \\
|D \rangle &= \int_{-\infty}^{\infty} e^{-x^2} |x\rangle \, \mathrm{d}x \,.
\end{align}$$
Note how the last line above involves infinitely many different kets, one for each real number `{{math|''x''}}`{=mediawiki}.
Since the ket is an element of a vector space, a **bra** $\langle A|$ is an element of its dual space, i.e. a bra is a linear functional which is a linear map from the vector space to the complex numbers. Thus, it is useful to think of kets and bras as being elements of different vector spaces (see below however) with both being different useful concepts.
A bra $\langle\phi|$ and a ket $|\psi\rangle$ (i.e. a functional and a vector), can be combined to an operator $|\psi\rangle\langle\phi|$ of rank one with outer product
$$|\psi\rangle\langle\phi| \colon |\xi\rangle \mapsto |\psi\rangle\langle\phi|\xi\rangle ~.$$
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# Bra–ket notation
## Vector spaces {#vector_spaces}
### Inner product and bra--ket identification on Hilbert space {#inner_product_and_braket_identification_on_hilbert_space}
The bra--ket notation is particularly useful in Hilbert spaces which have an inner product that allows Hermitian conjugation and identifying a vector with a continuous linear functional, i.e. a ket with a bra, and vice versa (see Riesz representation theorem). The inner product on Hilbert space $(\ , \ )$ (with the first argument anti linear as preferred by physicists) is fully equivalent to an (anti-linear) identification between the space of kets and that of bras in the bra--ket notation: for a vector ket $\psi = |\psi\rangle$ define a functional (i.e. bra) $f_\phi = \langle\phi|$ by
$$(\phi,\psi) = (|\phi\rangle, |\psi\rangle) =: f_\phi(\psi) = \langle\phi| \, \bigl(|\psi\rangle\bigr) =: \langle\phi{\mid}\psi\rangle$$
#### Bras and kets as row and column vectors {#bras_and_kets_as_row_and_column_vectors}
In the simple case where we consider the vector space $\Complex^n$, a ket can be identified with a column vector, and a bra as a row vector. If, moreover, we use the standard Hermitian inner product on $\Complex^n$, the bra corresponding to a ket, in particular a bra `{{math|{{bra|''m''}}}}`{=mediawiki} and a ket `{{math|{{ket|''m''}}}}`{=mediawiki} with the same label are conjugate transpose. Moreover, conventions are set up in such a way that writing bras, kets, and linear operators next to each other simply imply matrix multiplication. In particular the outer product $|\psi\rangle\langle\phi|$ of a column and a row vector ket and bra can be identified with matrix multiplication (column vector times row vector equals matrix).
For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector: $\langle A | B \rangle \doteq A_1^* B_1 + A_2^* B_2 + \cdots + A_N^* B_N =
\begin{pmatrix} A_1^* & A_2^* & \cdots & A_N^* \end{pmatrix}
\begin{pmatrix} B_1 \\ B_2 \\ \vdots \\ B_N \end{pmatrix}$ Based on this, the bras and kets can be defined as: $\begin{align}
\langle A | &\doteq \begin{pmatrix} A_1^* & A_2^* & \cdots & A_N^* \end{pmatrix} \\
| B \rangle &\doteq \begin{pmatrix} B_1 \\ B_2 \\ \vdots \\ B_N \end{pmatrix}
\end{align}$ and then it is understood that a bra next to a ket implies matrix multiplication.
The conjugate transpose (also called *Hermitian conjugate*) of a bra is the corresponding ket and vice versa: $\langle A |^\dagger = |A \rangle, \quad |A \rangle^\dagger = \langle A |$ because if one starts with the bra $\begin{pmatrix} A_1^* & A_2^* & \cdots & A_N^* \end{pmatrix} \,,$ then performs a complex conjugation, and then a matrix transpose, one ends up with the ket $\begin{pmatrix} A_1 \\ A_2 \\ \vdots \\ A_N \end{pmatrix}$
Writing elements of a finite dimensional (or mutatis mutandis, countably infinite) vector space as a column vector of numbers requires picking a basis. Picking a basis is not always helpful because quantum mechanics calculations involve frequently switching between different bases (e.g. position basis, momentum basis, energy eigenbasis), and one can write something like \"`{{math|{{ket|''m''}}}}`{=mediawiki}\" without committing to any particular basis. In situations involving two different important basis vectors, the basis vectors can be taken in the notation explicitly and here will be referred simply as \"`{{math|{{ket|''−''}}}}`{=mediawiki}\" and \"`{{math|{{ket|''+''}}}}`{=mediawiki}\".
### Non-normalizable states and non-Hilbert spaces {#non_normalizable_states_and_non_hilbert_spaces}
Bra--ket notation can be used even if the vector space is not a Hilbert space.
In quantum mechanics, it is common practice to write down kets which have infinite norm, i.e. non-normalizable wavefunctions. Examples include states whose wavefunctions are Dirac delta functions or infinite plane waves. These do not, technically, belong to the Hilbert space itself. However, the definition of \"Hilbert space\" can be broadened to accommodate these states (see the Gelfand--Naimark--Segal construction or rigged Hilbert spaces). The bra--ket notation continues to work in an analogous way in this more general context.
Banach spaces are a different generalization of Hilbert spaces. In a Banach space `{{math|{{mathcal|B}}}}`{=mediawiki}, the vectors may be notated by kets and the continuous linear functionals by bras. Over any vector space without a given topology, we may still notate the vectors by kets and the linear functionals by bras. In these more general contexts, the bracket does not have the meaning of an inner product, because the Riesz representation theorem does not apply.
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# Bra–ket notation
## Usage in quantum mechanics {#usage_in_quantum_mechanics}
The mathematical structure of quantum mechanics is based in large part on linear algebra:
- Wave functions and other quantum states can be represented as vectors in a separable complex Hilbert space. (The exact structure of this Hilbert space depends on the situation.) In bra--ket notation, for example, an electron might be in the \"state\" `{{math|{{ket|''ψ''}}}}`{=mediawiki}. (Technically, the quantum states are *rays* of vectors in the Hilbert space, as `{{math|''c''{{ket|''ψ''}}}}`{=mediawiki} corresponds to the same state for any nonzero complex number `{{math|''c''}}`{=mediawiki}.)
- Quantum superpositions can be described as vector sums of the constituent states. For example, an electron in the state `{{math|{{sfrac|1|√2}}{{ket|1}} + {{sfrac|''i''|√2}}{{ket|2}}}}`{=mediawiki} is in a quantum superposition of the states `{{math|{{ket|1}}}}`{=mediawiki} and `{{math|{{ket|2}}}}`{=mediawiki}.
- Measurements are associated with linear operators (called observables) on the Hilbert space of quantum states.
- Dynamics are also described by linear operators on the Hilbert space. For example, in the Schrödinger picture, there is a linear time evolution operator `{{math|''U''}}`{=mediawiki} with the property that if an electron is in state `{{math|{{ket|''ψ''}}}}`{=mediawiki} right now, at a later time it will be in the state `{{math|''U''{{ket|''ψ''}}}}`{=mediawiki}, the same `{{math|''U''}}`{=mediawiki} for every possible `{{math|{{ket|''ψ''}}}}`{=mediawiki}.
- Wave function normalization is scaling a wave function so that its norm is 1.
Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra--ket notation. A few examples follow:
### Spinless position--space wave function {#spinless_positionspace_wave_function}
The Hilbert space of a spin-0 point particle can be represented in terms of a \"position basis\" `{{math|{ {{ket|'''r'''}} }<nowiki/>}}`{=mediawiki}, where the label `{{math|'''r'''}}`{=mediawiki} extends over the set of all points in position space. These states satisfy the eigenvalue equation for the position operator: $\hat{\mathbf{r}}|\mathbf{r}\rangle = \mathbf{r}|\mathbf{r}\rangle.$ The position states are \"generalized eigenvectors\", not elements of the Hilbert space itself, and do not form a countable orthonormal basis. However, as the Hilbert space is separable, it does admit a countable dense subset within the domain of definition of its wavefunctions. That is, starting from any ket `{{math|{{ket|Ψ}}}}`{=mediawiki} in this Hilbert space, one may *define* a complex scalar function of `{{math|'''r'''}}`{=mediawiki}, known as a wavefunction, $\Psi(\mathbf{r}) \ \stackrel{\text{def}}{=}\ \lang \mathbf{r}|\Psi\rang \,.$
On the left-hand side, `{{math|Ψ('''r''')}}`{=mediawiki} is a function mapping any point in space to a complex number; on the right-hand side, $\left|\Psi\right\rangle = \int d^3\mathbf{r} \, \Psi(\mathbf{r}) \left|\mathbf{r}\right\rangle$ is a ket consisting of a superposition of kets with relative coefficients specified by that function.
It is then customary to define linear operators acting on wavefunctions in terms of linear operators acting on kets, by $\hat A(\mathbf{r}) ~ \Psi(\mathbf{r}) \ \stackrel{\text{def}}{=}\ \lang \mathbf{r}|\hat A|\Psi\rang \,.$
For instance, the momentum operator $\hat \mathbf {p}$ has the following coordinate representation, $\hat{\mathbf{p} } (\mathbf{r}) ~ \Psi(\mathbf{r}) \ \stackrel{\text{def}}{=}\ \lang \mathbf{r} |\hat \mathbf{p}|\Psi\rang = - i \hbar \nabla \Psi(\mathbf{r}) \,.$
One occasionally even encounters an expression such as $\nabla |\Psi\rang$, though this is something of an abuse of notation. The differential operator must be understood to be an abstract operator, acting on kets, that has the effect of differentiating wavefunctions once the expression is projected onto the position basis, $\nabla \lang\mathbf{r}|\Psi\rang \,,$ even though, in the momentum basis, this operator amounts to a mere multiplication operator (by `{{math|''iħ'''''p'''}}`{=mediawiki}). That is, to say, $\langle \mathbf{r} |\hat \mathbf{p} = - i \hbar \nabla \langle \mathbf{r}| ~,$ or $\hat \mathbf{p} = \int d^3 \mathbf{r} ~| \mathbf{r}\rangle ( - i \hbar \nabla) \langle \mathbf{r}| ~.$
### Overlap of states {#overlap_of_states}
In quantum mechanics the expression `{{math|{{bra-ket|''φ''|''ψ''}}}}`{=mediawiki} is typically interpreted as the probability amplitude for the state `{{math|''ψ''}}`{=mediawiki} to collapse into the state `{{math|''φ''}}`{=mediawiki}. Mathematically, this means the coefficient for the projection of `{{math|''ψ''}}`{=mediawiki} onto `{{math|''φ''}}`{=mediawiki}. It is also described as the projection of state `{{math|''ψ''}}`{=mediawiki} onto state `{{math|''φ''}}`{=mediawiki}.
### Changing basis for a spin-1/2 particle {#changing_basis_for_a_spin_12_particle}
A stationary spin-`{{1/2}}`{=mediawiki} particle has a two-dimensional Hilbert space. One orthonormal basis is: $|{\uparrow}_z \rangle \,, \; |{\downarrow}_z \rangle$ where `{{math|{{ket|↑<sub>''z''</sub>}}}}`{=mediawiki} is the state with a definite value of the spin operator `{{math|''S<sub>z</sub>''}}`{=mediawiki} equal to +`{{1/2}}`{=mediawiki} and `{{math|{{ket|↓<sub>''z''</sub>}}}}`{=mediawiki} is the state with a definite value of the spin operator `{{math|''S<sub>z</sub>''}}`{=mediawiki} equal to −`{{1/2}}`{=mediawiki}.
Since these are a basis, *any* quantum state of the particle can be expressed as a linear combination (i.e., quantum superposition) of these two states: $|\psi \rangle = a_{\psi} |{\uparrow}_z \rangle + b_{\psi} |{\downarrow}_z \rangle$ where `{{math|''a<sub>ψ</sub>''}}`{=mediawiki} and `{{math|''b<sub>ψ</sub>''}}`{=mediawiki} are complex numbers.
A *different* basis for the same Hilbert space is: $|{\uparrow}_x \rangle \,, \; |{\downarrow}_x \rangle$ defined in terms of `{{math|''S<sub>x</sub>''}}`{=mediawiki} rather than `{{math|''S<sub>z</sub>''}}`{=mediawiki}.
Again, *any* state of the particle can be expressed as a linear combination of these two: $|\psi \rangle = c_{\psi} |{\uparrow}_x \rangle + d_{\psi} |{\downarrow}_x \rangle$
In vector form, you might write $|\psi\rangle \doteq \begin{pmatrix} a_\psi \\ b_\psi \end{pmatrix} \quad \text{or} \quad |\psi\rangle \doteq \begin{pmatrix} c_\psi \\ d_\psi \end{pmatrix}$ depending on which basis you are using. In other words, the \"coordinates\" of a vector depend on the basis used.
There is a mathematical relationship between $a_\psi$, $b_\psi$, $c_\psi$ and $d_\psi$; see change of basis.
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# Bra–ket notation
## Pitfalls and ambiguous uses {#pitfalls_and_ambiguous_uses}
There are some conventions and uses of notation that may be confusing or ambiguous for the non-initiated or early student.
### Separation of inner product and vectors {#separation_of_inner_product_and_vectors}
A cause for confusion is that the notation does not separate the inner-product operation from the notation for a (bra) vector. If a (dual space) bra-vector is constructed as a linear combination of other bra-vectors (for instance when expressing it in some basis) the notation creates some ambiguity and hides mathematical details. We can compare bra--ket notation to using bold for vectors, such as $\boldsymbol \psi$, and $(\cdot,\cdot)$ for the inner product. Consider the following dual space bra-vector in the basis $\{|e_n\rangle\}$, where $\{\psi_n\}$ are the complex number coefficients of $\langle \psi |$: $\langle\psi| = \sum_n \langle e_n| \psi_n$
It has to be determined by convention if the complex numbers $\{\psi_n\}$ are inside or outside of the inner product, and each convention gives different results.
$\langle\psi| \equiv (\boldsymbol\psi, \cdot ) = \sum_n (\boldsymbol e_n, \cdot ) \, \psi_n$ $\langle\psi| \equiv (\boldsymbol\psi, \cdot ) = \sum_n (\boldsymbol e_n \psi_n, \cdot ) = \sum_n (\boldsymbol e_n, \cdot ) \, \psi_n^*$
### Reuse of symbols {#reuse_of_symbols}
It is common to use the same symbol for *labels* and *constants*. For example, $\hat \alpha |\alpha\rangle = \alpha |\alpha \rangle$, where the symbol $\alpha$ is used simultaneously as the *name of the operator* $\hat \alpha$, its *eigenvector* $|\alpha\rangle$ and the associated *eigenvalue* $\alpha$. Sometimes the *hat* is also dropped for operators, and one can see notation such as $A |a\rangle = a |a \rangle$.
### Hermitian conjugate of kets {#hermitian_conjugate_of_kets}
It is common to see the usage $|\psi\rangle^\dagger = \langle\psi|$, where the dagger ($\dagger$) corresponds to the Hermitian conjugate. This is however not correct in a technical sense, since the ket, $|\psi\rangle$, represents a vector in a complex Hilbert-space $\mathcal{H}$, and the bra, $\langle\psi|$, is a linear functional on vectors in $\mathcal{H}$. In other words, $|\psi\rangle$ is just a vector, while $\langle\psi|$ is the combination of a vector and an inner product.
### Operations inside bras and kets {#operations_inside_bras_and_kets}
This is done for a fast notation of scaling vectors. For instance, if the vector $|\alpha \rangle$ is scaled by $1/\sqrt{2}$, it may be denoted $|\alpha/\sqrt{2} \rangle$. This can be ambiguous since $\alpha$ is simply a label for a state, and not a mathematical object on which operations can be performed. This usage is more common when denoting vectors as tensor products, where part of the labels are moved **outside** the designed slot, e.g. $|\alpha \rangle = |\alpha/\sqrt{2} \rangle_1 \otimes |\alpha/\sqrt{2} \rangle_2$.
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# Bra–ket notation
## Linear operators {#linear_operators}
### Linear operators acting on kets {#linear_operators_acting_on_kets}
A linear operator is a map that inputs a ket and outputs a ket. (In order to be called \"linear\", it is required to have certain properties.) In other words, if $\hat A$ is a linear operator and $|\psi\rangle$ is a ket-vector, then $\hat A |\psi\rangle$ is another ket-vector.
In an $N$-dimensional Hilbert space, we can impose a basis on the space and represent $|\psi\rangle$ in terms of its coordinates as a $N \times 1$ column vector. Using the same basis for $\hat A$, it is represented by an $N \times N$ complex matrix. The ket-vector $\hat A |\psi\rangle$ can now be computed by matrix multiplication.
Linear operators are ubiquitous in the theory of quantum mechanics. For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.
### Linear operators acting on bras {#linear_operators_acting_on_bras}
Operators can also be viewed as acting on bras *from the right hand side*. Specifically, if `{{math|'''''A'''''}}`{=mediawiki} is a linear operator and `{{math|{{bra|''φ''}}}}`{=mediawiki} is a bra, then `{{math|{{bra|''φ''}}'''''A'''''}}`{=mediawiki} is another bra defined by the rule $\bigl(\langle\phi|\boldsymbol{A}\bigr) |\psi\rangle = \langle\phi| \bigl(\boldsymbol{A}|\psi\rangle\bigr) \,,$ (in other words, a function composition). This expression is commonly written as (cf. energy inner product) $\langle\phi| \boldsymbol{A} |\psi\rangle \,.$
In an `{{math|''N''}}`{=mediawiki}-dimensional Hilbert space, `{{math|{{bra|''φ''}}}}`{=mediawiki} can be written as a `{{math|1 × ''N''}}`{=mediawiki} row vector, and `{{math|'''''A'''''}}`{=mediawiki} (as in the previous section) is an `{{math|''N'' × ''N''}}`{=mediawiki} matrix. Then the bra `{{math|{{bra|''φ''}}'''''A'''''}}`{=mediawiki} can be computed by normal matrix multiplication.
If the same state vector appears on both bra and ket side, $\langle\psi|\boldsymbol{A}|\psi\rangle \,,$ then this expression gives the expectation value, or mean or average value, of the observable represented by operator `{{math|'''''A'''''}}`{=mediawiki} for the physical system in the state `{{math|{{ket|''ψ''}}}}`{=mediawiki}.
### Outer products {#outer_products}
A convenient way to define linear operators on a Hilbert space `{{math|{{mathcal|H}}}}`{=mediawiki} is given by the outer product: if `{{math|{{bra|''ϕ''}}}}`{=mediawiki} is a bra and `{{math|{{ket|''ψ''}}}}`{=mediawiki} is a ket, the outer product $|\phi\rang \, \lang \psi|$ denotes the rank-one operator with the rule $\bigl(|\phi\rang \lang \psi|\bigr)(x) = \lang \psi | x \rang |\phi \rang.$
For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication: $|\phi \rangle \, \langle \psi | \doteq
\begin{pmatrix} \phi_1 \\ \phi_2 \\ \vdots \\ \phi_N \end{pmatrix}
\begin{pmatrix} \psi_1^* & \psi_2^* & \cdots & \psi_N^* \end{pmatrix}
= \begin{pmatrix}
\phi_1 \psi_1^* & \phi_1 \psi_2^* & \cdots & \phi_1 \psi_N^* \\
\phi_2 \psi_1^* & \phi_2 \psi_2^* & \cdots & \phi_2 \psi_N^* \\
\vdots & \vdots & \ddots & \vdots \\
\phi_N \psi_1^* & \phi_N \psi_2^* & \cdots & \phi_N \psi_N^* \end{pmatrix}$ The outer product is an `{{math|''N'' × ''N''}}`{=mediawiki} matrix, as expected for a linear operator.
One of the uses of the outer product is to construct projection operators. Given a ket `{{math|{{ket|''ψ''}}}}`{=mediawiki} of norm 1, the orthogonal projection onto the subspace spanned by `{{math|{{ket|''ψ''}}}}`{=mediawiki} is $|\psi\rangle \, \langle\psi| \,.$ This is an idempotent in the algebra of observables that acts on the Hilbert space.
### Hermitian conjugate operator {#hermitian_conjugate_operator}
Just as kets and bras can be transformed into each other (making `{{math|{{ket|''ψ''}}}}`{=mediawiki} into `{{math|{{bra|''ψ''}}}}`{=mediawiki}), the element from the dual space corresponding to `{{math|''A''{{ket|''ψ''}}}}`{=mediawiki} is `{{math|{{bra|''ψ''}}''A''<sup>†</sup>}}`{=mediawiki}, where `{{math|''A''<sup>†</sup>}}`{=mediawiki} denotes the Hermitian conjugate (or adjoint) of the operator `{{math|''A''}}`{=mediawiki}. In other words, $|\phi\rangle = A |\psi\rangle \quad \text{if and only if} \quad \langle\phi| = \langle \psi | A^\dagger \,.$
If `{{math|''A''}}`{=mediawiki} is expressed as an `{{math|''N'' × ''N''}}`{=mediawiki} matrix, then `{{math|''A''<sup>†</sup>}}`{=mediawiki} is its conjugate transpose.
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# Bra–ket notation
## Properties
Bra--ket notation was designed to facilitate the formal manipulation of linear-algebraic expressions. Some of the properties that allow this manipulation are listed herein. In what follows, `{{math|''c''<sub>1</sub>}}`{=mediawiki} and `{{math|''c''<sub>2</sub>}}`{=mediawiki} denote arbitrary complex numbers, `{{math|''c''*}}`{=mediawiki} denotes the complex conjugate of `{{math|''c''}}`{=mediawiki}, `{{math|''A''}}`{=mediawiki} and `{{math|''B''}}`{=mediawiki} denote arbitrary linear operators, and these properties are to hold for any choice of bras and kets.
### Linearity
- Since bras are linear functionals, $\langle\phi| \bigl( c_1|\psi_1\rangle + c_2|\psi_2\rangle \bigr) = c_1\langle\phi|\psi_1\rangle + c_2\langle\phi|\psi_2\rangle \,.$
- By the definition of addition and scalar multiplication of linear functionals in the dual space, $\bigl(c_1 \langle\phi_1| + c_2 \langle\phi_2|\bigr) |\psi\rangle = c_1 \langle\phi_1|\psi\rangle + c_2 \langle\phi_2|\psi\rangle \,.$
### Associativity
Given any expression involving complex numbers, bras, kets, inner products, outer products, and/or linear operators (but not addition), written in bra--ket notation, the parenthetical groupings do not matter (i.e., the associative property holds). For example:
$$\begin{align}
\lang \psi| \bigl(A |\phi\rang\bigr) = \bigl(\lang \psi|A\bigr)|\phi\rang \, &\stackrel{\text{def}}{=} \, \lang \psi | A | \phi \rang \\
\bigl(A|\psi\rang\bigr)\lang \phi| = A\bigl(|\psi\rang \lang \phi|\bigr) \, &\stackrel{\text{def}}{=} \, A | \psi \rang \lang \phi |
\end{align}$$ and so forth. The expressions on the right (with no parentheses whatsoever) are allowed to be written unambiguously *because* of the equalities on the left. Note that the associative property does *not* hold for expressions that include nonlinear operators, such as the antilinear time reversal operator in physics.
### Hermitian conjugation {#hermitian_conjugation}
Bra--ket notation makes it particularly easy to compute the Hermitian conjugate (also called *dagger*, and denoted `{{math|†}}`{=mediawiki}) of expressions. The formal rules are:
- The Hermitian conjugate of a bra is the corresponding ket, and vice versa.
- The Hermitian conjugate of a complex number is its complex conjugate.
- The Hermitian conjugate of the Hermitian conjugate of anything (linear operators, bras, kets, numbers) is itself---i.e., $\left(x^\dagger\right)^\dagger=x \,.$
- Given any combination of complex numbers, bras, kets, inner products, outer products, and/or linear operators, written in bra--ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.
These rules are sufficient to formally write the Hermitian conjugate of any such expression; some examples are as follows:
- Kets:
\\bigl(c_1\|\\psi_1\\rangle + c_2\|\\psi_2\\rangle\\bigr)\^\\dagger = c_1\^\* \\langle\\psi_1\| + c_2\^\* \\langle\\psi_2\| \\,.
- Inner products: $\langle \phi | \psi \rangle^* = \langle \psi|\phi\rangle \,.$ Note that `{{math|{{bra-ket|''φ''|''ψ''}}}}`{=mediawiki} is a scalar, so the Hermitian conjugate is just the complex conjugate, i.e., $\bigl(\langle \phi | \psi \rangle\bigr)^\dagger = \langle \phi | \psi \rangle^*$
- Matrix elements: \\begin{align}
\\langle \\phi\| A \| \\psi \\rangle\^\\dagger &= \\left\\langle \\psi \\left\| A\^\\dagger \\right\|\\phi \\right\\rangle \\\\ \\left\\langle \\phi\\left\| A\^\\dagger B\^\\dagger \\right\| \\psi \\right\\rangle\^\\dagger &= \\langle \\psi \| BA \|\\phi \\rangle \\,. \\end{align}
- Outer products: $\Big(\bigl(c_1|\phi_1\rangle\langle \psi_1|\bigr) + \bigl(c_2|\phi_2\rangle\langle\psi_2|\bigr)\Big)^\dagger = \bigl(c_1^* |\psi_1\rangle\langle \phi_1|\bigr) + \bigl(c_2^*|\psi_2\rangle\langle\phi_2|\bigr) \,.$
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# Bra–ket notation
## Composite bras and kets {#composite_bras_and_kets}
Two Hilbert spaces `{{math|''V''}}`{=mediawiki} and `{{math|''W''}}`{=mediawiki} may form a third space `{{math|''V'' ⊗ ''W''}}`{=mediawiki} by a tensor product. In quantum mechanics, this is used for describing composite systems. If a system is composed of two subsystems described in `{{math|''V''}}`{=mediawiki} and `{{math|''W''}}`{=mediawiki} respectively, then the Hilbert space of the entire system is the tensor product of the two spaces. (The exception to this is if the subsystems are actually identical particles. In that case, the situation is a little more complicated.)
If `{{math|{{ket|''ψ''}}}}`{=mediawiki} is a ket in `{{math|''V''}}`{=mediawiki} and `{{math|{{ket|''φ''}}}}`{=mediawiki} is a ket in `{{math|''W''}}`{=mediawiki}, the tensor product of the two kets is a ket in `{{math|''V'' ⊗ ''W''}}`{=mediawiki}. This is written in various notations:
$$|\psi\rangle|\phi\rangle \,,\quad |\psi\rangle \otimes |\phi\rangle\,,\quad|\psi \phi\rangle\,,\quad|\psi ,\phi\rangle\,.$$
See quantum entanglement and the EPR paradox for applications of this product.
## The unit operator {#the_unit_operator}
Consider a complete orthonormal system (*basis*), $\{ e_i \ | \ i \in \mathbb{N} \} \,,$ for a Hilbert space `{{math|''H''}}`{=mediawiki}, with respect to the norm from an inner product `{{math|{{angbr|·,·}}}}`{=mediawiki}.
From basic functional analysis, it is known that any ket $|\psi\rangle$ can also be written as $|\psi\rangle = \sum_{i \in \mathbb{N}} \langle e_i | \psi \rangle | e_i \rangle,$ with `{{math|{{bra-ket|·|·}}}}`{=mediawiki} the inner product on the Hilbert space.
From the commutativity of kets with (complex) scalars, it follows that $\sum_{i \in \mathbb{N}} | e_i \rangle \langle e_i | = \mathbb{I}$ must be the *identity operator*, which sends each vector to itself.
This, then, can be inserted in any expression without affecting its value; for example $\begin{align}
\langle v | w \rangle &= \langle v | \left( \sum_{i \in \mathbb{N}} | e_i \rangle \langle e_i| \right) | w \rangle \\
&= \langle v | \left( \sum_{i \in \mathbb{N}} | e_i \rangle \langle e_i| \right) \left( \sum_{j \in \mathbb{N}} | e_j \rangle \langle e_j |\right)| w \rangle \\
&= \langle v | e_i \rangle \langle e_i | e_j \rangle \langle e_j | w \rangle \,,
\end{align}$ where, in the last line, the Einstein summation convention has been used to avoid clutter.
In quantum mechanics, it often occurs that little or no information about the inner product `{{math|{{bra-ket|''ψ''|''φ''}}}}`{=mediawiki} of two arbitrary (state) kets is present, while it is still possible to say something about the expansion coefficients `{{math|1={{bra-ket|''ψ''|''e<sub>i</sub>''}} = {{bra-ket|''e<sub>i</sub>''|''ψ''}}*}}`{=mediawiki} and `{{math|{{bra-ket|''e<sub>i</sub>''|''φ''}}}}`{=mediawiki} of those vectors with respect to a specific (orthonormalized) basis. In this case, it is particularly useful to insert the unit operator into the bracket one time or more.
For more information, see Resolution of the identity, ${\mathbb I} = \int\! dx~ | x \rangle \langle x |= \int\! dp ~| p \rangle \langle p |,$ where $|p\rangle = \int dx \frac{e^{ixp / \hbar} |x\rangle}{\sqrt{2\pi\hbar}}.$
Since `{{math|1={{bra-ket|''x''{{prime}}|''x''}} = ''δ''(''x'' − ''x''{{prime}})}}`{=mediawiki}, plane waves follow, $\langle x | p \rangle = \frac{e^{ixp / \hbar}}{\sqrt{2\pi\hbar}}.$
In his book (1958), Ch. III.20, Dirac defines the *standard ket* which, up to a normalization, is the translationally invariant momentum eigenstate $|\varpi\rangle=\lim_{p\to 0} |p\rangle$ in the momentum representation, i.e., $\hat{p}|\varpi\rangle=0$. Consequently, the corresponding wavefunction is a constant, $\langle x|\varpi\rangle \sqrt{2\pi \hbar}=1$, and $|x\rangle= \delta(\hat{x}-x) |\varpi\rangle \sqrt{2\pi \hbar},$ as well as $|p\rangle= \exp (ip\hat{x}/\hbar ) |\varpi\rangle.$
Typically, when all matrix elements of an operator such as $\langle x| A |y\rangle$ are available, this resolution serves to reconstitute the full operator, $\int dx \, dy \, |x\rangle \langle x| A |y\rangle \langle y | = A \,.$
## Notation used by mathematicians {#notation_used_by_mathematicians}
The object physicists are considering when using bra--ket notation is a Hilbert space (a complete inner product space).
Let $(\mathcal H, \langle\cdot,\cdot\rangle)$ be a Hilbert space and `{{math|''h'' ∈ {{mathcal|H}}}}`{=mediawiki} a vector in `{{math|{{mathcal|H}}}}`{=mediawiki}. What physicists would denote by `{{math|{{ket|''h''}}}}`{=mediawiki} is the vector itself. That is, $|h\rangle\in \mathcal{H} .$
Let `{{math|{{mathcal|H}}*}}`{=mediawiki} be the dual space of `{{math|{{mathcal|H}}}}`{=mediawiki}. This is the space of linear functionals on `{{math|{{mathcal|H}}}}`{=mediawiki}. The embedding $\Phi:\mathcal H \hookrightarrow \mathcal H^*$ is defined by $\Phi(h) = \varphi_h$, where for every `{{math|''h'' ∈ {{mathcal|H}}}}`{=mediawiki} the linear functional $\varphi_h:\mathcal H\to\mathbb C$ satisfies for every `{{math|''g'' ∈ {{mathcal|H}}}}`{=mediawiki} the functional equation $\varphi_h(g) = \langle h, g\rangle = \langle h\mid g\rangle$. Notational confusion arises when identifying `{{math|''φ<sub>h</sub>''}}`{=mediawiki} and `{{math|''g''}}`{=mediawiki} with `{{math|{{bra|''h''}}}}`{=mediawiki} and `{{math|{{ket|''g''}}}}`{=mediawiki} respectively. This is because of literal symbolic substitutions. Let $\varphi_h = H = \langle h\mid$ and let `{{math|1=''g'' = G = {{ket|''g''}}}}`{=mediawiki}. This gives $\varphi_h(g) = H(g) = H(G)=\langle h|(G) = \langle h|\bigl(|g\rangle\bigr) \,.$
One ignores the parentheses and removes the double bars.
Moreover, mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they usually use not an asterisk but an overline (which the physicists reserve for averages and the Dirac spinor adjoint) to denote complex conjugate numbers; i.e., for scalar products mathematicians usually write $\langle\phi ,\psi\rangle=\int \phi (x)\overline{\psi(x)}\, dx \,,$ whereas physicists would write for the same quantity $\langle\psi |\phi \rangle = \int dx \, \psi^*(x) \phi(x)~
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# Blizzard
A **blizzard** is a severe snowstorm characterized by strong sustained winds and low visibility, lasting for a prolonged period of time---typically at least three or four hours. A ground blizzard is a weather condition where snow that has already fallen is being blown by wind. Blizzards can have an immense size and usually stretch to hundreds or thousands of kilometres.
## Definition and etymology {#definition_and_etymology}
In the United States, the National Weather Service defines a blizzard as a severe snow storm characterized by strong winds causing blowing snow that results in low visibilities. The difference between a blizzard and a snowstorm is the strength of the wind, not the amount of snow. To be a blizzard, a snow storm must have sustained winds or frequent gusts that are greater than or equal to 56 km/h with blowing or drifting snow which reduces visibility to 400 m or less and must last for a prolonged period of time---typically three hours or more.
Environment Canada defines a blizzard as a storm with wind speeds exceeding 40 km/h accompanied by visibility of 400 m or less, resulting from snowfall, blowing snow, or a combination of the two. These conditions must persist for a period of at least four hours for the storm to be classified as a blizzard, except north of the arctic tree line, where that threshold is raised to six hours. The Australia Bureau of Meteorology describes a blizzard as, \"Violent and very cold wind which is laden with snow, some part, at least, of which has been raised from snow covered ground.\"
While severe cold and large amounts of drifting snow may accompany blizzards, they are not required. Blizzards can bring whiteout conditions, and can paralyze regions for days at a time, particularly where snowfall is unusual or rare.
A severe blizzard has winds over 72 km/h, near zero visibility, and temperatures of -12 C or lower. In Antarctica, blizzards are associated with winds spilling over the edge of the ice plateau at an average velocity of 160 km/h.
Ground blizzard refers to a weather condition where loose snow or ice on the ground is lifted and blown by strong winds. The primary difference between a ground blizzard as opposed to a regular blizzard is that in a ground blizzard no precipitation is produced at the time, but rather all the precipitation is already present in the form of snow or ice at the surface.
The *Oxford English Dictionary* concludes the term *blizzard* is likely onomatopoeic, derived from the same sense as *blow, blast, blister, and bluster*; the first recorded use of it for weather dates to 1829, when it was defined as a \"violent blow\". It achieved its modern definition by 1859, when it was in use in the western United States. The term became common in the press during the harsh winter of 1880--81.
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# Blizzard
## United States storm systems {#united_states_storm_systems}
In the United States, storm systems powerful enough to cause blizzards usually form when the jet stream dips far to the south, allowing cold, dry polar air from the north to clash with warm, humid air moving up from the south.
When cold, moist air from the Pacific Ocean moves eastward to the Rocky Mountains and the Great Plains, and warmer, moist air moves north from the Gulf of Mexico, all that is needed is a movement of cold polar air moving south to form potential blizzard conditions that may extend from the Texas Panhandle to the Great Lakes and Midwest. A blizzard also may be formed when a cold front and warm front mix together and a blizzard forms at the border line.
Another storm system occurs when a cold core low over the Hudson Bay area in Canada is displaced southward over southeastern Canada, the Great Lakes, and New England. When the rapidly moving cold front collides with warmer air coming north from the Gulf of Mexico, strong surface winds, significant cold air advection, and extensive wintry precipitation occur.
Low pressure systems moving out of the Rocky Mountains onto the Great Plains, a broad expanse of flat land, much of it covered in prairie, steppe and grassland, can cause thunderstorms and rain to the south and heavy snows and strong winds to the north. With few trees or other obstructions to reduce wind and blowing, this part of the country is particularly vulnerable to blizzards with very low temperatures and whiteout conditions. In a true whiteout, there is no visible horizon. People can become lost in their own front yards, when the door is only 10 ft away, and they would have to feel their way back. Motorists have to stop their cars where they are, as the road is impossible to see.
### Nor\'easter blizzards {#noreaster_blizzards}
A nor\'easter is a macro-scale storm that occurs off the New England and Atlantic Canada coastlines. It gets its name from the direction the wind is coming from. The usage of the term in North America comes from the wind associated with many different types of storms, some of which can form in the North Atlantic Ocean and some of which form as far south as the Gulf of Mexico. The term is most often used in the coastal areas of New England and Atlantic Canada. This type of storm has characteristics similar to a hurricane. More specifically, it describes a low-pressure area whose center of rotation is just off the coast and whose leading winds in the left-forward quadrant rotate onto land from the northeast. High storm waves may sink ships at sea and cause coastal flooding and beach erosion. Notable nor\'easters include The Great Blizzard of 1888, one of the worst blizzards in U.S. history. It dropped 40 - of snow and had sustained winds of more than 45 mph that produced snowdrifts in excess of 50 ft. Railroads were shut down and people were confined to their houses for up to a week. It killed 400 people, mostly in New York.
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# Blizzard
## Historic events {#historic_events}
### 1972 Iran blizzard {#iran_blizzard}
The 1972 Iran blizzard, which caused 4,000 reported deaths, was the deadliest blizzard in recorded history. Dropping as much as 26 feet of snow, it completely covered 200 villages. After a snowfall lasting nearly a week, an area the size of Wisconsin was entirely buried in snow.
### 2008 Afghanistan blizzard {#afghanistan_blizzard}
The 2008 Afghanistan blizzard, was a fierce blizzard that struck Afghanistan on 10 January 2008. Temperatures fell to a low of -30 C, with up to 180 cm of snow in the more mountainous regions, killing at least 926 people. The weather also claimed more than 100,000 sheep and goats, and nearly 315,000 cattle died.
### The Snow Winter of 1880--1881 {#the_snow_winter_of_18801881}
The winter of 1880--1881 is widely considered the most severe winter ever known in many parts of the United States.
The initial blizzard in October 1880 brought snowfalls so deep that two-story homes experienced *accumulations*, as opposed to drifts, up to their second-floor windows. No one was prepared for deep snow so early in the winter. Farmers from North Dakota to Virginia were caught flat with fields unharvested, what grain that had been harvested unmilled, and their suddenly all-important winter stocks of wood fuel only partially collected. By January train service was almost entirely suspended from the region. Railroads hired scores of men to dig out the tracks but as soon as they had finished shoveling a stretch of line a new storm arrived, burying it again.
There were no winter thaws and on February 2, 1881, a second massive blizzard struck that lasted for nine days. In towns the streets were filled with solid drifts to the tops of the buildings and tunneling was necessary to move about. Homes and barns were completely covered, compelling farmers to construct fragile tunnels in order to feed their stock.
When the snow finally melted in late spring of 1881, huge sections of the plains experienced flooding. Massive ice jams clogged the Missouri River, and when they broke the downstream areas were inundated. Most of the town of Yankton, in what is now South Dakota, was washed away when the river overflowed its banks after the thaw.
#### Novelization
Many children---and their parents---learned of \"The Snow Winter\" through the children\'s book *The Long Winter* by Laura Ingalls Wilder, in which the author tells of her family\'s efforts to survive. The snow arrived in October 1880 and blizzard followed blizzard throughout the winter and into March 1881, leaving many areas snowbound throughout the winter. Accurate details in Wilder\'s novel include the blizzards\' frequency and the deep cold, the Chicago and North Western Railway stopping trains until the spring thaw because the snow made the tracks impassable, the near-starvation of the townspeople, and the courage of her future husband Almanzo and another man, Cap Garland, who ventured out on the open prairie in search of a cache of wheat that no one was even sure existed.
### The Storm of the Century {#the_storm_of_the_century}
The Storm of the Century, also known as the Great Blizzard of 1993, was a large cyclonic storm that formed over the Gulf of Mexico on March 12, 1993, and dissipated in the North Atlantic Ocean on March 15. It is unique for its intensity, massive size and wide-reaching effect. At its height, the storm stretched from Canada towards Central America, but its main impact was on the United States and Cuba. The cyclone moved through the Gulf of Mexico, and then through the Eastern United States before moving into Canada. Areas as far south as northern Alabama and Georgia received a dusting of snow and areas such as Birmingham, Alabama, received up to 12 in with hurricane-force wind gusts and record low barometric pressures. Between Louisiana and Cuba, hurricane-force winds produced high storm surges across northwestern Florida, which along with scattered tornadoes killed dozens of people. In the United States, the storm was responsible for the loss of electric power to over 10 million customers. It is purported to have been directly experienced by nearly 40 percent of the country\'s population at that time. A total of 310 people, including 10 from Cuba, perished during this storm. The storm cost \$6 to \$10 billion in damages.
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# Blizzard
## List of blizzards {#list_of_blizzards}
### North America {#north_america}
#### 1700 to 1799 {#to_1799}
- The Great Snow 1717 series of four snowstorms between February 27 and March 7, 1717. There were reports of about five feet of snow already on the ground when the first of the storms hit. By the end, there were about ten feet of snow and some drifts reaching 25 ft, burying houses entirely. In the colonial era, this storm made travel impossible until the snow simply melted.
- Blizzard of 1765. March 24, 1765. Affected area from Philadelphia to Massachusetts. High winds and over 2 ft of snowfall recorded in some areas.
- Blizzard of 1772. \"The Washington and Jefferson Snowstorm of 1772\". January 26--29, 1772. One of largest D.C. and Virginia area snowstorms ever recorded. Snow accumulations of 3 ft recorded.
- The \"Hessian Storm of 1778\". December 26, 1778. Severe blizzard with high winds, heavy snows and bitter cold extending from Pennsylvania to New England. Snow drifts reported to be 15 ft high in Rhode Island. Storm named for stranded Hessian troops in deep snows stationed in Rhode Island during the Revolutionary War.
- The Great Snow of 1786. December 4--10, 1786. Blizzard conditions and a succession of three harsh snowstorms produced snow depths of 2 ft to 4 ft from Pennsylvania to New England. Reportedly of similar magnitude of 1717 snowstorms.
- The Long Storm of 1798. November 19--21, 1798. Heavy snowstorm produced snow from Maryland to Maine.
#### 1800 to 1850 {#to_1850}
- Blizzard of 1805. January 26--28, 1805. Cyclone brought heavy snowstorm to New York City and New England. Snow fell continuously for two days where over 2 ft of snow accumulated.
- New York City Blizzard of 1811. December 23--24, 1811. Severe blizzard conditions reported on Long Island, in New York City, and southern New England. Strong winds and tides caused damage to shipping in harbor.
- Luminous Blizzard of 1817. January 17, 1817. In Massachusetts and Vermont, a severe snowstorm was accompanied by frequent lightning and heavy thunder. St. Elmo\'s fire reportedly lit up trees, fence posts, house roofs, and even people. John Farrar professor at Harvard, recorded the event in his memoir in 1821.
- Great Snowstorm of 1821. January 5--7, 1821. Extensive snowstorm and blizzard spread from Virginia to New England.
- Winter of Deep Snow in 1830. December 29, 1830. Blizzard storm dumped 36 in in Kansas City and 30 in in Illinois. Areas experienced repeated storms thru mid-February 1831.
- \"The Great Snowstorm of 1831\" January 14--16, 1831. Produced snowfall over widest geographic area that was only rivaled, or exceeded by, the 1993 Blizzard. Blizzard raged from Georgia, to Ohio Valley, all the way to Maine.
- \"The Big Snow of 1836\" January 8--10, 1836. Produced 30 in to 40 in of snowfall in interior New York, northern Pennsylvania, and western New England. Philadelphia got a reported 15 in and New York City 2 ft of snow.
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# Blizzard
## List of blizzards {#list_of_blizzards}
### North America {#north_america}
#### 1851 to 1900 {#to_1900}
- Plains Blizzard of 1856. December 3--5, 1856. Severe blizzard-like storm raged for three days in Kansas and Iowa. Early pioneers suffered.
- \"The Cold Storm of 1857\" January 18--19, 1857. Produced severe blizzard conditions from North Carolina to Maine. Heavy snowfalls reported in east coast cities.
- Midwest Blizzard of 1864. January 1, 1864. Gale-force winds, driving snow, and low temperatures all struck simultaneously around Chicago, Wisconsin and Minnesota.
- Plains Blizzard of 1873. January 7, 1873. Severe blizzard struck the Great Plains. Many pioneers from the east were unprepared for the storm and perished in Minnesota and Iowa.
- Great Plains Easter Blizzard of 1873. April 13, 1873
- Seattle Blizzard of 1880. January 6, 1880. Seattle area\'s greatest snowstorm to date. An estimated 4 ft fell around the town. Many barns collapsed and all transportation halted.
- The Hard Winter of 1880-81. October 15, 1880. A blizzard in eastern South Dakota marked the beginning of this historically difficult season. Laura Ingalls Wilder\'s book *The Long Winter* details the effects of this season on early settlers.
- In the three year winter period from December 1885 to March 1888, the Great Plains and Eastern United States suffered a series of the worst blizzards in this nation\'s history ending with the Schoolhouse Blizzard and the Great Blizzard of 1888. The massive explosion of the volcano Krakatoa in the South Pacific late in August 1883 is a suspected cause of these huge blizzards during these several years. The clouds of ash it emitted continued to circulate around the world for many years. Weather patterns continued to be chaotic for years, and temperatures did not return to normal until 1888. Record rainfall was experienced in Southern California during July 1883 to June 1884. The Krakatoa eruption injected an unusually large amount of sulfur dioxide (SO2) gas high into the stratosphere which reflects sunlight and helped cool the planet over the next few years until the suspended atmospheric sulfur fell to ground.
- Plains Blizzard of late 1885. In Kansas, heavy snows of late 1885 had piled drifts 10 ft high.
- Kansas Blizzard of 1886. First week of January 1886. Reported that 80 percent of the cattle were frozen to death in that state alone from the cold and snow.
- January 1886 Blizzard. January 9, 1886. Same system as Kansas 1886 Blizzard that traveled eastward.
- Great Plains Blizzards of late 1886. On November 13, 1886, it reportedly began to snow and did not stop for a month in the Great Plains region.
- Great Plains Blizzard of 1887. January 9--11, 1887. Reported 72-hour blizzard that covered parts of the Great Plains in more than 16 in of snow. Winds whipped and temperatures dropped to around -50 F. So many cows that were not killed by the cold soon died from starvation. When spring arrived, millions of the animals were dead, with around 90 percent of the open range\'s cattle rotting where they fell. Those present reported carcasses as far as the eye could see. Dead cattle clogged up rivers and spoiled drinking water. Many ranchers went bankrupt and others simply called it quits and moved back east. The \"Great Die-Up\" from the blizzard effectively concluded the romantic period of the great Plains cattle drives.
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- Schoolhouse Blizzard of 1888 North American Great Plains. January 12--13, 1888. What made the storm so deadly was the timing (during work and school hours), the suddenness, and the brief spell of warmer weather that preceded it. In addition, the very strong wind fields behind the cold front and the powdery nature of the snow reduced visibilities on the open plains to zero. People ventured from the safety of their homes to do chores, go to town, attend school, or simply enjoy the relative warmth of the day. As a result, thousands of people---including many schoolchildren---got caught in the blizzard.
- Great Blizzard of March 1888 March 11--14, 1888. One of the most severe recorded blizzards in the history of the United States. On March 12, an unexpected northeaster hit New England and the mid-Atlantic, dropping up to 50 in of snow in the space of three days. New York City experienced its heaviest snowfall recorded to date at that time, all street railcars were stranded, and the storm led to the creation of the NYC subway system. Snowdrifts reached up to the second story of some buildings. Some 400 people died from this blizzard, including many sailors aboard vessels that were beset by gale-force winds and turbulent seas.
- Great Blizzard of 1899 February 11--14, 1899. An extremely unusual blizzard in that it reached into the far southern states of the US. It hit in February, and the area around Washington, D.C., experienced 51 hours straight of snowfall. The port of New Orleans was totally iced over; revelers participating in the New Orleans Mardi Gras had to wait for the parade routes to be shoveled free of snow. Concurrent with this blizzard was the extremely cold arctic air. Many city and state record low temperatures date back to this event, including all-time records for locations in the Midwest and South. State record lows: Nebraska reached -47 F, Ohio experienced -39 F, Louisiana bottomed out at -16 F, and Florida dipped below zero to -2 F.
#### 1901 to 1939 {#to_1939}
- Great Lakes Storm of 1913 November 7--10, 1913. \"The White Hurricane\" of 1913 was the deadliest and most destructive natural disaster ever to hit the Great Lakes Basin in the Midwestern United States and the Canadian province of Ontario. It produced 90 mph wind gusts, waves over 35 ft high, and whiteout snowsqualls. It killed more than 250 people, destroyed 19 ships, and stranded 19 others.
- Blizzard of 1918. January 11, 1918. Vast blizzard-like storm moved through Great Lakes and Ohio Valley.
- 1920 North Dakota blizzard March 15--18, 1920
- Knickerbocker Storm January 27--28, 1922
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# Blizzard
## List of blizzards {#list_of_blizzards}
### North America {#north_america}
#### 1940 to 1949 {#to_1949}
- Armistice Day Blizzard of 1940 November 10--12, 1940. Took place in the Midwest region of the United States on Armistice Day. This \"Panhandle hook\" winter storm cut a 1000 mi through the middle of the country from Kansas to Michigan. The morning of the storm was unseasonably warm but by mid afternoon conditions quickly deteriorated into a raging blizzard that would last into the next day. A total of 145 deaths were blamed on the storm, almost a third of them duck hunters who had taken time off to take advantage of the ideal hunting conditions. Weather forecasters had not predicted the severity of the oncoming storm, and as a result the hunters were not dressed for cold weather. When the storm began many hunters took shelter on small islands in the Mississippi River, and the 50 mph winds and 5 ft waves overcame their encampments. Some became stranded on the islands and then froze to death in the single-digit temperatures that moved in over night. Others tried to make it to shore and drowned.
- North American blizzard of 1947 December 25--26, 1947. Was a record-breaking snowfall that began on Christmas Day and brought the Northeast United States to a standstill. Central Park in New York City got 26 in of snowfall in 24 hours with deeper snows in suburbs. It was not accompanied by high winds, but the snow fell steadily with drifts reaching 10 ft. Seventy-seven deaths were attributed to the blizzard.
- The Blizzard of 1949 - The first blizzard started on Sunday, January 2, 1949; it lasted for three days. It was followed by two more months of blizzard after blizzard with high winds and bitter cold. Deep drifts isolated southeast Wyoming, northern Colorado, western South Dakota and western Nebraska, for weeks. Railroad tracks and roads were all drifted in with drifts of 20 ft and more. Hundreds of people that had been traveling on trains were stranded. Motorists that had set out on January 2 found their way to private farm homes in rural areas and hotels and other buildings in towns; some dwellings were so crowded that there was not enough room for all to sleep at once. It would be weeks before they were plowed out. The Federal government quickly responded with aid, airlifting food and hay for livestock. The total rescue effort involved numerous volunteers and local agencies plus at least ten major state and federal agencies from the U.S. Army to the National Park Service. Private businesses, including railroad and oil companies, also lent manpower and heavy equipment to the work of plowing out. The official death toll was 76 people and one million livestock. [Youtube video *Storm of the Century - the Blizzard of \'49*](https://www.youtube.com/watch?v=gl6Iz4dXGdg) [Storm of the Century - the Blizzard of \'49](https://www.weather.gov/unr/1949-01)
#### 1950 to 1959 {#to_1959}
- Great Appalachian Storm of November 1950 November 24--30, 1950
- March 1958 Nor\'easter blizzard March 18--21, 1958.
- The Mount Shasta California Snowstorm of 1959 -- The storm dumped 189 in of snow on Mount Shasta. The bulk of the snow fell on unpopulated mountainous areas, barely disrupting the residents of the Mount Shasta area. The amount of snow recorded is the largest snowfall from a single storm in North America.
#### 1960 to 1969 {#to_1969}
- March 1960 Nor\'easter blizzard March 2--5, 1960
- December 1960 Nor\'easter blizzard December 12--14, 1960. Wind gusts up to 50 mph.
- March 1962 Nor\'easter Great March Storm of 1962 -- Ash Wednesday. North Carolina and Virginia blizzards. Struck during Spring high tide season and remained mostly stationary for almost 5 days causing significant damage along eastern coast, Assateague island was under water, and dumped 42 in of snow in Virginia.
- North American blizzard of 1966 January 27--31, 1966
- Chicago Blizzard of 1967 January 26--27, 1967
- February 1969 nor\'easter February 8--10, 1969
- March 1969 Nor\'easter blizzard March 9, 1969
- December 1969 Nor\'easter blizzard December 25--28, 1969.
#### 1970 to 1979 {#to_1979}
- The Great Storm of 1975 known as the \"Super Bowl Blizzard\" or \"Minnesota\'s Storm of the Century\". January 9--12, 1975. Wind chills of -50 F to -80 F recorded, deep snowfalls.
- Groundhog Day gale of 1976 February 2, 1976
- Buffalo Blizzard of 1977 January 28 -- February 1, 1977. There were several feet of packed snow already on the ground, and the blizzard brought with it enough snow to reach Buffalo\'s record for the most snow in one season -- 199.4 in.
- Great Blizzard of 1978 also called the \"Cleveland Superbomb\". January 25--27, 1978. Was one of the worst snowstorms the Midwest has ever seen. Wind gusts approached 100 mph, causing snowdrifts to reach heights of 25 ft in some areas, making roadways impassable. Storm reached maximum intensity over southern Ontario Canada.
- Northeastern United States Blizzard of 1978 -- February 6--7, 1978. Just one week following the Cleveland Superbomb blizzard, New England was hit with its most severe blizzard in 90 years since 1888.
- Chicago Blizzard of 1979 January 13--14, 1979
#### 1980 to 1989 {#to_1989}
- February 1987 Nor\'easter blizzard February 22--24, 1987
#### 1990 to 1999 {#to_1999}
- 1991 Halloween blizzard Upper Mid-West US, October 31 -- November 3, 1991
- December 1992 Nor\'easter blizzard December 10--12, 1992
- 1993 Storm of the Century March 12--15, 1993. While the southern and eastern U.S. and Cuba received the brunt of this massive blizzard, the Storm of the Century impacted a wider area than any in recorded history.
- February 1995 Nor\'easter blizzard February 3--6, 1995
- Blizzard of 1996 January 6--10, 1996
- April Fool\'s Day Blizzard March 31 -- April 1, 1997. US East Coast
- 1997 Western Plains winter storms October 24--26, 1997
- Mid West Blizzard of 1999 January 2--4, 1999
#### 2000 to 2009 {#to_2009}
- January 25, 2000 Southeastern United States winter storm January 25, 2000. North Carolina and Virginia
- December 2000 Nor\'easter blizzard December 27--31, 2000
- North American blizzard of 2003 February 14--19, 2003 (Presidents\' Day Storm II)
- December 2003 Nor\'easter blizzard December 6--7, 2003
- North American blizzard of 2005 January 20--23, 2005
- North American blizzard of 2006 February 11--13, 2006
- Early winter 2006 North American storm complex Late November 2006
- Colorado Holiday Blizzards (2006--07) December 20--29, 2006 Colorado
- February 2007 North America blizzard February 12--20, 2007
- January 2008 North American storm complex January, 2008 West Coast US
- North American blizzard of 2008 March 6--10, 2008
- 2009 Midwest Blizzard 6--8 December 2009, a bomb cyclogenesis event that also affected parts of Canada
- North American blizzard of 2009 December 16--20, 2009
- 2009 North American Christmas blizzard December 22--28, 2009
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# Blizzard
## List of blizzards {#list_of_blizzards}
### North America {#north_america}
#### 2010 to 2019 {#to_2019}
- February 5--6, 2010 North American blizzard February 5--6, 2010 Referred to at the time as Snowmageddon was a Category 3 (\"major\") nor\'easter and severe weather event.
- February 9--10, 2010 North American blizzard February 9--10, 2010
- February 25--27, 2010 North American blizzard February 25--27, 2010
- October 2010 North American storm complex October 23--28, 2010
- December 2010 North American blizzard December 26--29, 2010
- January 31 -- February 2, 2011 North American blizzard January 31 -- February 2, 2011. Groundhog Day Blizzard of 2011
- 2011 Halloween nor\'easter October 28 -- Nov 1, 2011
- Hurricane Sandy October 29--31, 2012. West Virginia, western North Carolina, and southwest Pennsylvania received heavy snowfall and blizzard conditions from this hurricane
- November 2012 nor\'easter November 7--10, 2012
- December 17--22, 2012 North American blizzard December 17--22, 2012
- Late December 2012 North American storm complex December 25--28, 2012
- February 2013 nor\'easter February 7--20, 2013
- February 2013 Great Plains blizzard February 19 -- March 6, 2013
- March 2013 nor\'easter March 6, 2013
- October 2013 North American storm complex October 3--5, 2013
- Buffalo, NY blizzard of 2014. Buffalo got over 6 ft of snow during November 18--20, 2014.
- January 2015 North American blizzard January 26--27, 2015
- Late December 2015 North American storm complex December 26--27, 2015 Was one of the most notorious blizzards in the state of New Mexico and West Texas ever reported. It had sustained winds of over 30 mph and continuous snow precipitation that lasted over 30 hours. Dozens of vehicles were stranded in small county roads in the areas of Hobbs, Roswell, and Carlsbad New Mexico. Strong sustained winds destroyed various mobile homes.
- January 2016 United States blizzard January 20--23, 2016
- February 2016 North American storm complex February 1--8, 2016
- February 2017 North American blizzard February 6--11, 2017
- March 2017 North American blizzard March 9--16, 2017
- Early January 2018 nor'easter January 3--6, 2018
- March 2019 North American blizzard March 8--16, 2019
- April 2019 North American blizzard April 10--14, 2019
#### 2020 to present {#to_present}
- December 5--6, 2020 nor\'easter December 5--6, 2020
- January 31 -- February 3, 2021 nor\'easter January 31 -- February 3, 2021
- February 13--17, 2021 North American winter storm February 13--17, 2021
- March 2021 North American blizzard March 11--14, 2021
- January 2022 North American blizzard January 27--30, 2022
- December 2022 North American winter storm December 21--26, 2022
- March 2023 North American winter storm March 12--15, 2023
- January 8--10, 2024 North American storm complex January 8--10, 2024
- January 10--13, 2024 North American storm complex January 10--13, 2024
- January 5--6, 2025 United States blizzard January 5--6, 2025
- 2025 Gulf Coast blizzard January 20--22, 2025
### Canada
- The Eastern Canadian Blizzard of 1971 -- Dumped a foot and a half (45.7 cm) of snow on Montreal and more than 2 ft elsewhere in the region. The blizzard caused the cancellation of a Montreal Canadiens hockey game for the first time since 1918
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# Bank of China Tower (Hong Kong)
The **Bank of China Tower** (**BOC Tower**) is a skyscraper located in Central, Hong Kong. Located at 1 Garden Road on Hong Kong Island, the tower houses the headquarters of the Bank of China (Hong Kong) Limited. One of the most recognisable landmarks in Hong Kong, the building is notable for its distinct shape and design, consisting of triangular frameworks covered by glass curtain walls.
The building was designed by Chinese-American architect I. M. Pei and L. C. Pei of I. M. Pei and Partners. At a height of 315 m, reaching 367.4 m high including a 52.4 m spire, the building is the fourth tallest skyscraper in Hong Kong, after International Commerce Centre, Two International Finance Centre (2 IFC) and Central Plaza. It was the tallest building in Hong Kong and Asia from 1990 to 1992, and it was the first supertall skyscraper outside the United States, the first to break the 305 m (1,000 ft) mark. It was surpassed by Central Plaza on the same island in 1992.
Construction began on 18 April 1985 on the former site of Murray House, and was completed five years later in 1990. Sporting a steel-column design, the building is accessible from the MTR\'s Central station. The building lies between Cotton Tree Drive and Garden Road.
## History
### Site
The 6700 m2 site on which the building is constructed was formerly the location of Murray House. After its brick-by-brick relocation to Stanley, the site was sold by the Government for \"only HK\$1 billion\" in August 1982 amidst growing concern over the future of Hong Kong in the run-up to the transfer of sovereignty.
The building was initially built by the Hong Kong Branch of the Bank of China; its Garden Road entrance continues to display the name \"Bank of China\", rather than BOCHK. The top four and the bottom 19 stories are used by the Bank, while the other floors are leased out. Ownership has since been transferred to BOCHK, although the Bank of China has leased back several floors for use by its own operations in Hong Kong.
### Favouritism controversy {#favouritism_controversy}
The Government had apparently given preferential treatment to Chinese companies, and was again criticised for the apparent preferential treatment to the BOCHK.
The price paid was half the amount of the 6250 m2 Admiralty II plot, for which the MTR Corporation paid HK\$1.82 billion in cash. The BOC would make initial payment of \$60 million, with the rest payable over 13 years at 6% interest. The announcement of the sale was also poorly handled, and a dive in business confidence ensued. The Hang Seng Index fell 80 points, and the HK\$ lost 1.5% of its value the next day.
### Construction
The tower was built by Japanese contractor Kumagai Gumi. Superstructure work began in May 1986. The tower is a steel-frame structure.
The Tiananmen Square protests of 1989 interrupted publicity surrounding the building\'s design and construction. A press conference scheduled for 24 May 1989, two weeks before the incident, was intended to show off the building\'s \"designer socialist furnishings\", but was called off as the student demonstrations in Beijing escalated. The public relations firm that organised the conference explained to the *South China Morning Post* that \"under the circumstances, it has been decided to stop any publicity to do with the Bank of China.\"
Once developed, gross floor area was expected to be 100000 m2. The original project was intended for completion on the auspicious date of 8 August 1988. However, owing to project delays, groundbreaking took place in March 1985, almost two years late, with the completion also facing a nearly two-year delay. It was topped out in 1989, and occupied on 15 June 1990.
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# Bank of China Tower (Hong Kong)
## Architecture
Designed by Pritzker Prize-winning architect I. M. Pei, the building is 315.0 m high with two masts reaching 367.4 m high. The 72-storey building is located near Central MTR station. This was the tallest building in Hong Kong and Asia from 1990 to 1992, the first building outside the United States to break the 305 m (1,000 ft) mark, and the first composite space frame high-rise building. That also means it was the tallest outside the United States from its completion year, 1990. It is now the fourth tallest skyscraper in Hong Kong, after International Commerce Centre, Two International Finance Centre and Central Plaza.
A small observation deck on the 43rd floor of the building was once open to the public, but is now closed.
The whole structure is supported by the four steel columns at the corners of the building, with the triangular frameworks transferring the weight of the structure onto these four columns. It is covered with glass curtain walls. Structural engineer Leslie E. Robertson, best known for his work on the Twin Towers of the original World Trade Center, provided the structural engineering design, while Jaros, Baum & Bolles was the mechanical, electrical and plumbing engineer.
While its distinctive look makes it one of Hong Kong\'s most identifiable landmarks today, it was the source of some controversy at one time, as the bank is the only major building in Hong Kong to have bypassed the convention of consulting with feng shui masters on matters of design prior to construction.
The building has been criticised by some practitioners of feng shui for its sharp edges and its negative symbolism by the numerous \'X\' shapes in its original design, though Pei modified the design to some degree before construction following this feedback. The building\'s profile from some angles resembles that of a meat cleaver and it is sometimes referred to as a \"vertical knife\". This earned it the nickname *一把刀* (*yaat baa dou*) in Cantonese, literally meaning \'one knife\'.
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# Bank of China Tower (Hong Kong)
## Transport
The Bank of China Tower can be accessed by the Mass Transit Railway (MTR) by walking through Chater Garden from Central station Exit J2.
## In popular culture {#in_popular_culture}
- In the 1988 film *Police Story 2*, the building was shown during its construction
- In the 2012 film *Battleship*, the building is torn in half by a crashing alien spaceship and its spire falls into the streets of Hong Kong, killing many people.
- In *Star Trek: Voyager*, the building is used as the exterior of Starfleet Communications Research Center.
- The building is seen on the attraction It\'s a Small World at Hong Kong Disneyland.
- The building was featured in the film *Transformers: Age of Extinction*, where Bumblebee and Dinobot Strafe makes their final stand against the Decepticon drone Stinger.
- The building appears in *Cardcaptor Sakura: The Movie* for several scenes.
- The building was featured in the city-building games *SimCity 3000* and *SimCity 4* as a placeable landmark.
- The building was featured in the 2017 mobile game *TheoTown* as a vanilla landmark.
- The building (renamed to Mortensen Electric) appears in the 2012 action-adventure video game *Sleeping Dogs* in the Central District.
- In the 2021 movie *Godzilla vs. Kong*, the building is featured prominently throughout the battle between Godzilla and Kong in Hong Kong. Despite being in close proximity to the battle, the tower is not destroyed and is still standing at the end of the battle
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# Bugzilla
**Bugzilla** is a web-based general-purpose bug tracking system and testing tool originally developed and used by the Mozilla project, and licensed under the Mozilla Public License.
Released as open-source software by Netscape Communications in 1998, it has been adopted by a variety of organizations for use as a bug tracking system for both free and open-source software and proprietary projects and products. Bugzilla is used, among others, by the Mozilla Foundation, WebKit, Linux kernel, FreeBSD, KDE, Apache, Eclipse and LibreOffice. Red Hat uses it, but is gradually migrating its product to use Jira. It is also self-hosting.
## History
Bugzilla was originally devised by Terry Weissman in 1998 for the nascent Mozilla.org project, as an open source application to replace the in-house system then in use at Netscape Communications for tracking defects in the Netscape Communicator suite. Bugzilla was originally written in Tcl, but Weissman decided to port it to Perl before its release as part of Netscape\'s early open-source code drops, in the hope that more people would be able to contribute to it, given that Perl seemed to be a more popular language at the time.
Bugzilla 2.0 was the result of that port to Perl, and the first version was released to the public via anonymous CVS. In April 2000, Weissman handed over control of the Bugzilla project to Tara Hernandez. Under her leadership, some of the regular contributors were coerced into taking more responsibility, and Bugzilla development became more community-driven. In July 2001, facing distraction from her other responsibilities in Netscape, Hernandez handed control to Dave Miller, who was still in charge `{{as of|2020|lc=on}}`{=mediawiki}.
Bugzilla 3.0 was released on May 10, 2007, and brought a refreshed UI, an XML-RPC interface, custom fields and resolutions, mod_perl support, shared saved searches, and improved UTF-8 support, along with other changes.
Bugzilla 4.0 was released on February 15, 2011, and Bugzilla 5.0 was released in July 2015.
### Timeline
Bugzilla\'s release timeline:
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| 1,119 |
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# Bugzilla
## History
### Timeline
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## Requirements
Bugzilla\'s system requirements include:
- A compatible database management system
- A suitable release of Perl 5
- An assortment of Perl modules
- A compatible web server
- A suitable mail transfer agent, or any SMTP server
Currently supported database systems are MariaDB, MySQL, PostgreSQL, Oracle, and SQLite. Bugzilla is usually installed on Linux using the Apache HTTP Server, but any web server that supports CGI such as Lighttpd, Hiawatha, Cherokee can be used. Bugzilla\'s installation process is command line driven and runs through a series of stages where system requirements and software capabilities are checked.
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# Bugzilla
## Design
While the potential exists in the code to turn Bugzilla into a technical support ticket system, task management tool, or project management tool, Bugzilla\'s developers have chosen to focus on the task of designing a system to track software defects.
## Zarro Boogs {#zarro_boogs}
Bugzilla returns the string \"zarro boogs found\" instead of \"0 bugs found\" when a search for bugs returns no results. \"Zarro Boogs\" is intended as a \'buggy\' statement itself (a misspelling of \"zero bugs\") and is thus a meta-statement about the nature of software debugging, implying that even when no bugs have been identified, some may exist.
The following comment is provided in the Bugzilla source code to developers who may be confused by this behaviour:
: ***Zarro Boogs Found***
: This is just a goofy way of saying that there were no bugs found matching your query. When asked to explain this message, Terry Weissman had the following to say:
```{=html}
<!-- -->
```
: I\'ve been asked to explain this \... way back when, when Netscape released version 4.0 of its browser, we had a release party. Naturally, there had been a big push to try and fix every known bug before the release. Naturally, that hadn\'t actually happened. (This is not unique to Netscape or to 4.0; the same thing has happened with every software project I\'ve ever seen.) Anyway, at the release party, T-shirts were handed out that said something like \"Netscape 4.0: Zarro Boogs\". Just like the software, the T-shirt had no known bugs. Uh-huh. So, when you query for a list of bugs, and it gets no results, you can think of this as a friendly reminder. Of \*course\* there are bugs matching your query, they just aren\'t in the bugsystem yet\...
: --- Terry Weissman
: *From The Bugzilla Guide -- 2.16.10 Release: Glossary*
## WONTFIX
WONTFIX is used as a label on issues in Bugzilla and other systems. It indicates that a verified issue will not be resolved for one of several possible reasons including fixing would be too expensive, complicated or risky
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# Baryon
In particle physics, a **baryon** is a type of composite subatomic particle that contains an odd number of valence quarks, conventionally three. Protons and neutrons are examples of baryons; because baryons are composed of quarks, they belong to the hadron family of particles. Baryons are also classified as fermions because they have half-integer spin.
The name \"baryon\", introduced by Abraham Pais, comes from the Greek word for \"heavy\" (βαρύς, *barýs*), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark.
Baryons participate in the residual strong force, which is mediated by particles known as mesons. The most familiar baryons are protons and neutrons, both of which contain three quarks, and for this reason they are sometimes called *triquarks*. These particles make up most of the mass of the visible matter in the universe and compose the nucleus of every atom (electrons, the other major component of the atom, are members of a different family of particles called leptons; leptons do not interact via the strong force). Exotic baryons containing five quarks, called pentaquarks, have also been discovered and studied.
A census of the Universe\'s baryons indicates that 10% of them could be found inside galaxies, 50 to 60% in the circumgalactic medium, and the remaining 30 to 40% could be located in the warm--hot intergalactic medium (WHIM).
## Background
Baryons are strongly interacting fermions; that is, they are acted on by the strong nuclear force and are described by Fermi--Dirac statistics, which apply to all particles obeying the Pauli exclusion principle. This is in contrast to the bosons, which do not obey the exclusion principle.
Baryons, alongside mesons, are hadrons, composite particles composed of quarks. Quarks have baryon numbers of *B* = `{{sfrac|1|3}}`{=mediawiki} and antiquarks have baryon numbers of *B* = −`{{sfrac|1|3}}`{=mediawiki}. The term \"baryon\" usually refers to *triquarks*---baryons made of three quarks (*B* = `{{sfrac|1|3}}`{=mediawiki} + `{{sfrac|1|3}}`{=mediawiki} + `{{sfrac|1|3}}`{=mediawiki} = 1).
Other exotic baryons have been proposed, such as pentaquarks---baryons made of four quarks and one antiquark (*B* = `{{sfrac|1|3}}`{=mediawiki} + `{{sfrac|1|3}}`{=mediawiki} + `{{sfrac|1|3}}`{=mediawiki} + `{{sfrac|1|3}}`{=mediawiki} − `{{sfrac|1|3}}`{=mediawiki} = 1), but their existence is not generally accepted. The particle physics community as a whole did not view their existence as likely in 2006, and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks. However, in July 2015, the LHCb experiment observed two resonances consistent with pentaquark states in the Λ`{{su|p=0|b=b}}`{=mediawiki} → J/ψK`{{su|p=−}}`{=mediawiki}p decay, with a combined statistical significance of 15σ .
In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist.
## Baryonic matter {#baryonic_matter}
Nearly all matter that may be encountered or experienced in everyday life is baryonic matter, which includes atoms of any sort, and provides them with the property of mass. Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include neutrinos and free electrons, dark matter, supersymmetric particles, axions, and black holes.
The very existence of baryons is also a significant issue in cosmology because it is assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons came to outnumber their antiparticles is called baryogenesis.
## Baryogenesis
Experiments are consistent with the number of quarks in the universe being conserved alongside the total baryon number, with antibaryons being counted as negative quantities. Within the prevailing Standard Model of particle physics, the number of baryons may change in multiples of three due to the action of sphalerons, although this is rare and has not been observed under experiment. Some grand unified theories of particle physics also predict that a single proton can decay, changing the baryon number by one; however, this has not yet been observed under experiment. The excess of baryons over antibaryons in the present universe is thought to be due to non-conservation of baryon number in the very early universe, though this is not well understood.
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# Baryon
## Properties
### Isospin and charge {#isospin_and_charge}
The concept of isospin was first proposed by Werner Heisenberg in 1932 to explain the similarities between protons and neutrons under the strong interaction. Although they had different electric charges, their masses were so similar that physicists believed they were the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbed *isospin* by Eugene Wigner in 1937.
This belief lasted until Murray Gell-Mann proposed the quark model in 1964 (containing originally only the u, d, and s quarks). The success of the isospin model is now understood to be the result of the similar masses of u and d quarks. Since u and d quarks have similar masses, particles made of the same number then also have similar masses. The exact specific u and d quark composition determines the charge, as u quarks carry charge +`{{sfrac|2|3}}`{=mediawiki} while d quarks carry charge −`{{sfrac|1|3}}`{=mediawiki}. For example, the four Deltas all have different charges (`{{SubatomicParticle|Delta++}}`{=mediawiki} (uuu), `{{SubatomicParticle|Delta+}}`{=mediawiki} (uud), `{{SubatomicParticle|Delta0}}`{=mediawiki} (udd), `{{SubatomicParticle|Delta-}}`{=mediawiki} (ddd)), but have similar masses (\~1,232 MeV/c^2^) as they are each made of a combination of three u or d quarks. Under the isospin model, they were considered to be a single particle in different charged states.
The mathematics of isospin was modeled after that of spin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a \"charged state\". Since the \"Delta particle\" had four \"charged states\", it was said to be of isospin *I* = `{{sfrac|3|2}}`{=mediawiki}. Its \"charged states\" `{{SubatomicParticle|Delta++}}`{=mediawiki}, `{{SubatomicParticle|Delta+}}`{=mediawiki}, `{{SubatomicParticle|Delta0}}`{=mediawiki}, and `{{SubatomicParticle|Delta-}}`{=mediawiki}, corresponded to the isospin projections *I*~3~ = +`{{sfrac|3|2}}`{=mediawiki}, *I*~3~ = +`{{sfrac|1|2}}`{=mediawiki}, *I*~3~ = −`{{sfrac|1|2}}`{=mediawiki}, and *I*~3~ = −`{{sfrac|3|2}}`{=mediawiki}, respectively. Another example is the \"nucleon particle\". As there were two nucleon \"charged states\", it was said to be of isospin `{{sfrac|1|2}}`{=mediawiki}. The positive nucleon `{{SubatomicParticle|Nucleon+}}`{=mediawiki} (proton) was identified with *I*~3~ = +`{{sfrac|1|2}}`{=mediawiki} and the neutral nucleon `{{SubatomicParticle|Nucleon0}}`{=mediawiki} (neutron) with *I*~3~ = −`{{sfrac|1|2}}`{=mediawiki}. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:
: $I_\mathrm{3}=\frac{1}{2}[(n_\mathrm{u}-n_\mathrm{\bar{u}})-(n_\mathrm{d}-n_\mathrm{\bar{d}})],$
where the *n*\'s are the number of up and down quarks and antiquarks.
In the \"isospin picture\", the four Deltas and the two nucleons were thought to be the different states of two particles. However, in the quark model, Deltas are different states of nucleons (the N^++^ or N^−^ are forbidden by Pauli\'s exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature.
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# Baryon
## Properties
### Flavour quantum numbers {#flavour_quantum_numbers}
The strangeness flavour quantum number *S* (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds octet and decuplet figures on the right). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works well only for octet and decuplet made of one u, one d, and one other quark, and breaks down for the other octets and decuplets (for example, ucb octet and decuplet). If the quarks all had the same mass, their behaviour would be called *symmetric*, as they would all behave in the same way to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.
It was noted that charge (*Q*) was related to the isospin projection (*I*~3~), the baryon number (*B*) and flavour quantum numbers (*S*, *C*, *B*′, *T*) by the Gell-Mann--Nishijima formula:
: $Q = I_3 +\frac{1}{2}\left(B + S + C + B^\prime + T\right),$
where *S*, *C*, *B*′, and *T* represent the strangeness, charm, bottomness and topness flavour quantum numbers, respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
: \\begin{align}
` S &= -\left(n_\mathrm{s} - n_\mathrm{\bar{s}}\right), \\`\
` C &= +\left(n_\mathrm{c} - n_\mathrm{\bar{c}}\right), \\`\
` B^\prime &= -\left(n_\mathrm{b} - n_\mathrm{\bar{b}}\right), \\`\
` T &= +\left(n_\mathrm{t} - n_\mathrm{\bar{t}}\right),`
\\end{align} meaning that the Gell-Mann--Nishijima formula is equivalent to the expression of charge in terms of quark content:
: $Q = \frac{2}{3}\left[(n_\mathrm{u} - n_\mathrm{\bar{u}}) + (n_\mathrm{c} - n_\mathrm{\bar{c}}) + (n_\mathrm{t} - n_\mathrm{\bar{t}})\right] - \frac{1}{3}\left[(n_\mathrm{d} - n_\mathrm{\bar{d}}) + (n_\mathrm{s} - n_\mathrm{\bar{s}}) + (n_\mathrm{b} - n_\mathrm{\bar{b}})\right].$
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# Baryon
## Properties
### Spin, orbital angular momentum, and total angular momentum {#spin_orbital_angular_momentum_and_total_angular_momentum}
Spin (quantum number *S*) is a vector quantity that represents the \"intrinsic\" angular momentum of a particle. It comes in increments of `{{sfrac|1|2}}`{=mediawiki} ħ (pronounced \"h-bar\"). The ħ is often dropped because it is the \"fundamental\" unit of spin, and it is implied that \"spin 1\" means \"spin 1 ħ\". In some systems of natural units, ħ is chosen to be 1, and therefore does not appear anywhere.
Quarks are fermionic particles of spin `{{sfrac|1|2}}`{=mediawiki} (*S* = `{{sfrac|1|2}}`{=mediawiki}). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length `{{sfrac|1|2}}`{=mediawiki}, and has two spin projections (*S*~z~ = +`{{sfrac|1|2}}`{=mediawiki} and *S*~z~ = −`{{sfrac|1|2}}`{=mediawiki}). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length *S* = 1 and three spin projections (*S*~z~ = +1, *S*~z~ = 0, and *S*~z~ = −1). If two quarks have unaligned spins, the spin vectors add up to make a vector of length *S* = 0 and has only one spin projection (*S*~z~ = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length *S* = `{{sfrac|3|2}}`{=mediawiki}, which has four spin projections (*S*~z~ = +`{{sfrac|3|2}}`{=mediawiki}, *S*~z~ = +`{{sfrac|1|2}}`{=mediawiki}, *S*~z~ = −`{{sfrac|1|2}}`{=mediawiki}, and *S*~z~ = −`{{sfrac|3|2}}`{=mediawiki}), or a vector of length *S* = `{{sfrac|1|2}}`{=mediawiki} with two spin projections (*S*~z~ = +`{{sfrac|1|2}}`{=mediawiki}, and *S*~z~ = −`{{sfrac|1|2}}`{=mediawiki}).
There is another quantity of angular momentum, called the orbital angular momentum (azimuthal quantum number *L*), that comes in increments of 1 ħ, which represent the angular moment due to quarks orbiting around each other. The total angular momentum (total angular momentum quantum number *J*) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum. It can take any value from `{{nowrap|''J'' {{=}}`{=mediawiki} {{!}}*L* − *S*{{!}}}} to `{{nowrap|''J'' {{=}}`{=mediawiki} {{!}}*L* + *S*{{!}}}}, in increments of 1.
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| Spin,\ | Orbital angular\ | Total angular\ | Parity,\ | Condensed\ |
| *S* | momentum, *L* | momentum, *J* | *P* | notation, *J*^*P*^ |
+========+==================+=========================================================================================+==========+=====================================================================================================+
| | 0 | | \+ | ^+^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 1 | , `{{sfrac|1|2}}`{=mediawiki} | − | ^−^, `{{sfrac|1|2}}`{=mediawiki}^−^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 2 | , `{{sfrac|3|2}}`{=mediawiki} | \+ | ^+^, `{{sfrac|3|2}}`{=mediawiki}^+^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 3 | , `{{sfrac|5|2}}`{=mediawiki} | − | ^−^, `{{sfrac|5|2}}`{=mediawiki}^−^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 0 | | \+ | ^+^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 1 | , `{{sfrac|3|2}}`{=mediawiki}, `{{sfrac|1|2}}`{=mediawiki} | − | ^−^, `{{sfrac|3|2}}`{=mediawiki}^−^, `{{sfrac|1|2}}`{=mediawiki}^−^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 2 | , `{{sfrac|5|2}}`{=mediawiki}, `{{sfrac|3|2}}`{=mediawiki}, `{{sfrac|1|2}}`{=mediawiki} | \+ | ^+^, `{{sfrac|5|2}}`{=mediawiki}^+^, `{{sfrac|3|2}}`{=mediawiki}^+^, `{{sfrac|1|2}}`{=mediawiki}^+^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
| | 3 | , `{{sfrac|7|2}}`{=mediawiki}, `{{sfrac|5|2}}`{=mediawiki}, `{{sfrac|3|2}}`{=mediawiki} | − | ^−^, `{{sfrac|7|2}}`{=mediawiki}^−^, `{{sfrac|5|2}}`{=mediawiki}^−^, `{{sfrac|3|2}}`{=mediawiki}^−^ |
+--------+------------------+-----------------------------------------------------------------------------------------+----------+-----------------------------------------------------------------------------------------------------+
: Baryon angular momentum quantum numbers for *L* = 0, 1, 2, 3
Particle physicists are most interested in baryons with no orbital angular momentum (*L* = 0), as they correspond to ground states---states of minimal energy. Therefore, the two groups of baryons most studied are the *S* = `{{sfrac|1|2}}`{=mediawiki}; *L* = 0 and *S* = `{{sfrac|3|2}}`{=mediawiki}; *L* = 0, which corresponds to *J* = `{{sfrac|1|2}}`{=mediawiki}^+^ and *J* = `{{sfrac|3|2}}`{=mediawiki}^+^, respectively, although they are not the only ones. It is also possible to obtain *J* = `{{sfrac|3|2}}`{=mediawiki}^+^ particles from *S* = `{{sfrac|1|2}}`{=mediawiki} and *L* = 2, as well as *S* = `{{sfrac|3|2}}`{=mediawiki} and *L* = 2. This phenomenon of having multiple particles in the same total angular momentum configuration is called *degeneracy*. How to distinguish between these degenerate baryons is an active area of research in baryon spectroscopy.
### Parity
If the universe were reflected in a mirror, most of the laws of physics would be identical---things would behave the same way regardless of what we call \"left\" and what we call \"right\". This concept of mirror reflection is called \"intrinsic parity\" or simply \"parity\" (*P*). Gravity, the electromagnetic force, and the strong interaction all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P-symmetry). However, the weak interaction does distinguish \"left\" from \"right\", a phenomenon called parity violation (P-violation).
Based on this, if the wavefunction for each particle (in more precise terms, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to have negative or odd parity (*P* = −1, or alternatively *P* = --), while the other particles are said to have positive or even parity (*P* = +1, or alternatively *P* = +).
For baryons, the parity is related to the orbital angular momentum by the relation:
: $P=(-1)^L.\$
As a consequence, baryons with no orbital angular momentum (*L* = 0) all have even parity (*P* = +).
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# Baryon
## Nomenclature
Baryons are classified into groups according to their isospin (*I*) values and quark (*q*) content. There are six groups of baryons: nucleon (`{{SubatomicParticle|Nucleon}}`{=mediawiki}), Delta (`{{SubatomicParticle|Delta}}`{=mediawiki}), Lambda (`{{SubatomicParticle|Lambda}}`{=mediawiki}), Sigma (`{{SubatomicParticle|Sigma}}`{=mediawiki}), Xi (`{{SubatomicParticle|Xi}}`{=mediawiki}), and Omega (`{{SubatomicParticle|Omega}}`{=mediawiki}). The rules for classification are defined by the Particle Data Group. These rules consider the up (`{{SubatomicParticle|Up quark}}`{=mediawiki}), down (`{{SubatomicParticle|Down quark}}`{=mediawiki}) and strange (`{{SubatomicParticle|Strange quark}}`{=mediawiki}) quarks to be *light* and the charm (`{{SubatomicParticle|Charm quark}}`{=mediawiki}), bottom (`{{SubatomicParticle|Bottom quark}}`{=mediawiki}), and top (`{{SubatomicParticle|Top quark}}`{=mediawiki}) quarks to be *heavy*. The rules cover all the particles that can be made from three of each of the six quarks, even though baryons made of top quarks are not expected to exist because of the top quark\'s short lifetime. The rules do not cover pentaquarks.
- Baryons with (any combination of) three `{{SubatomicParticle|link=yes|Up quark}}`{=mediawiki} and/or `{{SubatomicParticle|link=yes|Down quark}}`{=mediawiki} quarks are `{{SubatomicParticle|link=yes|Nucleon}}`{=mediawiki}s (*I* = `{{sfrac|1|2}}`{=mediawiki}) or `{{SubatomicParticle|link=yes|Delta}}`{=mediawiki} baryons (*I* = `{{sfrac|3|2}}`{=mediawiki}).
- Baryons containing two `{{SubatomicParticle|link=yes|Up quark}}`{=mediawiki} and/or `{{SubatomicParticle|link=yes|Down quark}}`{=mediawiki} quarks are `{{SubatomicParticle|link=yes|Lambda}}`{=mediawiki} baryons (*I* = 0) or `{{SubatomicParticle|link=yes|Sigma}}`{=mediawiki} baryons (*I* = 1). If the third quark is heavy, its identity is given by a subscript.
- Baryons containing one `{{SubatomicParticle|link=yes|Up quark}}`{=mediawiki} or `{{SubatomicParticle|link=yes|Down quark}}`{=mediawiki} quark are `{{SubatomicParticle|link=yes|Xi}}`{=mediawiki} baryons (*I* = `{{sfrac|1|2}}`{=mediawiki}). One or two subscripts are used if one or both of the remaining quarks are heavy.
- Baryons containing no `{{SubatomicParticle|link=yes|Up quark}}`{=mediawiki} or `{{SubatomicParticle|link=yes|Down quark}}`{=mediawiki} quarks are `{{SubatomicParticle|link=yes|Omega}}`{=mediawiki} baryons (*I* = 0), and subscripts indicate any heavy quark content.
- Baryons that decay strongly have their masses as part of their names. For example, Σ^0^ does not decay strongly, but Δ^++^(1232) does.
It is also a widespread (but not universal) practice to follow some additional rules when distinguishing between some states that would otherwise have the same symbol.
- Baryons in total angular momentum *J* = `{{sfrac|3|2}}`{=mediawiki} configuration that have the same symbols as their *J* = `{{sfrac|1|2}}`{=mediawiki} counterparts are denoted by an asterisk ( \* ).
- Two baryons can be made of three different quarks in *J* = `{{sfrac|1|2}}`{=mediawiki} configuration. In this case, a prime ( ′ ) is used to distinguish between them.
- *Exception*: When two of the three quarks are one up and one down quark, one baryon is dubbed Λ while the other is dubbed Σ.
Quarks carry a charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a `{{SubatomicParticle|charmed Lambda+}}`{=mediawiki} contains a c quark and some combination of two u and/or d quarks. The c quark has a charge of (*Q* = +`{{sfrac|2|3}}`{=mediawiki}), therefore the other two must be a u quark (*Q* = +`{{sfrac|2|3}}`{=mediawiki}), and a d quark (*Q* = −`{{sfrac|1|3}}`{=mediawiki}) to have the correct total charge (*Q* = +1)
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# Braille embosser
A **braille embosser** is an impact printer that renders text as tactile braille cells. Using braille translation software, a document or digital text can be embossed with relative ease. This makes braille production efficient and cost-effective. Braille translation software may be free and open-sourced or paid. Braille embossers can emboss single-sided or double-sided (called interpoint) and can produce 6- or 8-dot braille.
Blind users tend to call other printers \"ink printers,\" to distinguish them from their braille counterparts. This is often the case regardless of the type of printer being discussed (e.g., thermal printers being called \"ink printers\" even though they use no ink).
As with ink printers and presses, embossers range from those intended for consumers to those used by large publishers. The price of embossers increase with the volume of braille it produces .
## Types
The fastest industrial braille embosser is probably the \$92,000 Belgian-made NV Interpoint 55, first produced in 1991, which uses a separate air compressor to drive the embossing head and can output up to 800 braille characters per second. Adoption was slow at first; in 2000 the National Federation of the Blind said there were only three of these in the US, one owned by the NFB itself and the other two by the Watchtower Bible and Tract Society. As of 2008, there are more than 60 in use across the world.
Smaller desktop braille embossers are more common and can be found in libraries, universities, and specialist education centers, as well as being privately owned by blind individuals. It may be necessary to use an acoustic cabinet or hood to dampen the noise level.
Braille embossers usually need special braille paper which is thicker and more expensive than normal paper. Some high-end embossers are capable of printing on normal paper. Embossers can be either one-sided or two-sided. Two-sided embossing requires lining up the dots so they do not overlap (called \"interpoint\" because the points on the other side are placed in between the points on the first side). Two-sided embossing uses less paper and reduces the size of the output.
Once one copy of a document has been produced, printing further copies is often quicker by means of a device called a thermoform, which produces copies on soft plastic. However, the resulting braille is not as easily readable as braille that has been freshly embossed, in much the same way that a poor-quality photocopy is not as readable as the original. Hence large publishers do not generally use thermoforms.
Some embossers can produce \"dotty Moon\", i.e., Moon type shapes formed by dots
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# Basic Role-Playing
***Basic Role-Playing*** (***BRP***) is a tabletop role-playing game which originated in the *RuneQuest* fantasy role-playing game. Chaosium released the *BRP* standalone booklet in 1980 in the boxed set release of the second edition of *RuneQuest*. Greg Stafford and Lynn Willis are credited as the authors. Chaosium used the percentile skill-based system as the basis for most of their games, including *Call of Cthulhu*, *Stormbringer*, and *Elfquest*.
## History
The core rules were written by Steve Perrin as part of his game *RuneQuest*. It was Greg Stafford\'s idea to simplify the rules (eliminating such mechanics as Strike Ranks and Hit Locations) and issue them in a 16-page booklet called *Basic Role-Playing*. Since the first *BRP* release, designers including Sandy Petersen, Lynn Willis, and Steve Henderson, have contributed to the system.
The system was notable for being the first role-playing game system to introduce a full skill system to characters regardless of their profession. This was developed in *RuneQuest* but was also later adopted by the more skill-oriented *Call of Cthulhu* RPG.
*BRP* was conceived of as a generic system. Specific rule systems for support differing genres could be added to the core rules in a modular fashion. In order to underscore this, in 1982 Chaosium released the *Worlds of Wonder* box set, which contained a revised main booklet and several booklets providing the additional rules for playing in specific genres. The superhero-themed *Superworld* originated as part of this set. A third edition of the core booklet, now entitled *Basic Roleplaying: The Chaosium System*, was released in 2002.
In 2004, Chaosium began publishing the *Basic Roleplaying* monographs, a series of paperback booklets. The first four monographs (*Players Book*, *Magic Book*, *Creatures Book*, and *Gamemaster Book*) was the same as *RuneQuest* third Edition, but with trademarked elements removed, as Chaosium had lost the rights to the name but retained copyright to the rules text. Additional monographs allowing for new mechanics, thereby extending the system to other genres, were released in the following years. Many of these monographs reproduced rules from other Chaosium-published *BRP* games that had gone out of print.
Jason Durall and Sam Johnson gathered up previous works and updated them to a new edition. published in 2008. This comprehensive book, *Basic Roleplaying: The Chaosium System* was nicknamed the \"Big Gold Book\". It allowed game masters to build their own game out of the included subsystems. A quickstart booklet for new players accompanied it. In 2011, it was updated to a second edition.
In 2020, Chaosium released *Basic Roleplaying* in abbreviated form (vs. the 2008 edition) as a System Reference Document (SRD).
A new edition, updating the 2008/2011 editions and titled *Basic Roleplaying: Universal Game Engine*, appeared in 2023, initially as a PDF, later as a hardbound book, and later still as a standalone SRD under the \"ORC License\" (Open RPG Creative) and has since spun off a market of multiple commercial products, both standalone BRP adventures and full-fledged RPG\'s, published under the terms of the ORC license. The full text (not the art, trade dress, etc.) of the PDF and print version was also ORC-licensed as a SRD.
## Licensed adaptations {#licensed_adaptations}
Preexisting RPG and fiction settings converted to the system by Chaosium using the *BRP* ruleset include *Ringworld*, *Hawkmoon*, and an adaptation of the French RPG *Nephilim*.
## Rules system {#rules_system}
*BRP* is similar to other generic systems such as *GURPS*, *Hero System*, or *Savage Worlds* in that it uses a simple resolution method which can be broadly applied. It uses a core set of seven characteristics: Size, Strength, Dexterity, Constitution, Intelligence, Power, and Appearance or Charisma. From these, a character derives scores in various skills, expressed as percentages. These skill scores are the basis of play. When attempting an action, the player rolls percentile dice to attempt to get a result equal to or lower than the character\'s skill score. Each incarnation of the *BRP* rules changed or added to the core ideas and mechanics, so that games are not identical. For example, in *Call of Cthulhu*, skills may never be over 100%, while in *Stormbringer* skills in excess of 100% are within reach for all characters. Scores can increase through experience checks, the mechanics of which vary in an individual game.
The system treats armor and defense as separate: the act of parrying is a defensive skill that reduces an opponent\'s chance to successfully land an attack, and the purpose of armor is to absorb damage.
In most *BRP* games there is no difference between the player character race systems and that of monsters or other opponents. By varying ability scores, the same system is used for a human hero as a troll villain. This approach allows for players to play a variety of nonhuman species.
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# Basic Role-Playing
## Adaptations of the system {#adaptations_of_the_system}
Chaosium was an early adopter of licensing out its *BRP* system to other companies, something that was unique at the time they began but commonplace now thanks to the d20 licenses. This places *BRP* in the notable position of being one of the first products to allow other game companies to develop games or game aids for their work. For example, *Other Suns*, published by Fantasy Games Unlimited, used them under license. *BRP* was also used as the base for the Swedish game *Drakar och Demoner* from Target Games.
## Reception
In the July 1981 edition of *The Space Gamer* (Issue No. 41), Ronald Pehr commented that \"*Basic Role-Playing* is too little too late. *RuneQuest* is long established, does an adequate job of teaching role-playing, and there are now even more games to choose from. If you want to teach role-playing to a very young, but literate, child, *Basic Role-Playing* is excellent. Otherwise, for all its charm, it\'s not much use.\".
In the August 1981 edition of *Dragon* (Issue 52), John Sapienza noted that *Basic Roleplaying* was \"not a fantasy role-playing game as such, but a handbook on how to role-play and a simple combat system to help the beginner get into the act.\" Despite this, Sapienza called it \"one of the best introductions to the practical social interactions in gaming that I have read, and will give beginning gamers the kind of guidance they typically do not get in the full-scale games they will graduate to, since game writers usually spend their time on mechanics instead of on the proper relationships between player and player, player and referee, or player and character.\" He concluded, \"*Basic Role-Playing* is a truly universal introduction to the hobby --- highly recommended.\"
### Awards
The *BRP* itself has been the recipient, via its games, of many awards. Most notable was the 1981 Origins Award for *Best Roleplaying Rules of 1981* for *Call of Cthulhu*. Other editions of *Call of Cthulhu* have also won Origins Awards including the Hall of Fame award. The *BRP* Character Generation software has also won awards for its design
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# Wireless broadband
thumb \|right \|upright=1.3 \|Three fixed wireless dishes with protective covers on top of 307 W. 7th Street, Fort Worth, Texas, around 2001
**Wireless broadband** is a telecommunications technology that provides high-speed wireless Internet access or computer networking access over a wide area. The term encompasses both fixed and mobile broadband.
## The term broadband {#the_term_broadband}
Originally the word \"broadband\" had a technical meaning, but became a marketing term for any kind of relatively high-speed computer network or Internet access technology. According to the 802.16-2004 standard, broadband means \"having instantaneous bandwidths greater than 1 MHz and supporting data rates greater than about 1.5 Mbit/s.\" The Federal Communications Commission (FCC) recently re-defined the word to mean download speeds of at least 25 Mbit/s and upload speeds of at least 3 Mbit/s.
## Technology and speeds {#technology_and_speeds}
thumb\|right \|A typical WISP Customer Premises Equipment (CPE) installed on a residence A wireless broadband network is an outdoor fixed and/or mobile wireless network providing point-to-multipoint or point-to-point terrestrial wireless links for broadband services.
Wireless networks can feature data rates exceeding 1 Gbit/s. Many fixed wireless networks are exclusively half-duplex (HDX), however, some licensed and unlicensed systems can also operate at full-duplex (FDX) allowing communication in both directions simultaneously.
Outdoor fixed wireless broadband networks commonly use a priority TDMA based protocol in order to divide communication into timeslots. This timeslot technique eliminates many of the issues common to 802.11 Wi-Fi protocol in outdoor networks such as the hidden node problem.
Few wireless Internet service providers (WISPs) provide download speeds of over 100 Mbit/s; most broadband wireless access (BWA) services are estimated to have a range of 50 km from a tower. Technologies used include Local Multipoint Distribution Service (LMDS) and Multichannel Multipoint Distribution Service (MMDS), as well as heavy use of the industrial, scientific and medical (ISM) radio bands and one particular access technology was standardized by IEEE 802.16, with products known as WiMAX.
WiMAX is highly popular in Europe but has not been fully accepted in the United States because cost of deployment. In 2005 the Federal Communications Commission adopted a Report and Order that revised the FCC\'s rules to open the 3650 MHz band for terrestrial wireless broadband operations.
Another system that is popular with cable internet service providers uses point-to-multipoint wireless links that extend the existing wired network using a transparent radio connection. This allows the same DOCSIS modems to be used for both wired and wireless customers.
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# Wireless broadband
## Development in the United States {#development_in_the_united_states}
On November 14, 2007, the Commission released Public Notice DA 07--4605 in which the Wireless Telecommunications Bureau announced the start date for licensing and registration process for the 3650--3700 MHz band. In 2010 the FCC adopted the TV White Space Rules (TVWS) and allowed some of the better no line of sight frequency (700 MHz) into the FCC Part-15 Rules. The Wireless Internet Service Providers Association, a national association of WISPs, petitioned the FCC and won.
Initially, WISPs were found only in rural areas not covered by cable or DSL. These early WISPs would employ a high-capacity T-carrier, such as a T1 or DS3 connection, and then broadcast the signal from a high elevation, such as at the top of a water tower. To receive this type of Internet connection, consumers mount a small dish to the roof of their home or office and point it to the transmitter. Line of sight is usually necessary for WISPs operating in the 2.4 and 5 GHz bands with 900 MHz offering better NLOS (non-line-of-sight) performance.
### Residential Wireless Internet {#residential_wireless_internet}
Providers of fixed wireless broadband services typically provide equipment to customers and install a small antenna or dish somewhere on the roof. This equipment is usually deployed as a service and maintained by the company providing that service. Fixed wireless services have become particularly popular in many rural areas where cable, DSL or other typical home internet services are not available.
### Business Wireless Internet {#business_wireless_internet}
Many companies in the US and worldwide have started using wireless alternatives to incumbent and local providers for internet and voice service. These providers tend to offer competitive services and options in areas where there is a difficulty getting affordable Ethernet connections from terrestrial providers such as ATT, Comcast, Verizon and others. Also, companies looking for full diversity between carriers for critical uptime requirements may seek wireless alternatives to local options.
### Demand for spectrum {#demand_for_spectrum}
To cope with increased demand for wireless broadband, increased spectrum would be needed. Studies began in 2009, and while some unused spectrum was available, it appeared broadcasters would have to give up at least some spectrum. This led to strong objections from the broadcasting community. In 2013, auctions were planned, and for now any action by broadcasters is voluntary.
## Mobile wireless broadband {#mobile_wireless_broadband}
In the United States, mobile broadband technologies include services from providers such as Verizon, AT&T Mobility, and T-Mobile which allow a more mobile version of Internet access. Consumers can purchase a PC card, laptop card, USB equipment, or mobile broadband modem, to connect their PC or laptop to the Internet via cell phone towers. This type of connection would be stable in almost any area that could also receive a strong cell phone connection. These connections can cost more for portable convenience as well as having speed limitations in all but urban environments.
On June 2, 2010, after months of discussion, AT&T became the first wireless Internet provider in the US to announce plans to charge according to usage. As the only iPhone service in the United States, AT&T experienced the problem of heavy Internet use more than other providers. About 3 percent of AT&T smart phone customers account for 40 percent of the technology\'s use. 98 percent of the company\'s customers use less than 2 gigabytes (4000 page views, 10,000 emails or 200 minutes of streaming video), the limit under the \$25 monthly plan, and 65 percent use less than 200 megabytes, the limit for the \$15 plan. For each gigabyte in excess of the limit, customers would be charged \$10 a month starting June 7, 2010, though existing customers would not be required to change from the \$30 a month unlimited service plan. The new plan would become a requirement for those upgrading to the new iPhone technology later in the summer.
## Licensing
A wireless connection can be either licensed or unlicensed. In the US, licensed connections use a private spectrum the user has secured rights to from the Federal Communications Commission (FCC). The unlicensed mobile wireless broadband, in US operates on CBRS Which has three tiers. Tier 1 -- Incumbent Access, reserved for US Federals Government, Tier 2 -- Priority Access, a paid access with priority on the spectrum, Tier 3 -- General Authorized Access (GAA), a shared spectrum. In other countries, spectrum is licensed from the country\'s national radio communications authority (such as the ACMA in Australia or Nigerian Communications Commission in Nigeria (NCC)). Licensing is usually expensive and often reserved for large companies who wish to guarantee private access to spectrum for use in point to point communication. Because of this, most wireless ISP\'s use unlicensed spectrum which is publicly shared
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# Bilinear transform
The **bilinear transform** (also known as **Tustin\'s method**, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa.
The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used for converting a transfer function $H_a(s)$ of a linear, time-invariant (LTI) filter in the continuous-time domain (often named an analog filter) to a transfer function $H_d(z)$ of a linear, shift-invariant filter in the discrete-time domain (often named a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters). It maps positions on the $j \omega$ axis, $\mathrm{Re}[s]=0$, in the s-plane to the unit circle, $|z| = 1$, in the z-plane. Other bilinear transforms can be used for warping the frequency response of any discrete-time linear system (for example to approximate the non-linear frequency resolution of the human auditory system) and are implementable in the discrete domain by replacing a system\'s unit delays $\left( z^{-1} \right)$ with first order all-pass filters.
The transform preserves stability and maps every point of the frequency response of the continuous-time filter, $H_a(j \omega_a)$ to a corresponding point in the frequency response of the discrete-time filter, $H_d(e^{j \omega_d T})$ although to a somewhat different frequency, as shown in the Frequency warping section below. This means that for every feature that one sees in the frequency response of the analog filter, there is a corresponding feature, with identical gain and phase shift, in the frequency response of the digital filter but, perhaps, at a somewhat different frequency. The change in frequency is barely noticeable at low frequencies but is quite evident at frequencies close to the Nyquist frequency.
## Discrete-time approximation {#discrete_time_approximation}
The bilinear transform is a first-order Padé approximant of the natural logarithm function that is an exact mapping of the *z*-plane to the *s*-plane. When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the result is precisely the Z transform of the discrete-time sequence with the substitution of
$$\begin{align}
z &= e^{sT} \\
&= \frac{e^{sT/2}}{e^{-sT/2}} \\
&\approx \frac{1 + s T / 2}{1 - s T / 2}
\end{align}$$
where $T$ is the numerical integration step size of the trapezoidal rule used in the bilinear transform derivation; or, in other words, the sampling period. The above bilinear approximation can be solved for $s$ or a similar approximation for $s = (1/T) \ln(z)$ can be performed.
The inverse of this mapping (and its first-order bilinear approximation) is
$$\begin{align}
s &= \frac{1}{T} \ln(z) \\
&= \frac{2}{T} \left[\frac{z-1}{z+1} + \frac{1}{3} \left( \frac{z-1}{z+1} \right)^3 + \frac{1}{5} \left( \frac{z-1}{z+1} \right)^5 + \frac{1}{7} \left( \frac{z-1}{z+1} \right)^7 + \cdots \right] \\
&\approx \frac{2}{T} \frac{z - 1}{z + 1} \\
&= \frac{2}{T} \frac{1 - z^{-1}}{1 + z^{-1}}
\end{align}$$
The bilinear transform essentially uses this first order approximation and substitutes into the continuous-time transfer function, $H_a(s)$
$$s \leftarrow \frac{2}{T} \frac{z - 1}{z + 1}.$$
That is
$$H_d(z) = H_a(s) \bigg|_{s = \frac{2}{T} \frac{z - 1}{z + 1}}= H_a \left( \frac{2}{T} \frac{z-1}{z+1} \right). \$$
## Stability and minimum-phase property preserved {#stability_and_minimum_phase_property_preserved}
A continuous-time causal filter is stable if the poles of its transfer function fall in the left half of the complex s-plane. A discrete-time causal filter is stable if the poles of its transfer function fall inside the unit circle in the complex z-plane. The bilinear transform maps the left half of the complex s-plane to the interior of the unit circle in the z-plane. Thus, filters designed in the continuous-time domain that are stable are converted to filters in the discrete-time domain that preserve that stability.
Likewise, a continuous-time filter is minimum-phase if the zeros of its transfer function fall in the left half of the complex s-plane. A discrete-time filter is minimum-phase if the zeros of its transfer function fall inside the unit circle in the complex z-plane. Then the same mapping property assures that continuous-time filters that are minimum-phase are converted to discrete-time filters that preserve that property of being minimum-phase.
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# Bilinear transform
## Transformation of a General LTI System {#transformation_of_a_general_lti_system}
A general LTI system has the transfer function $H_a(s) = \frac{b_0 + b_1s + b_2s^2 + \cdots + b_Qs^Q}{a_0 + a_1s + a_2s^2 + \cdots + a_Ps^P}$ The order of the transfer function `{{math|''N''}}`{=mediawiki} is the greater of `{{math|''P''}}`{=mediawiki} and `{{math|''Q''}}`{=mediawiki} (in practice this is most likely `{{math|''P''}}`{=mediawiki} as the transfer function must be proper for the system to be stable). Applying the bilinear transform $s = K\frac{z - 1}{z + 1}$ where `{{math|''K''}}`{=mediawiki} is defined as either `{{math|2/''T''}}`{=mediawiki} or otherwise if using frequency warping, gives $H_d(z) = \frac{b_0 + b_1\left(K\frac{z - 1}{z + 1}\right) + b_2\left(K\frac{z - 1}{z + 1}\right)^2 + \cdots + b_Q\left(K\frac{z - 1}{z + 1}\right)^Q}
{a_0 + a_1\left(K\frac{z - 1}{z + 1}\right) + a_2\left(K\frac{z - 1}{z + 1}\right)^2 + \cdots + b_P\left(K\frac{z - 1}{z + 1}\right)^P}$ Multiplying the numerator and denominator by the largest power of `{{math|(''z'' + 1)<sup>−1</sup>}}`{=mediawiki} present, `{{math|(''z'' + 1)<sup>−''N''</sup>}}`{=mediawiki}, gives $H_d(z) = \frac{b_0(z+1)^N + b_1K(z-1)(z+1)^{N-1} + b_2K^2(z-1)^2(z+1)^{N-2} + \cdots + b_QK^Q(z-1)^Q(z+1)^{N-Q}}
{a_0(z+1)^N + a_1K(z-1)(z+1)^{N-1} + a_2K^2(z-1)^2(z+1)^{N-2} + \cdots + a_PK^P(z-1)^P(z+1)^{N-P}}$ It can be seen here that after the transformation, the degree of the numerator and denominator are both `{{math|''N''}}`{=mediawiki}.
Consider then the pole-zero form of the continuous-time transfer function $H_a(s) = \frac{(s - \xi_1)(s - \xi_2) \cdots (s - \xi_Q)}{(s - p_1)(s - p_2) \cdots (s - p_P)}$ The roots of the numerator and denominator polynomials, `{{math|''ξ<sub>i</sub>''}}`{=mediawiki} and `{{math|''p<sub>i</sub>''}}`{=mediawiki}, are the zeros and poles of the system. The bilinear transform is a one-to-one mapping, hence these can be transformed to the z-domain using $z = \frac{K + s}{K - s}$ yielding some of the discretized transfer function\'s zeros and poles `{{math|''ξ'<sub>i</sub>''}}`{=mediawiki} and `{{math|''p'<sub>i</sub>''}}`{=mediawiki} $\begin{aligned}
\xi'_i &= \frac{K + \xi_i}{K - \xi_i} \quad 1 \leq i \leq Q \\
p'_i &= \frac{K + p_i}{K - p_i} \quad 1 \leq i \leq P
\end{aligned}$ As described above, the degree of the numerator and denominator are now both `{{math|''N''}}`{=mediawiki}, in other words there is now an equal number of zeros and poles. The multiplication by `{{math|(''z'' + 1)<sup>−''N''</sup>}}`{=mediawiki} means the additional zeros or poles are $\begin{aligned}
\xi'_i &= -1 \quad Q < i \leq N \\
p'_i &= -1 \quad P < i \leq N
\end{aligned}$ Given the full set of zeros and poles, the z-domain transfer function is then $H_d(z) = \frac{(z - \xi'_1)(z - \xi'_2) \cdots (z - \xi'_N)}
{(z - p'_1)(z - p'_2) \cdots (z - p'_N)}$
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# Bilinear transform
## Example
As an example take a simple low-pass RC filter. This continuous-time filter has a transfer function
$$\begin{align}
H_a(s) &= \frac{1/sC}{R+1/sC} \\
&= \frac{1}{1 + RC s}.
\end{align}$$
If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for $s$ the formula above; after some reworking, we get the following filter representation:
: {\|
\|- \|$H_d(z) \$ \|$=H_a \left( \frac{2}{T} \frac{z-1}{z+1}\right) \$ \|- \| \|$= \frac{1}{1 + RC \left( \frac{2}{T} \frac{z-1}{z+1}\right)} \$ \|- \| \|$= \frac{1 + z}{(1 - 2 RC / T) + (1 + 2RC / T) z} \$ \|- \| \|$= \frac{1 + z^{-1}}{(1 + 2RC / T) + (1 - 2RC / T) z^{-1}}. \$ \|}
The coefficients of the denominator are the \'feed-backward\' coefficients and the coefficients of the numerator are the \'feed-forward\' coefficients used for implementing a real-time digital filter.
## Transformation for a general first-order continuous-time filter {#transformation_for_a_general_first_order_continuous_time_filter}
It is possible to relate the coefficients of a continuous-time, analog filter with those of a similar discrete-time digital filter created through the bilinear transform process. Transforming a general, first-order continuous-time filter with the given transfer function
$$H_a(s) = \frac{b_0 s + b_1}{a_0 s + a_1} = \frac{b_0 + b_1 s^{-1}}{a_0 + a_1 s^{-1}}$$
using the bilinear transform (without prewarping any frequency specification) requires the substitution of
$$s \leftarrow K \frac{1 - z^{-1}}{1 + z^{-1}}$$
where
$$K \triangleq \frac{2}{T}$$.
However, if the frequency warping compensation as described below is used in the bilinear transform, so that both analog and digital filter gain and phase agree at frequency $\omega_0$, then
$$K \triangleq \frac{\omega_0}{\tan\left(\frac{\omega_0 T}{2}\right)}$$.
This results in a discrete-time digital filter with coefficients expressed in terms of the coefficients of the original continuous time filter:
$$H_d(z)=\frac{(b_0 K + b_1) + (-b_0 K + b_1)z^{-1}}{(a_0 K + a_1) + (-a_0 K + a_1)z^{-1}}$$
Normally the constant term in the denominator must be normalized to 1 before deriving the corresponding difference equation. This results in
$$H_d(z)=\frac{\frac{b_0 K + b_1}{a_0 K + a_1} + \frac{-b_0 K + b_1}{a_0 K + a_1}z^{-1}}{1 + \frac{-a_0 K + a_1}{a_0 K + a_1}z^{-1}}.$$
The difference equation (using the Direct form I) is
$$y[n] = \frac{b_0 K + b_1}{a_0 K + a_1} \cdot x[n] + \frac{-b_0 K + b_1}{a_0 K + a_1} \cdot x[n-1] - \frac{-a_0 K + a_1}{a_0 K + a_1} \cdot y[n-1] \ .$$
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# Bilinear transform
## General second-order biquad transformation {#general_second_order_biquad_transformation}
A similar process can be used for a general second-order filter with the given transfer function
$$H_a(s) = \frac{b_0 s^2 + b_1 s + b_2}{a_0 s^2 + a_1 s + a_2} = \frac{b_0 + b_1 s^{-1} + b_2 s^{-2}}{a_0 + a_1 s^{-1} + a_2 s^{-2}} \ .$$
This results in a discrete-time digital biquad filter with coefficients expressed in terms of the coefficients of the original continuous time filter:
$$H_d(z)=\frac{(b_0 K^2 + b_1 K + b_2) + (2b_2 - 2b_0 K^2)z^{-1} + (b_0 K^2 - b_1 K + b_2)z^{-2}}{(a_0 K^2 + a_1 K + a_2) + (2a_2 - 2a_0 K^2)z^{-1} + (a_0 K^2 - a_1 K + a_2)z^{-2}}$$
Again, the constant term in the denominator is generally normalized to 1 before deriving the corresponding difference equation. This results in
$$H_d(z)=\frac{\frac{b_0 K^2 + b_1 K + b_2}{a_0 K^2 + a_1 K + a_2} + \frac{2b_2 - 2b_0 K^2}{a_0 K^2 + a_1 K + a_2}z^{-1} + \frac{b_0 K^2 - b_1 K + b_2}{a_0 K^2 + a_1 K + a_2}z^{-2}}{1 + \frac{2a_2 - 2a_0 K^2}{a_0 K^2 + a_1 K + a_2}z^{-1} + \frac{a_0 K^2 - a_1 K + a_2}{a_0 K^2 + a_1 K + a_2}z^{-2}}.$$
The difference equation (using the Direct form I) is
$$y[n] = \frac{b_0 K^2 + b_1 K + b_2}{a_0 K^2 + a_1 K + a_2} \cdot x[n] + \frac{2b_2 - 2b_0 K^2}{a_0 K^2 + a_1 K + a_2} \cdot x[n-1] + \frac{b_0 K^2 - b_1 K + b_2}{a_0 K^2 + a_1 K + a_2} \cdot x[n-2] - \frac{2a_2 - 2a_0 K^2}{a_0 K^2 + a_1 K + a_2} \cdot y[n-1] - \frac{a_0 K^2 - a_1 K + a_2}{a_0 K^2 + a_1 K + a_2} \cdot y[n-2] \ .$$
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# Bilinear transform
## Frequency warping {#frequency_warping}
To determine the frequency response of a continuous-time filter, the transfer function $H_a(s)$ is evaluated at $s = j \omega_a$ which is on the $j \omega$ axis. Likewise, to determine the frequency response of a discrete-time filter, the transfer function $H_d(z)$ is evaluated at $z = e^{ j \omega_d T}$ which is on the unit circle, $|z| = 1$. The bilinear transform maps the $j \omega$ axis of the *s*-plane (which is the domain of $H_a(s)$) to the unit circle of the *z*-plane, $|z| = 1$ (which is the domain of $H_d(z)$), but it is **not** the same mapping $z = e^{sT}$ which also maps the $j \omega$ axis to the unit circle. When the actual frequency of $\omega_d$ is input to the discrete-time filter designed by use of the bilinear transform, then it is desired to know at what frequency, $\omega_a$, for the continuous-time filter that this $\omega_d$ is mapped to.
$$H_d(z) = H_a \left( \frac{2}{T} \frac{z-1}{z+1}\right)$$
: {\|
\|- \|$H_d(e^{ j \omega_d T})$ \|$= H_a \left( \frac{2}{T} \frac{e^{ j \omega_d T} - 1}{e^{ j \omega_d T} + 1}\right)$ \|- \| \|$= H_a \left( \frac{2}{T} \cdot \frac{e^{j \omega_d T/2} \left(e^{j \omega_d T/2} - e^{-j \omega_d T/2}\right)}{e^{j \omega_d T/2} \left(e^{j \omega_d T/2} + e^{-j \omega_d T/2 }\right)}\right)$ \|- \| \|$= H_a \left( \frac{2}{T} \cdot \frac{\left(e^{j \omega_d T/2} - e^{-j \omega_d T/2}\right)}{\left(e^{j \omega_d T/2} + e^{-j \omega_d T/2 }\right)}\right)$ \|- \| \|$= H_a \left(j \frac{2}{T} \cdot \frac{ \left(e^{j \omega_d T/2} - e^{-j \omega_d T/2}\right) /(2j)}{\left(e^{j \omega_d T/2} + e^{-j \omega_d T/2 }\right) / 2}\right)$ \|- \| \|$= H_a \left(j \frac{2}{T} \cdot \frac{ \sin(\omega_d T/2) }{ \cos(\omega_d T/2) }\right)$ \|- \| \|$= H_a \left(j \frac{2}{T} \cdot \tan \left( \omega_d T/2 \right) \right)$ \|}
This shows that every point on the unit circle in the discrete-time filter z-plane, $z = e^{ j \omega_d T}$ is mapped to a point on the $j \omega$ axis on the continuous-time filter s-plane, $s = j \omega_a$. That is, the discrete-time to continuous-time frequency mapping of the bilinear transform is
$$\omega_a = \frac{2}{T} \tan \left( \omega_d \frac{T}{2} \right)$$
and the inverse mapping is
$$\omega_d = \frac{2}{T} \arctan \left( \omega_a \frac{T}{2} \right).$$
The discrete-time filter behaves at frequency $\omega_d$ the same way that the continuous-time filter behaves at frequency $(2/T) \tan(\omega_d T/2)$. Specifically, the gain and phase shift that the discrete-time filter has at frequency $\omega_d$ is the same gain and phase shift that the continuous-time filter has at frequency $(2/T) \tan(\omega_d T/2)$. This means that every feature, every \"bump\" that is visible in the frequency response of the continuous-time filter is also visible in the discrete-time filter, but at a different frequency. For low frequencies (that is, when $\omega_d \ll 2/T$ or $\omega_a \ll 2/T$), then the features are mapped to a *slightly* different frequency; $\omega_d \approx \omega_a$.
One can see that the entire continuous frequency range
: $-\infty < \omega_a < +\infty$
is mapped onto the fundamental frequency interval
: $-\frac{\pi}{T} < \omega_d < +\frac{\pi}{T}.$
The continuous-time filter frequency $\omega_a = 0$ corresponds to the discrete-time filter frequency $\omega_d = 0$ and the continuous-time filter frequency $\omega_a = \pm \infty$ correspond to the discrete-time filter frequency $\omega_d = \pm \pi / T.$
One can also see that there is a nonlinear relationship between $\omega_a$ and $\omega_d.$ This effect of the bilinear transform is called **frequency warping**. The continuous-time filter can be designed to compensate for this frequency warping by setting $\omega_a = \frac{2}{T} \tan \left( \omega_d \frac{T}{2} \right)$ for every frequency specification that the designer has control over (such as corner frequency or center frequency). This is called **pre-warping** the filter design.
It is possible, however, to compensate for the frequency warping by pre-warping a frequency specification $\omega_0$ (usually a resonant frequency or the frequency of the most significant feature of the frequency response) of the continuous-time system. These pre-warped specifications may then be used in the bilinear transform to obtain the desired discrete-time system. When designing a digital filter as an approximation of a continuous time filter, the frequency response (both amplitude and phase) of the digital filter can be made to match the frequency response of the continuous filter at a specified frequency $\omega_0$, as well as matching at DC, if the following transform is substituted into the continuous filter transfer function. This is a modified version of Tustin\'s transform shown above.
$$s \leftarrow \frac{\omega_0}{\tan\left(\frac{\omega_0 T}{2}\right)} \frac{z - 1}{z + 1}.$$
However, note that this transform becomes the original transform
$$s \leftarrow \frac{2}{T} \frac{z - 1}{z + 1}$$
as $\omega_0 \to 0$.
The main advantage of the warping phenomenon is the absence of aliasing distortion of the frequency response characteristic, such as observed with Impulse invariance
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# Brian Boitano
**Brian Anthony Boitano** (born October 22, 1963) is an American figure skater from Sunnyvale, California. He is the 1988 Olympic champion, the 1986 and 1988 World Champion, and the 1985--1988 U.S. National Champion.
Boitano turned professional following the 1988 season. Under new rules by the ISU, he returned to competition in 1993 and competed at the 1994 Winter Olympics, where he placed sixth. In 1996, he was inducted into the World Figure Skating Hall of Fame and the United States Figure Skating Hall of Fame.
## Early life {#early_life}
Brian Boitano was born in 1963 and raised in Mountain View, California. Boitano is a graduate of Marian A. Peterson High School in Sunnyvale, California. He is of Italian American descent, with family from northern Italy. As an adult, he has lived in San Francisco.
## Figure skating career {#figure_skating_career}
### Early career {#early_career}
Beginning skating as a child, Brian Boitano won a gold medal at the Junior U.S. Championships in 1978 and first made his mark on the international scene when he won the bronze medal at the 1978 World Junior Figure Skating Championships, beating future rival Brian Orser for that medal.
Early in his career, Boitano was known primarily for his jumping. He, along with several other skaters, helped push the technical envelope of men\'s skating. In 1982, Boitano became the first American to land a triple Axel. In 1987, he introduced his signature jump, the \'Boitano triple Lutz\', in which the skater raises his left arm above his head. He attempted a quadruple jump throughout the 1986--87 season and at the 1988 World Figure Skating Championships, but did not cleanly land the jump; he double-footed the landing on two occasions.
At the 1983 World Championships, he became the first skater to ever land all six triple jumps in competition. He would eventually include and successfully land eight triple jumps in his free skate program, the maximum number possible (see Zayak rule). He would jump two flip jumps and two triple Axels to compete with his rival, Brian Orser, who jumped one triple flip and one triple Axel. It was not until failing to defend his World title in 1987 that Boitano focused specifically on improving his artistry. Toward this end, he worked with renowned choreographer Sandra Bezic.
Boitano placed second at the 1984 United States Figure Skating Championships, earning a place in the 1984 Winter Olympics. He placed 5th at the Olympics, setting the stage for his success over the next four years.
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# Brian Boitano
## Figure skating career {#figure_skating_career}
### World Champion {#world_champion}
Following the 1984 Olympics, several skaters emerged as likely medal hopes following the retirement of Scott Hamilton.
Boitano won the 1985 United States Figure Skating Championships, the first of his four titles. At the first World Championships of the post-Hamilton era in 1985, Alexander Fadeev won, with Brian Orser finishing in second place and Boitano in third place. He had injured tendons in his right ankle a few weeks before the 1986 U.S. Championships but went on to win his second national title. At the 1986 World Championships, Boitano took the title, while Fadeev had a disastrous free skate despite having been in an excellent position to win; Orser finished in second place once again.
During the 1986--87 season, Boitano had introduced three new elements to his programs: the \'Tano triple lutz and a quadruple toe loop, as well as wearing a blindfold, although he never succeeded in landing a clean quadruple jump in competition. The 1987 World Championships were held in Cincinnati, giving the defending world champion a home-field advantage. The outcome of the event would set the tone for the 1988 Olympics. He fell on his quadruple toe loop attempt and placed second.
After losing the world title to Orser at home, Boitano and his coach Linda Leaver decided that some changes needed to be made if he was to become the Olympic champion. He had always been good at the technical requirements (\"The first mark\"), but he was weak on the artistic (\"the second mark\"). He was a self-described \"jumping robot.\" In order to help his growth as an artist, he hired choreographer Sandra Bezic to choreograph his programs for the 1987--1988 Olympic season.
Bezic choreographed two programs that featured clean lines and accentuated the skating abilities of the 5\' 11\" Boitano. The short program was based on Giacomo Meyerbeer\'s ballet *Les Patineurs*, in which he plays a cocky young man showing off his tricks, using movements dating to the 19th century. In one moment, he wipes ice shavings, also called snow, off his skate blade and tosses it over his shoulder after landing a triple Axel combination. The free skating program was based on the film score, *Napoleon*, detailing various phases of a soldier\'s life.
Boitano debuted his new programs at 1987 Skate Canada, held in the Saddledome in Calgary, Alberta, Canada. This was where he would compete against Brian Orser for the Olympic title three months later. His new programs were received with standing ovations by the audience. Although Orser won the competition, Boitano skated clean, landing seven triple jumps, including a footwork section into a jump, but popped his planned second triple Axel. The team was so confident about the strength of his new programs that they omitted the quadruple toe loop which, if landed, could have put him a shoulder above Orser in technical merit.
The short program at the 1988 United States Figure Skating Championships proved to be a highlight. Boitano received marks of 6.0 from eight of the nine judges for presentation, the second mark. His free skate was flawed. Due to delays, he did not skate until after midnight. Still, he won the competition, and went into the Olympics as the national champion (U.S.), as did Orser (representing Canada).
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# Brian Boitano
## Figure skating career {#figure_skating_career}
### 1988 Olympics: Battle of the Brians {#olympics_battle_of_the_brians}
Going into the Olympics, Boitano and Brian Orser each had won a world title and each had an excellent, balanced repertoire. Boitano was known as the slightly better technician and Orser as the better artist. `{{according to whom|date=March 2023}}`{=mediawiki} Adding to the rivalry, Boitano and Orser were both performing military-themed programs. Boitano\'s free skate was set to music from *Napoleon and Josephine*, the television miniseries. For his free skate, Boitano wore a blue stretch suit with red braids and epaulets, and used military gestures and postures as much as his music allowed.
The Battle of the Brians at the 1988 Winter Olympics was the highlight of Boitano\'s amateur career. Boitano and Orser were effectively tied going into the free skating portion of the event and whoever won that portion would win the event. Alexander Fadeev had won the compulsory figures section of the competition, with Boitano second and Orser third. In the short program, Orser placed first and Boitano second. The free skating was, at the time, worth 50% of the score, and so Boitano\'s lead would not be enough to hold him in first place if he lost the free skate.
Boitano skated a clean, technically excellent long program, with eight triple jumps, including two axels, and a triple flip-triple toe loop combination. Landing his second triple axel jump cleanly was probably a critical factor in the battle. Orser made one small mistake on a jump and omitted his planned second triple axel. Boitano won the battle in a 5--4 split. It was later discovered that the Canadian Figure Skating Association had engaged in \"vote trading\" with several countries on the judging panel, particularly East Germany and the USSR. This ultimately backfired, as the Soviet judge refused to follow this agreement and voting \"with his conscience,\" placing Boitano first. Had he followed his federation\'s directive, Boitano would have lost the gold medal. The judge was promptly suspended by his federation. Experts questioned why the scores were so close between the two skaters because Boitano had two triple axels, two triple flips and a triple triple combination, elements that were not included in Orser\'s program.
With his win, Boitano became the first Olympic champion to land the full complement of six types of triple jumps. Boitano won the gold medal, wearing skates with American flag appliqués. These are now part of the collections of the National Museum of American History at the Smithsonian Institution.
Following the Olympics, both Orser and Boitano went to the 1988 World Championships, which Boitano won. Boitano turned professional soon after.
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# Brian Boitano
## Figure skating career {#figure_skating_career}
### Professional career and return to amateur standing {#professional_career_and_return_to_amateur_standing}
Following the Olympics, Boitano went on to dominate competitions in the professional ranks, winning ten straight professional competitions, including five consecutive World Professional Championship titles and four consecutive wins at the Challenge of Champions. Boitano also appeared in *Carmen on Ice*, for which he won an Emmy. He performed with Champions on Ice for many years. He wanted to return to amateur competition and make another run at the Olympics.
In June 1993, the International Skating Union (ISU) introduced a clause, commonly known as the \"Boitano rule,\" which allowed professionals to reinstate as \"amateur\" or \"eligible\" skaters. Many others joined Boitano, including Ukrainian Viktor Petrenko, 1988 bronze medalist and 1992 gold medalist. The ISU decision was the result of Boitano\'s active involvement during the early 1990s, when the International Olympic Committee lifted the remaining limits on athletes\' remuneration. Previously, the committee had been accused of rejecting Western professionals, while allowing Eastern Bloc state-sponsored \"amateurs\" to compete. Boitano reinstated as an amateur to compete in the 1994 Winter Olympics in Lillehammer, Norway.
Boitano competed at the 1994 United States Figure Skating Championships, led after the short program, but lost to Scott Davis in the long program in a 6--3 split decision. Boitano was named to the Olympic team. Going into the Olympics as a medal favorite in a strong field, Boitano missed his triple Axel combination during the short program for the first time in his career. This mistake proved extremely costly, and knocked Boitano out of medal contention. He skated a good long program and finished 6th.
Boitano returned to the professional ranks afterward. In 1996 he was inducted into the World Figure Skating Hall of Fame and the United States Figure Skating Hall of Fame.
## Personal life {#personal_life}
In December 2013, Boitano was named to the United States delegation to the 2014 Winter Olympics in Sochi, Russia. In conjunction with that appointment, Boitano publicly came out as gay.
The Sochi games and Russia were the targets of criticism and LGBT activism because of a Russian anti-gay \"propaganda\" law passed in June 2013. In January 2014, Boitano told the Associated Press that he had never wanted to come out until he was named to the delegation.
Boitano\'s older brother, Mark Boitano, is a real estate agent and former politician. He served as a member of the New Mexico Senate from 1997 to 2013.
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# Brian Boitano
## Celebrity and popular culture career {#celebrity_and_popular_culture_career}
### *South Park* song {#south_park_song}
A caricature of Boitano as a superhero appears as a semi-recurring character in the cartoon series *South Park*. The film *South Park: Bigger, Longer & Uncut* (1999) features a musical number titled \"What Would Brian Boitano Do?\". He was also featured in *Jesus vs. Santa*.
### Food Network show {#food_network_show}
On August 23, 2009, Food Network debuted a new series entitled *What Would Brian Boitano Make?*, which borrows both its name and opening musical theme from the *South Park: Bigger, Longer & Uncut* song. The show features Boitano preparing meals for his friends. The series was picked up for a ten-episode second season.
### Other television and film appearances {#other_television_and_film_appearances}
- Boitano starred, along with Katarina Witt and archrival Brian Orser, in the 1990 German dance film *Carmen on Ice*; Boitano played Don Jose. All three won an Emmy Award for \"Outstanding performance in classical music/dance programming\".
- He was featured in the Super Bowl XXVI halftime show \"Winter Magic\", along with Gloria Estefan and Dorothy Hamill.
- Boitano had a cameo in the 2007 film *Blades of Glory* as a world skating federation judge.
- He and fellow figure skater Michelle Kwan had a cameo as themselves in the 2005 Disney film, *Ice Princess*, appearing as commentators during the Sectionals competition.
- He appeared on *Giada at Home* for one episode.
- He appeared as a guest judge on *Top Chef Masters*, Season 4 episode 3. The episode is titled \"What would Brian Boitano Make?\"
- He appeared on Fox Business Network\'s *Stossel*, episode \"Spontaneous Order\" (February 10, 2011).
- He appeared in an episode of *Check, Please! Bay Area*, a restaurant review program which airs on KQED-TV in San Francisco.
- He hosted a series on HGTV, called *The Brian Boitano Project*, which premiered January 16, 2014, in which he purchased a near derelict ancestral home in Northern Italy, home to many Boitanos. During the series he gives the home in Favale di Malvaro a sympathetic restoration/renovation and shops flea markets with two nieces to find decor and furnishings. Local artisans, carpenters, masons and painters create a gem where he can live part-time and host Boitanos from afar.
- Boitano appeared as a guest on Season 18 of the reality series *Hell\'s Kitchen*, where he along with Gordon Ramsay and Traci Des Jardins co-judged the team challenge in the episode \"Hell Freezes Over\".
## Programs
+------------+-----------------+------------------------------------------+--------------------------------------------+
| Season | Short program | Free skating | Exhibition |
+============+=================+==========================================+============================================+
| 1993--1994 | Carousel Waltz\ | Appalachian Spring/Lincoln Portrait\ | Elegy For Harp And Strings\ |
| | Richard Rodgers | by Aaron Copland | Lee Holdridge |
+------------+-----------------+------------------------------------------+--------------------------------------------+
| 1987--1988 | Les Patineurs\ | Silent movie Napoleon\ | Adventures of Don Juan\ |
| | (Meyerbeer) | (Carmine Coppola / Francis Ford Coppola) | from the Errol Flynn movie\ |
| | | | Parlami d\'amore Mariu (Italian love song) |
+------------+-----------------+------------------------------------------+--------------------------------------------+
## Results
International
-----------------------
Event
Olympics
Worlds
Skate America
Skate Canada
NHK Trophy
St. Ivel
Nebelhorn
St. Gervais
International: Junior
Junior Worlds
National
U.S. Champ
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# List of political scandals in the United Kingdom
This is a **list of political scandals in the United Kingdom** in chronological order. Scandals implicating political figures or governments of the UK, often reported in the mass media, have long had repercussions for their popularity. Issues in political scandals have included alleged or proven financial and sexual matters, or various other allegations or actions taken by politicians that led to controversy. In British media and political discourse, such scandals have sometimes been referred to as **political sleaze** since the 1990s. Notable scandals include the Marconi scandal, Profumo affair and the 2009 expenses scandal. `{{Dynamic list}}`{=mediawiki}
## 1890s
- Liberator Building Society scandal, in which the Liberal Party MP Jabez Balfour was exposed as running several fraudulent companies to conceal financial losses. Balfour fled to Argentina, but was eventually arrested and imprisoned.
## 1910s {#s_1}
- Marconi scandal of insider trading by Liberal Party Ministers including:
- Rufus Isaacs, 1st Marquess of Reading, the Attorney General
- The Master of Elibank, Lord Murray, the Treasurer of the Liberal Party,
- David Lloyd George, 1st Earl Lloyd-George of Dwyfor, the Chancellor of the Exchequer
- Herbert Samuel, 1st Viscount Samuel, Postmaster General; was falsely implicated. (1912)
- Shell Crisis of 1915, which led to the fall of H. H. Asquith\'s Liberal Party government during World War I.
## 1920s {#s_2}
- Lloyd George and the honours scandal. Honours sold for large campaign contributions (1922)
- Zinoviev Letter (1924)
## 1930s {#s_3}
- Jimmy Thomas budget leak (1936)
## 1940s {#s_4}
- Hugh Dalton budget leak (1947)
- John Belcher corruptly influenced -- led to Lynskey Tribunal
## 1950s {#s_5}
- British Malayan headhunting scandal (1952). Involved generals, politicians, and activists, sparked by the *Daily Worker\'s* leaked photos of war crimes (notably headhunting) committed by British troops during the Malayan Emergency.
- Crichel Down and the resignation of Thomas Dugdale (1954)
- Suez Crisis (1956)
## 1960s {#s_6}
- Vassall affair (1963): civil servant John Vassall, working for Minister Tam Galbraith, was revealed to be a spy for the Soviet Union and was arrested. The affair was investigated in the Vassall tribunal.
- Profumo affair (1963): Secretary of State for War John Profumo had an affair with Christine Keeler (to whom he had been introduced by artist Stephen Ward) who was having an affair with a Soviet spy at the same time.
- The Robert Boothby (Conservative), Tom Driberg (Labour), Kray brothers affair and consequent cover-up involving senior politicians of both parties. The *Daily Mirror* published some details of the matter and was falsely sued for libel.
## 1970s {#s_7}
- Corrupt architect John Poulson and links to Conservative Home Secretary Reginald Maudling, Labour council leader T. Dan Smith and others (1972--1974): Maudling resigned, Smith sentenced to imprisonment.
- Earl Jellicoe and Lord Lambton sex scandal (1973): Conservatives, junior defence minister Lambton is arrested for using prostitutes and Cabinet minister Jellicoe also confesses.
- Labour MP John Stonehouse\'s faked suicide (1974)
- Harold Wilson\'s Prime Minister\'s Resignation Honours (known satirically as the \"Lavender List\") gives honours to a number of wealthy businessmen. (May 1976)
- Peter Jay\'s appointment as British Ambassador to the US by his father in law, the then Labour Prime Minister James Callaghan. At the time Jay was a journalist with little diplomatic experience. (1976)
- \"Rinkagate\": the Thorpe affair. Liberal Party leader Jeremy Thorpe was arrested and tried for allegedly paying a hitman to murder his lover, model Norman Scott, while walking his dog on Exmoor; the hitman only shot the dog, Rinka. Thorpe was forced to resign due to his clandestine gay affairs, but was acquitted of conspiracy to murder.
## 1980s {#s_8}
- Joseph Kagan, Baron Kagan, earlier ennobled by the Labour Prime Minister Harold Wilson\'s notorious Lavender List (1976), was convicted of fraud (1980)
- Cecil Parkinson affair with secretary Sara Keays resulting in their child, Flora Keays (1983)
- Al Yamamah contract alleged to have been obtained by bribery (1985)
- Westland affair (1986): The Defence Secretary, Michael Heseltine, resigned from his Cabinet job in a disagreement with Prime Minister Margaret Thatcher over the Westland affair. Heseltine walked out of a meeting at Number 10 as his views on the future of the Westland helicopter company were being ignored at the time.
- Jeffrey Archer and the prostitute allegations (1986), and his subsequent conviction for perjury (2001)
- Westminster cemeteries scandal (1987)
- Edwina Currie resigns as a junior Health minister after claiming that millions of British eggs were infected with salmonella, stating that \"most of \[British\] egg production\" was infected (1988)
- \"Homes for votes\" gerrymandering scandal (1987--1989)
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# List of political scandals in the United Kingdom
## 1990s {#s_9}
- Arms-to-Iraq and the closely connected Iraqi Supergun affair (1990)
- David Mellor resignation after press disclosure of his affair with Antonia de Sancha and gratis holiday from a daughter of a PLO official (1992)
- Michael Mates gift of a watch (\"Don\'t let the bastards grind you down\") to Asil Nadir (1993)
- Monklandsgate dominated the 1994 Monklands East by-election. It mainly consisted of allegations of sectarian spending discrepancies between Protestant Airdrie and Catholic Coatbridge, fuelled by the fact that all 17 of the ruling Labour group were Roman Catholics. (1994)
- *Back to Basics*, a government policy slogan portrayed by opponents and the press as a morality campaign to compare it with a contemporaneous succession of sex scandals in John Major\'s government which led to the resignation of Tim Yeo and the Earl of Caithness, among others (1994)
- Cash-for-questions affair involving Neil Hamilton, Tim Smith and Mohamed Al-Fayed (1994)
- Jonathan Aitken and the Paris Ritz Hotel bill allegations, and his subsequent conviction for perjury after his failed libel action against *The Guardian*, resulting in Aitken being only the third person to have to resign from the Privy Council in the 20th century. (1995)
- Conservative MP Jerry Hayes was \"outed\" as a homosexual by the *News of the World* with the headline \"TORY MP 2-TIMED WIFE WITH UNDER-AGE GAY LOVER\". Hayes had met Young Conservative Paul Stone at the 1991 Conservative conference and that same evening, \"committed a lewd act which was in breach of the law at the time\". Stone had been 18 at the time, whilst the legal age for homosexual sex in 1991 was 21. Hayes had previously supported Section 28. (1997)
- Bernie Ecclestone was involved in a political scandal when it transpired he had given the Labour Party a million pound donation -- which raised eyebrows when the incoming Labour government changed its policy to allow Formula One to continue being sponsored by tobacco manufacturers. The Labour Party returned the donation when the scandal came to light. (1997)
- Peter Mandelson, Trade and Industry Secretary, resigned after failing to disclose £373,000 loan from Paymaster General Geoffrey Robinson. (1998)
- Ron Davies resigned from the cabinet after being robbed by a man he met at Clapham Common (a well-known gay cruising ground) and then lying about it (1998)
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# List of political scandals in the United Kingdom
## 2000s {#s_10}
- Officegate (2001). Henry McLeish, Labour First Minister of Scotland, failed to refund the House of Commons for income he had received from the sub-let of his constituency office in Glenrothes while still a Westminster MP.
- Keith Vaz, Peter Mandelson and the Hinduja brothers. Mandelson was forced to resign for a second time due to misleading statements. (2001)
- Jo Moore, within an hour of the September 11 attacks, sent an email to the press office of her department suggesting: \"It\'s now a very good day to get out anything we want to bury. Councillors\' expenses?\" Although prior to the catastrophic collapse of the towers, the phrase \"a good day to bury bad news\" (not actually used by Moore) has since been used to refer to other instances of attempting to hide one item of news behind a more publicised issue.
- Betsygate (2002), which revolved around the level of pay that Iain Duncan Smith\'s wife Elisabeth received as his diary secretary.
- In 2002, Edwina Currie revealed that she had had an affair, beginning in 1984, with John Major before he became Prime Minister of the United Kingdom. Major had frequently pushed his *Back To Basics* agenda (see above), which was taken by the media as a form of moral absolutism.
- The Burrell affair -- allegations about the behaviour of the British royal family and their servants with possible constitutional implications. (2002)
- Ron Davies stood down from the Welsh assembly following accusations of illicit gay sex. Davies had claimed he had been badger-watching in the area. (2003)
- The apparent suicide of Dr. David Kelly and the *Hutton Inquiry*. On 17 July 2003, Kelly, an employee of the Ministry of Defence, apparently committed suicide after being misquoted by BBC journalist Andrew Gilligan as saying that Tony Blair\'s Labour government had knowingly \"sexed up\" the \"September Dossier\", a report into Iraq and weapons of mass destruction. The government was cleared of wrongdoing, while the BBC was strongly criticised by the subsequent inquiry, leading to the resignation of the BBC\'s chairman and director-general.
- In April 2004, Beverly Hughes was forced to resign as minister for Immigration, Citizenship and Counter Terrorism when it was shown that she had been informed of procedural improprieties concerning the granting of visas to certain categories of workers from Eastern Europe. She had earlier told the House of Commons that if she had been aware of such facts she would have done something about it.
- In 2005, David McLetchie, leader of the Scottish Conservatives, was forced to resign after claiming the highest taxi expenses of any MSP. These included personal journeys, journeys related solely with his second job as a solicitor, and Conservative Party business, for example travel to Conservative conferences. Conservative backbench MSP Brian Monteith had the whip withdrawn for briefing against his leader to the *Scotland on Sunday* newspaper.
- Liberal Democrats Home Affairs spokesman Mark Oaten resigned after it was revealed by the *News of the World* that he paid rentboys to perform sexual acts on him.
- David Mills financial allegations (2006). Tessa Jowell, Labour cabinet minister, was embroiled in a scandal about a property remortgage allegedly arranged to enable her husband, David Mills, to realise £350,000 from an off-shore hedge fund, money he allegedly received as a gift following testimony he had provided for Silvio Berlusconi in the 1990s. Nicknamed by the press as \"Jowellgate\".
- Cash for Honours (2006). In March 2006 it emerged that the Labour Party had borrowed millions of pounds in 2005 to help fund their general election campaign. While not illegal, on 15 March the Treasurer of the party, Jack Dromey, stated publicly that he had neither knowledge of nor involvement in these loans and had only become aware when he read about it in the newspapers. A story was running at the time that Dr Chai Patel and others had been recommended for life peerages after lending the Labour party money. He called on the Electoral Commission to investigate the issue of political parties taking out loans from non-commercial sources.
- Angus McNeil (2007). The married SNP MP who made the initial police complaint over the cash for honours scandal was forced to make an apology after it was revealed that in 2005 he had a \"heavy petting\" session with two teenage girls aged 17 and 18`{{bsn|reason=low quality tabloid newspaper|date=April 2025}}`{=mediawiki} in a hotel room at the same time his wife was pregnant with their third child.
- News of the World royal phone hacking scandal
- In November 2007, it emerged that more than £400,000 had been accepted by the Labour Party from one person through a series of third parties, causing the Electoral Commission to seek an explanation. Peter Watt resigned as the General Secretary of the party the day after the story broke and was quoted as saying that he knew about the arrangement but had not appreciated that he had failed to comply with the reporting requirements.
- On 24 January 2008, Peter Hain resigned his two cabinet posts (Secretary of State for Work and Pensions and Secretary of State for Wales) after the Electoral Commission referred donations to his Deputy Leadership campaign to the police.
- Derek Conway (2008): The Conservative Party MP was found to have reclaimed salaries he had paid to his two sons who had in fact not carried out the work to the extent claimed. He was ordered to repay £16,918, suspended from the House of Commons for 10 days and removed from the party whip.
- Cash for influence (2009): Details of covertly recorded discussions with four Labour Party peers which covered their ability to influence legislation and the consultancy fees that they charged (including retainer payments of up to £120,000) were published by *The Sunday Times*.
- United Kingdom parliamentary expenses scandal (2009): Widespread actual and alleged misuse of the permitted allowances and expenses claimed by Members of Parliament and attempts by MPs and peers to exempt themselves from Freedom of Information legislation.
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# List of political scandals in the United Kingdom
## 2010s {#s_11}
### 2010
- The Iris Robinson scandal in which First Minister of Northern Ireland Peter Robinson stepped aside for six weeks in January 2010 following revelations of his wife\'s involvement in an extramarital affair, her attempted suicide, and allegations that he had failed to properly declare details of loans she had procured for her lover to develop a business venture.
- Red Sky scandal, involving contracts given to company Red Sky by the Northern Ireland Housing Executive.
- The 2010 cash for influence scandal, in which undercover reporters for the *Dispatches* television series posed as political lobbyists offering to pay Members of Parliament to influence policy.
- On 29 May 2010 Chief Secretary to the Treasury David Laws resigned from the Cabinet and was referred to the Parliamentary Commissioner for Standards after *The Daily Telegraph* newspaper published details of Laws claiming around £40,000 in expenses on a second home owned by a secret partner between 2004 and 2009, whilst House of Commons rules have prevented MPs from claiming second home expenses on properties owned by a partner since 2006. By resigning Laws became the shortest serving Minister in modern British political history with less than 18 days\' service as a Cabinet Minister.
### 2011 {#section_1}
- On 14 October 2011 Secretary of State for Defence Liam Fox resigned from the Cabinet after he \"mistakenly allowed the distinction between \[his\] personal interest and \[his\] government activities to become blurred\" over his friendship with Adam Werritty. (He again served as a cabinet minister under Theresa May.)
- News International phone hacking scandal
- The Ed Balls document leak was exposed by *The Daily Telegraph* and showed that shadow chancellor Ed Balls was involved in a supposed plot known as \'Project Volvo\' to oust Tony Blair as leader and replace him with Gordon Brown shortly after the 2005 election.
### 2012 {#section_2}
- Conservative Party \'cash for access\' scandal involving Peter Cruddas and Sarah Southern, March 2012.
- In February 2012, Liberal Democrat MP Chris Huhne resigned from the Cabinet when he was charged with perverting the course of justice over a 2003 speeding case. His wife Vicky Pryce had claimed that she was driving the car, and accepted the licence penalty points on his behalf so that he could avoid being banned from driving. Huhne pleaded guilty at his trial, resigned as a member of parliament, and he and Pryce were sentenced to eight months in prison for perverting the course of justice.
- In October 2012, Andrew Mitchell resigned from his post as Chief Whip following allegations made about his conduct during an altercation with police at Downing Street on 19 September, the incident becoming known as \"plebgate\".
### 2013 {#section_3}
- In the 2013 Labour Party Falkirk candidate selection, which began following the announcement that the incumbent MP Eric Joyce was to step down at the 2015 general election, allegations were made on the significant infiltration of the selection process by the Unite trade union, the Labour Party\'s largest financial backer.
### 2014 {#section_4}
- In April 2014 Maria Miller, the Culture Secretary, resigned following pressure relating to the results of an investigation into her past expenses claims.
- On 20 November 2014 Emily Thornberry resigned her shadow cabinet position shortly after polls closed in the Rochester and Strood by-election. Earlier in the day, she had received criticism after tweeting a photograph of a house in the constituency adorned with three flags of St. George and the owner\'s white van parked outside on the driveway, under the caption \"Image from #Rochester\", provoking accusations of snobbery. She was criticised by fellow Labour Party MPs, including leader Ed Miliband who said her tweet conveyed a \"sense of disrespect\".
- Namagate, involving allegations that First Minister of Northern Ireland Peter Robinson may have financially benefitted from a deal with National Asset Management Agency (NAMA).
### 2015 {#section_5}
- In September 2015, Lord Ashcroft published a biography of David Cameron, which suggested that the then Prime Minister took drugs regularly and performed an \"outrageous initiation ceremony\" which involved inserting \"a private part of his anatomy\" into the mouth of a dead pig during his time in university. This became known as \"piggate\". It also led to questions about the Prime Minister\'s honesty with party donors\' known tax statuses as Lord Ashcroft suggested he had openly discussed his non-domiciled status with him in 2009, earlier than previously thought.
### 2017 {#section_6}
- In 2017 the contaminated blood scandal, in which many haemophiliacs died from infected Factor medicine, hit the headlines and Parliament with allegations of an \"industrial scale\" criminal cover-up. MP Ken Clarke retracted remarks from his autobiography relating to the scandal and a public inquiry was initiated.
- The Renewable Heat Incentive scandal in Northern Ireland, in which Arlene Foster set up a green energy scheme but failed to introduce cost controls, creating perverse incentives which eventually led to a £480m bill to the Northern Ireland budget. There were allegations that members of the Democratic Unionist Party attempted to postpone the closure of the scheme, which gave way to a spike in applications and causing the public purse millions of pounds. In January 2017, the scandal caused the resignation of the deputy First Minister, Martin McGuinness, after Foster refused to stand aside as First Minister pending an investigation, collapsing the Executive Office and triggering an early election of the Northern Ireland Assembly. The resulting political rifts meant the Assembly did not meet again until 2020.
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# List of political scandals in the United Kingdom
## 2010s {#s_11}
### 2018 {#section_7}
- The 2018 Windrush scandal, involving members of the Windrush generation being wrongly detained, deported, or threatened with deportation which caused the resignation of the then Home Secretary, Amber Rudd.
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# List of political scandals in the United Kingdom
## 2020s {#s_12}
### 2020 {#section_8}
- The Dominic Cummings scandal, where Dominic Cummings, chief strategist of prime minister Boris Johnson, broke COVID-19 pandemic restrictions during the UK\'s first nationwide lockdown while experiencing symptoms of the disease. Cummings and Johnson rejected calls for the former to resign. It was suggested that the scandal undermined the public\'s compliance with pandemic restrictions.
- The Alex Salmond scandal concerned how the Scottish Government, led by incumbent first minister of Scotland Nicola Sturgeon, breached its own guidelines in its investigation into the harassment claims against Sturgeon\'s predecessor as first minister, Alex Salmond. The Scottish Government lost a judicial review into their actions and had to pay over £500,000 to Salmond for legal expenses. Salmond claimed that senior figures in Sturgeon\'s government and the ruling Scottish National Party (SNP) conspired against him for political reasons. Critics accused Sturgeon of breaking the ministerial code which resulted in calls for her resignation. Sturgeon disputed the allegations, arguing that while mistakes had been made, her government acted appropriately.
### 2021 {#section_9}
- The Greensill scandal, in which former prime minister David Cameron approached a number of government ministers on behalf of Greensill Capital to lobby for the company to receive Covid Corporate Financing Facility loans.
- *The Sun* published pictures and then video of leaked CCTV footage from inside the Department of Health of health secretary Matt Hancock and Gina Coladangelo kissing in a breach of COVID-19 social distancing guidance. Boris Johnson accepted Matt Hancock\'s apology and stated that he \"considers the matter closed\", but Hancock resigned as health secretary the following day.
- In November 2021, the Parliamentary Commissioner for Standards found that Conservative MP Owen Paterson had broken paid advocacy rules, but instead of approving his suspension, the government enforced a three-line whip on Conservative MPs to pass a motion that the investigation was \"clearly flawed\". After an outcry from opposition parties, the government made a U-turn and Paterson resigned.
- Partygate, involving social gatherings by Downing Street and Conservative Party staff during COVID-19 restrictions in late 2020.
### 2022 {#section_10}
- Neil Parish, Conservative MP for Tiverton and Honiton, was forced to resign in April after it was discovered that he had watched pornography in the House of Commons on at least two occasions.
- Chris Pincher scandal: The deputy chief whip of the Conservative Party, Chris Pincher, resigned on 30 June following allegations about him groping two men.`{{Cite news |date=2 July 2022 |title=Tory MP Chris Pincher suspended by party over 'drunken groping' claims |work=[[Sky News]] |url=https://news.sky.com/story/tory-mp-chris-pincher-suspended-by-party-over-drunken-groping-claims-12643558}}`{=mediawiki}
Further allegations of harassment emerged against Pincher, along with claims that prime minister Boris Johnson had already been informed of his behaviour. The incremental effect of this and other recent controversies led to the resignation of 59 Conservative politicians, including Rishi Sunak as chancellor and Sajid Javid as health secretary. This in turn led to Boris Johnson committing to resign as leader of the Conservative Party, and thus as prime minister when his replacement as leader had been chosen by his party.
### 2023 {#section_11}
- Operation Branchform: A Police Scotland investigation into possible fundraising fraud in the Scottish National Party begun in 2021 came to a head in 2023 with the arrests of SNP Chief Executive Peter Murrell, Party Treasurer Colin Beattie, and former Party Leader and First Minister of Scotland Nicola Sturgeon over a three-month period. Both Peter Murrell and Colin Beattie resigned their party roles immediately after their arrests. The highly-publicised arrests and perceived delays in bringing the investigation (which continued for nearly two more years) to a conclusion led both the SNP\'s supporters and its opponents to claim that the investigation had been politicised. Murrell was ultimately charged with embezzlement in 2024 and appeared in court for the first time in March 2025.
- Michael Matheson iPad scandal: Scottish Health Secretary Michael Matheson incurred nearly £11,000 in roaming charges after taking a Scottish Parliamentary iPad on a family holiday to Morocco. When this was publicised, Matheson initially attempted to claim the charges as a parliamentary expense, but later admitted that the iPad had been used by his sons to stream football matches and agreed to personally pay back the full cost of the data roaming bill. Following an investigation by the Scottish Parliament Corporate Body, Matheson resigned as Health Secretary in February 2024. Matheson was subsequently banned from Holyrood for 27 days and had his salary withdrawn for 54 days, the heaviest sanction ever given to an MSP.
### 2024 {#section_12}
- In March 2024, *The Guardian* reported that Frank Hester, the largest ever donor to the Conservative Party, had made comments in a 2019 company meeting about the MP Diane Abbott. The paper reported that he said that looking at Abbott makes you \"want to hate all black women\" and that she \"should be shot\", as well as making comments about a female executive from another organisation, saying \"it would be much better if she died\", and about his own Asian female employees, saying \"we take the piss out of the fact that all our Chinese girls sit together in Asian corner\".
- Election betting scandal: Following the scheduling of the 2024 general election for 4 July, it was discovered that Craig Williams, Parliamentary Private Secretary to Prime Minister Rishi Sunak, had placed a £100 bet on the election being in July. Further investigation uncovered multiple similar bets made by Conservative Party members and MPs, including cabinet minister Alister Jack, as well as police officers on Sunak\'s protection detail. The Gambling Commission ultimately charged Williams and fourteen other people with criminal offences under the Gambling Act 2005.
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## 2020s {#s_12}
### 2025 {#section_13}
- Tulip Siddiq, City Minister and Economic Secretary to the Treasury, was implicated in corruption investigations into her aunt, the deposed Prime Minister of Bangladesh Sheikh Hasina. Siddiq was accused of helping her aunt to embezzle £3.9 billion during the construction of a nuclear power plant in 2013. She ultimately resigned on 14 January
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# British Steel (1967–1999)
**British Steel** was a major British steel producer. It originated from the nationalised **British Steel Corporation** (**BSC**), formed in 1967, which was privatised as a public limited company, **British Steel plc**, in 1988. It was once a constituent of the FTSE 100 Index. The company merged with Koninklijke Hoogovens to form Corus Group in 1999.
## History
The Labour Party came to power at the 1945 general election, pledging to bring several industries into state ownership. In 1946, it put the first steel development plan into practice with the aim of increasing capacity. It passed the Iron and Steel Act 1949, which meant nationalisation of the industry, as the government bought out the shareholders, and created the Iron and Steel Corporation of Great Britain. American Marshall Plan aid in 1948--50 reinforced modernisation efforts and provided funding for them. However, the nationalisation was reversed by the Conservative government after 1952.
The industry was re-nationalised in 1967 under another Labour government, becoming British Steel Corporation (BSC). But by then, 20 years of political manipulation had left companies, such as British Steel, with serious problems: a complacency with existing equipment, plants operating below full capacity (hence the low efficiency), poor-quality assets, outdated technology, government price controls, higher coal and oil costs, lack of funds for capital improvement, and increasing competition on the world market.
By the 1970s, the Labour government\'s main goal for the declining industry was to keep employment high. Since British Steel was a major employer in depressed regions, it was decided to keep many mills and facilities operating at a loss. In the 1980s, Conservative Prime Minister Margaret Thatcher re-privatised BSC as British Steel. Under private control, the company dramatically cut its workforce and underwent a radical reorganisation and massive capital investment to again become competitive in the world marketplace.
Alasdair M. Blair (1997), Professor of International Relations and Head of the Department of Politics and Public Policy at De Montfort University, has explored the history of British Steel since the Second World War to evaluate the impact of government intervention in a market economy. He suggests that entrepreneurship was lacking in the 1940s; the government could not persuade the industry to upgrade its plants. For generations, the industry had followed a piecemeal growth pattern that proved relatively inefficient in the face of world competition.
### Nationalisation
BSC was formed from the assets of former private companies which had been nationalised, largely under the Labour government of Harold Wilson, on 28 July 1967. Wilson\'s was the second attempt at nationalisation; the post-war government of Clement Attlee had created the Iron and Steel Corporation of Great Britain in 1951 taking public ownership of 80 companies but this had been largely reversed by the following Conservative governments of the 1950s with only Britain\'s largest steel company, Richard Thomas and Baldwins, remaining in public ownership.
BSC was established under the Iron and Steel Act 1967, which vested in the corporation the shares of the fourteen major UK-based steel companies then in operation, being:
- David Colville & Sons;
- Consett Iron Company Ltd;
- Dorman Long & Company Ltd;
- English Steel Corporation Ltd;
- GKN Steel Company Ltd;
- John Summers & Sons Ltd;
- The Lancashire Steel Corporation Ltd;
- The Park Gate Iron and Steel Company Ltd;
- Richard Thomas and Baldwins Ltd;
- Round Oak Steelworks Ltd;
- South Durham Steel & Iron Company Ltd;
- The Steel Company of Wales Ltd;
- Stewarts & Lloyds, Ltd; and
- The United Steel Companies Ltd.
At the time of its formation, BSC comprised around ninety per cent of the UK\'s steelmaking capacity; it had around 268,500 employees and around 200 wholly or partly-owned subsidiaries based in the United Kingdom, Australia, New Zealand, Canada, Africa, South Asia, and South America.
Dorman Long, South Durham and Stewarts and Lloyds had merged as British Steel and Tube Ltd before vesting took place. BSC later arranged an exchange deal with Guest, Keen and Nettlefolds Ltd (GKN), the parent company of GKN Steel, under which BSC acquired Dowlais Ironworks at Merthyr Tydfil and GKN took over BSC\'s Brymbo Steelworks near Wrexham.
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# British Steel (1967–1999)
## History
### Restructuring
According to Blair (1997), British Steel faced serious problems at the time of its formation, including obsolescent plants; plants operating under capacity and thus at low efficiency; outdated technology; price controls that reduced marketing flexibility; soaring coal and oil costs; lack of capital investment funds; and increasing competition on the world market. By the 1970s, the government adopted a policy of keeping employment high in the declining industry. This especially impacted BSC since it was a major employer in a number of depressed regions.
One of the arguments made in favour of nationalisation was that it would enable steel production to be rationalised. This involved concentrating investment on major integrated plants, placed near the coast for ease of access by sea, and closing older, smaller plants, especially those that had been located inland for proximity to coal supplies.
From the mid-1970s, British Steel pursued a strategy of concentrating steelmaking in five areas: South Wales, South Yorkshire, Scunthorpe, Teesside and Scotland. This policy continued following the Conservative victory at the 1979 general election. Other traditional steelmaking areas faced cutbacks. Under the Labour government of James Callaghan, a review by Lord Beswick had led to the reprieve of the so-called \'Beswick plants\', for social reasons, but subsequent governments were obliged under EU rules to withdraw subsidies. Major changes resulted across Europe, including in the UK:
- At Consett, the closure of the British Steel works in 1980 marked the end of steel production in Derwent Valley and the sharp decline of the area.
- At Corby, the closure of the former Stewarts & Lloyds site in the early-1980s saw the loss of 11,000 jobs, leading to an initial unemployment rate of over 30%.
- In Wales, works at East Moors (Cardiff) closed in 1978.
- Shotton closure of the heavy end with the loss of over 6,000 jobs.
- In Scotland, Western Europe\'s largest hot strip steel mill Ravenscraig steelworks, near Motherwell, North Lanarkshire, was closed by British Steel in 1992, leading to high levels of unemployment in the area. It also led to the closure of several local support and satellite businesses, such as the nearby British Steel Clydesdale Works in Mossend, Clyde Alloy in Netherton and equipment maker Anderson Strathclyde. Demolition of the site\'s landmark blue gasometer in 1996, and the subsequent cleanup operation, has created the largest brownfield site in Europe. This huge area between Motherwell and Wishaw is in line to be transformed into the new town of Ravenscraig, a project partly funded by Corus.
### Privatisation
The Conservative manifesto for the 1987 general election noted that \"British Steel has more than doubled its productivity since 1979 and made a profit last year for the first time in over ten years.\"
Following Margaret Thatcher\'s re-election, on 3 December 1987 the Conservative government formally announced in a statement by Kenneth Clarke, Minister of State for Trade and Industry, that it intended to privatise the British Steel Corporation.
On 5 September 1988 the assets, rights and liabilities of British Steel Corporation were transferred to British Steel plc, registered under the Companies Act as company number 2280000, by the British Steel Act 1988.
The government retained a special share which carried no voting rights but until 31 December 1993, permitted the government to stop any one party controlling more than 15% of the shares.
British Steel employees were given a free allocation of shares, and offered two free shares for each they purchased up to £165, discounted shares up to £2,200, and priority on applying for shares up to £10,000.
Dealing in shares opened on the London Stock Exchange on 5 December 1988.
### Post-privatisation {#post_privatisation}
The privatised company later merged with the Dutch steel producer Koninklijke Hoogovens to form Corus Group on 6 October 1999. Corus itself was taken over in March 2007 by the Indian steel operator Tata Steel.
## Chairmen
- Lord Melchett (1967--1973)
- Monty Finniston (1973--1976)
- Charles Villiers (1976--1980)
- Ian MacGregor (1980--1983)
- Robert Haslam (1983--1986)
- Robert Scholey (1986--1992)
- Sir Brian Moffat (1992--1999)
Ian MacGregor later became famous for his role as Chairman of the National Coal Board during the UK miners\' strike (1984--1985). During the strike the \"Battle of Orgreave\" took place at British Steel\'s coking plant.
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# British Steel (1967–1999)
## Sponsorships
In 1971 British Steel sponsored Sir Chay Blyth in his record-making non-stop circumnavigation against the winds and currents, known as \'The Impossible Voyage\'. In 1992 they sponsored the British Steel Challenge, the first of a series of \'wrong way\' races for amateur crews.
British Steel had agreed a sponsorship deal with Middlesbrough Football Club during the 1994--95 season, with a view to British Steel-sponsored Middlesbrough shirts making their appearance the following season. But the sponsorship deal was terminated before it commenced after it was revealed that British steel only made up a tiny fraction of steel used in construction of the stadium, and that the bulk of the steel had been imported from Germany.
## In popular culture {#in_popular_culture}
The English rock band XTC mentioned British Steel in their 1979 song Making Plans for Nigel.
The heavy metal band Judas Priest named their 1980 album *British Steel* after the British Steel Corporation. Lead singer Rob Halford explained in an interview that the \'sounds of heavy metal\' have been with him since childhood, due to the close proximity of the BSC plant where he grew up
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# Broch
In archaeology, a **broch** `{{IPAc-en|b|r|ɒ|x}}`{=mediawiki} is an Iron Age drystone hollow-walled structure found in Scotland. Brochs belong to the classification \"complex Atlantic roundhouse\" devised by Scottish archaeologists in the 1980s.
Brochs are roundhouse buildings found throughout Atlantic Scotland. The word broch is derived from the Lowland Scots \'brough\', meaning fort. In the mid-19th century, Scottish antiquaries called brochs \'burgs\', after Old Norse borg, with the same meaning. Brochs are often referred to as dùns in the west, and they are the most spectacular of a complex class of buildings found in northern Scotland. There are approximately 571 candidate broch sites throughout the country, according to the Royal Commission on the Ancient and Historical Monuments of Scotland.
The origin of brochs is still subject to ongoing research. While most archaeologists believed 80 years ago that brochs were built by immigrants, there is now little doubt that the hollow-walled broch tower was an invention in what is now Scotland. The first brochs may have been built circa 300 BCE, and there is evidence to suggest that they were used primarily for defensive or offensive purposes.
The distribution of brochs is centred on northern Scotland, with the densest concentrations found in Caithness, Sutherland, and the Northern Isles. A few examples occur in the Scottish Borders and on the west coast of Dumfries and Galloway, and near Stirling. The original interpretation of brochs was that they were defensive structures, places of refuge for the community and their livestock. They were sometimes regarded as the work of Danes or Picts, and from the 1930s to the 1960s, archaeologists regarded them as castles where local landowners held sway over a subject population.
However, the castle theory fell from favour among Scottish archaeologists in the 1980s, due to a lack of supporting archaeological evidence. These archaeologists suggested defensibility was never a major concern in the siting of a broch, and argued that they may have been the \"stately homes\" of their time, objects of prestige and very visible demonstrations of superiority for important families. Once again, however, there is a lack of archaeological proof for this reconstruction, and the sheer number of brochs makes it problematic. The article concludes by stating that the purpose of brochs may have been a combination of defensive, offensive, and symbolic functions.
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# Broch
## Origin and definition {#origin_and_definition}
The word *broch* is derived from Lowland Scots \'brough\', meaning (among other things) fort. In the mid-19th century Scottish antiquaries called brochs \'burgs\', after Old Norse **borg**, with the same meaning. Place names in Scandinavian Scotland such as Burgawater and Burgan show that Old Norse **borg** is the older word used for these structures in the north. Brochs are often referred to as *dùn* in the west. Antiquarians began to use the spelling *broch* in the 1870s.
A precise definition for the word has proved elusive. Brochs are the most spectacular of a complex class of roundhouse buildings found throughout Atlantic Scotland. The Shetland Amenity Trust lists about 120 sites in Shetland as candidate brochs, while the Royal Commission on the Ancient and Historical Monuments of Scotland (RCAHMS) identifies a total of 571 candidate broch sites throughout the country. Researcher Euan MacKie, using a restricted definition, has proposed a much smaller total for Scotland of 104.
The origin of brochs is a subject of continuing research. Eighty years ago most archaeologists believed that brochs, usually regarded as the \'castles\' of Iron Age chieftains, were built by immigrants who had been pushed northward after being displaced first by the intrusions of Belgic tribes into what is now southeast England at the end of the 2nd century BC and later by the Roman invasion of southern Britain beginning in AD 43. Yet there is now little doubt that the hollow-walled broch tower was an invention in what is now Scotland; even the kinds of pottery found inside them that most resembled south British styles were local hybrid forms.
The first of the modern review articles on the subject (MacKie 1965) did not, as is commonly believed, propose that brochs were built by immigrants, but rather that a hybrid culture formed from the blending of a small number of immigrants with the native population of the Hebrides produced them in the 1st century BC, basing them on earlier, simpler, promontory forts. This view contrasted, for example, with that of Sir W. Lindsay Scott, who argued, following V. Gordon Childe (1935), for a wholesale migration into Atlantic Scotland of people from southwest England.
MacKie\'s theory has fallen from favour too, mainly because starting in the 1970s there was a general move in archaeology away from \'diffusionist\' explanations towards those pointing to exclusively indigenous development. Meanwhile, the increasing number -- albeit still pitifully few -- of radiocarbon dates for the primary use of brochs (as opposed to their later, secondary use) still suggests that most of the towers were built in the 1st centuries BC and AD. A few may be earlier, notably the one proposed for Old Scatness Broch in Shetland, where a sheep bone dating to between 390 and 200 BC has been reported.
The other broch claimed to be substantially older than the 1st century BC is Crosskirk in Caithness, but a recent review of the evidence suggests that it cannot plausibly be assigned a date earlier than the 1st centuries BC/AD.
## Distribution
The distribution of brochs is centred on northern Scotland. Caithness, Sutherland and the Northern Isles have the densest concentrations, but there are many examples in the west of Scotland and the Hebrides. Although mainly concentrated in the northern Highlands and the Islands, a few examples occur in the Borders (for example Edin\'s Hall Broch and Bow Castle Broch), on the west coast of Dumfries and Galloway, and near Stirling. In a c. 1560 sketch there appears to be a broch by the river next to Annan Castle in Dumfries and Galloway. This small group of southern brochs has never been satisfactorily explained.
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# Broch
## Purposes
The original interpretation of brochs, favoured by 19th-century antiquarians, was that they were defensive structures, places of refuge for the community and their livestock. They were sometimes regarded as the work of Danes or Picts. From the 1930s to the 1960s, archaeologists such as V. Gordon Childe and later John Hamilton regarded them as castles where local landowners held sway over a subject population.
The castle theory fell from favour among Scottish archaeologists in the 1980s, due to a lack of supporting archaeological evidence. These archaeologists suggested defensibility was never a major concern in the siting of a broch, and argued that they may have been the \"stately homes\" of their time, objects of prestige and very visible demonstrations of superiority for important families (Armit 2003). Once again, however, there is a lack of archaeological proof for this reconstruction, and the sheer number of brochs, sometimes in places with a lack of good land, makes it problematic.
Brochs\' close groupings and profusion in many areas may indeed suggest that they had a primarily defensive or even offensive function. Some of them were sited beside precipitous cliffs and were protected by large ramparts, artificial or natural: a good example is at Burland near Gulberwick in Shetland, on a clifftop and cut off from the mainland by huge ditches. Often they are at key strategic points. In Shetland they sometimes cluster on each side of narrow stretches of water: the Broch of Mousa, for instance, is directly opposite another at Burraland in Sandwick. In Orkney there are more than a dozen on the facing shores of Eynhallow Sound, and many at the exits and entrances of the great harbour of Scapa Flow. In Sutherland quite a few are placed along the sides and at the mouths of deep valleys. Writing in 1956 John Stewart suggested that brochs in Shetland were forts put up by a military society to scan and protect the countryside and seas.
Finally, some archaeologists consider broch sites individually, doubting that there ever was a single common purpose for which every broch was constructed. There are differences in the positions, dimensions and likely status of broch in the various areas in which brochs are found. For example, the broch \"villages\" which occur at a few places in Orkney have no parallel in the Western Isles.
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# Broch
## Structures
thumb\|upright=1.2\|Broch of Mousa in the Shetland Isles
Generally, brochs have a single entrance with bar-holes, door-checks and lintels. There are mural cells and there is a scarcement (ledge), perhaps for timber-framed lean-to dwellings lining the inner face of the wall. Also there is a spiral staircase winding upwards between the inner and outer wall and connecting the galleries. Brochs vary from 5 to in internal diameter, with 3 m walls. On average, the walls only survive to a few metres in height. There are five extant examples of towers with significantly higher walls: Dun Carloway on Lewis, Dun Telve and Dun Troddan in Glenelg, Mousa in Shetland and Dun Dornaigil in Sutherland, all of whose walls exceed 6.5 m in height.
Mousa\'s walls are the best preserved and are still 13 m tall; it is not clear how many brochs originally stood so high. A frequent characteristic is that the walls are galleried: with an open space between, the outer and inner wall skins are separate but tied together with linking stone slabs; these linking slabs may in some cases have served as steps to higher floors. It is normal for there to be a cell breaking off from the passage beside the door; this is known as the guard cell. It has been found in some Shetland brochs that guard cells in entrance passageways are close to large door-check stones. Although there was much argument in the past, it is now generally accepted among some archaeologists that brochs were roofed, perhaps with a conical timber framed roof covered with a locally sourced thatch. The evidence for this assertion is still very scanty, although excavations at Dun Bharabhat, Lewis, may support it. The main difficulty with the interpretation continues to be identifying potential sources of structural timber, though bog and driftwood may have been sources.
Very few of the brochs on the islands of Orkney and Shetland have cells on the ground floor. Most brochs have scarcements (ledges) which may have allowed the construction of a wooden first floor (spotted by the antiquary George Low in Shetland in 1774), and excavations at Loch na Berie on the Isle of Lewis may show signs of a further, second floor (e.g. stairs on the first floor, which head upwards). Some brochs such as Dun Dornaigil and Culswick in Shetland have unusual triangular lintels above the entrance door.
thumb\|upright=1.2\|Dun Telve Broch, Glenelg
As in the case of Old Scatness in Shetland (near Jarlshof) and Burroughston on Shapinsay, brochs were sometimes located close to arable land and a source of water (some have wells or natural springs rising within their central space). Sometimes, on the other hand, they were sited in wilderness areas (e.g. Levenwick and Culswick in Shetland, Castle Cole in Sutherland). Brochs are often built beside the sea (Carn Liath, Sutherland); sometimes they are on islands in lochs (e.g. Clickimin in Shetland).
About 20 Orcadian broch sites include small settlements of stone buildings surrounding the main tower. Examples include Howe, near Stromness, Gurness Broch in the north west of Mainland, Orkney, Midhowe on Rousay and Lingro near Kirkwall (destroyed by a farmer in the 1980s). There are \"broch village\" sites in Caithness, but elsewhere they are unknown.
Most brochs are unexcavated. The end of the broch building period seems to have come around AD 100--200. Those that have been properly examined show that they continued to be in use for many centuries, with the interiors often modified and changed, and that they underwent many phases of habitation and abandonment.
## Heritage status {#heritage_status}
The Crucible of Iron Age Shetland\'s Mousa, Old Scatness and Jarlshof sites are on the United Kingdom \"Tentative List\" of possible nominations for the UNESCO World Heritage Programme list of sites of outstanding cultural or natural importance to the common heritage of humankind. This list, published in July 2010, includes sites that may be nominated for inscription over the next 5--10 years.
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# Broch
## New broch planned {#new_broch_planned}
The Caithness Broch Project was set up in 2013 as a project in experimental archaeology to build a broch using traditional techniques such as drystone walling. Purposes of the project include possible insights into the purpose of brochs, preservation of local skills in techniques such as drystone wall building, and to attract tourists. `{{As of|2022}}`{=mediawiki} a site had not been acquired, and the funding required, estimated at £1m--£3m, had not yet been arranged
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# The Beano
***The Beano*** (formerly ***The Beano Comic***) is a British anthology comic magazine created by Scottish publishing company DC Thomson. Its first issue was published on 30 July 1938, and it published its 4000th issue in August 2019. Popular and well-known comic strips and characters include *Dennis the Menace*, *Minnie the Minx*, *The Bash Street Kids*, *Roger the Dodger*, *Billy Whizz*, *Lord Snooty and His Pals*, *Ivy the Terrible*, *General Jumbo*, *Jonah*, and *Biffo the Bear*.
*The Beano* was planned as a pioneering children\'s magazine that contained mostly comic strips, in the style of American newspaper gag-a-days, as opposed to the more text-based story papers that were immensely popular before the Second World War. In the present, its legacy is its misbehaving characters, escapist tales and anarchic humour with an audience of all ages. *Beano* is a multimedia franchise with spin-off books and Christmas annuals, a website, theme park rides, games, cartoon adaptations, and a production company.
*The Beano* is the best-selling comic magazine outside Japan, having sold over 2 billion copies since its inception, and is the world's longest-running comic magazine, having been run on a weekly basis since 1938, alongside its sister comic *The Dandy* until 2012.
It has had three characters as the mascot throughout the years: Big Eggo (1938--1948), Biffo the Bear (1948--1974), and the current, Dennis the Menace and Gnasher (1974--present).
## History
### Creation (1920s--1939) {#creation_1920s1939}
Throughout the 1920s, DC Thomson dominated the British comics industry. Dubbed \"the big five\", the publisher\'s most successful comics were *Adventure* (1921), *The Rover* and *The Wizard* (1922), *The Skipper* (1930) and *The Hotspur* (1933).`{{refn|group=Note|Original contender was 1924's ''The Vanguard'', which discontinued two years later.}}`{=mediawiki} These were weekly issued boys\' magazines for preteen males, containing anthologies by DC Thomson\'s creator staff designed in various formats and genres. They became popular throughout the United Kingdom, notably in English industrial cities, helped through the company\'s ability to view sales and promotions in the areas much more easily than the rival publishers in London. Although many were about \"super men\" the young readers could idolise, the rest of the stories would be comic strips inspired by the gag-a-day strips in American newspapers full of stylised characters, slapstick and puns.
Overseeing the magazines was the Managing Editor of Children\'s Publications, R. D. Low, who first joined the company in 1913. Almost a decade into the big five\'s success, the stories shifted to comedic and included more comic strips, which gave Low an idea of creating a new \"big five\" which focused on the funnies more than drama. The suggestion was approved; editors Bill Blain and (sub-editor) Albert Barnes of *The Wizard* and *The Hotspur*, respectively, joined Low\'s project. The new team placed a newspaper advertisement into *The Daily Telegraph*`{{refn|group=Note|''[[The Daily Telegraph]]'' had a reputation of being the best news source to find the artist jobs in the world.}}`{=mediawiki} asking for artists and/or comic ideas. With the help of the advertisement responses and employed artists at DC Thomson, *The Dandy* was published in 1937, the New Big Five\'s first member. For *The Beano* (initially called \"The Beano Comic\" until issue 412), Low received comic strip suggestions by Reg Carter, an English illustrator in Sussex who had created funnies for several British comics and designed humorous postcards. After an in-person interview, Low and Carter planned the front cover for *The Beano*{{\'s}} first issue, eventually creating the character Big Eggo (originally named Oswald the Ostrich). It would be in colour whilst the inside of the magazine would be black and white,`{{refn|group=Note|[[Wee Peem]] also had slight red colouring.}}`{=mediawiki} a tactic used for *The Dandy*{{\'s}} first issue (black and white stories inside, colourful Korky the Cat strip on the front). Joining the *Big Eggo* strip would be many funnies, such as Hugh McNeill\'s *Ping the Elastic Man*, James Jewell\'s *Wee Peem*, Allan Morley\'s *Big Fat Joe*, Eric Roberts\' *Rip Van Wink*, Dudley D. Watkins\' *Lord Snooty and His Pals*, and Roland Davies\' *Contrary Mary*. Despite the aim to make a new comic series full of American-inspired comic strips, *The Beano* also contained short stories, serial fiction and adventure stories similar to the Big Five\'s magazines; *Morgyn the Mighty* was previously in *The Rover*. *Tin-Can Tommy* and *Brave Captain Kipper* were reprints, co-produced by the Italian art agency Torelli Bros.
Worth 2d with a free prize of a \"whoopee mask\", issue 1 of *The Beano* was released on 26 July 1938 for the 30th, selling roughly 443,000 copies. Like *The Dandy*, its name is from a Low-led DC Thomson office party called The DB Club (The Dandy Beano Club). DC Thomson had several office party clubs that hosted different types of staff gatherings to choose from (e.g. The Prancers would hike hills), but Low\'s DB Club preferred playing golf and dining throughout Dundee. The two magazines also followed the one-word titles of other comics by rival companies, such as Amalgamated Press\' *Crackers*, *Sparkler*, *Puck* and some books from its *Union Jack* series (*The Marvel*, *The Magnet* and *The Gem*); and Target Publications\' *Chuckler*, *Rattler* and *Dazzler*. *Beano* editor-in-chief was George Moonie, former sub-editor of *The Wizard*, who would be editor until the summer of 1959. He later explained DC Thomson was a competitive company that wanted to make the best children\'s literature in the United Kingdom, but there was also competition within itself as *Beano* offices was determined to beat *The Dandy*{{\'s}} popularity.
### World War Two, reaching million sales (1939--1945) {#world_war_two_reaching_million_sales_19391945}
Drastic changes occurred behind the scenes of *The Beano* during the Second World War: George Moonie and editing partner Ron Fraser left to join the Royal Marines and Air Force respectively, both not returning until c. 1946. Stuart Gilchrist became sole editor-in-chief after Moonie\'s other sub-editor Freddie Simpson became ill and resigned. Contact was also lost with Torelli Bros. so in-house creations of *Tin-Can Tommy* began from issue 69 by Sam Fair. Paper rationing caused the rest of Low\'s New Big Five to be cancelled (it stopped at three published, the third member being *The Magic Comic* (1939), which ended with 80 issues in 1941), and *The Beano* to fluctuate its page count instead of its usual 28. Eventually, *The Beano* became a fortnightly magazine (alternating with The Dandy comic) until 23 July 1949.
Comic strips would encourage readers to help their parents and other adults with the war effort, and to be optimistic about the war\'s outcome. New comic strips mocked Mussolini and propagandist William Joyce, *Lord Snooty and His Pals* stories would be about the protagonists outsmarting the Axis leaders, and other stories would be about characters recycling paper. *Big Eggo* front covers were often about Eggo pranking servicemen during the Blitz, and Pansy Potter received a medal for single-handedly capturing a Nazi U-boat. Issue 192 would debut a 16-part prose story about a boy and his mother being evacuated to the United States and becoming the enemy of a Chicago gangster\'s widow.
Issues published weekly every Tuesday in 1938,`{{refn|group=Note|The date of the Saturday of that week is written on the front.<ref name="issue1"/>}}`{=mediawiki} and when the magazine changed distribution to every two weeks, the day remained unchanged. From issue 366, the day changed to Friday until issue 375 which began the Thursday publication day schedule.
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## History
### Post-war changes (1945--1988) {#post_war_changes_19451988}
December 1945 marked a milestone: issue 272 became the first *Beano* issue to sell over a million copies. The end of the war also ushered in a new era for the comic, debuting superhero Jack Flash, the debut of Biffo the Bear as new cover star and a new generation of trouble-making kids: Dennis the Menace, Minnie the Minx, The Bash Street Kids, and Roger the Dodger. DC Thomson also introduced new comic magazines like *The Beezer* and *The Topper* that a few *Beano* artists also created characters and stories for.
After the war saw a drift away from text stories and adventure comics, with the last text story published in 1955; adventure comics lasted longer with 1975 being the last year to feature them as *General Jumbo*{{\'s}} eighth series drew to a close in issue 1734.
George Moonie resigned as editor-in-chief in 1959 to develop comics for girls. Sub-editor of *The Beezer* Harry Cramond succeeded Moonie until retiring in 1984, described as the most influential editor in *The Beano*{{\'s}} history. He oversaw new merchandising, high sales,`{{refn|group="Note"|''The Beano'' eventually passed ''The Dandy''{{'s}}`{=mediawiki} sales by 100,000 copies. but both magazines sometimes sold up to four million issues per week.}} and the thousandth and two thousandth issues. DC Thomson\'s *Beano* offices featured on documentary television and Cramond\'s successor Euan Kerr guest-starred on television for the magazine\'s 50th anniversary.
### Move to full colour (1988--present) {#move_to_full_colour_1988present}
*The Beano* began to advertise outside of DC Thomson\'s products in 1988 in order to keep both it and *The Dandy* \"pocket money\" cheap, beginning with issue 2407. Issue 2674 in 1993 was the first issue to feature every page in colour.
A notable revamp was the 50th birthday issue, which had an abnormally larger page count with more coloured sections and printed on wider sheets. A decade later, issues gained eight extra pages with computer-based art. In the 21st century, there were seven changes within a five-year span: logo updates, fonts assigned for certain design roles,`{{refn|group="Note"|New headline fonts were introduced (CCZoinks), circa 2007; the balloon font was also changed to Cloudsplitter by [[Blambot]].}}`{=mediawiki} and the magazine started using glossy paper.
From issue 3442 in 2008 (and as of 2020), the day the comic was released was changed to Wednesday.
Outside of the magazine, *Beano*{{\'}}s brand expanded into a multimedia franchise. Theme park tie-ins, a website, spin-off magazines, and animated television programmes starring the popular comic characters (several for Dennis the Menace) became common, keeping *The Beano* in popular culture. The turn of the millennium began a sales decline and led to friendly rival *The Dandy* being discontinued in 2012. Eventually, *The Beano* recovered after the creation of its magazine subscription service, which also shipped internationally.
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# The Beano
## Stories
Plots and dialogue are written into a script by an (often) uncredited DC Thomson writer, a formerly common practice for DC Thomson magazines. Uncredited artists assigned to a strip(s) will design all its stories into a \"series\" that the chief editor will arrange into an order to publish for each issue. Strips are sometimes ghostwritten by other artists who imitate the original designer\'s style, which is helpful if artists retire or die unexpectedly, otherwise the strip is discontinued. \"When I started I was drawing two pages a week and thinking \'Phew, that\'s quite a lot\'. Now I do 10 or 12 pages a week. You have to do more all the time to stay where you are,\" explained Nigel Parkinson. From March 2016, authors and illustrators are now credited in issues.
There have been over a thousand stories throughout the magazine\'s history told through various ways. Since November 1975, the magazine has contained only comic strips in the style of American newspaper \"funnies\", but it began with other genres. The last genre to leave *Beano* was adventure stories: short tales eleven-pictures long in text comics format. The stories were either dramatic or dramedies, but heavily featured hobbies and interests young boys had (war and the military, hunting, sailing, jungle men). They also stood out because the illustrations of backgrounds, animals and human characters were photorealistic. Although artists like Dudley D. Watkins drew for a few series, the most prolific illustrator was Irish artist Paddy Brennan, who notably drew for *The Daring Deeds of Sinbad the Sailor*, *Red Rory of the Eagles* and *General Jumbo* in the 1950s. Comic adventure stories were a hybrid: adventure stories presented as a comic strip.
Prose stories were a page of text with an illustration at the top. Some stories were about animals with artwork by former Big Five illustrator Richard \"Toby\" Baines, but the longest-running prose character in the magazine\'s history was Prince Ivor, who first starred in *Follow the Secret Hand*. The last prose story to appear was *Ace From Space* in 1955.
Although comic strips have featured in *The Beano* since issue 1, their contents has changed throughout. Anthropomorphic animals were common stars that would partake in human activities, and the punchlines occurred from the failures to do so. Misbehaving children showed most popular with *Lord Snooty and His Pals* becoming the first longest-running strip when it concluded in 1991, but the most well known that continue to appear in issues are *Dennis the Menace*, *Minnie the Minx*, *The Bash Street Kids*, and *Roger the Dodger*. Some adult-starring characters also misbehaved but they were usually portrayed as incompetent, notably Jonah. In the late 20th century, merging comic strip characters in the same vicinity became common in the franchise, such as the video game *Beanotown Racing*, but characters living together in \"Beanotown\" became a prominent feature of comic strips into the present.`{{r|Beanotown1|Beanotown2}}`{=mediawiki}`{{refn|group="Note"|Notably, Lord Snooty lives in Bunkerton, General Jumbo lives in Dinchester, Billy the Cat lives in Burnham, etc. Lord Snooty's returns in the 21st century retcons Bunkerton as a district in Beanotown.}}`{=mediawiki}
Due to the initial target audience of *The Beano* being schoolboys, masculine interests, hobbies, and values dominated issues constantly. Aside from aforementioned adventure stories and comedic characters, there were cowboys, aliens, kings, the supernatural, fantasy creatures (and talking animals), and men whose lifestyle or jobs require physical strength (despite the story making their careers incidental). *The Beano* alternated between mocking or idolising these characters through story formats; wealthy characters causing mischief, caring about their families or being shown underprivileged lives made the working-class audience relate and sympathise with them. Female characters were usually supporting a male character, joint protagonist with a male character, or the antagonist. Prose stories starring girls and women were about the protagonist searching out the truth to a secret, usually over a friend\'s/family disappearance, or they were witches cursing or tormenting the male protagonists. Female comic characters were also in supporting roles with or join-protagonist with a male character, but the starring characters notably had binary stereotypical traits: drawn as tall and flowy, *Swanky, Lanky Liz* is obsessed with fashion and makeup and acts vain and snobbish, whereas Pansy Potter, Minnie the Minx and Toots from *The Bash Street Kids* share the round-faced and snub-nosed art style of the boys in their stories and are unruly tomboys (in Pansy Potter\'s case, showcases the strength she inherited from her father). Non-White characters starred in their stories either set in Africa, Asia, or South America, or were about the character adapting to a new life in the United Kingdom.
Stories used to vary in length and layout, but in 2012, *The Beano* debuted a chapter called Funsize Funnies where shorter comic strips shared some pages. In some instances, these extremely short strips were brand new (*Stunt Gran*, *BamBeanos*, *BSK CCTV*, *Gnash Gnews*, *Winston*), but others were tiny reboots of older comic strips that the new audience could not recall reading before. Quiet reboots included *Simply Smiffy* (cancelled 1987), *Rasher* (cancelled 1995), *Little Plum* (cancelled 2007), *Les Pretend* (cancelled 2007), *Baby Face Finlayson* (cancelled 2005), *Biffo the Bear* (cancelled 1999), *Pansy Potter* (cancelled 1993), and *Lord Snooty* (cancelled 1991).
### Crossovers
*The Beano* allows its characters from different strips to interact with each other. Reprinting old stories or redistributing characters into other magazines is common throughout DC Thomson\'s history, as if the stories are set in the same universe. The *Lord Snooty* series discontinued old characters and replaced them with *Beano* strip characters of the past; *Dennis the Menace* featured in DC Thomson\'s *Champ* magazine in the mid-1980s and *The Weekly News* tabloid-magazine for four years in the 1950s. *Morgyn the Mighty*, *Tricky Dicky*, *Bananaman* and *Corporal Clott* were stories previously from *The Rover*, *The Topper*, *Nutty* and *The Dandy*, respectively, whereas one of Gnasher\'s puppies had her own strip in *The Beezer and Topper* and *Jackie* magazine.
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# The Beano
## Stories
### Anniversary issues {#anniversary_issues}
Along with guest editors, anniversary issues are frequently contained with crossovers. The 2000th issue had the \"Hall of Fame\" strip which showed framed portraits of characters from the past, and issue 3443\'s *Fred\'s Bed* featured Fred crawling under his bed and time travelling through the magazine\'s comic strips. For the 80th anniversary, issue 3945 was guest edited by actor-turned children\'s author David Walliams and had a large crossover story about Bash Street School opening the Beanotown\'s 1938 time capsule and discovering a map, which leads to robots and a giant tentacle monster breaking out to attack the residents. There was also a flashback panel of the time capsule being sealed which featured a handful of comic strip characters from the first issue, later helping the present day characters discover how to defeat the tentacle monster, named Simon. Issue 4000\'s crossover was a time travel story where the Beanotown characters of the present helped their future selves save the world.
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# The Beano
## Creators
### Chief Editor history {#chief_editor_history}
As of 2020, there have been seven official chief editors:
- George Moonie (1938--1939, c. 1946--1959)
- Harold Cramond (1959--1984)
- Euan Kerr (1984--2006)
- Alan Digby (2006--2011)
- Michael Stirling (2011--2012)
- Craig Graham (2012--2016)
- John Anderson (2016--present)
Temporary chief editors:
- Stuart Gilchrist (1939--c. 1946) stood in as editor when George Moonie joined the Navy for World War Two.
- Dick and Dom (2006) edited issue 3311 and chose their favourite strips from the available 2005 waiting list.
- Nick Park (2008) edited issue 3443 to celebrate *Beano*{{\'s}} 70th anniversary.
- Harry Hill (published 6 March 2013) edited the 2013 Red Nose Day special.
- Andy Murray (28 June 2014) edited the Wimbledon special.
- David Walliams (2018) edited issue 3945 to celebrate the 80th anniversary.
- Joe Sugg (2021) edited issue 4077 for *Dennis the Menace*{{\'s}} 70th anniversary.
- Marcus Rashford (2022) edited issue 4146 following the release of his book, *You Can Do It: How to Find Your Voice and Make a Difference.*
- Leah Williamson (2023) edited issue 4212 to celebrate *Minnie The Mix* 70th anniversary.
### Notable artists {#notable_artists}
strips, but also has writer credits for other strips.
- Leo Baxendale created The Bash Street Kids and Minnie the Minx
- Gordon Bell
- Basil Blackaller
- Paddy Brennan
- Nick Brennan
- Sid Burgon
- Reg Carter created the first cover star Big Eggo.
- James Crighton also designed the first logo.
- Wilbur Dawbarn
- Hunt Emerson
- Sam Fair created comic strips for the spin-off annuals.
- Andy Fanton
- John Geering
- Barry Glennard
- Charlie Grigg
- Harry Hargreaves
- Ken H. Harrison
- Laura Howell became the first female artist to create strips for the magazine in 2007.
- Diego Jourdan
- Malcolm Judge
- David Law
- Trevor Metcalfe
- Allan Morley
- David Mostyn
- Vic Neill
- Robert Nixon
- Gary Northfield
- David Parkins
- Nigel Parkinson is considered the *Beano* ambassador, creating up to 20 strips for different stories a week.
- Tom Paterson
- Mike Pearse
- Jim Petrie made 2000 Minnie the Minx stories.
- Dean Rankine
- Ken Reid
- Bill Ritchie
- Zoom Rockman became the youngest artist to have their work in *The Beano* at 12-years-old. His comic strips appeared exclusively in the 75th anniversary issue.
- Jon Rushby
- Cavan Scott
- Duncan Scott
- Jamie Smart
- Lew Stringer
- David Sutherland
- Kev F. Sutherland
- Dudley D. Watkins was an employee of DC Thomson who had designed stories for a variety of the company\'s magazines over a decade before *The Beano*{{\'s}} first issue. He was the original creator of *Morgyn the Mighty* during its run in *The Rover*.
- Stevie White
}}
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# The Beano
## Merchandise
From the first issue, readers have received free gifts from *The Beano*: toy masks, sweets, posters, and toys. Originally, free gifts would be attached inside the cover or strategically on the front so that it could distract the buyer from other comics next to *The Beano* on the shelves, hopefully excited for the next issue after reading it and eating/playing with the toys. Gifts were intentionally sporadic, especially during the Christmas period when families\' money would be saved for food and presents. Issue 90 would be the last issue with a gift (licorice \"black eye\") due to rationing, the next free gift being the Flying Snorter Balloon in issue 953. The most popular free gift was issue 2201\'s Gnasher Snapper, a prank toy that would make a bang sound when unfolded, and was re-gifted occasionally in later issues, as well as the 60th anniversary.
During the 25th anniversary of *Dennis the Menace*, The Dennis the Menace Fan Club was formed. The fan club was instantly popular, recalls Euan Kerr in 1984; \"The club enrolled over 2000 new members every week, well into the 90s\[.\]\" Membership was 30p, and new members received a membership card full of classified communication tactics and two badges: a red one with Dennis\' face on the front and a furry one of a googly-eyed Gnasher face---the latter was the most sought-after badge in the club\'s history. For two years, there was a tie-in agony aunt page called *Dear Dennis* (issue 1679--1767) where fan club members sent Dennis their problems that Dennis would reply to in the following issue; thousands of letters would arrive at DC Thomson per week and the authors of the messages would receive prizes. The club would be renamed The Beano Club, which ended in 2010, but had over 1.5 million members. A spin-off was introduced called Gnasher\'s Fang Club, and Gnasher would ask readers to send him stories about their pets\' adventures which could be printed into the next issue. \"The mailbag of little drawings of pets was several thousand per week,\" remembers sub-editor Morris Heggie. \"And the popularity lasted and lasted.\"
The 21st century celebrated anniversaries with more memorabilia. For *The Beano*{{\'s}} 70th birthday, DC Thomson published *The Beano Special Collectors Edition: 70 Years of Fun* (2008), and *The History of The Beano* (2008) was published by Waverly Books, both documenting the magazine\'s history; two exhibitions at the University of Dundee (*Happy Birthday, Beano!*) and The Cartoon Museum (*Beano and Dandy Birthday Bash!*) showed the public private DC Thomson artwork and the history of the magazine. For 2018, readers could buy a box for the 80th anniversary containing posters, reprints of selected older issues, and two books updating the previous documentation of the magazine\'s history, as well as *Minnie the Minx*{{\'s}} origins. Both anniversaries had tie-in museum exhibitions that also told their audiences the magazine\'s history. Limited-edition figurines from Robert Harrop were available to buy from their official website in late 2008. The 21st century also began *Beano*{{\'s}} branching into different mediums: their first website, Beanotown.com, formed in 2000, and Chessington World of Adventures opened Beanoland in the same year. Both would later discontinue but Beanotown.com would be revamped as beano.com, a website full of games, *Beano* secrets and other activities for children. Gulliver\'s Travels opened the Beano 6 Super Ride in May 2021. *The Beano* was also the face of the United Kingdom\'s 2018 Summer Reading Challenge, called Mischief Makers, which included a special Dennis the Menace novel tie-in called *Dennis the Menace and the Chamber of Mischief* by Beano artist Nigel Auchterlounie. The Dennis the Menace Fan Club was re-launched as a phone app, rebranded as The Dennis and Gnasher Fan Club, and allowed readers free membership, printable badges, and pranks. On television, the Sky Kids show *SO Beano!* aired; a TV show with special guests, children presenters, and fun and games, in a similar style to *Friday Download* and *Scrambled!*
### Annuals
The first Beano annual hardcover book was published as far back as 1939, a year after the first weekly comic was published. In 2018, it was estimated that an original first issue Beano annual in relatively good condition could fetch between £1,200 to £1,500.
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# The Beano
## Merchandise
### Spin-off comics {#spin_off_comics}
#### Comic libraries {#comic_libraries}
Since 1982 the comic, along with *The Dandy*, has also run \"Comic Library\" titles. Released monthly, these titles are a feature-length (usually about 64-page) adventure, featuring a character from the comic itself. They are available in A5 size only. In 1998, these were replaced by the *Fun Size Beano*. Fun Size Comics were discontinued in late 2010.
#### *Beano Specials* {#beano_specials}
The comic also ran A4-sized *Beano Specials* in 1987 with full coloured pages, which later were replaced by *Beano Superstars* which ran for 121 issues from 1992 to 2002. These were similar to the Comic Library series. Some of the last issues were printed versions of episodes from the 1996--1998 *Dennis and Gnasher* animated TV series. A *Beano Poster Comic* series was also printed in the early 1990s.
The Beano Specials returned in 2003, and are now published seasonally. The issues were numbered, and the first one was a Dennis and Friends special, the last a Christmas reprint special. These were replaced by BeanoMAX in early 2007.
#### BeanoMAX
On 15 February 2007, the first issue of a monthly comic entitled *BeanoMAX* was published. The sister comic features many of the same characters; however, the stories in *BeanoMAX* are written in a longer format meant for 10- to 13-year-olds. The first issue was a Comic Relief special featuring assorted celebrity guests. The magazine has been rebranded several times since 2013, and is currently known as *EPIC Magazine*.
#### *Plug*
*Plug* was a comic based on the eponymous character from *The Bash Street Kids* that began with issue dated 24 September 1977, and is notable for being the first comic to make use of rotogravure printing. The magazine similar in style to I.P.C\'s *Krazy* which had started the previous year. It contained uncharacteristically outlandish material for D C. Thomson, as well as later including celebrity appearances in the comic.
The comic revealed Plug\'s full name to be Percival Proudfoot Plugsley and also gave him a pet monkey by the name of Chumkee. Plug\'s strip was mostly drawn by Vic Neill but other artists, including Dave Gudgeon drew some later strips. Other strips included *Antchester United*, *Violent Elizabeth*, *Eebagoom*, *Hugh\'s Zoo* and *D\'ye Ken John Squeal and his Hopeless Hounds*.
The venture was unsuccessful, in part because the comic cost 9p, with the *Beano* at the time only costing 4p and most of its rivals priced similarly. It merged with *The Beezer* on 24 February 1979.
#### *Dennis and Gnasher* {#dennis_and_gnasher}
The brand new *Dennis and Gnasher* was launched separately from *The Beano* in September 2009. It coincided with their new cartoon on CBBC of the same name.
#### *BeanOLD*
44-page special issue 4062, with cover date 21 November 2020, during a lockdown in the COVID-19 pandemic had an eight-page adult pullout named *BeanOLD*, with cartoons poking fun at British politicians such as Boris Johnson and Dominic Cummings, and with appearances by Greta Thunberg, Captain Tom, and footballer Marcus Rashford. The slogan was \"2020 has been tough. So tough that even grown-ups need *Beano*\".
## Beano Studios {#beano_studios}
In June 2016, DC Thomson launched Beano Studios, a spin-off media studio based in London and Dundee, to create media for children and expand The Beano franchise. The launch was marked in The Beano issue 3854, featuring a new cover design, updated logo, and the introduction of the website beano.com.
Michael Stirling, former chief editor, returned as head of the Dundee studio, with Jodie Morris, James Neal, Nigel Pickard, and Emma Scott joining in key roles. The website beano.com offers games, news, videos, and content that appeals to children and nostalgic parents alike, drawing over two million annual visitors. This online presence contributed to a 10% rise in comic sales by 2018.
Beano Studios quickly expanded its reach with the popular CBBC series Dennis & Gnasher: Unleashed! in 2017, which aired in over 90 countries and earned an International Emmy nomination. Building on this success, Beano Studios pursued new projects including a live-action Minnie the Minx show, another Dennis the Menace adaptation, and a Bananaman cartoon in collaboration with Fox Entertainment.
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# The Beano
## Reception and legacy {#reception_and_legacy}
*The Beano* was an instant success upon release, and became the longest-running, weekly-issued comic of all time in 2018. Although interest in comic magazines dwindled, it survived surrounding setbacks. In the 1950s, it (and *The Dandy*) were unaffected by DC Thomson\'s magazine cancellations (selling over 100 million per year) that were caused by both paper rationing and public lack of interest. Alan Digby\'s attempt to boost sales with the 8-week \"Missing Gnasher\" plot in *Dennis the Menace* failed, but the story featured in newspapers and on radio broadcasts, causing people of all ages to contact *Beano* offices to voice their concerns. Roughly 31,000--41,000 copies are sold per week in the present day, but an estimated 2 billion *Beano* comic magazines have been sold in its lifetime. A 1997 television poll by the National Comics Awards selected it for the Best British Comic Ever award. Dennis the Menace would represent the comic when Royal Mail launched a special stamp collection in 2012, celebrating Britain\'s rich comic book history. *The Dandy*, *Eagle*, *The Topper*, *Roy of the Rovers*, *Bunty*, *Buster*, *Valiant*, *Twinkle* and *2000 AD* were also featured.
Like *The Dandy*, *The Beano* is a definitive part of British pop culture. \"It\'s refreshing to see how the \[zany\] principles that made it such a hit all those years ago have remained to this day.\" writes *Coventry Evening Telegraph*. *Beano* annuals are the most popular Christmas annual sold, and old issues sell for thousands at auctions. Lord Snooty is often used as a pejorative in British politics. DC Thomson considers the 1950s *Beano*{{\'s}} golden age possibly because of many commemorations based on the strips that first appeared from that decade: Dennis became the literal and metaphorical mascot of the magazine, his increasing popularity making him the last consistent cover star and his strips spawning three BBC animated adaptations; Minnie and the Bash Street Kids have a statue and a street named after the strip, respectively. The \"anarchic\" humour is credited as the key to the magazine\'s longevity, as well as its refusal to be condescending to its readers: \"*The Beano* may have changed since the \'30s but has always maintained its anti-authoritarian stance and steadfast refusal to treat children like idiots,\" theorised Morris Heggie. `{{quote box|quote=My British-born grandparents made sure they passed down an important part of their culture by giving out ''Beano'' Annuals every year. I grew up on ''Beano''s and ''Dandy''s in 1970s Canada, and become one of my country's leading kids' cartoonists, writing and drawing for [[Chickadee (magazine)|''Chickadee'' magazines]] and annuals, and creating a weekly comic strip for the ''[[Toronto Star]]''. I'm forever in debt to the lowbrow lessons gleaned from Dennis and his ilk.
|author=[[Jay Stephens]], 2003<ref name=Appleby>{{cite news |title=BBC NEWS {{!}} UK {{!}}`{=mediawiki} Magazine {{!}} Drawing Dennis: The Beano at 65 \|url=<http://news.bbc.co.uk/1/hi/magazine/3090659.stm> \|work=news.bbc.co.uk \|access-date=18 July 2021 \|archive-date=5 July 2004 \|archive-url=<https://web.archive.org/web/20040705002748/http://news.bbc.co.uk/1/hi/magazine/3090659.stm> \|url-status=live }}
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}} The magazine is cited as an inspiration to many readers. *Beano* artists Emily McGorman-Bruce, Zoom Rockman, Jess Bradley, and Barrie Appleby were avid readers of the magazine and/or its annuals before they became creators of its new strips. Meanwhile, *The Beano* inspired comic artists Jay Stephens, Carolyn Edwards (Titan Comics) and webcomic creator Sarah Millman (*NPC Tea*, *The Heart of Time*) to either work in the creative industry or create their own stories. Alan Moore theorised the magazine influenced numerous British comic artists into reimagining American comics in the 1980s by pioneering the Dark Age. Guest chief-editors Nick Park, David Walliams, Joe Sugg, and Harry Hill are also fans of *The Beano*, with Park admitting \"My dream job was always to work on *The Beano* and it\'s such an honour for me to be Guest Editor\[.\]\"
Notable famous members of the old Dennis the Menace/Beano Club include Auberon Waugh, Mike Read, and Mark Hamill, as well as honorary members Paul Gascoigne, and Princes William and Harry. Chris Tarrant cited Dennis as his role model when he was a child, and Paul Rudd revealed *Roger the Dodger* was his favourite strip. Stella McCartney created tribute fashion to both *The Beano* and *The Dandy*, explaining they were \"a huge part of my childhood\" and wanted to celebrate \"the next generation of *Beano* fans with a sustainable and practical range for kids who still share that 'Beano' spirit of these iconic characters\". In music pop culture, the album *Blues Breakers with Eric Clapton* is nicknamed \"The Beano Album\" because Eric Clapton is holding issue 1242 on its cover.
### Audience participation {#audience_participation}
Interaction with the audience is a historic practice in *The Beano*{{\'s}} history. Excluding fan clubs and merchandise, *Comic Idol* is a sporadic election in which readers vote for their favourite strips to keep in the magazine. Cancelled strips with the least votes include *Little Plum*, *Baby Face Finlayson*, *Les Pretend*, *Calamity James*,`{{refn|group=Note|name=Return}}`{=mediawiki} *Crazy for Daisy*, and *Lord Snooty*.`{{refn|group=Note|name=Return}}`{=mediawiki} *Super School* and *Meebo and Zuky* were nominees who won polls and became official strips in the following issues. Readers would find a voting slip covered with the candidates printed in an issue that they would fill out and mail to DC Thomson, but the creation of *Beano*{{\'s}} websites would allow real-time opinions from readers. *Pets\' Picture Gallery* invited readers to send drawings of their pets to feature in the following issue.
Readers participated in the magazine\'s record-breaking stunts. In 1988, 100 children helped Euan Kerr and *Beano* scriptwriter Al Bernard recreate the front cover of issue 2396 on Scarborough Beach with Hann-Made Productions. It was awarded the Largest Comic Strip at 39950 square feet. *Beano*{{\'s}} 2018 comic competition to celebrate the opening of V&A Dundee was awarded the biggest competition to finish a comic strip with 650 participants.
Along with Nick Park\'s guest editor issue, the 70th anniversary coincided with Gnashional Menace Day, a CLIC Sargent-partnered event where readers could be sponsored \"behaving like Dennis\" for charity.
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# The Beano
## Reception and legacy {#reception_and_legacy}
### Controversy
*The Beano* has had a few controversies throughout its lifetime, but aspects have either been discontinued, phased out or changed to not cause offence. Its infamous changes are the removal of corporal punishment (e.g. Dennis the Menace often depicted receiving bottom spanks with a slipper by his furious father) and misbehaving characters abandoning slingshots---the latter irritating former readers for being a \"politically correct\" notion, usually highlighted with claim \"Dennis has lost his menace\". Racist depictions and terminology have been removed through the years as well. *Little Plum*{{\'s}} sub-title \"Your redskin chum\" was not included in its 2002 revival. The first masthead character was a caricatured design of a black boy named Peanut, mascot of the *Little Peanut\'s Page of Fun* joke page (appeared from issues 1 to 112), usually eating watermelon. His last masthead feature was in December 1947, but subsequent reprints of the first issues have removed him. *Hard-Nut the Nigger* and *Musso the Wop* have not had reprints since their last appearances, the latter being printed during World War II when Britain was at war with Fascist Italy.`{{refn|group=Note|''Mussolini the Wop''{{'s}}`{=mediawiki} example reprint in *The History of The Beano* has \"Wop\" conspicuously hidden underneath a drawing of war planes flying past the Leaning Tower of Pisa.}}
Some changes were to not convince readers bullying was acceptable. Dennis and Gnasher\'s constant targeting of passive, diligent Walter \"the Softy\" (who was also a knitting and flower-picking hobbyist) was accused of encouraging playground homophobia, so it was toned down. Walter was also rewritten to be a bit less soft, becoming more antagonistic and stood up to Dennis sometimes, eventually having his first girlfriend. Fatty from the Bash Street Kids was renamed Freddy (his real name) in 2021, causing backlash from former readers, including then government minister Jacob Rees-Mogg who accused the change of being \"publicity-seeking\". Former chief-editor Mike Stirling explained it was due to fan letters from young readers asking why he was nicknamed so: \"although it\'s always been used affectionately, and never pejoratively, we agreed it\'s time it changed.\" A *News of the World* report contained accusations of *Uh Oh, Si Co!* encouraging readers to mock children with anger issues or mental illness, which caused the strip to be cancelled
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# Banach algebra
In mathematics, especially functional analysis, a **Banach algebra**, named after Stefan Banach, is an associative algebra $A$ over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy $\|x \, y\| \ \leq \|x\| \, \|y\| \quad \text{ for all } x, y \in A.$
This ensures that the multiplication operation is continuous with respect to the metric topology.
A Banach algebra is called *unital* if it has an identity element for the multiplication whose norm is $1,$ and *commutative* if its multiplication is commutative. Any Banach algebra $A$ (whether it is unital or not) can be embedded isometrically into a unital Banach algebra $A_e$ so as to form a closed ideal of $A_e$. Often one assumes *a priori* that the algebra under consideration is unital because one can develop much of the theory by considering $A_e$ and then applying the outcome in the original algebra. However, this is not the case all the time. For example, one cannot define all the trigonometric functions in a Banach algebra without identity.
The theory of real Banach algebras can be very different from the theory of complex Banach algebras. For example, the spectrum of an element of a nontrivial complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.
Banach algebras can also be defined over fields of $p$-adic numbers. This is part of $p$-adic analysis.
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# Banach algebra
## Examples
The prototypical example of a Banach algebra is $C_0(X)$, the space of (complex-valued) continuous functions, defined on a locally compact Hausdorff space $X$, that vanish at infinity. $C_0(X)$ is unital if and only if $X$ is compact. The complex conjugation being an involution, $C_0(X)$ is in fact a C\*-algebra. More generally, every C\*-algebra is a Banach algebra by definition.
- The set of real (or complex) numbers is a Banach algebra with norm given by the absolute value.
- The set of all real or complex $n$-by-$n$ matrices becomes a unital Banach algebra if we equip it with a sub-multiplicative matrix norm.
- Take the Banach space $\R^n$ (or $\Complex^n$) with norm $\|x\| = \max_{} |x_i|$ and define multiplication componentwise: $\left(x_1, \ldots, x_n\right) \left(y_1, \ldots, y_n\right) = \left(x_1 y_1, \ldots, x_n y_n\right).$
- The quaternions form a 4-dimensional real Banach algebra, with the norm being given by the absolute value of quaternions.
- The algebra of all bounded real- or complex-valued functions defined on some set (with pointwise multiplication and the supremum norm) is a unital Banach algebra.
- The algebra of all bounded continuous real- or complex-valued functions on some locally compact space (again with pointwise operations and supremum norm) is a Banach algebra.
- The algebra of all continuous linear operators on a Banach space $E$ (with functional composition as multiplication and the operator norm as norm) is a unital Banach algebra. The set of all compact operators on $E$ is a Banach algebra and closed ideal. It is without identity if $\dim E = \infty.$
- If $G$ is a locally compact Hausdorff topological group and $\mu$ is its Haar measure, then the Banach space $L^1(G)$ of all $\mu$-integrable functions on $G$ becomes a Banach algebra under the convolution $x y(g) = \int x(h) y\left(h^{-1} g\right) d \mu(h)$ for $x, y \in L^1(G).$
- Uniform algebra: A Banach algebra that is a subalgebra of the complex algebra $C(X)$ with the supremum norm and that contains the constants and separates the points of $X$ (which must be a compact Hausdorff space).
- Natural Banach function algebra: A uniform algebra all of whose characters are evaluations at points of $X.$
- C\*-algebra: A Banach algebra that is a closed \*-subalgebra of the algebra of bounded operators on some Hilbert space.
- Measure algebra: A Banach algebra consisting of all Radon measures on some locally compact group, where the product of two measures is given by convolution of measures.
- The algebra of the quaternions $\H$ is a real Banach algebra, but it is not a complex algebra (and hence not a complex Banach algebra) for the simple reason that the center of the quaternions is the real numbers, which cannot contain a copy of the complex numbers.
- An affinoid algebra is a certain kind of Banach algebra over a nonarchimedean field. Affinoid algebras are the basic building blocks in rigid analytic geometry.
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# Banach algebra
## Properties
Several elementary functions that are defined via power series may be defined in any unital Banach algebra; examples include the exponential function and the trigonometric functions, and more generally any entire function. (In particular, the exponential map can be used to define abstract index groups.) The formula for the geometric series remains valid in general unital Banach algebras. The binomial theorem also holds for two commuting elements of a Banach algebra.
The set of invertible elements in any unital Banach algebra is an open set, and the inversion operation on this set is continuous (and hence is a homeomorphism), so that it forms a topological group under multiplication.
If a Banach algebra has unit $\mathbf{1},$ then $\mathbf{1}$ cannot be a commutator; that is, $xy - yx \neq \mathbf{1}$ for any $x, y \in A.$ This is because $x y$ and $y x$ have the same spectrum except possibly $0.$
The various algebras of functions given in the examples above have very different properties from standard examples of algebras such as the reals. For example:
- Every real Banach algebra that is a division algebra is isomorphic to the reals, the complexes, or the quaternions. Hence, the only complex Banach algebra that is a division algebra is the complexes. (This is known as the Gelfand--Mazur theorem.)
- Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
- Every commutative real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers.
- Every commutative real unital Noetherian Banach algebra (possibly having zero divisors) is finite-dimensional.
- Permanently singular elements in Banach algebras are topological divisors of zero, that is, considering extensions $B$ of Banach algebras $A$ some elements that are singular in the given algebra $A$ have a multiplicative inverse element in a Banach algebra extension $B.$ Topological divisors of zero in $A$ are permanently singular in any Banach extension $B$ of $A.$
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# Banach algebra
## Spectral theory {#spectral_theory}
Unital Banach algebras over the complex field provide a general setting to develop spectral theory. The *spectrum* of an element $x \in A,$ denoted by $\sigma(x)$, consists of all those complex scalars $\lambda$ such that $x - \lambda \mathbf{1}$ is not invertible in $A.$ The spectrum of any element $x$ is a closed subset of the closed disc in $\Complex$ with radius $\|x\|$ and center $0,$ and thus is compact. Moreover, the spectrum $\sigma(x)$ of an element $x$ is non-empty and satisfies the spectral radius formula: $\sup \{|\lambda| : \lambda \in \sigma(x)\} = \lim_{n \to \infty} \|x^n\|^{1/n}.$
Given $x \in A,$ the holomorphic functional calculus allows to define $f(x) \in A$ for any function $f$ holomorphic in a neighborhood of $\sigma(x).$ Furthermore, the spectral mapping theorem holds: $\sigma(f(x)) = f(\sigma(x)).$
When the Banach algebra $A$ is the algebra $L(X)$ of bounded linear operators on a complex Banach space $X$ (for example, the algebra of square matrices), the notion of the spectrum in $A$ coincides with the usual one in operator theory. For $f \in C(X)$ (with a compact Hausdorff space $X$), one sees that: $\sigma(f) = \{f(t) : t \in X\}.$
The norm of a normal element $x$ of a C\*-algebra coincides with its spectral radius. This generalizes an analogous fact for normal operators.
Let $A$ be a complex unital Banach algebra in which every non-zero element $x$ is invertible (a division algebra). For every $a \in A,$ there is $\lambda \in \Complex$ such that $a - \lambda \mathbf{1}$ is not invertible (because the spectrum of $a$ is not empty) hence $a = \lambda \mathbf{1}:$ this algebra $A$ is naturally isomorphic to $\Complex$ (the complex case of the Gelfand--Mazur theorem).
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# Banach algebra
## Ideals and characters {#ideals_and_characters}
Let $A$ be a unital *commutative* Banach algebra over $\Complex.$ Since $A$ is then a commutative ring with unit, every non-invertible element of $A$ belongs to some maximal ideal of $A.$ Since a maximal ideal $\mathfrak m$ in $A$ is closed, $A / \mathfrak m$ is a Banach algebra that is a field, and it follows from the Gelfand--Mazur theorem that there is a bijection between the set of all maximal ideals of $A$ and the set $\Delta(A)$ of all nonzero homomorphisms from $A$ to $\Complex.$ The set $\Delta(A)$ is called the \"structure space\" or \"character space\" of $A,$ and its members \"characters\".
A character $\chi$ is a linear functional on $A$ that is at the same time multiplicative, $\chi(a b) = \chi(a) \chi(b),$ and satisfies $\chi(\mathbf{1}) = 1.$ Every character is automatically continuous from $A$ to $\Complex,$ since the kernel of a character is a maximal ideal, which is closed. Moreover, the norm (that is, operator norm) of a character is one. Equipped with the topology of pointwise convergence on $A$ (that is, the topology induced by the weak-\* topology of $A^*$), the character space, $\Delta(A),$ is a Hausdorff compact space.
For any $x \in A,$ $\sigma(x) = \sigma(\hat x)$ where $\hat x$ is the Gelfand representation of $x$ defined as follows: $\hat x$ is the continuous function from $\Delta(A)$ to $\Complex$ given by $\hat x(\chi) = \chi(x).$ The spectrum of $\hat x,$ in the formula above, is the spectrum as element of the algebra $C(\Delta(A))$ of complex continuous functions on the compact space $\Delta(A).$ Explicitly, $\sigma(\hat x) = \{\chi(x) : \chi \in \Delta(A)\}.$
As an algebra, a unital commutative Banach algebra is semisimple (that is, its Jacobson radical is zero) if and only if its Gelfand representation has trivial kernel. An important example of such an algebra is a commutative C\*-algebra. In fact, when $A$ is a commutative unital C\*-algebra, the Gelfand representation is then an isometric \*-isomorphism between $A$ and $C(\Delta(A)).$
## Banach \*-algebras {#banach__algebras}
A Banach \*-algebra $A$ is a Banach algebra over the field of complex numbers, together with a map ${}^* : A \to A$ that has the following properties:
1. $\left(x^*\right)^* = x$ for all $x \in A$ (so the map is an involution).
2. $(x + y)^* = x^* + y^*$ for all $x, y \in A.$
3. $(\lambda x)^* = \bar{\lambda}x^*$ for every $\lambda \in \Complex$ and every $x \in A;$ here, $\bar{\lambda}$ denotes the complex conjugate of $\lambda.$
4. $(x y)^* = y^* x^*$ for all $x, y \in A.$
In other words, a Banach \*-algebra is a Banach algebra over $\Complex$ that is also a \*-algebra.
In most natural examples, one also has that the involution is isometric, that is, $\|x^*\| = \|x\| \quad \text{ for all } x \in A.$ Some authors include this isometric property in the definition of a Banach \*-algebra.
A Banach \*-algebra satisfying $\|x^* x\| = \|x^*\| \|x\|$ is a C\*-algebra
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# Bill Holbrook
**Bill Holbrook** (born 1958) is an American cartoonist and webcomic writer and artist, best known for his syndicated comic strip *On the Fastrack*.
Born in Los Angeles, Holbrook grew up in Huntsville, Alabama, and began drawing at an early age. While majoring in illustration and visual design at Auburn University, Holbrook served as art director of the student newspaper, doing editorial cartoons and a weekly comic strip. At the same time, his work was being published in the *Huntsville Times* and the *Monroe Journal*. After graduation in 1980, he joined the *Atlanta Constitution* as an editorial staff artist.
During a 1982 visit to relatives on the West Coast, Holbrook met *Peanuts* creator, Charles Schulz. Following his advice and encouragement, Holbrook created a strip in the fall of that year about a college graduate working in a rundown diner. It did not stir syndicate interest, but what he learned on the strip helped him when he created *On the Fastrack*.
Eleven days before *On the Fastrack* made its syndicated debut (March 19, 1984), Holbrook met Teri Peitso on a blind date. They were married on Pearl Harbor Day, 1985. They have two daughters, Chandler and Haviland. Peitso-Holbrook\'s novels have been nominated for both Edgar Awards and Agatha Awards. She is currently an assistant professor in literacy education at Georgia State University. The family lives in the Atlanta area.
On October 3, 1988, Holbrook began his second strip, *Safe Havens*, and his third strip, *Kevin and Kell* was launched in September 1995.
## Comic strips {#comic_strips}
Every week Holbrook writes the story line for the next three weeks for one of his strips and draws the next three weeks\' worth of strips for another. In 2010, characters from *On the Fastrack* and *Safe Havens* began appearing in both strips.
- *On the Fastrack* - About the misadventures at Fastrack, Inc., *On the Fastrack* has been distributed by King Features Syndicate since 1984. It now appears in 75 newspapers nationwide.
- *Safe Havens* - Initially about a day care center, this strip evolved into the adventures of Samantha Argus and her friends and is now syndicated nationally to over 50 newspapers.
- *Kevin and Kell* - Originally an online-only strip but was also published in the *Atlanta Journal-Constitution* for some years, *Kevin and Kell* centers on the mixed marriage between a rabbit, Kevin and a grey wolf, Kell Dewclaw. The plot revolves around species-related humor, satire, and interpersonal conflict.
- *[Duel In The Somme](http://duelinthesomme.com/) `{{Webarchive|url=https://web.archive.org/web/20100904021112/http://duelinthesomme.com/ |date=2010-09-04 }}`{=mediawiki}* - Holbrook illustrated a story by Ben Bova and Rob Balder in this strip about a romantic rivalry between a computer-simulation designer and his boss
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# William M. Tweed
**William Magear \"Boss\" Tweed** (April 3, 1823 -- April 12, 1878) was an American politician most notable for being the political boss of Tammany Hall, the Democratic Party\'s political machine that played a major role in the politics of 19th-century New York City and State.
At the height of his influence, Tweed was the third-largest landowner in New York City, a director of the Erie Railroad, a director of the Tenth National Bank, a director of the New-York Printing Company, the proprietor of the Metropolitan Hotel, a significant stockholder in iron mines and gas companies, a board member of the Harlem Gas Light Company, a board member of the Third Avenue Railway Company, a board member of the Brooklyn Bridge Company, and the president of the Guardian Savings Bank.
Tweed was elected to the United States House of Representatives in 1852 and the New York County Board of Supervisors in 1858, the year that he became the head of the Tammany Hall political machine. He was also elected to the New York State Senate in 1867. However, Tweed\'s greatest influence came from being an appointed member of a number of boards and commissions, his control over political patronage in New York City through Tammany, and his ability to ensure the loyalty of voters through jobs he could create and dispense on city-related projects.
Boss Tweed was convicted for stealing an amount estimated by an aldermen\'s committee in 1877 at between \$25 million and \$45 million from New York City taxpayers by political corruption, but later estimates ranged as high as \$200 million (equivalent to \$`{{Inflation|US-GDP|0.2|1877|r=0}}`{=mediawiki} billion in `{{Inflation/year|US}}`{=mediawiki}). Unable to make bail, he escaped from jail once but was returned to custody. He died in the Ludlow Street Jail.
## Early life and education {#early_life_and_education}
Tweed was born April 3, 1823, at 1 Cherry Street, on the Lower East Side of Manhattan. The son of a third-generation Scottish chair-maker, Tweed grew up on Cherry Street. His grandfather arrived in the United States from a town near the River Tweed close to Edinburgh. Tweed\'s religious affiliation was not widely known in his lifetime, but at the time of his funeral *The New York Times*, quoting a family friend, reported that his parents had been Quakers and \"members of the old Rose Street Meeting house\". At the age of 11, he left school to learn his father\'s trade, and then became an apprentice to a saddler. He also studied to be a bookkeeper and worked as a brushmaker for a company he had invested in, before eventually joining in the family business in 1852. On September 29, 1844, he married Mary Jane C. Skaden and lived with her family on Madison Street for two years.
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# William M. Tweed
## Early career {#early_career}
Tweed became a member of the Odd Fellows and the Masons, and joined a volunteer fire company, Engine No. 12. In 1848, at the invitation of state assemblyman John J. Reilly, he and some friends organized the Americus Fire Company No. 6, also known as the \"Big Six\", as a volunteer fire company, which took as its symbol a snarling red Bengal tiger from a French lithograph, a symbol which remained associated with Tweed and Tammany Hall for many years. At the time, volunteer fire companies competed vigorously with each other; some were connected with street gangs and had strong ethnic ties to various immigrant communities. The competition could become so fierce, that burning buildings would sometimes be ignored as the fire companies fought each other. Tweed became known for his ax-wielding violence, and was soon elected the Big Six foreman. Pressure from Alfred Carlson, the chief engineer, got him thrown out of the crew. However, fire companies were also recruiting grounds for political parties at the time, thus Tweed\'s exploits came to the attention of the Democratic politicians who ran the Seventh Ward. The Seventh Ward put him up for Alderman in 1850, when Tweed was 26. He lost that election to the Whig candidate Morgan Morgans, but ran again the next year and won, garnering his first political position. Tweed then became associated with the \"Forty Thieves\", the group of aldermen and assistant aldermen who, up to that point, were known as some of the most corrupt politicians in the city\'s history.
Tweed was elected to the United States House of Representatives in 1852, but his two-year term was undistinguished. In an attempt by Republican reformers in Albany, the state capital, to control the Democratic-dominated New York City government, the power of the New York County Board of Supervisors was beefed up. The board had 12 members, six appointed by the mayor and six elected, and in 1858 Tweed was appointed to the board, which became his first vehicle for large-scale graft; Tweed and other supervisors forced vendors to pay a 15% overcharge to their \"ring\" in order to do business with the city. By 1853, Tweed was running the seventh ward for Tammany. The board also had six Democrats and six Republicans, but Tweed often just bought off one Republican to sway the board. One such Republican board member was Peter P. Voorhis, a coal dealer by profession who absented himself from a board meeting in exchange for \$2,500 so that the board could appoint city inspectors. Henry Smith was another Republican that was a part of the Tweed ring.
Although he was not trained as a lawyer, Tweed\'s friend, Judge George G. Barnard, certified him as an attorney, and Tweed opened a law office on Duane Street. He ran for sheriff in 1861 and was defeated, but became the chairman of the Democratic General Committee shortly after the election, and was then chosen to be the head of Tammany\'s general committee in January 1863. Several months later, in April, he became \"Grand Sachem\", and began to be referred to as \"Boss\", especially after he tightened his hold on power by creating a small executive committee to run the club. Tweed then took steps to increase his income: he used his law firm to extort money, which was then disguised as legal services; he had himself appointed deputy street commissioner -- a position with considerable access to city contractors and funding; he bought the New-York Printing Company, which became the city\'s official printer, and the city\'s stationery supplier, the Manufacturing Stationers\' Company, and had both companies begin to overcharge the city government for their goods and services. Among other legal services he provided, he accepted almost \$100,000 from the Erie Railroad in return for favors. He also became one of the largest owners of real estate in the city. He also started to form what became known as the \"Tweed Ring\", by having his friends elected to office: George G. Barnard was elected Recorder of New York City; Peter B. Sweeny was elected New York County District Attorney; and Richard B. Connolly was elected City Comptroller. Other judicial members of the Tweed ring included Albert Cardozo, John McCunn, and John K. Hackett.
When Grand Sachem Isaac Fowler, who had produced the \$2,500 to buy off the Republican Voorhis on the Board of Supervisors, was found to have stolen \$150,000 in post office receipts, the responsibility for Fowler\'s arrest was given to Isaiah Rynders, another Tammany operative who was serving as a United States marshal at the time. Rynders made enough ruckus upon entering the hotel where Fowler was staying that Fowler was able to escape to Mexico.
With his new position and wealth came a change in style: Tweed began to favor wearing a large diamond in his shirtfront -- a habit that Thomas Nast used to great effect in his attacks on Tweed in *Harper\'s Weekly* beginning in 1869 -- and he bought a brownstone to live in at 41 West 36th Street, then a very fashionable area. He invested his now considerable illegal income in real estate, so that by the late 1860s he ranked among the biggest landowners in New York City.
Tweed became involved in the operation of the New York Mutuals, an early professional baseball club, in the 1860s. He brought in thousands of dollars per home game by dramatically increasing the cost of admission and gambling on the team. He has been credited with originating the practice of spring training in 1869 by sending the club south to New Orleans to prepare for the season.
Tweed was a member of the New York State Senate (4th D.) from 1868 to 1873, sitting in the 91st, 92nd, 93rd, and 94th New York State Legislatures, but not taking his seat in the 95th and 96th New York State Legislatures. While serving in the State Senate, he split his time between Albany, New York and New York City. While in Albany, he stayed in a suite of seven rooms in Delevan House. Accompanying him in his rooms were his favorite canaries. Guests are presumed to have included members of the Black Horse Cavalry, thirty state legislators whose votes were up for sale. In the Senate he helped financiers Jay Gould and Big Jim Fisk to take control of the Erie Railroad from Cornelius Vanderbilt by arranging for legislation that legitimized fake Erie stock certificates that Gould and Fisk had issued. In return, Tweed received a large block of stock and was made a director of the company. Tweed was also subsequently elected to the board of the Gould-controlled Cleveland and Pittsburgh Railroad (future Pennsylvania Railroad) in January 1870.
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# William M. Tweed
## Corruption
After the election of 1869, Tweed took control of the New York City government. His protégé, John T. Hoffman, the former mayor of the city, won election as governor, and Tweed garnered the support of good-government reformers like Peter Cooper and the Union League Club, by proposing a new city charter which returned power to City Hall at the expense of the Republican-inspired state commissions. The new charter passed, thanks in part to \$600,000 in bribes Tweed paid to Republicans, and was signed into law by Hoffman in 1870. Mandated new elections allowed Tammany to take over the city\'s Common Council when they won all fifteen aldermanic contests.
The new charter put control of the city\'s finances in the hands of a Board of Audit, which consisted of Tweed, who was Commissioner of Public Works, Mayor A. Oakey Hall and Comptroller Richard \"Slippery Dick\" Connolly, both Tammany men. Hall also appointed other Tweed associates to high offices -- such as Peter B. Sweeny, who took over the Department of Public Parks -- providing what became known as the Tweed Ring with even firmer control of the New York City government and enabling them to defraud the taxpayers of many more millions of dollars. In the words of Albert Bigelow Paine, \"their methods were curiously simple and primitive. There were no skilful manipulations of figures, making detection difficult \... Connolly, as Controller, had charge of the books, and declined to show them. With his fellows, he also \'controlled\' the courts and most of the bar.\" Crucially, the new city charter allowed the Board of Audit to issue bonds for debt in order to finance opportunistic capital expenditures the city otherwise could not afford. This ability to float debt was enabled by Tweed\'s guidance and passage of the Adjusted Claims Act in 1868. Contractors working for the city -- \"Ring favorites, most of them -- were told to multiply the amount of each bill by five, or ten, or a hundred, after which, with Mayor Hall\'s \'O. K.\' and Connolly\'s endorsement, it was paid \... through a go-between, who cashed the check, settled the original bill and divided the remainder \... between Tweed, Sweeny, Connolly and Hall\".
For example, the construction cost of the New York County Courthouse, begun in 1861, grew to nearly \$13 million---about \$`{{Format price|{{Inflation|US-GDP|13000000|1861|r=-7}}}}`{=mediawiki} in `{{Inflation/year|US-GDP}}`{=mediawiki} dollars, and nearly twice the cost of the Alaska Purchase in 1867. \"A carpenter was paid \$360,751 (roughly \$`{{Format price|{{Inflation|US-GDP|360751|1861|r=-5}}}}`{=mediawiki} in `{{Inflation/year|US-GDP}}`{=mediawiki}) for one month\'s labor in a building with very little woodwork \... a plasterer got \$133,187 (\$`{{Format price|{{Inflation|US-GDP|133187|1861|r=-5}}}}`{=mediawiki}) for two days\' work\". Tweed bought a marble quarry in Sheffield, Massachusetts, to provide much of the marble for the courthouse at great profit to himself. After the Tweed Charter to reorganize the city\'s government was passed in 1870, four commissioners for the construction of the New York County Courthouse were appointed. The commission never held a meeting, though each commissioner received a 20% kickback from the bills for the supplies.
Tweed and his friends also garnered huge profits from the development of the Upper East Side, especially Yorkville and Harlem. They would buy up undeveloped property, then use the resources of the city to improve the area -- for instance by installing pipes to bring in water from the Croton Aqueduct -- thus increasing the value of the land, after which they sold and took their profits. The focus on the east side also slowed down the development of the west side, the topography of which made it more expensive to improve. The ring also took their usual percentage of padded contracts, as well as raking off money from property taxes. Despite the corruption of Tweed and Tammany Hall, they did accomplish the development of upper Manhattan, though at the cost of tripling the city\'s bond debt to almost \$90 million.
During the Tweed era, the proposal to build a suspension bridge between New York and Brooklyn, then an independent city, was floated by Brooklyn-boosters, who saw the ferry connections as a bottleneck to Brooklyn\'s further development. In order to ensure that the Brooklyn Bridge project would go forward, State Senator Henry Cruse Murphy approached Tweed to find out whether New York\'s aldermen would approve the proposal. Tweed\'s response was that \$60,000 for the aldermen would close the deal, and contractor William C. Kingsley put up the cash, which was delivered in a carpet bag. Tweed and two others from Tammany also received over half the private stock of the Bridge Company, the charter of which specified that only private stockholders had voting rights, so that even though the cities of Brooklyn and Manhattan put up most of the money, they essentially had no control over the project.
Tweed bought a mansion on Fifth Avenue and 43rd Street, and stabled his horses, carriages and sleighs on 40th Street. By 1871, he was a member of the board of directors of not only the Erie Railroad and the Brooklyn Bridge Company, but also the Third Avenue Railway Company and the Harlem Gas Light Company. He was president of the Guardian Savings Banks and he and his confederates set up the Tenth National Bank to better control their fortunes.
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# William M. Tweed
## Scandal
Tweed\'s downfall began in 1871. James Watson, who was a county auditor in Comptroller Dick Connolly\'s office and who also held and recorded the ring\'s books, died a week after his head was smashed by a horse in a sleigh accident on January 24, 1871. Although Tweed guarded Watson\'s estate in the week prior to Watson\'s death, and although another ring member attempted to destroy Watson\'s records, a replacement auditor, Matthew O\'Rourke, associated with former sheriff James O\'Brien, provided city accounts to O\'Brien. The Orange riot of 1871 in the summer of that year did not help the ring\'s popularity. The riot was prompted after Tammany Hall banned a parade of Irish Protestants celebrating a historical victory against Catholicism, namely the Battle of the Boyne. The parade was banned because of a riot the previous year in which eight people died when a crowd of Irish Catholic laborers attacked the paraders. Under strong pressure from the newspapers and the Protestant elite of the city, Tammany reversed course, and the march was allowed to proceed, with protection from city policemen and state militia. The result was an even larger riot in which over 60 people were killed and more than 150 injured.
Although Tammany\'s electoral power base was largely centered in the Irish immigrant population, it also needed both the city\'s general population and elite to acquiesce in its rule, and this was conditional on the machine\'s ability to control the actions of its people. The July riot showed that this capability was not nearly as strong as had been supposed.
Tweed had for months been under attack from *The New York Times* and Thomas Nast, the cartoonist from *Harper\'s Weekly* -- regarding Nast\'s cartoons, Tweed reportedly said, \"Stop them damned pictures. I don\'t care so much what the papers say about me. My constituents don\'t know how to read, but they can\'t help seeing them damned pictures!\" -- but their campaign had only limited success in gaining traction. They were able to force an examination of the city\'s books, but the blue-ribbon commission of six businessmen appointed by Mayor A. Oakey Hall, a Tammany man, which included John Jacob Astor III, banker Moses Taylor and others who benefited from Tammany\'s actions, found that the books had been \"faithfully kept\", letting the air out of the effort to dethrone Tweed.
The response to the Orange riot changed everything, and only days afterwards the *Times*/Nast campaign began to garner popular support. More important, the *Times* started to receive inside information from County Sheriff James O\'Brien, whose support for Tweed had fluctuated during Tammany\'s reign. O\'Brien had tried to blackmail Tammany by threatening to expose the ring\'s embezzlement to the press, and when this failed he provided the evidence he had collected to the *Times*. Shortly afterward, county auditor Matthew J. O\'Rourke supplied additional details to the *Times*, which was reportedly offered \$5 million to not publish the evidence. The *Times* also obtained the accounts of the recently deceased James Watson, who was the Tweed Ring\'s bookkeeper, and these were published daily, culminating in a special four-page supplement on July 29 headlined \"Gigantic Frauds of the Ring Exposed\". In August, Tweed began to transfer ownership in his real-estate empire and other investments to his family members.
The exposé provoked an international crisis of confidence in New York City\'s finances, and, in particular, in its ability to repay its debts. European investors were heavily positioned in the city\'s bonds and were already nervous about its management -- only the reputations of the underwriters were preventing a run on the city\'s securities. New York\'s financial and business community knew that if the city\'s credit were to collapse, it could potentially bring down every bank in the city with it.
Thus, the city\'s elite met at Cooper Union in September to discuss political reform: but for the first time, the conversation included not only the usual reformers, but also Democratic bigwigs such as Samuel J. Tilden, who had been thrust aside by Tammany. The consensus was that the \"wisest and best citizens\" should take over the governance of the city and attempt to restore investor confidence. The result was the formation of the executive committee of Citizens and Taxpayers for Financial Reform of the city (also known as \"the Committee of Seventy\"), which attacked Tammany by cutting off the city\'s funding. Property owners refused to pay their municipal taxes, and a judge---Tweed\'s old friend George Barnard---enjoined the city Comptroller from issuing bonds or spending money. Unpaid workers turned against Tweed, marching to City Hall demanding to be paid. Tweed doled out some funds from his own purse---\$50,000---but it was not sufficient to end the crisis, and Tammany began to lose its essential base.
Shortly thereafter, the Comptroller resigned, appointing Andrew Haswell Green, an associate of Tilden, as his replacement. Green loosened the purse strings again, allowing city departments not under Tammany control to borrow money to operate. Green and Tilden had the city\'s records closely examined, and discovered money that went directly from city contractors into Tweed\'s pocket. The following day, they had Tweed arrested.
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