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Eugène Terre'Blanche

Eugène Ney Terre'Blanche (, 31 January 1941 – 3 April 2010) was an Afrikaner nationalist who founded and led the Afrikaner Weerstandsbeweging (AWB; 'Afrikaner Resistance Movement'). Prior to founding the AWB, he served as a South African Police officer, was a farmer, and was an unsuccessful Herstigte Nasionale Party ('Reconstituted National Party') candidate for local office in the Transvaal. He was a major figure in the right-wing backlash against the collapse of apartheid. His beliefs and philosophy have continued to be influential amongst white supremacists in South Africa and across the world.

Background
Terre'Blanche's grandfather fought as a Cape Rebel for the Boer cause in the Second Boer War, while his father was a lieutenant colonel in the South African Defence Force and a leader of the local Commando.

The progenitor of the Terre'Blanche name (translatable as either 'white land' or 'white earth' in French) in the region was a French Huguenot refugee, Estienne Terre'Blanche from Toulon (Provence), who arrived at the Cape in 1704, fleeing anti-Protestant persecution in France. The Terre'Blanche name has generally retained its original spelling though other spellings include Terre Blanche, Terblanche and Terblans.

Born on a farm in the Transvaal town of Ventersdorp on 31 January 1941, Terre'Blanche attended Laerskool Ventersdorp and Hoër Volkskool in Potchefstroom, matriculating in 1962. While in school, he gave early expression to his political leanings by founding the cultural organisation Jong Afrikanerharte (Young Afrikaner Hearts).

He joined the South African Police, and was initially deployed in South West Africa (now Namibia), which had been given to South Africa under a League of Nations Trust mandate after World War I. Upon returning to South Africa, he became a Warrant Officer in the Special Guard Unit, which was assigned to members of the Cabinet.

Under Terre'Blanche, the AWB swore to use violence to preserve minority rule, opposing any concessions offered to the African National Congress – an organisation AWB supporters repeatedly branded as Marxist terrorists – and gaining notoriety for storming the Kempton Park Trade Centre during bilateral negotiations in 1993. AWB loyalists also clashed with South African security forces at the Battle of Ventersdorp, a bloody skirmish in 1991 where police opened fire on a white crowd for the first time since the Rand Rebellion, leaving three AWB members dead. Immediately prior to South Africa's first multiracial election, Terre'Blanche's followers were linked to a number of bombings and assassinations targeting the South African Communist Party; armed AWB commandos participated in the crisis in Bophuthatswana in 1994.

Terre'Blanche spent three years in a Rooigrond prison for assaulting a petrol station attendant and for the attempted murder of a black security guard around 1996. He was released in June 2004. On 3 April 2010, he was hacked and beaten to death on his Ventersdorp farm, by two of his black employees.

Herstigte Nasionale Party
During the late 1960s, Terre'Blanche increasingly opposed what he called the "liberal policies" of B. J. Vorster, then Prime Minister of South Africa. After four years of service in the South African Police, he resigned to pursue a career in politics, running unsuccessfully for local office in Heidelberg as a member of the far-right Herstigte Nasionale Party.

Afrikaner Weerstandsbeweging
Disillusioned with the established avenues for political participation, Terre'Blanche founded the Afrikaner Weerstandsbeweging (AWB) in Heidelberg with six other individuals in 1973. Initially a secret society, the AWB first appeared on the public scene after its members were charged and fined in connection with the tarring and feathering of Floors van Jaarsveld, a professor of history who had publicly voiced the opinion that the Day of the Vow, a religious public holiday in remembrance of the Battle of Blood River, was nothing more than a secular event with hardly any real reference point in history. Although Terre'Blanche would later express his regrets regarding the incident when testifying before the Truth and Reconciliation Commission, he suggested that his convictions relating to the sanctity of the Day of the Vow might make his actions more understandable. In the years that followed, Terre'Blanche's speeches at public gatherings often evoked the Battle of Blood River, and his oratorical skills earned him much support among the white right wing in South Africa; the AWB claimed 70,000 members at its height. In September 1977, Johannesburg newspaper The World reported that Terre'Blanche had been investigated on charges of bestiality involving a number of African bushpigs.

Throughout the 1980s, Terre'Blanche continued to present himself and the AWB as an alternative to both the National Party-led government and the Conservative Party, and he remained staunchly opposed to the reform policies of P. W. Botha to establish additional, albeit still separate, parliamentary chambers for non-whites, and to grant suffrage to Coloureds and South Africans of Indian origin. The organisation's strongest support was found in the rural communities of South Africa's North, with comparably few supporters in urban areas where his following was largely limited to middle and lower-income Afrikaners.

End of apartheid
Terre'Blanche viewed the end of apartheid as a surrender to communism, and threatened full-scale civil war if President F. W. de Klerk handed power to Nelson Mandela and the African National Congress. When De Klerk addressed a meeting in Terre'Blanche's hometown of Ventersdorp in 1991, Terre'Blanche led a protest, and the Battle of Ventersdorp ensued between the AWB and the police, with a number of people killed. Terre'Blanche claimed that it was only when he stood between the police and the AWB and demanded a ceasefire that the shooting ended. Terre'Blanche accused President de Klerk of instigating the riot for political gain.

In an attempt to disrupt the negotiation process in 1993, Terre'Blanche led an armed invasion of the World Trade Centre in Kempton Park while negotiations to end apartheid were in progress. After a memorandum of grievances was presented to National Party minister Roelf Meyer and Dawie de Villiers and after an agreement that no arrests would be made, the AWB withdrew from the premises. That evening several identified AWB leaders were arrested and their wives were incarcerated in Soweto, separately from their husbands. Vlakplaas General Krappies Engelbrecht was appointed to launch an investigation.

Terre'Blanche claimed he and President Lucas Mangope of the predominantly ethnic Tswana Homeland of Bophuthatswana came to a "mutual agreement" on 17 February 1992 to aid each other in the "event of a communist threat". On 4 March 1994 Mangope announced that Bophutatswana would not participate in the South African general election in an effort to maintain Bophutatswana's independence from the Republic of South Africa. Bophuthatswana's minister of justice, Godfrey Mothibe tried in vain to convince Mangope to participate in the election, but then accused the ANC of orchestrating the revolt, which was helped by the stance taken by South Africa's Minister of Foreign Affairs, Pik Botha. Thousands of ANC supporters were bussed in from outside Bophuthatswana to support the popular uprising. Terre'Blanche claimed a conspiracy by citing a "three-step plan" by the ANC in an effort to destabilise Bophuthatswana, which included ANC infiltration of the Bophuthatswana police and military. However, ANC candidate for the North West Province, Popo Molefe claimed the ANC was merely supporting the people of Bophuthatswana after it became clear that their political freedoms were limited.

The AWB were subsequently defeated while invading Bophuthatswana to prop up the autocratic leader of the Bantustan in 1994 and Terre'Blanche did not follow up on his earlier threats of war.

Terre'Blanche claimed he had personally communicated with Mangope on 10 March 1994, prior to mobilising his men to protect the capital Mmabatho against looting and unrest. Officers of the Bophuthatswana Defence Force initially received the AWB militia with "great joy and surprise".(Vuur en Verraad, Arthur Kemp) The AWB militia assembled in an airport hangar in Mmabatho, where they were to be provided with rations and firearms. Terre'Blanche ordered his men to remove their AWB badges upon the request of the Bophuthatswana Defence Force. While contained at the hangar, an unidentified and independent faction carrying the AWB emblems started shooting indiscriminately at the public. Terre'Blanche concluded that the South African intelligence services may have set up the shooting in order to discredit the AWB, since the media broadcast footage of the individuals' emblems, but did not publicise their identity. The Bophuthatswana police systematically began to remove the media from strategic locations, and the initial hospitality shown to the AWB militia was replaced by contempt. When Bophuthatswana fell into complete anarchy, the AWB withdrew.

1991 documentary and libel case
Terre'Blanche was the subject of the television documentary The Leader, His Driver and the Driver's Wife (1991), directed by British filmmaker Nick Broomfield. Broomfield's documentary claimed Terre'Blanche had an affair with Jani Allan, the journalist who had interviewed him for South Africa's Sunday Times; an assertion she disputed as well as her portrayal in the documentary. This provoked a scandal in the AWB. In July 1989, Cornelius Lottering, a member of the breakaway Orde van die Dood group, orchestrated a failed assassination attempt on Allan's life by placing a bomb outside her Sandton apartment.

This led to Allan taking libel proceedings against the documentary broadcaster Channel 4 in 1992 in the London's High Court. During the court hearings, several transcripts of their alleged sexual relationship appeared in the South African and British press. Terre'Blanche submitted a sworn statement to the London court denying he had had an affair with Allan. In a rare interview with the Afrikaans Sunday newspaper Die Rapport, his wife Martie Terre'Blanche denounced the rumours. Although the judge found that Channel 4's allegations had not defamed Allan, he did not rule on whether or not there had been an affair. The South African business newspaper Financial Mail published a lead story on 6 August detailing the theory that F.W. de Klerk had orchestrated the libel case to discredit Terre'Blanche and the far right movement in South Africa. Allan has continued to dismiss the claims.

Amnesty
Following the end of apartheid, Terre'Blanche and his supporters sought amnesty for the storming of the World Trade Centre, the 'Battle of Ventersdorp', and other acts. Amnesty was granted by the Truth and Reconciliation Commission.

Later years
In 2004, Terre'Blanche was voted No. 25 in SABC3's Great South Africans, a list of 100 South African personalities. Controversy over the list led the SABC to cancel the television series.

Terre'Blanche was much ridiculed after he was filmed falling off his horse during a parade in Pretoria. After his murder, the state-owned SABC said on the evening news that he would be remembered "as a failed horseman". Terre'Blanche claimed the media only showed part of the fall and explained that unedited footage of the incident would show that the horse had slipped. He accused the media of double standards in reporting when praising Mbhazima Shilowa when he fell from, but immediately remounted his horse.

Broomsfield's sequel to his 1991 documentary, His Big White Self, was first broadcast in February 2006. Terre'Blanche was also interviewed by Louis Theroux in episode 3.3 "Boer Separatists" of the BBC series Louis Theroux's Weird Weekends, and was characterized during the episode by Theroux speaking to a former follower of Terre'Blanche as "very hostile, deeply racist".

In March 2008, the AWB announced the re-activation of the political party for 'populist' reasons, citing the encouragement of the public. Reasons for the return have been attributed principally to attacks on commercial farmers and ethnic Boers, the electricity crisis, corruption across government departments and rampant crime. Throughout April 2008, Terre'Blanche was to be the speaker at several AWB rallies, encompassing Vryburg, Middelburg, Mpumalanga and Pretoria.

He had been calling for a "free Afrikaner republic", and vowed to take his campaign to the United Nations' International Court of Justice in The Hague in a bid to secure this. He favoured large tracts of land that he claimed had been purchased from the ethnic Swazis in the eastern portion of the South African Republic, from the Zulus in northern Natal, and others, as well as largely uninhabited portions of the interior that had been settled by the Voortrekkers. In June 2008, it was announced that the AWB Youth Wing would be launched and Terre'Blanche was to be its founding member.

In a video interview in 2008, he voiced his objection to a proposal to change the Springbok emblem of the South Africa national rugby union team (Springboks). He stated that the Springbok emblem could be replaced with an impala or kudu for sports teams representing the new Afrikaner republic.

In September 2009, he addressed a three-day convention attended by 300 Afrikaners which was intended to develop a strategy for "Boer liberation". Terre'Blanche reinforced earlier claims for land in Northern Natal and the Eastern Transvaal. In October 2009 several right-wing groups led by Terre'Blanche outlined their future plans at a Ventersdorp meeting. In an interview with the Mail and Guardian he said he wanted to unite 23 organisations under one umbrella, in order to take, as he had vowed, the fight of "the free Afrikaner" to the International Court of Justice.

In an interview with the Mail and Guardian, he stated that he would publish his biography, Blouberge van Nimmer (The Blue Mountains of Long Ago), in December 2009. The biography was ready for press at the time of his death and published under the name "My Storie", as told to author Amos van der Merwe. A complaint was lodged in December 2009 with the South African Human Rights Commission regarding inflammatory comments he was alleged to have made.

Conviction and prison sentence
On 17 June 2001, Terre'Blanche was sentenced to six years in prison, of which he served three years, for assaulting John Ndzima, a petrol station worker, and the attempted murder of Paul Motshabi, a security guard, in 1996. Terre'Blanche denied both accusations. One of only three whites in the Rooigrond prison near Mafikeng, during his time in prison he claimed to have become a born-again Christian and to have moderated many of his racist views.

Assault on Ndzima
The assault on Ndzima occurred after a confrontation over Ndzima's testimony against two white boys who had broken into a pharmacy in Ventersdorp. Terre'Blanche said that he merely argued with Ndzima after the burglary, questioning Ndzima's claims to have seen the burglars. According to Terre'Blanche, during the argument his dog broke loose and chased Ndzima. Terre'Blanche asked the state prosecution to explain why there was no blood on his overall after the alleged assault. He claimed that a bogus case had been built against him in order to "bury the conservative element of Afrikaner-nationalism in the shallow grave of injustice". The court rejected his claims, concluding that Terre'Blanche had assaulted Ndzima as retribution for testifying against whites. Terre'Blanche later said that his defence attorney had resigned as a member of the ultra-conservative white Conservative Party's Volksraad and joined the ANC shortly after the conclusion of the court case.

Attempted murder of Motshabi
Security Guard Paul Motshabi was permanently disabled when he was beaten by Terre'Blanche in 1996. He was crippled and intellectually impaired by brain damage sustained in the attack, and his wife left him. He was one of 16 victims of violence in the South Africa's North West who received new houses as part of the national government's campaign to mark 16 days of activism against violence against women and children.

Terre'Blanche also maintained his innocence in the Motshabi case, stating that he had discovered Motshabi already beaten in a park while patrolling Ventersdorp, after which he took him to hospital. Although he was not present when the alleged attack happened, Gabriel Kgosimang, an ex-employee of Terre'Blanche, testified that his former employer had repeatedly beaten Motshabi over the head, upper body, neck and shoulders after he crashed into him with his vehicle. The official medical report only cites a single hit to the head.

Motshabi passed away due to natural causes on 23 August 2017, aged 48.

Subsequent disputes
Terre'Blanche was released on 11 June 2004. The AWB website continued to claim that these accusations, along with other scandals involving him, were fabricated by the "Black Government and the left wing media". Terre'Blanche subsequently claimed that a policeman had identified the real attackers of Motshabi. The names were supposedly contained in a sealed envelope and kept in safekeeping with instructions given that this information would be released in case something "unnatural" should happen to him. Despite the murder of Terre'Blanche, no names have been released.

Poetry
Prior to the 1994 multi-racial elections, Terre'Blanche's Afrikaans-language works were on the state syllabus of Natal schools. Upon his release from jail, he quoted Wordsworth's poem I Wandered Lonely As a Cloud. He had previously released a CD of his poetry collection and most recently a DVD. The DVD was named "Inktrane", which is directly translated to English as "ink tears". This DVD was released through 11.3% Motion Pictures (Pty) Ltd.

Murder
Terre'Blanche, who had lived in relative obscurity since the decline of his organisation, was murdered on his farm Villana, just outside Ventersdorp, on 3 April 2010. He was beaten and hacked to death with pipes and panga machetes whilst napping. His body was found on his bed with severe facial and head injuries. His murder has been categorised as a typical and notable case of South African farm attacks.

South African President Jacob Zuma, who followed up an overnight statement with a televised address, called for calm and for "responsible leadership" following the murder, describing it as a "terrible deed;" and described the murderer as "cowardly." Zuma's words were echoed by the AWB and organisations including AfriForum and Solidarity. Minister of Police Nathi Mthethwa, Commissioner of police Bheki Cele and other high ranking police officials and politicians visited Terre'Blanche's family in Ventersdorp the morning after the murder to express sympathy with the family.

Two males, Chris Mahlangu, aged 28, and Patrick Ndlovu, aged 15, were arrested. Both were employees at Terre'Blanche's farm. They were both charged with murder, and one was released on bail. Terre'Blanche's daughter Bea told the media that the two workers had not been paid for March because her father could not get his banking in order before the Easter weekend, and that an arrangement had been made to pay them after the weekend. She stated that he had enjoyed a good relationship with his employees, which had been strengthened by their work with animals on the farm.

Aftermath
Chris Mahlangu's announcement to other farm workers that he was "now their boss" fuelled suspicions that the murder was politically motivated. The murder took place amid a racial controversy in South Africa involving the singing of a song by African National Congress Youth League leader Julius Malema, which includes the lyrics "Shoot the Boer" ("Dubul' ibhunu"). The ANC, which had previously defended its right to sing the song, announced that it would consider a moratorium on the singing of the song, following the murder, in the interests of national cohesion. Democratic Alliance leader Helen Zille said that the murder would "inflame tensions" in South Africa. Malema denied the song had anything to do with the murder, and defended his singing of it, saying he was "ready to die", and that he was not scared of Boers, in reference to threats, later retracted, that Terre'Blanche would be avenged. ANC leaders later announced a temporary ban on the singing of the song.

Thousands attended Terre'Blanche's funeral, held at noon on 9 April 2010 at Ventersdorp's Protestant Church. Later the same day, he was buried on his farm.

Court case
The two suspects appeared in court in Ventersdorp on 6 April 2010 amid racially charged scenes, and were charged with murder, robbery and crimen injuria, for injuring the dignity of Terre'Blanche by leaving his trousers pulled down after killing him. The AWB retracted earlier calls to avenge the murder as Zuma appealed for peace. Nevertheless, members of the ANC supported the accused by turning up at the court in huge numbers, and singing revolutionary songs. Terre'Blanche's supporters also turned up at the court, singing the former South African national anthem, "Die Stem van Suid Afrika".

On 22 May 2012, 29-year-old Chris Mahlangu was found guilty of the murder and sentenced to life in prison. 18-year-old Patrick Ndlovu, the other man accused in the case, was acquitted of murder due to a lack of forensic evidence, though he was found guilty of breaking-in. They had both pleaded not guilty, and declined to testify. Protesters from both sides were gathered outside the court when the verdict was read. Judge John Horn ruled that there was no evidence that Mahlangu had been acting in self-defence, and that the murder had been committed for financial reasons. Although Mahlangu claimed that he had been raped, Horn declared that if that was the case he should have raised it immediately, which he had not done. He also claimed that he had been acting in retaliation because he had been living in an "appalling condition... not fit for human habitation," as well as having experienced child exploitation on the farm.

In popular culture
In Harry Turtledove's 1992 science fiction novel The Guns of the South, Eugene Terre'Blanche is fictionalised as the minor character Eugen Blankaard, whose name is a literal Afrikaans translation. This character, a historian of AWB, does not appear directly, but his writings are read by other characters. A poster of Terre'Blanche appears in the 1992 Australian drama Romper Stomper, about a neo-Nazi group in suburban Melbourne.

Terre'Blanche is the subject of two Nick Broomfield documentaries: The Leader, His Driver, and the Driver's Wife and His Big White Self.

Louis Theroux interviewed Terre'Blanche in 2000 as part of his Weird Weekends documentary on the Boers.

title: Eugène Terre'Blanche


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Talk:Hamilton–Jacobi–Bellman equation

Physics and Optimal Control
Um, I don't think the Hamilton-Jacobi-Bellman equation is the Hamilton-Jacobi equation anymore than let's say Shannon information is the thermodynamic entropy. Phys 02:57, 15 Aug 2004 (UTC)

Phys is right. There is some mixing together here of Hamilton-Jacobi-Bellman and Hamilton-Jacobi, of Optimal Control and Physics. The result is confusing. I will rewrite from the point of view of O.C. only. Someone else can add the relation to physics and to the pre-Bellman work. Encyclops July 2005

The historical reason for the name is that Bellman got the idea from the mathematics book of Carathéodory on the Calculus of Variations which used the Hamilton-Jacobi theory. JFB80 (talk) 21:23, 13 November 2010 (UTC)

Bracket notation
Is there a reason for using the notation $$\langle a,b \rangle $$ to denote inner product here? I'd prefer ordinary matrix notation: $$ a^Tb $$. The latter is less confusing, since it can't be confused with other variations of scalar product, such as $$ \int a^\prime b \, \mathrm{d} x$$--PeR 12:08, 14 June 2006 (UTC)

$$ a^Tb $$ is very clear. But when a and b are somewhat messy expressions it becomes less readable. In our case what would we have $$\left(\frac{\partial}{\partial x}V(x,t)\right)^T F(x, u)$$ ? I don't know if I like it or not. Encyclops 00:23, 15 June 2006 (UTC)

 * I think really the notation used should be $$\nabla$$ and the $$\cdot$$. The notation for $$\frac {\delta} {\delta x}$$ where x is a vector is not particularly intuitive.- (User) Wolfkeeper (Talk) 18:28, 20 May 2009 (UTC)

 * Yes, $$\nabla$$ or $$\nabla_x$$ seems good to me, FWIW. And a dot for the inner product, I like also. Encyclops (talk) 19:08, 20 May 2009 (UTC)

Sufficient condition?
The current article claims that the HJB is a sufficient condition. That sounds wrong to me, because first of all the equation itself is not a sufficient condition: I assume what is meant is that "if V solves HJB, this suffices to conclude that it optimizes the objective". But is this true in general? I know that in discrete-time, infinite-horizon cases, a solution of the Bellman equation only serves to identify a candidate solution for the original sequence problem, that is, solving the Bellman equation is necessary but not sufficient for optimality. (See Stokey-Lucas-Prescott, Recursive Methods in Economic Dynamics. Theorem 4.3 shows that for an infinite horizon problem, satisfying the Bellman equation and an appropriate 'transversality condition' suffices for optimality; but the Bellman equation alone is not sufficient.)

Is the sufficiency claim in this article based on the fact that the example given has a finite horizon T? If so, this should be clarified, and it would be helpful to add more general cases too. --Rinconsoleao (talk) 08:07, 30 May 2008 (UTC)

 * The continuous time/continuous state case we are looking at here is more complex than the discrete time case you mention; there are some delicate technical issues that do not arise in d.t. control. A number of "verification theorems" have been proven, using various assumptions.  The simplest theorems, one of which goes back to Bellman, says that if a control satisfies HJB and the terminal condition, then that control is optimal.  HJB => optimality.  In this sense HJB is a sufficient condition.  However, there could exist optimal solutions that are not smooth (not continuous or not differentiable), do not satisfy HJB, but are nevertheless optimal. There are also other verification theorems that establish HJB as necessary and sufficient, but that requires additional assumptions, so they are more restrictive.  We also have to ask what kind of "solutions" of HJB we are talking about, the "classical" PDE solutions that Bellman used or the modern viscosity solutions. Frankly, my knowledge of this area is not sufficient ;-) to give an overview of all these theorems. Encyclops (talk) 23:49, 30 May 2008 (UTC)

Sufficient condition? A confirmation
I do agree with this remark. For me, HJB is a necessary condition i.e. an optimal control should necessarily satisfied HJB. I refer to Oksendal (Stochastic differential equations, theorem 11.2.1).

The important question is to know if the finding of a solution of a HJB equation is sufficient. No. Once found, the solution of the HJB PDE has to satisfies some criteria (a verification theorem, Oksendal 11.2.2).

HJB is necessary but not sufficient.

130.104.59.97 (talk) 09:31, 3 December 2009 (UTC)Devil may cry.

I am quite confused by this article. In my references the HJB equation is a sufficient not necessary condition. In the book of Bertsekas: Dynamic programming and optimal control, Athena Scientific at pag. 93 it is stated that the theorem about HJB is a sufficient condition. And in all my courses of optimal control, every professor always remarks the difference between the Pontryagin minimum principle (necessary) and the HJB (sufficient). Checking the book of Oksendal I saw that the formulation presented is for stochastic process from a stochastic/mathematical point of view. Now, I do not have the knowledge to understand where is the trick, however, I am quite sure that the HJB equation for optimal control problem, as formulated in this article and proved in Bertsekas, is a sufficient condition not necessary. Could someone make a more deep investigation? Pivs (talk) 20:43, 4 May 2012 (UTC)

Multiply by dt?
I wonder if the two last terms (before the big O) of the last equation should not be multiplied by dt. —Preceding unsigned comment added by 61.26.5.133 (talk) 03:18, 13 March 2009 (UTC)

 * I think you may be right. Any other opinions ? Encyclops (talk) 01:42, 16 March 2009 (UTC)

 * Agreed. Done. --Rinconsoleao (talk) 09:44, 8 June 2009 (UTC)

Terminal condition
In section The partial differential equation I see a terminal condition which does not quite look like a meaningful terminal condition. Is it actually meant to be

V(x(T),T) = D(x(T)) $$ and if so, may I correct that? Thank you --Andylong (talk) 11:32, 3 July 2012 (UTC)

Terminal Constraint
Here we have a control problem with x(0) = x0.

Okay. But often we solve control problems where in addition there is a terminal constraint x(T) = xE.

I ran through the literature and I must say that I fail at finding the HJB in that case. In particular, right now we use V(t,X) := min_(x,u){ int_t^T C(x(s),u(s)) ds + D(x(T)) s.t. x(t)=X }. If we were to attempt V(t,X) := min_(x,u){ int_t^T C(x(s),u(s)) ds + D(x(T)) s.t. x(t)=X, x(T)=xE } then V(T,X) for X!=xE would no longer be well-defined.

It would be crazy if that problem was unsolvable via the article's technique. Certainly, because xE can be chosen freely or as parameter of the optimization problem, once the case xE has been presented in this article, the one-sided case can be deleted afterwards in favour of brevity. — Preceding unsigned comment added by 2A02:908:1657:A860:71C7:F597:421E:F6B8 (talk) 21:47, 26 October 2021 (UTC)

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

title: Talk:Hamilton–Jacobi–Bellman equation


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Conrad Gozzo

Conrad Joseph Gozzo (February 6, 1922 – October 8, 1964) was an American trumpet player. He was a member of the NBC Hollywood staff orchestra at the time of his death.

Early life
Gozzo was born in New Britain, Connecticut on February 6, 1922, to Mildred Katz and Jimmy Gozzo. Son of Sicilian parents from Canicattini Bagni (SR). His father played trumpet, and Gozzo began learning the instrument around the age of 5. He played in his junior and senior high school bands, but left school in 1938 or 1939 at the recommendation of Isham Jones to join bandleader and clarinetist Tommy Reynolds in Boston, Massachusetts.

Career
Gozzo was quickly noted for his exceptional technical ability and style. He played under Reynolds for nine months, leaving to play with Red Norvo in November 1939; he played under Norvo until February 1941, but with a brief interlude playing with trumpeter Johnnie Davis. He had a brief tenure with the orchestra of Bob Chester, with whom he first recorded; then performed and recorded with Claude Thornhill's band. There he met vocalist Betty Claire, who he married in late 1941. Thornhill's band dissolved in October 1942.

Gozzo briefly worked with Benny Goodman, then enlisted in the U.S. Navy in mid-November 1942, where clarinetist Artie Shaw had formed a band, the Rangers No. 501. They were first assigned to San Francisco and left for Hawaii in late December. They toured in the South Pacific, the U.K. and the mainland U.S. until being discharged in October 1945. Gozzo briefly rejoined Goodman along with fellow trumpet players from Shaw's band.

Gozzo, lead trumpeter on the Glen Gray, Stan Kenton, and Harry James "remakes", and in Dan Terry's 1954 Columbia sessions, recorded extensively with arrangers Van Alexander, Nelson Riddle, Billy May, Ray Conniff, Jerry Fielding and Shorty Rogers, and also with performers Dean Martin and Frank Sinatra. He played first trumpet on all of the recordings of composer Henry Mancini. He performed on many major live television shows broadcast on the NBC network, including the Dinah Shore Show (1955 through 1964). He also performed on motion picture soundtracks including The Glenn Miller Story, The Benny Goodman Story, Bye Bye Birdie, Call Me Madam, Ben-Hur and Cleopatra. He played on the Ella Fitzgerald two-record set on Verve, Ella Fitzgerald Sings the Harold Arlen Songbook.

Gozzo's nicknames were "Goz" and "Gopher", due to his resemblance to a gopher when viewed from the front while he was playing. He was considered by his colleagues as being an exceptionally strong trumpeter with a well-developed range and tonal quality. For most of his recording career, he played a Besson Meha trumpet with a custom Bert Herrick mouthpiece. Occasionally, he played a Chicago Benge or a LeBlanc Gozzo model trumpet.

In March 1955, Gozzo released his own album, Goz the Great!, signed with RCA Victor and played by "Conrad Gozzo and his Orchestra", directed by Billy May. Three of the twelve tracks were written together by Gozzo and May. The album was not particularly successful and was reviewed as mediocre.

Death and legacy
Gozzo died on October 8, 1964, of liver disease at Providence Saint Joseph Medical Center in Burbank, California. On November 15, 1964, a fundraising concert for his widow was held at the Hollywood Palladium, featuring singers Frank Sinatra, Peggy Lee and Dinah Shore.

"A Trumpeter's Prayer" (1957) by Tutti Camarata originally featured Gozzo, and was performed on November 19, 1989, in New Britain for the 25th anniversary of his death. Jazz composer Sammy Nestico dedicated "Portrait of a Trumpet" to Gozzo.

Discography
With Georgie Auld With Louis Bellson With Buddy Bregman With Ray Brown With Hoagy Carmichael With Benny Carter With Sammy Davis Jr With Henry Mancini With Shorty Rogers With Pete Rugolo
 * In the Land of Hi-Fi with Georgie Auld and His Orchestra (EmArcy, 1955)
 * Skin Deep (Norgran, 1953)
 * Swinging Kicks (Verve, 1957)
 * Bass Hit! (Verve, 1957)
 * Hoagy Sings Carmichael (Pacific Jazz, 1956)
 * Aspects (United Artists, 1959)
 * It's All Over but the Swingin' (Decca, 1957)
 * The Music from Peter Gunn (RCA Victor, 1959)
 * More Music from Peter Gunn (RCA Victor, 1959)
 * The Blues and the Beat (RCA Victor, 1960)
 * Music from Mr. Lucky (RCA Victor, 1960)
 * Uniquely Mancini (RCA Victor, 1963)
 * Cool and Crazy (RCA Victor, 1953)
 * Shorty Rogers Courts the Count (RCA Victor, 1954)
 * Portrait of Shorty (RCA Victor, 1957)
 * Introducing Pete Rugolo (Columbia, 1954)
 * Adventures in Rhythm (Columbia, 1954)
 * Rugolomania (Columbia, 1955)
 * New Sounds by Pete Rugolo (Harmony, 1954–55, [1957])

title: Conrad Gozzo


text:
Maltodextrin

Maltodextrin is a name shared by two different families of chemicals. Both families are glucose polymers (called dextrose or dextrins), but have little chemical or nutritional similarity.

The digestible maltodextrins (or simply maltodextrins) are manufactured as white solids derived from chemical processing of plant starches. They are used as food additives, which are digested rapidly, providing glucose as food energy. They are generally recognized as safe (GRAS) for food and beverage manufacturing in numerous products. Due to their rapid production of glucose, digestible maltodextrins are potential risks for people with diabetes.

The digestion-resistant maltodextrins (also called resistant maltodextrins) are defined as nutritional food additives due to their ability upon fermentation in the colon to yield short-chain fatty acids, which contribute to gastrointestinal health. Digestion-resistant maltodextrins are also white solids resulting from the chemical processing of plant starches, but are processed using methods specifically to be resistant to digestion. They are used as ingredients in many consumer products, such as low-calorie sweeteners, and are considered GRAS.

Consumers may find the shared name for different maltodextrin food additives to be confusing.

Definition
Digestible maltodextrins are well-defined chemically, understood, and documented. By contrast, digestion-resistant maltodextrins – being the newer and more complex chemical family – are less defined chemically, researched and documented.

Maltodextrins are classified by a dextrose equivalent (DE), a number between 3 and 20 that corresponds to the number of free chain ends in a certain sample. A lower DE value means the polymer chains are longer (contain more glucose units) whereas a higher DE value means the chains are shorter. This is an inverse concept compared with the degree of polymerization of the chain. A high-DE maltodextrin is sweeter, more soluble, and has lower heat resistance. Above DE 20, the European Union's CN code calls it glucose syrup; at DE 10 or lower, the customs CN code nomenclature classifies maltodextrins as dextrins.

Digestible maltodextrin
Maltodextrins consist of D -glucose units connected in chains of variable length. The glucose units are primarily linked with α(1→4) glycosidic bonds, like those seen in the linear derivative of glycogen (after the removal of α1,6- branching). Commercial maltodextrin is typically composed of a mixture of chains that vary from three to 17 glucose units long. Properties of maltodextrin, such as sweetness, viscosity, and texture, can be manipulated during manufacturing by altering the extent of starch hydrolysis.

Maltodextrins are digested into glucose units, contributing a food energy value of 4 calories per gram (or 16 kiloJoules per gram). Maltodextrin manufacturing produces a high-purity product with microbiological safety, making it applicable to varied food, beverage, sports, and baked products.

Digestion-resistant maltodextrin
Digestion-resistant maltodextrins are a chemical family much larger than the family of digestible maltodextrins. A definition of a digestion-resistant maltodextrin is: "Resistant maltodextrin/dextrin is a glucose oligosaccharide. Resistant maltodextrin and dextrin products are composed of non-digestible oligosaccharides of glucose molecules that are joined by digestible linkages and non-digestible α-1,2 and α-1,3 linkages." The chemical is of greater structural complexity than a digestible maltodextrin. The two families of maltodextrins have little in common chemically or nutritionally.

Names used to identify digestion-resistant maltodextrin as an ingredient in foods for regulatory purposes include soluble fiber, resistant dextrin, or dextrin. Names may include the food starch used to fabricate the ingredient.

The chemical family has had a history of changes in classification. As of 2023, a digestion-resistant maltodextrin is considered a resistant dextrin and a resistant starch of type 5. Another study contrasted resistant dextrins and resistant maltodextrins, finding them to differ chemically and functionally. In that study, the final maltodextrin product required further processing of the resistant dextrin. The chemical family is effectively defined by the food starch and the manufacturing process, both of which may vary according to manufacturing preferences.

The digestion-resistant maltodextrin ingredient has several properties exploited in food or beverage manufacturing: it is a low-moisture (5% water), free-flowing, fine white powder that disperses readily in water; it is clear in solution with low viscosity; it is odorless, slightly acidic, and has a bland flavor; it is 90% dietary fiber. The average molecular mass of the digestion-resistant maltodextrin molecule is 2,000 daltons.

Digestion-resistant maltodextrin is a soluble (fermentable) dietary fiber with numerous non-starch glycosidic bonds, allowing it to pass through the digestive tract unchanged in physical properties without undergoing digestion, supplying no food energy. In the colon, it is a prebiotic fiber fermented by gut microbiota, resulting in the formation of short-chain fatty acids contributing to gastrointestinal health.

History
After development of food ingredients from starch sources around 1950, digestible maltodextrins were first produced between 1967 and 1973. Digestion-resistant maltodextrins were developed in the 1990s from studies of starch nutrition, leading to the definition of resistant starch. This was accompanied by the detection of digestion-resistant components in food products and manufacturing methods. Some sources typically referred to digestible maltodextrin when describing maltodextrin without further definition of which maltodextrin was used.

Digestible maltodextrin production
Maltodextrin can be enzymatically derived from any starch, such as corn, potato, rice or cassava. In the United States, this starch is usually corn; in Europe, it is common to use wheat. A food starch is boiled. The resulting paste is treated with a combination of acid and enzymes to produce maltodextrins.

Digestion-resistant maltodextrin production
Digestion-resistant maltodextrins are manufactured by a process superficially similar to that for digestible maltodextrins. A food starch is exposed to a combination of heat, acid and enzymes before purification. Part of the process deliberately resembles human digestion – thus, the result is digestion-resistant by design. Neither the food starch source nor the process is standardized.

A list of 14 preparation methods included three to four different methods, including microwave heating. Similar methods differed in detail, possibly because methods are optimized for the plant starch source. One study provided a detailed description of a laboratory method for producing digestion-resistant maltodextrins, combining several of the listed preparation methods.

A step in one method of preparing digestion-resistant maltodextrins is roasting the plant starch in acid conditions. The process breaks the starch molecules into small units, which then recombine with different, more digestion-resistant bonds. Enzymes can be used to break starches apart as an alternative to roasting.

A 2023 review found that use of different starch sources and different manufacturing techniques may produce digestion-resistant maltodextrins with varied properties, concluding that manufacturing methods for digestion-resistant maltodextrin lacked standardization. Another 2023 review of methods examined digestion-resistant maltodextrins from three different starch sources (potato, cassava, and sweet potato) using identical manufacturing techniques. The resulting digestion-resistant maltodextrins were measured to have small physical and chemical differences, such as in formation of dextrin crystals and surface porosity, digestion resistance (80-85%), thermal stabilities, solubility, and formation of pastes. The significance of such differences to the quality of processed foods and health is unknown. A third 2023 study showed maltodextrin digestion rates to be a function of molecular structure.

Food uses
In the European Union, wheat-derived maltodextrin is exempt from wheat allergen labeling, as set out in Annex II of EC Regulation No 1169/2011. In the United States, however, it is not exempt from allergen declaration per the Food Allergen Labeling and Consumer Protection Act, and its effect on a voluntary gluten-free claim must be evaluated on a case-by-case basis per the applicable FDA policy.

Digestible maltodextrin
Maltodextrin has varied applications for food and beverage processing, including medical food, baby food, hospital food, and sports supplement products. It is also used as a substitute for lactose.

Maltodextrin is used to improve the texture and mouthfeel of food and beverage products, such as potato chips and "light" peanut butter to reduce the fat content. It is an effective flavorant, bulking agent, and sugar substitute.

Maltodextrin is easily digestible and can provide a quick source of food energy. Due to its rapid absorption, maltodextrin is used by athletes as an ingredient in sports drinks or recovery supplements to replenish glycogen stores and enhance performance during prolonged exercise. It can be taken as a dietary supplement in powder form, gel packets, energy drinks or oral rinse. Maltodextrin has a high glycemic index of 110, compared to glucose (100) and table sugar (80).

In the United States, maltodextrin is considered a safe ingredient (GRAS) for food manufacturing.

Digestion-resistant maltodextrin
Digestion-resistant maltodextrin is included among other sources as functional fiber, meaning its use in foods may provide improved function of the gastrointestinal system. The low molecular weight, low viscosity, high water solubility, and resistance to enzymatic activity allow digestion-resistant maltodextrin to avoid digestion in the gastrointestinal tract. Such properties may be advantageous to add digestion-resistant maltodextrin as a source of fermentable dietary fiber in food manufacturing, while maintaining the sensory qualities of processed foods.

Digestion-resistant maltodextrins, as prebiotic dietary fiber, are additives used in processed foods primarily as bulking agents or with the intent to confer a health effect. The characteristics of digestion-resistant maltodextrins allow them to be added to diverse kinds of food products, such as beverages, dairy products, and desserts.

They are also relatively low-calorie, colorless, odorless and tasteless. They are nontoxic, chemically stable, and nonreactive with other food ingredients over the range of temperatures required for food preparation and storage.

In Europe, the United States, and Canada, industrial digestion-resistant maltodextrin is recognized as a safe ingredient for food manufacturing.

Digestible maltodextrin
Due to its liberation of glucose molecules when digested, maltodextrin can cause a rapid increase in blood sugar levels when consumed in large quantities, especially for individuals with diabetes or insulin resistance. As maltodextrin is quickly digested and absorbed, excessive consumption may contribute to weight gain, impaired insulin sensitivity, and elevated blood lipids, if not balanced with an appropriate lifestyle or diet.

Digestion-resistant maltodextrin
Digestion-resistant maltodextrin is a fermentable dietary fiber under research for its potential to lower the risk of hypoglycemia, obesity, and associated disorders of metabolic syndrome. While traversing the colon, digestion-resistant maltodextrin is a substrate for producing short-chain fatty acids – the main energy source of cells lining the colon, thereby contributing to health of the gastrointestinal system. Consumption of foods containing digestion-resistant maltodextrin increases the frequency and volume of bowel movements, potentially relieving constipation.

Reviews have concluded that digestion-resistant maltodextrin is classified as a type 5 resistant starch (RS5), a prebiotic dietary fiber having properties that may improve management of diabetes and other disorders of metabolic syndrome. Consumption of food or beverage products containing fermentable dietary fibers, such as digestion-resistant maltodextrin, may cause abdominal discomfort, bloating, and flatulence.

Health claim regulation
In 2014, a scientific panel for the European Food Safety Authority concluded that manufactured foods containing a commercial digestion-resistant dextrin were eligible for a health claim of reducing post-meal blood glucose levels.

In 2017, Health Canada included digestion-resistant maltodextrin among manufactured sources of dietary fiber having desirable physiological effects eligible for product labeling.

In 2018, the United States FDA issued an industry guidance document stating that foods made with digestion-resistant maltodextrin could be advertised as providing a health benefit from fermentable dietary fiber.

Other uses
Maltodextrin is used to coat pills and tablets, and to formulate powders, in the manufacturing of prescription drugs and dietary supplement products. It is also used as a horticultural insecticide both in the field and in greenhouses. Having no biochemical action, its efficacy is based upon spraying a dilute solution upon the pest insects, whereupon the solution dries, blocks insect spiracles, and causes death by asphyxiation.

title: Maltodextrin


text:
IGA

IGA or IgA may refer to:

Businesses and organizations

 * IGA (supermarkets) (initially Independent Grocers Alliance), a name used by many independent supermarkets throughout the world
 * IGA (Australian supermarket group), the local Australian variant of the international IGA
 * International Island Games Association, an organization that organizes the Island Games (a friendly competition between teams from several islands and other small territories)
 * International Grenfell Association, an organization providing health care, education, religious and other services to the fishermen and coastal communities in Newfoundland and Labrador
 * Interscope-Geffen-A&M, an American record label
 * Irish Games Association, a non-profit body which is dedicated to promoting gaming in Ireland
 * International Gay Association, the original name of the International Lesbian, Gay, Bisexual, Trans and Intersex Association

In government

 * Illinois General Assembly
 * Indiana General Assembly
 * Iowa General Assembly

In science and technology

 * Immunoglobulin A (IgA), an antibody playing a critical role in mucosal immunity
 * Intergranular attack, another term for intergranular corrosion (a form of corrosion where the boundaries of crystallites of the material are more susceptible to corrosion than their insides)

Other uses

 * Identity Governance and Administration, the organisational policies, processes and procedures controlling identity management
 * In-game advertising, the use of computer and video games as a medium in which to deliver advertising
 * International Gamers Award, an award for strategy board games and historical simulation games
 * Islamic Golden Age, a period in the history of the Muslim world
 * Koji Igarashi, a Japanese video game producer, nicknamed IGA

title: IGA


text:
Paixhans gun

The Paixhans gun (French: Canon Paixhans, ) was the first naval gun designed to fire explosive shells. It was developed by the French general Henri-Joseph Paixhans in 1822–1823. The design furthered the evolution of naval artillery into the modern age. Its use presaged the end of wood as the preferred material in naval warships, and the rise of the ironclad.

Explosive shells had been used in ground warfare and against stationary targets, but not in high-velocity, flat-trajectory guns due to safety concerns. Henri-Joseph Paixhans developed a delaying mechanism that allowed explosive shells to be safely fired in high-powered guns, first demonstrated in trials in 1824. The French Navy adopted the first Paixhans guns in 1841, and the weapons eventually saw use in the 1840s by France, Britain, Russia, and the United States. The guns' effectiveness in naval combat was demonstrated in battles such as Veracruz in 1838, Campeche in 1843, and Sinop in 1853.

Although the idea was innovative, metallurgy at the time had not advanced enough for safe operation, leading to catastrophic failures in naval guns. Further developments by John A. Dahlgren and Thomas Jackson Rodman improved the weapon for both solid shot and shell use.

Background
Explosive shells had long been in use in ground warfare (in howitzers and mortars) and on bomb vessels against stationary targets, but they were fired only at high angles and with relatively low velocities. The shells of that time were inherently dangerous to handle, and no method had been found to safely fire the explosive shells with the high power and flatter trajectory of a high-velocity gun.

However, before the advent of radar and modern optical controlled firing, high trajectories were not practical for ship-to-ship combat. Such combat essentially required flat-trajectory guns in order to have a reasonable chance of hitting the target. Therefore, ship-to-ship combat had consisted for centuries of encounters between flat-trajectory cannons using inert cannonballs, which could inflict only local damage, even on wooden hulls.

Mechanism
Paixhans advocated using flat-trajectory shell guns against warships in 1822 in his Nouvelle force maritime et artillerie.

Paixhans developed a delaying mechanism that, for the first time, allowed shells to be fired safely in high-powered flat-trajectory guns. The effect of explosive shells lodging into wooden hulls and then detonating was potentially devastating. Henri-Joseph Paixhans first demonstrated this in trials against the two-decker Pacificateur in 1824, in which he successfully broke up the ship. Two prototype Paixhans guns had been cast in 1823 and 1824 for this test. Paixhans reported the results in Experiences faites sur une arme nouvelle. The shells had a fuze that ignited automatically when the gun was fired; they lodged in the wooden hull of the target, and exploded a moment later:

"The shells which produced those very extensive ravages upon the Pacificator hulk in the experiments made at Brest, in 1821 and 1824, upon the evidences of which the French naval shell system was founded, were loaded shells, having fuzes attached, which, ignited by the explosion of the discharge in the gun, continued to burn for a time somewhat greater than that of the estimated flight, and then exploded; thus producing the maximum effect which any shell is capable of producing on a ship."

The first Paixhans guns for the French Navy were made in 1841. The barrel of the guns weighed about (10,000 lb), and proved accurate to about (2 mi). In the 1840s, France, Britain, Russia, and the United States adopted the new naval guns.

The effect of the guns in an operational context was first demonstrated during the actions at Veracruz in 1838, at Campeche in 1843, Eckernförde in 1849 during the Danish–Prussian War, and especially at the Battle of Sinop in 1853 during the Crimean War. The Naval Battle of Campeche made history because it was the first time both sides used explosive shells and the only time sailing ships defeated steamers.

According to the Penny Cyclopaedia (1858):

"General Paixhans made important improvements in the construction of heavy ordnance, and also in the projectiles, in the carriages, and in the mode of working the guns. The Paixhans-guns are especially adapted for the projection of shells and hollow shot, and were first adopted in France about the year 1824. Similar pieces of ordnance have since been introduced into the British service. They are suitable either for ships of war, or for fortresses which defend coasts. The original Paixhans-gun was 9'4' long [2.84 m], and weighed nearly 74 cwts [3,800 kg]. The bore was 22 cm. By judicious distribution of the metal it was so much strengthened about the chamber, or place of charge, that it could bear firing with solid shot weighing from 86 to 88 lbs [39–40 kg], or with hollow shot weighing about 60 lbs [27 kg]. The charge varied from 10 lbs. 12 oz to 18 lbs [4.9-8.2 kg] of powder. General Paixhans was one of the first to recommend cylindro-conical projectiles, as having the advantage of encountering less resistance from the air than round balls, having a more direct flight, and striking the object aimed at with much greater force, when discharged from a piece of equal calibre, whether musket or great gun. As large ships of war, particularly three-decked ships, offer a mark which can hardly be missed, even at considerable distances, and as their wooden walls are so thick and strong that a shell projected horizontally could not pass through them, an explosion taking place would produce the destructive effects of springing a mine, and far exceeding those of a shell projected vertically, and acting by concussion or percussion."

Development
While the idea was notable in the advance of artillery, metallurgy had not advanced to the level needed for safe operation. The naval guns of this type were known for catastrophic failures: the chambers would burst in use. The long shells and large blackpowder charges needed to propel the shells put a stress on cast-iron cannon that often could not be contained. Further work by John A. Dahlgren, and Thomas Jackson Rodman improved the weapon to use both solid shot and shell safely.

France
In 1827, the French navy ordered fifty large guns on the Paixhans model from the arsenals at Ruelle and at Indret near Nantes. The gun chosen, the canon-obusier de 80, was so called because it was of the 22 cm bore diameter which would have fired an 80-pound solid shot. The gun barrel weighed 3,600 kg and the bore was of 23 cm diameter and 2.8 m long, firing a shell weighing 23.12 kg. The guns were produced slowly and were tested afloat through the 1830s. They formed a small part of the armament on larger ships, with only two or four guns being carried, although on smaller, experimental steam vessels they, and the much larger canon-obusier de 150 of 27 cm bore, were proportionately more important. The paddle steamer Météore, for example, carried three canon-obusier de 80 pieces and six small carronades in 1833. Alongside the large guns which Paixhans had called for, the French navy also used a smaller shell gun, of the same 164 mm bore as its standard solid shot-firing 30 pounder guns and carronades, in larger numbers with first rate ships carrying over 30 of these guns.

United States
The United States Navy adopted the design, and equipped several ships with 8-inch guns of 63 and 55 cwt. in 1845, and later a 10-inch shell gun of 86 cwt. Paixhans guns were used on USS Constitution (four Paixhans guns) in 1842, under the command of Foxhall A. Parker, Sr., USS Constellation in 1854, and were also installed on the USS Mississippi (10 Paixhans guns), and USS Susquehanna (six Paixhans guns) during Commodore Perry's mission to open Japan in 1853.

The Dahlgren gun was developed by John A. Dahlgren in 1846, with advantages over Paixhans guns:

"Paixhans had so far satisfied naval men of the power of shell guns as to obtain their admission on shipboard; but by unduly developing the explosive element, he had sacrificed accuracy and range.... The difference between the system of Paixhans and my own was simply that Paixhans guns were strictly shell guns, and were not designed for shot, nor for great penetration or accuracy at long ranges. They were, therefore, auxiliary to, or associates of, the shot-guns. This made a mixed armament, was objectionable as such, and never was adopted to any extent in France... My idea was, to have a gun that should generally throw shells far and accurately, with the capacity to fire solid shot when needed. Also to compose the whole battery entirely of such guns."

Russia
The Russian Navy was the first to use the guns extensively in combat. At the Battle of Sinop in 1853, Russian ships attacked and annihilated a Turkish fleet with their Paixhans explosive shell guns. The shells penetrated deep inside the wooden planking of Turkish ships, exploding and igniting the hulls. The defeat was instrumental in convincing the naval powers of the shell's efficacy, and hastened the development of the ironclad to counter it.

title: Paixhans gun


text:
Yakovlev (surname)

Yakovlev (Яковлев, ) is an East Slavic surname derived from the masculine given name Yakov. Yakovleva is the feminine form.

Notable people with the surname include:

 * Alexander Yakovlev (disambiguation), several people
 * Anatoli Yakovlev (1913–1993), Soviet spymaster in New York City
 * Andrei Yakovlev (born 1995), Russian footballer
 * Boris Yakovlev (1945–2014), Soviet Ukrainian race walker
 * Dmitry Yakovlev, Kazakhstani beach volleyball player
 * Egor Yakovlev (born 1991), Russian ice hockey player
 * Elena Yakovleva (born 1961), Russian actress
 * Gennady Yakovlev (born 1938), Russian botanist
 * Ivan Yakovlev (1848–1930), Chuvash enlightener, educator, and writer
 * Lora Yakovleva (born 1932), Russian chess grandmaster
 * Maksim Sergeyevich Yakovlev (born 1991), Russian footballer
 * Mikhail Iakovlev (born 2000), Israeli racing cyclist
 * Mikhail Yakovlev (footballer, born 1892) (1892–1942), Russian footballer
 * Natalya Yakovleva (handballer) (born 1986), Kazakhstani handball player
 * Nataliya Yakovleva (swimmer) (born 1971), Russian Olympic Swimmer
 * Nikolai Dmitriyevich Yakovlev (1898–1972), Soviet military leader
 * Oleg Yakovlev (footballer, born 1970), Russian football player and manager
 * Oleg Yakovlev (footballer, born 1997), Russian footballer
 * Olga Vitalevna Yakovleva (1970–2015), Russian singer known as Origa
 * Pavel Yakovlev (disambiguation), several people
 * Postnik Yakovlev, Russian architect of St Basil's Cathedral in Moscow, active 1555–1588
 * Roman Yakovlev (born 1976), Russian volleyball player
 * Sergei Yakovlev (disambiguation), several people
 * Vadim Yakovlev, Russian Cossack cavalry commander, active 1914–1923
 * Valentina Yakovleva (born 1947), Soviet Olympic Swimmer
 * Varvara Yakovleva (died 1918), Russian Orthodox nun and saint
 * Varvara Yakovleva (politician) (1884–1941), Russian Bolshevik leader
 * Vasily Yakovlev (1885–1938), Finnish Bolshevik revolutionary and politician
 * Vasily Evgrafovich Yakovlev (1839–1908), Russian entomologist
 * Vasyl Yakovlev (born 1972), Ukrainian Olympic cyclist
 * Vitali Yakovlev (born 1985), Russian footballer
 * Vladimir Anatolyevich Yakovlev (born 1944), Russian politician
 * Vladimir Yakovlev (general) (born 1954), Russian military commander
 * Vladimir Yakovlev (journalist) (born 1959), Russian journalist and editor
 * Vladislav Yakovlev (rower) (born 1993), Kazakhstani rower
 * Yakov Yakovlev (1896–1938), Soviet statesman and politician
 * Yegor Yakovlev (1930–2005), Russian journalist
 * Yuriy Yakovlev (disambiguation), several people

title: Yakovlev (surname)


text:
Close-packing of equal spheres

In geometry, close-packing of equal spheres is a dense arrangement of congruent spheres in an infinite, regular arrangement (or lattice). Carl Friedrich Gauss proved that the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is
 * $$\frac{\pi}{3\sqrt 2} \approx 0.74048$$.

The same packing density can also be achieved by alternate stackings of the same close-packed planes of spheres, including structures that are aperiodic in the stacking direction. The Kepler conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was proven by T. C. Hales. Highest density is known only for 1, 2, 3, 8, and 24 dimensions.

Many crystal structures are based on a close-packing of a single kind of atom, or a close-packing of large ions with smaller ions filling the spaces between them. The cubic and hexagonal arrangements are very close to one another in energy, and it may be difficult to predict which form will be preferred from first principles.

FCC and HCP lattices
There are two simple regular lattices that achieve this highest average density. They are called face-centered cubic (FCC) (also called cubic close packed) and hexagonal close-packed (HCP), based on their symmetry. Both are based upon sheets of spheres arranged at the vertices of a triangular tiling; they differ in how the sheets are stacked upon one another. The FCC lattice is also known to mathematicians as that generated by the A3 root system.

Cannonball problem
The problem of close-packing of spheres was first mathematically analyzed by Thomas Harriot around 1587, after a question on piling cannonballs on ships was posed to him by Sir Walter Raleigh on their expedition to America. Cannonballs were usually piled in a rectangular or triangular wooden frame, forming a three-sided or four-sided pyramid. Both arrangements produce a face-centered cubic lattice – with different orientation to the ground. Hexagonal close-packing would result in a six-sided pyramid with a hexagonal base.

The cannonball problem asks which flat square arrangements of cannonballs can be stacked into a square pyramid. Édouard Lucas formulated the problem as the Diophantine equation $$\sum_{n=1}^{N} n^2 = M^2$$ or $$\frac{1}{6} N(N+1)(2N+1) = M^2$$ and conjectured that the only solutions are $$N = 1, M = 1,$$ and $$N = 24, M = 70$$. Here $$N$$ is the number of layers in the pyramidal stacking arrangement and $$M$$ is the number of cannonballs along an edge in the flat square arrangement.

Positioning and spacing
In both the FCC and HCP arrangements each sphere has twelve neighbors. For every sphere there is one gap surrounded by six spheres (octahedral) and two smaller gaps surrounded by four spheres (tetrahedral). The distances to the centers of these gaps from the centers of the surrounding spheres is √$3/2$ for the tetrahedral, and √2 for the octahedral, when the sphere radius is 1.

Relative to a reference layer with positioning A, two more positionings B and C are possible. Every sequence of A, B, and C without immediate repetition of the same one is possible and gives an equally dense packing for spheres of a given radius.

The most regular ones are
 * FCC = ABC ABC ABC... (every third layer is the same)
 * HCP = AB AB AB AB... (every other layer is the same).

There is an uncountably infinite number of disordered arrangements of planes (e.g. ABCACBABABAC...) that are sometimes collectively referred to as "Barlow packings", after crystallographer William Barlow.

In close-packing, the center-to-center spacing of spheres in the xy plane is a simple honeycomb-like tessellation with a pitch (distance between sphere centers) of one sphere diameter. The distance between sphere centers, projected on the z (vertical) axis, is:

 * $$\text{pitch}_Z = \sqrt{6} \cdot {d\over 3}\approx0.816\,496\,58 d,$$

where d is the diameter of a sphere; this follows from the tetrahedral arrangement of close-packed spheres.

The coordination number of HCP and FCC is 12 and their atomic packing factors (APFs) are equal to the number mentioned above, 0.74.

Lattice generation
When forming any sphere-packing lattice, the first fact to notice is that whenever two spheres touch a straight line may be drawn from the center of one sphere to the center of the other intersecting the point of contact. The distance between the centers along the shortest path namely that straight line will therefore be r1 + r2 where r1 is the radius of the first sphere and r2 is the radius of the second. In close packing all of the spheres share a common radius, r. Therefore, two centers would simply have a distance 2r.

Simple HCP lattice

To form an A-B-A-B-... hexagonal close packing of spheres, the coordinate points of the lattice will be the spheres' centers. Suppose, the goal is to fill a box with spheres according to HCP. The box would be placed on the x-y-z coordinate space.

First form a row of spheres. The centers will all lie on a straight line. Their x-coordinate will vary by 2r since the distance between each center of the spheres are touching is 2r. The y-coordinate and z-coordinate will be the same. For simplicity, say that the balls are the first row and that their y- and z-coordinates are simply r, so that their surfaces rest on the zero-planes. Coordinates of the centers of the first row will look like (2r, r, r), (4r, r, r), (6r ,r, r), (8r ,r, r), ... .

Now, form the next row of spheres. Again, the centers will all lie on a straight line with x-coordinate differences of 2r, but there will be a shift of distance r in the x-direction so that the center of every sphere in this row aligns with the x-coordinate of where two spheres touch in the first row. This allows the spheres of the new row to slide in closer to the first row until all spheres in the new row are touching two spheres of the first row. Since the new spheres touch two spheres, their centers form an equilateral triangle with those two neighbors' centers. The side lengths are all 2r, so the height or y-coordinate difference between the rows is √3r. Thus, this row will have coordinates like this:

 * $$\left(r, r + \sqrt{3}r, r\right),\ \left(3r, r + \sqrt{3}r, r\right),\ \left(5r, r + \sqrt{3}r, r\right),\ \left(7r, r + \sqrt{3}r, r\right), \dots.$$

The first sphere of this row only touches one sphere in the original row, but its location follows suit with the rest of the row.

The next row follows this pattern of shifting the x-coordinate by r and the y-coordinate by √3. Add rows until reaching the x and y maximum borders of the box.

In an A-B-A-B-... stacking pattern, the odd numbered planes of spheres will have exactly the same coordinates save for a pitch difference in the z-coordinates and the even numbered planes of spheres will share the same x- and y-coordinates. Both types of planes are formed using the pattern mentioned above, but the starting place for the first row's first sphere will be different.

Using the plane described precisely above as plane #1, the A plane, place a sphere on top of this plane so that it lies touching three spheres in the A-plane. The three spheres are all already touching each other, forming an equilateral triangle, and since they all touch the new sphere, the four centers form a regular tetrahedron. All of the sides are equal to 2r because all of the sides are formed by two spheres touching. The height of which or the z-coordinate difference between the two "planes" is $√6r2⁄3$. This, combined with the offsets in the x and y-coordinates gives the centers of the first row in the B plane:

 * $$\left(r, r + \frac{\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(3r, r + \frac{\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(5r, r + \frac{\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(7r, r + \frac{\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right), \dots. $$

The second row's coordinates follow the pattern first described above and are:

 * $$\left(2r, r + \frac{4\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(4r, r + \frac{4\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(6r, r + \frac{4\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\ \left(8r,r + \frac{4\sqrt{3}r}{3}, r + \frac{\sqrt{6}r2}{3}\right),\dots. $$

The difference to the next plane, the A plane, is again $√6r2⁄3$ in the z-direction and a shift in the x and y to match those x- and y-coordinates of the first A plane.

In general, the coordinates of sphere centers can be written as:

 * $$\begin{bmatrix}

2i + ((j\ +\ k) \bmod 2)\\ \sqrt{3}\left[j + \frac{1}{3}(k \bmod 2)\right]\\ \frac{2\sqrt{6}}{3}k \end{bmatrix}r$$

where i, j and k are indices starting at 0 for the x-, y- and z-coordinates.

Miller indices
Crystallographic features of HCP systems, such as vectors and atomic plane families, can be described using a four-value Miller index notation ( hkil ) in which the third index i denotes a degenerate but convenient component which is equal to −h − k. The h, i and k index directions are separated by 120°, and are thus not orthogonal; the l component is mutually perpendicular to the h, i and k index directions.

Filling the remaining space
The FCC and HCP packings are the densest known packings of equal spheres with the highest symmetry (smallest repeat units). Denser sphere packings are known, but they involve unequal sphere packing. A packing density of 1, filling space completely, requires non-spherical shapes, such as honeycombs.

Replacing each contact point between two spheres with an edge connecting the centers of the touching spheres produces tetrahedrons and octahedrons of equal edge lengths. The FCC arrangement produces the tetrahedral-octahedral honeycomb. The HCP arrangement produces the gyrated tetrahedral-octahedral honeycomb. If, instead, every sphere is augmented with the points in space that are closer to it than to any other sphere, the duals of these honeycombs are produced: the rhombic dodecahedral honeycomb for FCC, and the trapezo-rhombic dodecahedral honeycomb for HCP.

Spherical bubbles appear in soapy water in a FCC or HCP arrangement when the water in the gaps between the bubbles drains out. This pattern also approaches the rhombic dodecahedral honeycomb or trapezo-rhombic dodecahedral honeycomb. However, such FCC or HCP foams of very small liquid content are unstable, as they do not satisfy Plateau's laws. The Kelvin foam and the Weaire–Phelan foam are more stable, having smaller interfacial energy in the limit of a very small liquid content.

There are two types of interstitial holes left by hcp and fcc conformations; tetrahedral and octahedral void. Four spheres surround the tetrahedral hole with three spheres being in one layer and one sphere from the next layer. Six spheres surround an octahedral voids with three spheres coming from one layer and three spheres coming from the next layer. Structures of many simple chemical compounds, for instance, are often described in terms of small atoms occupying tetrahedral or octahedral holes in closed-packed systems that are formed from larger atoms.

Layered structures are formed by alternating empty and filled octahedral planes. Two octahedral layers usually allow for four structural arrangements that can either be filled by an hpc of fcc packing systems. In filling tetrahedral holes a complete filling leads to fcc field array. In unit cells, hole filling can sometimes lead to polyhedral arrays with a mix of hcp and fcc layering.

title: Close-packing of equal spheres


text:
Silverwing

Silverwing or Silver Wing may refer to:

 * Silverwing, a series of children's novels by Kenneth Oppel
 * Silverwing (TV series), a 2003 animated TV series based on the first book in the novel series
 * Silverwing (band), later known as Pet Hate, a 1980s British heavy metal band
 * "Silverwing", a song by Arch Enemy from Burning Bridges
 * Silver Wing Medal, a Philippine military decoration
 * Silver Wing Service, a luxury air service offered by Imperial Airways
 * Honda Silver Wing (disambiguation), a line of motorcycles and scooters

title: Silverwing


text: User talk:68.82.140.174

title: User talk:68.82.140.174


text:
Théophile Corret de la Tour d'Auvergne

Théophile Malo Corret de la Tour d'Auvergne (23 November 1743 – 28 June 1800) was a French officer named by Napoleon as the "first grenadier of France". He was also a celtomaniac antiquarian who introduced the words "dolmen" and "menhir" into general archaeological usage.

Career
He was the son of a lawyer named Corret, and was certainly baptised and perhaps born at Carhaix-Plouguer in Brittany, though nearby Saint-Hernin where his father had a position is one of a number of other places in the area put forward as his place of birth. His desire for a military career being strongly marked, he was enabled by the not uncommon device of producing a certificate of nobility signed by his friends, first to be nominally enlisted in the Maison du Roi, and soon afterwards to receive a commission in the line, under the name of Corret de Kerbaufret. Four years after joining, in 1771, he assumed with the help of a letter from the Duke of Bouillon the surname of La Tour d'Auvergne, claiming descent from an illegitimate half-brother of the great Marshal Henri de la Tour d'Auvergne, Vicomte de Turenne, one of Louis XIV's leading commanders. Many years of routine service with his regiment were broken only by his participation as a volunteer in the Duke de Crillon's Franco-Spanish expedition to Menorca in 1781. This led to an offer of promotion into the Spanish army, but he refused to change his allegiance.

In 1784 he was promoted captain, and in 1791 he received the Cross of St. Louis. In the early part of the French Revolution his patriotism was still more conspicuously displayed in his resolute opposition to the proposals of many of his brother officers in the Angoumois regiment to emigrate rather than to swear to the constitution, and he fought in the revolutionary army in the French Revolutionary Wars, refusing promotion beyond the grade of captain. In 1792 his lifelong interest in numismatics and questions of language was shown by a work which he published on the Bretons. At this time he was serving under Montesquiou in the Alps, and although there was only outpost fighting he distinguished himself by his courage and audacity, qualities which were displayed in more serious fighting in the Pyrenees the next year. He declined well-earned promotion to colonel, and, being broken in health and compelled, owing to the loss of his teeth, to live on milk, he left the army in 1795.

On his return by sea to Brittany he was captured by the English and held prisoner for two years. When released, he settled at Passy and published Origines gauloises (1796). In 1797, on the appeal of an old friend whose son had been taken as a conscript, he volunteered as the youth's substitute, and served on the Rhine (1797) and in Switzerland (1798–1799) as a captain. In recognition of his singular bravery and modesty Corret obtained a decree from Napoleon naming him the "first grenadier of France" (27 April 1800). This led him to volunteer again, and he was killed in action at the Battle of Neuburg on 27 June 1800.

Memory
La Tour d'Auvergne's almost legendary courage had captivated the imagination of the French soldier, and his memory was not allowed to die. It was customary for the French troops and their allies of the Rhine Confederation under Napoleon to march at attention when passing his burial place on the battlefield. His heart was long carried by the grenadier company of his regiment, the 46th. After being in the possession of Giuseppe Garibaldi for many years, it was finally deposited in the keeping of the city of Paris in 1883.

In 1800 Napoleon ordered, "His name is to be kept on the pay list and roll of his company. It will be called at all parades and a non-commissioned officer will reply,  'Mort au champ d'honneur.' " This custom, with little variation, is still observed in the 46th regiment on all occasions when the color is taken on parade. However, in early 1809, Napoleon himself put this tradition to an end. "What regiment has not had a general, a colonel, or finally, a brave man killed at its head? I have tolerated this singularity long enough" (Nap. Corr., vol 18, No. 14727). The urn was collected by the War Minister, showing that Napoleon preferred to celebrate the men who died to affirm his dynasty and build his Empire, rather than an individual whose association with the French Revolution was unmistakable.

title: Théophile Corret de la Tour d'Auvergne


text:
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