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January Uprising

The January Uprising was an insurrection principally in Russia's Kingdom of Poland that was aimed at putting an end to Russian occupation of part of Poland and regaining independence. It began on 22 January 1863 and continued until the last insurgents were captured by the Russian forces in 1864.

It was the longest-lasting insurgency in partitioned Poland. The conflict engaged all levels of society and arguably had profound repercussions on contemporary international relations and ultimately provoked a social and ideological paradigm shift in national events that went on to have a decisive influence on the subsequent development of Polish society.

A confluence of factors rendered the uprising inevitable in early 1863. The Polish nobility and urban bourgeois circles longed for the semi-autonomous status they had enjoyed in Congress Poland before the previous insurgency, a generation earlier in 1830, and youth encouraged by the success of the Italian independence movement urgently desired the same outcome. Russia had been weakened by its Crimean adventure and had introduced a more liberal attitude in its internal politics which encouraged Poland's underground National Government to plan an organised strike against their Russian occupiers no earlier than the spring of 1863. They had not reckoned with Aleksander Wielopolski, the pro-Russian archconservative head of the civil administration in the Russian partition. In an attempt to derail the Polish national movement, he brought forward to January the conscription of young Polish activists into the Imperial Russian Army for 20-year service. That decision is what triggered the January Uprising of 1863, the very outcome that Wielopolski had wanted to avoid. The rebellion by young Polish conscripts was soon joined by high-ranking Polish-Lithuanian officers and members of the political class. The insurrectionists, as yet ill-organised, were severely outnumbered and lacking sufficient foreign support and forced into hazardous guerrilla tactics. Reprisals were swift and ruthless. Public executions and deportations to Siberia eventually persuaded many Poles to abandon armed struggle. In addition, Tsar Alexander II hit the landed gentry hard and, as a result, the whole economy, with a sudden decision in 1864 for finally abolishing serfdom in Poland. The ensuing breakup of estates and destitution of many peasants convinced educated Poles to turn instead to the idea of "organic work", economic and cultural self-improvement.

Background
Despite the Russian Empire's loss of the Crimean War and weakened economic and political state, Alexander II warned in 1856 against further concessions with the words "forget any dreams". There were two prevailing streams of thought among the population of the Kingdom of Poland. One had patriotic stirrings within liberal-conservative usually landed and intellectual circles, centered around Andrzej Zamoyski and hoped for an orderly return to the constitutional status before 1830; they became characterized as the Whites. The alternative tendency, characterized as the Reds, represented a democratic movement uniting peasants, workers and some clergy. For both streams central to their dilemma was the peasant question. However, estate owners tended to favour the abolition of serfdom in exchange for compensation, but the democratic movement saw the overthrow of the Russian yoke as entirely dependent on an unconditional liberation of the peasantry. Just as the democrats organized the first religious and patriotic demonstrations in 1860, covert resistance groups began to form among educated youth. Blood was first to shed in Warsaw in February 1861, when the Russian Army attacked a demonstration in Castle Square on the anniversary of the Battle of Grochów. There were five fatalities. Fearing the spread of spontaneous unrest, Alexander II reluctantly agreed to accept a petition for a change in the system of governance. Ultimately, he agreed to the appointment of Aleksander Wielopolski to head a commission to look into Religious Observance and Public Education and announced the formation of a State Council and self-governance for towns and powiats. The concessions did not prevent further demonstrations. On 8 April, there were 200 killed and 500 wounded by Russian fire. Martial law was imposed in Warsaw, and brutally-repressive measures were taken against the organisers in Warsaw and Vilna by deporting them deep into Russia.

In Vilna alone, 116 demonstrations were held in 1861. That autumn, Russians had introduced a state of emergency in Vilna Governorate, Kovno Governorate and Grodno Governorate.

The events led to a speedier consolidation of the resistance. Future leaders of the uprising gathered secretly in St. Petersburg, Warsaw, Vilna, Paris and London. Two bodies emerged from those consultations. By October 1861, the urban "Movement Committee" (Komitet Ruchu Miejski) had been formed, followed in June 1862, by the Central National Committee (CNC). Its leadership included Stefan Bobrowski, Jarosław Dąbrowski, Zygmunt Padlewski, Agaton Giller and Bronisław Szwarce. The body directed the creation of national structures that were intended to become a new secret Polish state. The CNC had not planned an uprising before the spring of 1863 at the earliest. However, Wielopolski's move to start conscription to the Russian Army in mid-January forced its hand to call the uprising prematurely on the night of 22–23 January 1863.

Call to arms in the Kingdom of Poland
The uprising broke out at a moment when general peace prevailed in Europe, and although there was vociferous support for the Poles, powers such as France, Britain and Austria were unwilling to disturb the international calm. The revolutionary leaders did not have sufficient means to arm and equip the groups of young men hiding in forests to escape Alexander Wielopolski's order of conscription into the Russian Army. Initially, about 10,000 men rallied around the revolutionary banner. The volunteers came chiefly from city working classes and minor clerks, but there was also a significant number of the younger sons of the poorer szlachta (nobility) and a number of priests of lower rank. Initially, the Russian government had at its disposal an army of 90,000 men, under Russian General Anders Edvard Ramsay, in Poland.

It looked as if the rebellion might be crushed quickly. Undeterred, the CNC's provisional government issued a manifesto in which it declared "all sons of Poland are free and equal citizens without distinction of creed, condition or rank". It decreed that land cultivated by the peasants, whether on the basis of rent or service, should become their unconditional property, and compensation for it would be given to the landlords out of State general funds. The provisional government did its best to send supplies to the unarmed and scattered volunteers, who, in February, had fought in eighty bloody skirmishes with the Russians. Meanwhile, the CNC issued an appeal for assistance to the nations of Western Europe that was received everywhere with supportive sentiments from Norway to Portugal. The Confederate States of America sympathized with the Polish-Lithuanian rebels and viewed their struggles analogous. Italian, French and Hungarian officers answered the call. Pope Pius IX was against the 1863 uprising of which he informed Wsyslaw Czartoryski. The historian Jerzy Zdrada records that by the late spring and the early summer of 1863, there were 35,000 Poles under arms facing a Russian Army of 145,000 in the Polish Kingdom.

Uprising spreads to Lithuania
On 1 February 1863, the uprising erupted in the former Grand Duchy of Lithuania. In April and May, it had spread to Dinaburg, Latvia and Witebsk, Belarus, to the Kiev Governorate, northern Ukraine, and to the Wolynian Voivodship. Volunteers, weapons and supplies began to flow in over the borders from Galicia, in the Austrian Partition, and from the Prussian Partition. Volunteers also arrived from Italy, Hungary, France and Russia itself. The greatest setback was that in spite of the liberation manifesto from the KCN, without prior ideological agitation, the peasantry could not be mobilized to participate in the struggle except in those regions that were dominated by Polish units, which saw a gradual enrollment into the uprising of agricultural workers.

Secret State
The secret Polish state was directed by the Rada Narodowa (RN, National Council) to which the civil and military structures on the ground were accountable. It was a "virtual coalition government" formed of the Reds and the Whites and was led by Zygmunt Sierakowski, Antanas Mackevičius and Konstanty Kalinowski. The latter two supported their counterparts in Poland and adhered to common policies.

Its diplomatic corps was centered on Paris under the direction of Wladyslaw Czartoryski. The eruption of armed conflict in the former Commonwealth of Two Nations had surprised western European capitals, even if public opinion responded with sympathy for the rebel cause. It had dawned on Paris, London, Vienna and Saint Petersburg that the crisis could plausibly turn into an international war. For their part, Russian diplomats considered the uprising an internal matter, and European stability was generally predicated on the fate of Poland's aspiration.

International repercussions
The uncovering of the existence of the Alvensleben Convention, signed on 8 February 1863 by Prussia and Russia in St. Petersburg, to suppress the Poles jointly, internationalized the uprising. It enabled Western powers to take the diplomatic initiative for their own ends. Napoleon III of France, already a sympathizer with Poland, was concerned to protect his border on the Rhine and turned his political guns on Prussia with a view to provoking a war with it. He was simultaneously seeking an alliance with Austria. The United Kingdom, on the other hand, sought to prevent a Franco-Prussian war and to block an Austrian alliance with France and so looked to scupper any rapprochement between France and Russia. Austria was competing with Prussia for the leadership of the German territories but rejected French approaches for an alliance and spurned any support of Napoleon III as acting against German interests. There was no discussion of military intervention on behalf of the Poles, despite Napoleon's support for the continuation of the insurgency.France, the United Kingdom and Austria agreed to a diplomatic intervention in defense of Polish rights and in April issued diplomatic notes that were intended to be no more than persuasive in tone. The Polish RN hoped that the evolution of the insurgency would ultimately push western powers to adopt an armed intervention, which was the flavour of Polish diplomatic talks with those powers. The Polish line was that the establishment of continued peace in Europe was conditional on the return of an independent Polish state.

With the threat of war averted, St. Petersburg left the door open for negotiations but was adamant in its rejection of any western rights to armed conflict. In June 1863, western powers iterated the conditions: an amnesty for the insurgents, the creation of a national representative structure, the development of autonomous concessions across the Kingdom, a recall of a conference of Congress of Vienna (1815) signatories and a ceasefire for its duration. That fell well below the expectations of the leadership of the uprising. While concerned by the threat of war, Alexander II felt secure enough with the support of his people to reject the proposals. Although France and Britain were insulted, they did not proceed with further interventions, which enabled Russia to extend and finally to break off negotiations in September 1863.

Outcome on the ground
Apart from the efforts of Sweden, diplomatic intervention by foreign powers on behalf of Poland was on the balance unhelpful in drawing attention away from the aim of Polish national unity towards its social divisions. It alienated Austria, which had maintained friendly neutrality towards Poland and not interfered with Polish activities in Galicia. It prejudiced public opinion among radical groups in Russia that until then had been friendly because they regarded the uprising as a social, rather than a national, insurgency. It also stirred the Russian government to ever more brutal suppression of hostilities and repression against its Polish participants, who had grown in strength.

In addition to the thousands who fell in battle, 128 men were hanged under the personal supervision of Mikhail Muravyov 'Muravyov the Hangman', and 9,423 men and women were exiled to Siberia, 2,500 men according to Russia's own estimates. The historian Norman Davies gives the number as 80,000 and noted it was the single largest deportation in Russian history. Whole villages and towns were burned down. All economic and social activities were suspended, and the szlachta was ruined through the confiscation of property and exorbitant taxes. Such was the brutality of Russian troops that their actions were condemned throughout Europe. Count Fyodor Berg, the newly appointed governor, Namiestnik of Poland, and the successor to Muravyov, employed harsh measures against the population and intensified systematic Russification in an effort to eradicate Polish traditions and culture.

Social and ethnic divisions laid bare
Insurgents of landed background constituted 60% of the uprising's participants (in Lithuania and Belarus around 50%, in Ukraine some 75%). Records indicate that 95% of those punished for participation in the uprising were Catholic, which corresponded to the general proportion of participants.

Despite outreach to Rus (Ruthenian) peasants by the Polish gentry (szlachta), comparatively few partook in the January Uprising. In some cases they assisted the Russian forces in catching rebels. This has been cited as one of the primary reasons for the failure of the uprising.

During the first 24 hours of the uprising, armouries across the country were looted, and many Russian officials were executed on sight. On 2 February 1863, was the start of the first major military engagement of the uprising between Lithuanian peasants armed mostly with scythes and a squadron of Russian hussars outside Čysta Būda, near Marijampolė. It ended with the massacre of the unprepared peasants. While there was still hope of a short war, insurgent groups merged into larger formations and recruited new volunteers.

Evolution of events
The provisional government had counted on an insurgency erupting in Russia, where wide discontent with the autocratic regime then seemed to be brewing. It also counted on the active support of Napoleon III, particularly after Prussia, expecting the inevitable armed conflict with France, had made overtures to Russia sealed in the Alvensleben Convention and offered assistance in suppressing the Polish uprising. Arrangements had already been completed on 14 February and the British Ambassador to Berlin, Sir Alexander Malet, informed his government that a Prussian military envoy

"has concluded a military convention with the Russian Government, according to which the two governments will reciprocally afford facilities to each other for the suppression of the insurrectionary movements which have lately taken place in Poland and Lithuania. The Prussian railways are also to be placed at the disposal of the Russian military authorities for the transportation of troops through Prussian territory from one part of the former Polish-Lithuanian commonwealth to another."

That step by Otto von Bismarck led to protests from several governments and incensed the several constituent nations of the former Commonwealth. The result was the transformation of a relatively insignificant uprising into another "national war" against Russia. Encouraged by promises made by Napoleon III, all provinces of the erstwhile Commonwealth, acting on the advice of Władysław Czartoryski, had taken to arms. Moreover, to Indicate their solidarity, all Commonwealth citizens holding office under the Russian government, including the Archbishop of Warsaw, Zymunt Feliński, resigned their positions and signed their allegiance to the newly constituted Government, which was composed of the five most prominent representatives of the Whites. The Reds, meanwhile, criticised the Polish National Government for being reactionary with its policy to incentivise Polish peasants to fight in the uprising. The government justified its inaction on the back of hopes of foreign military intervention promised by Napoleon III that never materialised.

Romuald Traugutt
It was only after Polish General Romuald Traugutt had taken matters into his own hands on 17 October 1863 to unite all classes under a single national banner that the struggle could be upheld. His restructuring in preparation for an offensive in spring 1864 was banking on a European-wide war. On 27 December 1863, he enacted a decree of the former provisional government by granting peasants the land they worked. The land was to be provided by compensating the owners through state funds after the successful conclusion of the uprising. Traugutt called upon all Polish classes to rise against Russian oppression for the creation of a new Polish state. The response was moderate since the policy came too late. The Russian government had already begun working among peasants to grant them generous parcels of land for the asking. The peasants who had been bought off did not engage with Polish revolutionaries to any extent or provide them with support.

Fighting continued intermittently during the winter of 1863–1864 on the southern edge of the Kingdom, near the Galician border, from where assistance was still forthcoming. In late December in the Lublin Voivodeship, General Michał Heydenreich's unit was overwhelmed. The most determined resistance continued in the Świętokrzyskie Mountains, where General Józef Hauke-Bosak distinguished himself by taking several cities from the vastly superior Russian forces. However, he too succumbed to a crushing defeat on 21 February 1864 which presaged the end of the armed struggle. On 29 February, Austria imposed martial law, and on 2 March, the tsarist authorities brought in the abolition of serfdom in the Polish Kingdom. Both events neutralised Traugutt's concept of developing the uprising with a general mobilisation of the population in the Russian partition and reliance on assistance from Galicia. In April 1864, Napoleon III abandoned the Polish cause. Władysław Czartoryski wrote to Traugutt: "We are alone, and alone we shall remain".

Arrests eliminated key positions in the secret Polish state, and those who felt threatened sought refuge abroad. Traugutt was taken on the night of 10 April. After he and the last four members of the National Council, Antoni Jezioranski, Rafał Krajewski, Józef Toczyski and Roman Żuliński, had been apprehended by Russian troops, they were imprisoned and executed by hanging on 5 August at the Warsaw Citadel. That marked the symbolic closure of the Uprising. Only Aleksander Waszkowski, the head of the Warsaw insurgency eluded the police till December 1864, but he too joined the list of "the lost" in February 1865. The war consisting of 650 battles and skirmishes with 25,000 Polish and other insurgents killed, had lasted 18 months. The insurgency persisted in Samogitia and Podlasie, where the Greek Catholic population, outraged and persecuted for their religious observance, "Kryaki (those baptised into the Greek Orthodox Church), and others like the commander and priest Stanisław Brzóska, clung the longest to the revolutionary banner until the spring of 1865.

Decades of reprisals

After the collapse of the uprising, harsh reprisals followed. According to official Russian information, 396 persons were executed and 18,672 were exiled to Siberia. Large numbers of men and women were sent to the interior of Russia and to the Caucasus, Urals and other remote areas. Altogether over 60,000 persons were imprisoned and subsequently exiled from Poland and consigned to distant regions of Russia.

The abolition of serfdom in early 1864 was deliberately enacted in a move designed specifically to ruin the szlachta. The Russian government confiscated 1,660 estates in Poland and 1,794 in Lithuania. A 10% income tax was imposed on all estates as a war indemnity. Only in 1869 was the tax reduced to 5% on all incomes. It was the only time that peasants paid the market price for the redemption of the land (the average for the Russian Empire was 34% above the market price). All land taken from Polish peasants since 1864 was to be returned without rights of compensation. Former serfs could sell land only to other peasants, not to szlachta. Ninety percent of the ex-serfs in the empire who actually gained land after 1861 were confined to the eight western provinces. Along with Romania, Polish landless or domestic serfs were the only people who were eligible for land grants after serfdom had been abolished.

All of that was to punish the szlachta for its role in the uprisings of 1830 and 1863. In addition to the land granted to the peasants, the Russian government gave them a forest, pasture and other privileges, known under the name of servitutes, which proved to be a source of incessant irritation between the landowners and peasants over the ensuing decades and impeded economic development. The government took over all church estates and funds and abolished monasteries and convents. With the exception of religious instruction, all teaching in schools was ordered to be in Russian. That also became the official language of the country, to be used exclusively in all offices of central and local government. All traces of former Polish autonomy were removed, and the Kingdom was divided into ten provinces, each with an appointed Russian military governor under the control of the Governor-General in Warsaw. All former Polish government functionaries were deprived of their positions and replaced by Russian officials. According to George Kennan, "thousands of Polish insurgents" were transported to the "Nerchinsk silver-mining district... after the unsuccessful insurrection of 1863".

Legacy
These measures of cultural eradication proved to be only partially effective. In 1905, 41 years after Russia crushed the uprising, the next generation of Poles rose once again in the Łódź insurrection, which too failed.

The January Uprising was one in a centuries-long series of Polish uprisings. In its aftermath, two new movements began to evolve that set the political agenda for the next century. One, led by the descendant of Lithuanians, Józef Piłsudski emerged as the Polish Socialist Party. The other, led by Roman Dmowski, became the National Democracy movement; sometimes referred to as Endecja, its roots lay in Catholic conservatism that sought national sovereignty, along with the reversal of forced Russification and Germanisation by the Polonisation of the partitioned territories in the former Commonwealth.

Notable insurgents

 * Francišak Bahuševič (1840–1900), Belarusian poet and writer, one of the founders of modern Belarusian literature
 * Stanisław Brzóska (1832–1865), Polish priest and commander at the end of the insurrection.
 * Saint Albert Chmielowski (1845–1916), founder of the Albertine Brothers and Sisters.
 * Jarosław Dąbrowski (1836–1871), officer in the Russian Army, left-wing member of the "secret committee" of officers in St. Petersburg. He took over its leadership from Sierakowski. He died in Paris fighting for the Paris Commune.
 * Wincenty Kalinowski (also known as Kastus) (1838–1864), was one of the leaders of Lithuanian national revival, a founder of Belarusian nationalism, and the leader of the January Uprising in the lands of the former Grand Duchy of Lithuania.
 * Saint Raphael Kalinowski (1835–1907), born Joseph Kalinowski in Lithuania, resigned as a Captain from the Russian Army to become Minister of War for the Polish insurgents. He was arrested and sentenced to death by firing squad, but the sentence was then changed to 10 years in Siberia, including a grueling nine-month overland trek to get there.
 * Apollo Korzeniowski (1820–1869), Polish playwright and father of Joseph Conrad.
 * Marian Langiewicz (1827–1887), Military Commander of the uprising. He had an English wife, Suzanne, next to whom he was buried in Istanbul.
 * Antanas Mackevičius (1828–1863), Lithuanian priest who organized some two hundred and fifty men, armed with hunting rifles and straightened scythes. After a defeat near Vilkija, he was captured and taken to the prison in Kaunas. After Mackevičius refused to betray other leaders of the uprising, he was hanged on 28 December 1863.
 * Ludwik Mierosławski (1814–1878), veteran of the November Uprising and of the Greater Poland uprising (1846), general, strategist, writer and emigrant with wide foreign contacts.
 * Władysław Niegolewski (1819–1885), was a liberal Polish politician and member of parliament, an insurgent in the Greater Poland Uprising of 1846 and 1848 and of the January 1863 Uprising, and a co-founder (1861) of the Central Economic Society and (1880) the People's Libraries Society.
 * Francesco Nullo (1826–1863), Italian general who headed the Garibaldi Legion, and that carried huge symbolic value. Nullo died at the Battle of Krzykawka.
 * Bolesław Prus (1847–1912), leading Polish writer of historical novels.
 * Anna Henryka Pustowójtówna (1838–1881), alias "Michał Smok", adjutant to Marian Langiewicz. She was of Russian-Polish descent and an activist from 1861. She later took part in the Paris Commune and the Franco-Prussian War. Having had four children, she later died in Paris.
 * François Rochebrune, (1830–1870), one of several French officers in the Uprising, he formed and led a Polish rebel unit called the Zouaves of Death and was promoted to General.
 * Aleksander Sochaczewski (1843–1923), Polish painter.
 * Romuald Traugutt (1826–1864), a Lieutenant colonel of German descent in the Russian Army, he was promoted general in the insurrection, was its leader for a spell and held the Foreign Affairs portfolio in the underground government. He was tortured and hanged by the Russians with several of his colleagues.

Influence on art and literature
Falling into the late romantic period, the events and figures of the uprising inspired many Polish painters, including Artur Grottger, Juliusz Kossak and Michał Elwiro Andriolli, and marked the delineation with the positivism that followed.

 * The Polish poet Cyprian Norwid wrote a famous poem, "Chopin's Piano," describing the defenestration of the composer's piano during the January 1863 Uprising, when Russian soldiers maliciously threw the instrument out of a second-floor Warsaw apartment. Chopin had left Warsaw and Poland forever shortly before the outbreak of the November 1830 Uprising.
 * Eliza Orzeszkowa, a leading Polish positivist writer and nominee for the Nobel Prize in Literature wrote Nad Niemnem a novel set in and around the city of Grodno after the 1863 January Uprising.
 * Józef Jarzębowski has put together material from unknown people who lived through the uprising in his Mówią Ludzie Roku 1863: Antologia nieznanych i małoznanych Głosów Ludzi współczesnych. London: Veritas, 1963. ("Voices from 1863: An Anthology of unknown and little known contemporary Perspectives").
 * In the initial draft of Twenty Thousand Leagues Under the Seas by Jules Verne but not in the published version, Captain Nemo was a Polish nobleman whose family had been brutally murdered by the Russians during the January 1863 Uprising. Since France had only recently signed an alliance with the Russian Empire, for the novel's final version, Verne's editor, Pierre-Jules Hetzel, made him obscure Nemo's motives.
 * In Guy de Maupassant's novel Pierre et Jean, the protagonist Pierre has a friend, an old Polish chemist who is said to have come to France after the bloody events in his motherland. The story is believed to refer to the January Uprising.

title: January Uprising


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Tmesis

In its strictest sense, tmesis (plural tmeses ; Ancient Greek: τμῆσις tmēsis "a cutting" < τέμνω temnō, "I cut") is a word compound that is divided into two parts, with another word infixed between the parts, thus constituting a separate word compound. Example: "un-freaking-believable" (an emphatic way to say "unbelievable"). In a broader sense, tmesis is a recognizable phrase (such as a phrasal verb) or word that is divided into two parts, with one or more words interpolated between the parts, thus creating a separate phrase.

Verbs
Tmesis of prefixed verbs (whereby the prefix is separated from the simple verb) was thought to be an original feature of the Ancient Greek language, common in Homer (and later poetry), but not used in Attic prose. Such separable verbs are also part of the normal grammatical usage of some modern languages, such as Dutch and German.

Ancient Greek
Tmesis in Ancient Greek is something of a misnomer, since there is not necessarily a splitting of the prefix from the verb; rather the consensus now seems to be that the separate prefix or pre-verb reflects a stage in the language where the prefix had not yet joined onto the verb. There are many examples in Homer's epics, the Iliad and the Odyssey, both of which preserve archaic features. One common and oft-cited example is κατὰ δάκρυα λείβων (kata dakrua leibōn; "shedding tears"), in which the pre-verb/prefix κατά- kata- "down" has not yet joined the verbal participle λείβων leibōn "shedding". In later Greek, these would combine to form the compound verb καταλείβων kataleibōn "shedding (in a downwards direction)".

Latin
Tmesis is found as a poetic or rhetorical device in classical Latin poetry, such as Ovid's Metamorphoses. Words such as circumdare ("to surround") are split apart with other words of the sentence in between, e.g. circum virum dant: "they surround the man" (circumdant (circum- prefix + dant)). This device is used in this way to create a visual image of surrounding the man by means of the words on the line. In the work of the poet Ennius, the literal splitting of the word cerebrum creates a vivid image: saxo cere comminuit brum "he shattered his brain with a rock."

Old Irish
Tmesis can be found in some early Old Irish texts, such as Audacht Morainn (The Testament of Morann). Old Irish verbs are found at the beginning of clauses (in a VSO word order) and often possess prepositional pre-verbal particles, e.g. ad-midethar (ad- prefix) "evaluates, estimates". Tmesis occurs when the pre-verbal particle is separated from the verbal stem and the verbal stem is placed in clause final position while the pre-verbal particle/prefix remains at the beginning of the clause. This results in an abnormal word order, e.g. ad- cruth caín -cichither "[the] fair form will be seen" (where ad-chichither is the future third-person singular passive of ad-cí "sees").

Old Norse
Examples of tmesis have been found in skaldic poetry. In addition to the use of kennings, skalds used tmesis to obscure the meaning of the poem. One use of tmesis was to divide the elements of personal names.

English
Colloquial examples include un-bloody-believable, abso-bloody-lutely, and several variants. Numerous English words are joined with the vulgar infix -fucking-, such as unfuckingbelievable or fanfuckingtastic. Other examples: scrumdiddlyumptious, edumacation.

English employs a large number of phrasal verbs, consisting of a core verb and a particle. A phrasal verb is written as two words that are analyzed semantically as a unit, but the unit may be separable under certain circumstances. For example, regarding a phrasal verb that has a transitive sense:
 * Turn off the light OR  Turn the light off. (optional tmesis)
 * Hand in the application OR Hand it in. (optional tmesis)

Similarly, tmesis can occur regarding a phrasal verb that has an intransitive sense. For example:
 * Come back tomorrow OR Come on back tomorrow. (adjunctive tmesis)
 * Let's head out OR Let's head right out. (adjunctive tmesis)

The intervention of an adverb or transitive object in the middle of the phrasal verb can be viewed as a form of tmesis even though the semantic unit being separated is written as two words even when not separated.

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

title: Tmesis


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Free University of Brussels (1834–1969)

The Free University of Brussels (Université libre de Bruxelles, or ULB; Vrije Hogeschool te Brussel, later Vrije Universiteit Brussel) was a university in Brussels, Belgium. Founded in 1834 on the principle of "free inquiry" (libre examen), its founders envisaged the institution as a free-thinker reaction to the traditional dominance of Catholicism in Belgian education. The institution was avowedly secular and particularly associated with Liberal political movements during the era of pillarisation. The Free University was one of Belgium's major universities, together with the Catholic University of Leuven and the state universities of Liège and Ghent.

The "Linguistic Wars" affected the Free University, which split along language lines in 1969 in the aftermath of student unrest at Leuven the previous year. Today two institutions carry the "Free University of Brussels" name: the French-speaking Université libre de Bruxelles (ULB) and the Dutch-speaking Vrije Universiteit Brussel (VUB). Although separate, both institutions continue to collaborate under the auspices of an umbrella organisation known as Brussels Free Universities.

Establishment of a university in Brussels

The Free University of Brussels was founded as the Free University of Belgium (Université libre de Belgique) on 20 November 1834 in the aftermath of Belgium's independence in 1830. Belgium had possessed three State universities at Leuven, Ghent, and Liège under Dutch rule but teaching had been extensively disrupted by the revolution and continued hostilities with the Dutch. As early as 1831, Belgian freemasons of the Les Amis philanthropes lodge had considered founding a new private university. News of the imminent creation of the Catholic University of Mechelen revived the initiative among those with anti-clerical ideas, especially freemasons, liberals, and other freethinkers. Pierre-Théodore Verhaegen and Auguste Baron led the fundraising for the new institution from April 1834. It was officially founded on 20 November 1834 in the former Palace of Charles of Lorraine in Brussels with the help of the liberal mayor Nicolas-Jean Rouppe. The date of its establishment is still commemorated annually, by students of its successor institutions, as a holiday called Saint-Verhaegen/Sint-Verhaegen (often shortened to St V) for Pierre-Théodore Verhaegen.

The motivating principle behind the new institution was "free inquiry" (libre examen) which denoted freethinking ideas inherited from the European Enlightenment. This hostility to political and religious authority led to hostility from the Catholic Church and Catholic Party politicians, increasingly associated with the Mechelen university's successor, the Catholic University of Leuven founded in 1835. Under the system of pillarisation, the Free University became one of the principle institutions in the Liberal "pillar". It was renamed the Université libre de Bruxelles ("Free University of Brussels") in 1842.

After its establishment, the Free University faced difficult times, since it received no subsidies or grants from the government; yearly fundraising events and tuition fees provided the only financial means. Verhaegen, who became a professor and later head of the new university, gave it a mission statement which he summarised in a speech to King Leopold I: "the principle of free inquiry and academic freedom uninfluenced by any political or religious authority." In 1858, the Catholic Church established the Saint-Louis Institute in the city, which subsequently expanded into a university in its own right.

Growth, internal tensions and move

The Free University grew significantly over the following decades. In 1842, it moved to the Granvelle Palace, which it occupied until 1928. It expanded the number of subjects taught and, in 1880, became one of the first institutions in Belgium to allow female students to study in some faculties. In 1893, it received large grants from Ernest and Alfred Solvay and Raoul Warocqué to open new faculties in the city. A disagreement over an invite from the rector Hector Denis to the anarchist geographer Élisée Reclus to speak at the university in 1893 led to some of the liberal and socialist faculty splitting away from the Free University to form the New University of Brussels (Université nouvelle de Bruxelles) in 1894. The institution failed to displace the Free University, however, and closed definitively in 1919.

In 1900, the Free University's football team won the bronze medal at the Summer Olympics. After Racing Club de Bruxelles declined to participate, a student selection with players from the university was sent by the Federation. The team was enforced with a few non-students. The Institute of Sociology was founded in 1902, then in 1904 the Solvay School of Commerce, which would later become the Solvay Brussels School of Economics and Management. In 1911, the university obtained its legal personality under the name Université libre de Bruxelles - Vrije Hogeschool te Brussel.

The German occupation during World War I led to the suspension of classes for four years in 1914–1918. In the aftermath of the war, the Free University moved its principle activities to the Solbosch in the southern suburb of Ixelles and a purpose-built university campus was created, funded by the Belgian American Educational Foundation. The university was again closed by the German occupiers during World War II on 25 November 1941. Students from the university were involved in the Belgian Resistance, establishing Groupe G which focused on sabotage.

Splitting of the university

Until the early 20th century, courses at the Free University were taught exclusively in French, the language of the upper class in Belgium at that time, as well as of law and academia. However, with the Dutch-speaking population asking for more rights in Belgium (see Flemish Movement), some courses began being taught in both French and Dutch at the Faculty of Law as early as 1935. Nevertheless, it was not until 1963 that all faculties offered their courses in both languages. Tensions between French- and Dutch-speaking students in the country came to a head in 1968 when the Catholic University of Leuven split along linguistic lines, becoming the first of several national institutions to do so.

On 1 October 1969, the French and Dutch entities of the Free University separated into two distinct sister universities. This splitting became official with the act of 28 May 1970, of the Belgian Parliament, by which the French-speaking Université libre de Bruxelles (ULB) and the Dutch-speaking Vrije Universiteit Brussel (VUB) officially became two separate legal, administrative and scientific entities.

Notable faculty

 * Henri La Fontaine (1854–1943): Nobel Prize for Peace in 1913.
 * Jules Bordet (1870–1961): Nobel Prize in Physiology or Medicine in 1919.

title: Free University of Brussels (1834–1969)


text:
Alphabetical order

Alphabetical order is a system whereby character strings are placed in order based on the position of the characters in the conventional ordering of an alphabet. It is one of the methods of collation. In mathematics, a lexicographical order is the generalization of the alphabetical order to other data types, such as sequences of numbers or other ordered mathematical objects.

When applied to strings or sequences that may contain digits, numbers or more elaborate types of elements, in addition to alphabetical characters, the alphabetical order is generally called a lexicographical order.

To determine which of two strings of characters comes first when arranging in alphabetical order, their first letters are compared. If they differ, then the string whose first letter comes earlier in the alphabet comes before the other string. If the first letters are the same, then the second letters are compared, and so on. If a position is reached where one string has no more letters to compare while the other does, then the first (shorter) string is deemed to come first in alphabetical order.

Capital or upper case letters are generally considered to be identical to their corresponding lower case letters for the purposes of alphabetical ordering, although conventions may be adopted to handle situations where two strings differ only in capitalization. Various conventions also exist for the handling of strings containing spaces, modified letters, such as those with diacritics, and non-letter characters such as marks of punctuation.

The result of placing a set of words or strings in alphabetical order is that all of the strings beginning with the same letter are grouped together; within that grouping all words beginning with the same two-letter sequence are grouped together; and so on. The system thus tends to maximize the number of common initial letters between adjacent words.

History
Alphabetical order was first used in the 1st millennium BCE by Northwest Semitic scribes using the abjad system. However, a range of other methods of classifying and ordering material, including geographical, chronological, hierarchical and by category, were preferred over alphabetical order for centuries.

Parts of the Bible are dated to the 7th–6th centuries BCE. In the Book of Jeremiah, the prophet utilizes the Atbash substitution cipher, based on alphabetical order. Similarly, biblical authors used acrostics based on the (ordered) Hebrew alphabet.

The first effective use of alphabetical order as a cataloging device among scholars may have been in ancient Alexandria, in the Great Library of Alexandria, which was founded around 300 BCE. The poet and scholar Callimachus, who worked there, is thought to have created the world's first library catalog, known as the Pinakes, with scrolls shelved in alphabetical order of the first letter of authors' names.

In the 1st century BC, Roman writer Varro compiled alphabetic lists of authors and titles. In the 2nd century CE, Sextus Pompeius Festus wrote an encyclopedic epitome of the works of Verrius Flaccus, De verborum significatu, with entries in alphabetic order. In the 3rd century CE, Harpocration wrote a Homeric lexicon alphabetized by all letters. In the 10th century, the author of the Suda used alphabetic order with phonetic variations.

Alphabetical order as an aid to consultation started to enter the mainstream of Western European intellectual life in the second half of the 12th century, when alphabetical tools were developed to help preachers analyse biblical vocabulary. This led to the compilation of alphabetical concordances of the Bible by the Dominican friars in Paris in the 13th century, under Hugh of Saint Cher. Older reference works such as St. Jerome's Interpretations of Hebrew Names were alphabetized for ease of consultation. The use of alphabetical order was initially resisted by scholars, who expected their students to master their area of study according to its own rational structures; its success was driven by such tools as Robert Kilwardby's index to the works of St. Augustine, which helped readers access the full original text instead of depending on the compilations of excerpts which had become prominent in 12th century scholasticism. The adoption of alphabetical order was part of the transition from the primacy of memory to that of written works. The idea of ordering information by the order of the alphabet also met resistance from the compilers of encyclopaedias in the 12th and 13th centuries, who were all devout churchmen. They preferred to organise their material theologically – in the order of God's creation, starting with Deus (meaning God).

In 1604 Robert Cawdrey had to explain in Table Alphabeticall, the first monolingual English dictionary, "Nowe if the word, which thou art desirous to finde, begin with (a) then looke in the beginning of this Table, but if with (v) looke towards the end". Although as late as 1803 Samuel Taylor Coleridge condemned encyclopedias with "an arrangement determined by the accident of initial letters", many lists are today based on this principle.

Basic order and examples
The standard order of the modern ISO basic Latin alphabet is:
 * A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z

An example of straightforward alphabetical ordering follows: Another example: The above words are ordered alphabetically. As comes before Aster because they begin with the same two letters and As has no more letters after that whereas Aster does. The next three words come after Aster because their fourth letter (the first one that differs) is r, which comes after e (the fourth letter of Aster) in the alphabet. Those words themselves are ordered based on their sixth letters (l, n and p respectively). Then comes At, which differs from the preceding words in the second letter (t comes after s). Ataman comes after At for the same reason that Aster came after As. Attack follows Ataman based on comparison of their third letters, and Baa comes after all of the others because it has a different first letter.
 * As; Aster; Astrolabe; Astronomy; Astrophysics; At; Ataman; Attack; Baa
 * Barnacle; Be; Been; Benefit; Bent

Treatment of multiword strings
When some of the strings being ordered consist of more than one word, i.e., they contain spaces or other separators such as hyphens, then two basic approaches may be taken. In the first approach, all strings are ordered initially according to their first word, as in the sequence:
 * Oak; Oak Hill; Oak Ridge; Oakley Park; Oakley River
 * where all strings beginning with the separate word Oak precede all those beginning with Oakley, because Oak precedes Oakley in alphabetical order.

In the second approach, strings are alphabetized as if they had no spaces, giving the sequence:
 * Oak; Oak Hill; Oakley Park; Oakley River; Oak Ridge
 * where Oak Ridge now comes after the Oakley strings, as it would if it were written "Oakridge".

The second approach is the one usually taken in dictionaries, and it is thus often called dictionary order by publishers. The first approach has often been used in book indexes, although each publisher traditionally set its own standards for which approach to use therein; there was no ISO standard for book indexes (ISO 999) before 1975.

Modified letters
In French, modified letters (such as those with diacritics) are treated the same as the base letter for alphabetical ordering purposes. For example, rôle comes between rock and rose, as if it were written role. However, languages that use such letters systematically generally have their own ordering rules. See below.

Ordering by surname
In most cultures where family names are written after given names, it is still desired to sort lists of names (as in telephone directories) by family name first. In this case, names need to be reordered to be sorted correctly. For example, Juan Hernandes and Brian O'Leary should be sorted as "Hernandes, Juan" and "O'Leary, Brian" even if they are not written this way. Capturing this rule in a computer collation algorithm is complex, and simple attempts will fail. For example, unless the algorithm has at its disposal an extensive list of family names, there is no way to decide if "Gillian Lucille van der Waal" is "van der Waal, Gillian Lucille", "Waal, Gillian Lucille van der", or even "Lucille van der Waal, Gillian".

Ordering by surname is frequently encountered in academic contexts. Within a single multi-author paper, ordering the authors alphabetically by surname, rather than by other methods such as reverse seniority or subjective degree of contribution to the paper, is seen as a way of "acknowledg[ing] similar contributions" or "avoid[ing] disharmony in collaborating groups". The practice in certain fields of ordering citations in bibliographies by the surnames of their authors has been found to create bias in favour of authors with surnames which appear earlier in the alphabet, while this effect does not appear in fields in which bibliographies are ordered chronologically.

The and other common words
If a phrase begins with a very common word (such as "the", "a" or "an", called articles in grammar), that word is sometimes ignored or moved to the end of the phrase, but this is not always the case. For example, the book "The Shining" might be treated as "Shining", or "Shining, The" and therefore before the book title "Summer of Sam". However, it may also be treated as simply "The Shining" and after "Summer of Sam". Similarly, "A Wrinkle in Time" might be treated as "Wrinkle in Time", "Wrinkle in Time, A", or "A Wrinkle in Time". All three alphabetization methods are fairly easy to create by algorithm, but many programs rely on simple lexicographic ordering instead.

Mac prefixes
The prefixes M and Mc in Irish and Scottish surnames are abbreviations for Mac and are sometimes alphabetized as if the spelling is Mac in full. Thus McKinley might be listed before Mackintosh (as it would be if it had been spelled out as "MacKinley"). Since the advent of computer-sorted lists, this type of alphabetization is less frequently encountered, though it is still used in British telephone directories.

St prefix
The prefix St or St. is an abbreviation of "Saint", and is traditionally alphabetized as if the spelling is Saint in full. Thus in a gazetteer St John's might be listed before Salem (as if it would be if it had been spelled out as "Saint John's"). Since the advent of computer-sorted lists, this type of alphabetization is less frequently encountered, though it is still sometimes used.

Ligatures
Ligatures (two or more letters merged into one symbol) which are not considered distinct letters, such as Æ and Œ in English, are typically collated as if the letters were separate—"æther" and "aether" would be ordered the same relative to all other words. This is true even when the ligature is not purely stylistic, such as in loanwords and brand names.

Special rules may need to be adopted to sort strings which vary only by whether two letters are joined by a ligature.

Treatment of numerals
When some of the strings contain numerals (or other non-letter characters), various approaches are possible. Sometimes such characters are treated as if they came before or after all the letters of the alphabet. Another method is for numbers to be sorted alphabetically as they would be spelled: for example 1776 would be sorted as if spelled out "seventeen seventy-six", and 24 heures du Mans as if spelled "vingt-quatre..." (French for "twenty-four"). When numerals or other symbols are used as special graphical forms of letters, as 1337 for leet or the movie Seven (which was stylised as Se7en), they may be sorted as if they were those letters. Natural sort order orders strings alphabetically, except that multi-digit numbers are treated as a single character and ordered by the value of the number encoded by the digits.

In the case of monarchs and popes, although their numbers are in Roman numerals and resemble letters, they are normally arranged in numerical order: so, for example, even though V comes after I, the Danish king Christian IX comes after his predecessor Christian VIII.

Language-specific conventions
Languages which use an extended Latin alphabet generally have their own conventions for treatment of the extra letters. Also in some languages certain digraphs are treated as single letters for collation purposes. For example, the Spanish alphabet treats ñ as a basic letter following n, and formerly treated the digraphs ch and ll as basic letters following c and l, respectively. Now сh and ll are alphabetized as two-letter combinations. The new alphabetization rule was issued by the Royal Spanish Academy in 1994. These digraphs were still formally designated as letters but they are no longer so since 2010. On the other hand, the digraph rr follows rqu as expected (and did so even before the 1994 alphabetization rule), while vowels with acute accents (á, é, í, ó, ú) have always been ordered in parallel with their base letters, as has the letter ü.

In a few cases, such as Arabic and Kiowa, the alphabet has been completely reordered.

Alphabetization rules applied in various languages are listed below.
 * In Arabic, there are two main orders of the 28 letter alphabet used today. The standard and most commonly used is the hijāʾī order, which was created by the early Arab linguist Nasr ibn 'Asim al-Laythi and features a visual ordering method where letters are ordered based on their shapes. For example bāʾ (ب), tāʾ (ت), thāʾ (ث) are grouped as they have the same base shape or rasm (ٮ) and are differentiated only by consonant pointing known as iʻjām. The original ʾabjadī order, which phonetically resembles that of other Semitic languages as well as Latin, is still in use today, usually limited for ordering lists in a document, analogous to Roman Numerals. When the ʾabjadī order is used in numbering, letters are written in a modified form to distinguish them from letters used in words and from numerals. For example, ʾalif (ا) which looks identical to the Eastern Arabic numeral one (١), a small oval loop extends clockwise of the letter's bottom, followed by a short tail (�). Although these characters are rarely used digitally they are encoded in Unicode under Arabic Mathematical Alphabetic Symbols. A less common order, the ṣawtī order, is collated phonetically and was created by al-Khalil ibn Ahmad al-Farahidi.
 * In Azerbaijani, there are eight additional letters to the standard Latin alphabet. Five of them are vowels: i, ı, ö, ü, ə and three are consonants: ç, ş, ğ. The alphabet is the same as the Turkish, with the same sounds written with the same letters, except for three additional letters: q, x and ə for sounds that do not exist in Turkish. Although all the "Turkish letters" are collated in their "normal" alphabetical order like in Turkish, the three extra letters are collated arbitrarily after letters whose sounds approach theirs. So, q is collated just after k, x (pronounced like a German ch) is collated just after h and ə (pronounced roughly like an English short a) is collated just after e.
 * In Breton, there is no "c", "q", "x" but there are the digraphs "ch" and "c'h", which are collated between "b" and "d". For example: « buzhugenn, chug, c'hoar, daeraouenn » (earthworm, juice, sister, teardrop).
 * In Czech and Slovak, accented vowels have secondary collating weight – compared to other letters, they are treated as their unaccented forms (in Czech, A-Á, E-É-Ě, I-Í, O-Ó, U-Ú-Ů, Y-Ý, and in Slovak, A-Á-Ä, E-É, I-Í, O-Ó-Ô, U-Ú, Y-Ý), but then they are sorted after the unaccented letters (for example, the correct lexicographic order is baa, baá, báa, báá, bab, báb, bac, bác, bač, báč [in Czech] and baa, baá, baä, báa, báá, báä, bäa, bäá, bää, bab, báb, bäb, bac, bác, bäc, bač, báč, bäč [in Slovak]). Accented consonants have primary collating weight and are collated immediately after their unaccented counterparts, with exception of Ď, Ň and Ť (in Czech) and Ď, Ĺ, Ľ, Ň, Ŕ and Ť (in Slovak), which have again secondary weight. CH is considered to be a separate letter and goes between H and I. In Slovak, DZ and DŽ are also considered separate letters and are positioned between Ď and E.
 * In the Danish and Norwegian alphabets, the same extra vowels as in Swedish (see below) are also present but in a different order and with different glyphs (..., X, Y, Z, Æ, Ø, Å). Also, "Aa" collates as an equivalent to "Å". The Danish alphabet has traditionally seen "W" as a variant of "V", but today "W" is considered a separate letter.
 * In Dutch the combination IJ (representing Ĳ) was formerly to be collated as Y (or sometimes as a separate letter: Y < IJ < Z), but is currently mostly collated as 2 letters (II < IJ < IK). Exceptions are phone directories; IJ is always collated as Y here because in many Dutch family names Y is used where modern spelling would require IJ. Note that a word starting with ij that is written with a capital I is also written with a capital J, for example, the town IJmuiden, the river IJssel and the country IJsland (Iceland).
 * In Esperanto, consonants with circumflex accents (ĉ, ĝ, ĥ, ĵ, ŝ), as well as ŭ (u with breve), are counted as separate letters and collated separately (c, ĉ, d, e, f, g, ĝ, h, ĥ, i, j, ĵ ... s, ŝ, t, u, ŭ, v, z).
 * In Estonian õ, ä, ö and ü are considered separate letters and collate after w. Letters š, z and ž appear in loanwords and foreign proper names only and follow the letter s in the Estonian alphabet, which otherwise does not differ from the basic Latin alphabet.
 * The Faroese alphabet also has some of the Danish, Norwegian, and Swedish extra letters, namely Æ and Ø. Furthermore, the Faroese alphabet uses the Icelandic eth, which follows the D. Five of the six vowels A, I, O, U and Y can get accents and are after that considered separate letters. The consonants C, Q, X, W and Z are not found. Therefore, the first five letters are A, Á, B, D and Ð, and the last five are V, Y, Ý, Æ, Ø
 * In Filipino (Tagalog) and other Philippine languages, the letter Ng is treated as a separate letter. It is pronounced as in sing, ping-pong, etc. By itself, it is pronounced nang, but in general Filipino orthography, it is spelled as if it were two separate letters (n and g). Also, letter derivatives (such as Ñ) immediately follow the base letter. Filipino also is written with diacritics, but their use is very rare (except the tilde).
 * The Finnish alphabet and collating rules are the same as those of Swedish.
 * For French, the last accent in a given word determines the order. For example, in French, the following four words would be sorted this way: cote < côte < coté < côté. The letter e is ordered as e é è ê ë (œ considered as oe), same thing for o as ô ö.
 * In German letters with umlaut (Ä, Ö, Ü) are treated generally just like their non-umlauted versions; ß is always sorted as ss. This makes the alphabetic order Arbeit, Arg, Ärgerlich, Argument, Arm, Assistant, Aßlar, Assoziation. For phone directories and similar lists of names, the umlauts are to be collated like the letter combinations "ae", "oe", "ue" because a number of German surnames appear both with umlaut and in the non-umlauted form with "e" (Müller/Mueller). This makes the alphabetic order Udet, Übelacker, Uell, Ülle, Ueve, Üxküll, Uffenbach.
 * The Hungarian vowels have accents, umlauts, and double accents, while consonants are written with single, double (digraphs) or triple (trigraph) characters. In collating, accented vowels are equivalent with their non-accented counterparts and double and triple characters follow their single originals. Hungarian alphabetic order is: A=Á, B, C, Cs, D, Dz, Dzs, E=É, F, G, Gy, H, I=Í, J, K, L, Ly, M, N, Ny, O=Ó, Ö=Ő, P, Q, R, S, Sz, T, Ty, U=Ú, Ü=Ű, V, W, X, Y, Z, Zs. (Before 1984, dz and dzs were not considered single letters for collation, but two letters each, d+z and d+zs instead.) It means that e.g. nádcukor should precede nádcsomó (even though s normally precedes u), since c precedes cs in the collation. Difference in vowel length should only be taken into consideration if the two words are otherwise identical (e.g. egér, éger). Spaces and hyphens within phrases are ignored in collation. Ch also occurs as a digraph in certain words but it is not considered as a grapheme on its own right in terms of collation.
 * A particular feature of Hungarian collation is that contracted forms of double di- and trigraphs (such as ggy from gy + gy or ddzs from dzs + dzs) should be collated as if they were written in full (independently of the fact of the contraction and the elements of the di- or trigraphs). For example, kaszinó should precede kassza (even though the fourth character z would normally come after s in the alphabet), because the fourth "character" (grapheme) of the word kassza is considered a second sz (decomposing ssz into sz + sz), which does follow i (in kaszinó).
 * In Icelandic, Þ is added, and D is followed by Ð. Each vowel (A, E, I, O, U, Y) is followed by its correspondent with acute: Á, É, Í, Ó, Ú, Ý. There is no Z, so the alphabet ends: ... X, Y, Ý, Þ, Æ, Ö.
 * Both letters were also used by Anglo-Saxon scribes who also used the Runic letter Wynn to represent /w/.
 * Þ (called thorn; lowercase þ) is also a Runic letter.
 * Ð (called eth; lowercase ð) is the letter D with an added stroke.
 * Kiowa is ordered on phonetic principles, like the Brahmic scripts, rather than on the historical Latin order. Vowels come first, then stop consonants ordered from the front to the back of the mouth, and from negative to positive voice-onset time, then the affricates, fricatives, liquids, and nasals:
 * A, AU, E, I, O, U, B, F, P, V, D, J, T, TH, G, C, K, Q, CH, X, S, Z, L, Y, W, H, M, N

 * In Lithuanian, specifically Lithuanian letters go after their Latin originals. Another change is that Y comes just before J: ... G, H, I, Į, Y, J, K...
 * In Polish, specifically Polish letters derived from the Latin alphabet are collated after their originals: A, Ą, B, C, Ć, D, E, Ę, ..., L, Ł, M, N, Ń, O, Ó, P, ..., S, Ś, T, ..., Z, Ź, Ż. The digraphs for collation purposes are treated as if they were two separate letters.
 * In Pinyin alphabetical order, where words have the same basic letters in pinyin and differ only in modifying diacritics, the unmodified letter comes before the modified letter. For example, $⟨e⟩$ comes before $⟨ê⟩$ (額 (è) before 欸 (ê̄)), and $⟨u⟩$ comes before and $⟨ü⟩$ (路 (lù) before 驢 (lǘ) and 努 (nǔ) before 女 (nǚ)). Characters with the same pinyin letters (including modified letters $⟨ê⟩$ and $⟨ü⟩$) are arranged according to their tones in the order of "first tone (i.e., "flat tone"), second tone (rising tone), third tone (falling-rising tone), fourth tone (falling tone), fifth tone (neutral tone)", for example "媽 (mā), 麻 (má), 馬 (mǎ), 罵 (mà), 嗎 (ma)".
 * In Portuguese, the collating order is just like in English: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. Digraphs and letters with diacritics are not included in the alphabet.
 * In Romanian, special characters derived from the Latin alphabet are collated after their originals: A, Ă, Â, ..., I, Î, ..., S, Ș, T, Ț, ..., Z.
 * In Serbo-Croatian and other related South Slavic languages, the five accented characters and three conjoined characters are sorted after the originals: ..., C, Č, Ć, D, DŽ, Đ, E, ..., L, LJ, M, N, NJ, O, ..., S, Š, T, ..., Z, Ž.
 * Spanish treated (until 1994) "CH" and "LL" as single letters, giving an ordering of ,,  and , , . This is not true any more since in 1994 the RAE adopted the more conventional usage, and now LL is collated between LK and LM, and CH between CG and CI. The six characters with diacritics Á, É, Í, Ó, Ú, Ü are treated as the original letters A, E, I, O, U, for example: , , , , . The only Spanish-specific collating question is Ñ as a different letter collated after N.
 * In the Swedish alphabet, there are three extra vowels placed at its end (..., X, Y, Z, Å, Ä, Ö), similar to the Danish and Norwegian alphabet, but with different glyphs and a different collating order. The letter "W" has been treated as a variant of "V", but in the 13th edition of Svenska Akademiens ordlista (2006) "W" was considered a separate letter.
 * In the Turkish alphabet there are six additional letters: ç, ğ, ı, ö, ş, and ü (but no q, w, and x). They are collated with ç after c, ğ after g, ı before i, ö after o, ş after s, and ü after u. Originally, when the alphabet was introduced in 1928, ı was collated after i, but the order was changed later so that letters having shapes containing dots, cedilles or other adorning marks always follow the letters with corresponding bare shapes. Note that in Turkish orthography the letter I is the majuscule of dotless ı, whereas İ is the majuscule of dotted i.
 * In many Turkic languages (such as Azeri or the Jaꞑalif orthography for Tatar), there used to be the letter Gha (Ƣƣ), which came between G and H. It is now in disuse.
 * In Vietnamese, there are seven additional letters: ă, â, đ, ê, ô, ơ, ư while f, j, w, z are absent, even though they are still in some use (like Internet address, foreign loan language). "f" is replaced by the combination "ph". The same as for "w" is "qu".
 * In Volapük ä, ö and ü are counted as separate letters and collated separately (a, ä, b ... o, ö, p ... u, ü, v) while q and w are absent.
 * In Welsh the digraphs CH, DD, FF, NG, LL, PH, RH, and TH are treated as single letters, and each is listed after the first character of the pair (except for NG which is listed after G), producing the order A, B, C, CH, D, DD, E, F, FF, G, NG, H, and so on. It can sometimes happen, however, that word compounding results in the juxtaposition of two letters which do not form a digraph. An example is the word LLONGYFARCH (composed from LLON + GYFARCH). This results in such an ordering as, for example, LAWR, LWCUS, LLONG, LLOM, LLONGYFARCH (NG is a digraph in LLONG, but not in LLONGYFARCH). The letter combination R+H (as distinct from the digraph RH) may similarly arise by juxtaposition in compounds, although this tends not to produce any pairs in which misidentification could affect the ordering. For the other potentially confusing letter combinations that may occur – namely, D+D and L+L – a hyphen is used in the spelling (e.g. AD-DAL, CHWIL-LYS).

Automation
Collation algorithms (in combination with sorting algorithms) are used in computer programming to place strings in alphabetical order. A standard example is the Unicode Collation Algorithm, which can be used to put strings containing any Unicode symbols into (an extension of) alphabetical order. It can be made to conform to most of the language-specific conventions described above by tailoring its default collation table. Several such tailorings are collected in Common Locale Data Repository.

Similar orderings
The principle behind alphabetical ordering can still be applied in languages that do not strictly speaking use an alphabet – for example, they may be written using a syllabary or abugida – provided the symbols used have an established ordering.

For logographic writing systems, such as Chinese hanzi or Japanese kanji, the method of radical-and-stroke sorting is frequently used as a way of defining an ordering on the symbols. Japanese sometimes uses pronunciation order, most commonly with the Gojūon order but sometimes with the older Iroha ordering.

In mathematics, lexicographical order is a means of ordering sequences in a manner analogous to that used to produce alphabetical order.

Some computer applications use a version of alphabetical order that can be achieved using a very simple algorithm, based purely on the ASCII or Unicode codes for characters. This may have non-standard effects such as placing all capital letters before lower-case ones. See ASCIIbetical order.

A rhyming dictionary is based on sorting words in alphabetical order starting from the last to the first letter of the word.

title: Alphabetical order


text:
User:Wlievens

Me
My name is Wouter.

On Wikipedia
I am an inclusionist and eventualist when it comes to wikipedia.

Professional Interests
Among my professional interests are computer games, programming languages and software engineering. I'm especially interested in language engineering, particularly reflective programming (reflection) and metaprogramming. I believe intentional programming is the direction in which programming technologies should some day evolve.

Personal Interests
I'm interested in board games and tabletop wargames.

Hobby Projects
One of my projects is a geopolitical web-based simulation game called Particracy, where each player runs a political party.

title: User:Wlievens


text:
Joaquim Agostinho

Joaquim Fernandes Agostinho, OIH (7 April 1943 – 10 May 1984) was a Portuguese professional bicycle racer. He was champion of Portugal in six successive years. He rode the Tour de France 13 times and finished all but once, winning on Alpe d'Huez in 1979, and finishing third twice. All total he finished in the top 10 of a Grand Tour eleven times, made three podiums and won a total of seven stages between the Vuelta and Tour.

Youth
Agostinho was born in a small village, near Torres Vedras. He lived for several years in Casalinhos de Alfaiata. Out for a ride as a youth, he encountered Sporting Clube de Portugal's cycling team on a road near Casalinhos de Alfaiata – Torres Vedras. He began an impromptu race; the team could not catch him, even though Agostinho was riding a standard steel bicycle.

Agostinho fought for three years with the Portuguese army in Angola and Mozambique during the Portuguese Colonial War of 1961–1974. Jean-Pierre Douçot, who became his mechanic as a professional, said: "'It was his captain during the war in Mozambique who discovered him. When he carried messages on a heavy bike, he took two hours to ride 50km when the others took five.'"

Racing career
Joaquim Agostinho started racing as an amateur at the age of 25 years in some Portuguese races, wearing some borrowed cycling wear lent by João Roque. After winning some races, Agostinho signed a professional contract with Sporting Clube de Portugal. Then, when racing with the Sporting Clube de Portugal cycling team in São Paulo, Agostinho – a rider "of average height but with the build of a rhinoceros", according to the historian Pierre Chany – left Jean de Gribaldy, a team manager and former cyclist, in awe of him. They met in Brazil in 1968, when Agostinho won the Tour de São Paulo. De Gribaldy was managing an amateur team in the race. That year Agostinho rode the world professional road championship at Imola and came 16th after initiating the move which brought victory for the Italian, Vittorio Adorni. De Gribaldy and Agostinho became lifelong friends. De Gribaldy said in 1980:

"'At the end of my life, if I had to recall a single place in the world, I wouldn't hesitate long. I would choose the little Brazilian hotel, insignificant, discreet, in São Paulo, where I had arranged to meet Joaquim. It was in 1968. I had noticed him two months earlier at Imola, at the world championship, but it was in São Paulo that I spoke to him for the first time. I asked him simply: 'Do you want to come and race in France?' He didn't know a word of French but in his smile I understood immediately what he was trying to answer. What a long way we went together afterwards. What memories we created together.'"

De Gribaldy asked him to join his Frimatic team in France, promising a ride in the 1969 Tour de France. Agostinho was already 26, a late age to turn professional, he won two stages that year. He also had one of the heavy falls that characterised his career, crashing on the cinder track at Divonne-les-Bains and being carried away with concussion, amnesia and cuts. He restarted next morning and rode as far as Paris, finishing the race eighth. He rode 13 Tours de France from 1969 to 1983, came third in 1978 and 1979 and won four stages. He finished 12 times.

Agostinho stayed with de Gribaldy as his teams were successively sponsored by Frimatic, Hoover, and Van Cauter Magniflex. In 1973 he left de Gribaldy to ride for Bic and then Teka before re-associating with de Gribaldy when he joined Flandria's French team in 1978.

Raphaël Géminiani said: "'Joaquim Agostinho didn't know his own strength. He was a ball of muscles of out-of-the-ordinary power. He was built like a cast-iron founder. Having come to cycling fairly late, he had trouble integrating with it. It's a shame he didn't want to dedicate himself 100 per cent to being a professional cyclist. Now and then he showed his very great physical powers, but no more often than that. He didn't want to do more. The peloton scared him, which is why he fell so often. More than that, Tinho was never aggressive enough to impose himself totally. He had a legendary kindness and his only ambition was to be good, gentle Tinho. If he'd been ambitious, he would easily have written his name into the records of the Tour de France.'"

Pierre Martin said in International Cycle Sport: "He was a man of strange contradictions. Built like a sprinter, he was no good at sprinting. He was one of the great climbers. Eddy Merckx said in 1969, the year when he and Agostinho made their debuts in the Tour de France, that Agostinho was the rival who worried him most, indeed the only rival who had worried him at all.'"

Agostinho was Portuguese champion in six successive years, from 1968 to 1973. He was a gifted climber and a consistent leader in both in the Vuelta a España and the Tour de France where he was a winner at Alpe d'Huez. Martin said:

"'He loved the Tour de France. There were few other races which he took seriously, indeed he raced relatively little during an average season – enough to pay for and maintain life's dream, but no more. On the roads of the Tour, nobody ever knew when he would suddenly burst into action. He might be quiet for days on end, when suddenly the racing fever would grip him, not always in the mountains, and away he went. When he went, those with serious ambitions went with him, knowing that, otherwise, they would see him no more until the end of the stage. He didn't take cycling too seriously. It had brought him wealth and security, had allowed him to buy and stock a large farm about 20 miles from Lisbon. The farm and his family were his life; cycling was his hobby. When he was riding the Tour d'Indre-et-Loire once, news reached him that 20 cows had been stolen. Off he went, in mid-race, back to Portugal to organise a posse to hunt the cattle, chartering a light plane for himself to direct the search."

In 1982 he took a whole year off to look after his farm, demoralised by a fall in form the previous season.

Doping
Joaquim Agostinho was caught three times in drugs checks: in the Tour of Portugal in 1969 and 1973, and the Tour de France of 1977.

Death
Agostinho was leading the Tour of the Algarve at Quarteira in April 1984 when a dog ran into the road a few hundred metres before the finish. Agostinho hit it and fell to the ground, hitting his head. He remounted and crossed the line accompanied by other riders. He was dazed but seemed otherwise unhurt. He walked to an ambulance, holding his head. He then went to a hotel, where his head was dressed in ice. Two hours later he was taken to hospital in Faro, where an X-ray showed he had broken the parietal bone in his skull. He was conveyed by ambulance, four hours after the fall, 280 km to Lisbon, the nearest city that could treat him. He fell into a coma in the ambulance and subsequently died.

Monuments & tributes

 * In Torres Vedras, on top of the Parque Verde da Várzea, there is a monument built in honour of Joaquim Agostinho.

 * In the gardens of Silveira a monument was inaugurated on 14 May 1989.
 * The 'Avenida Joaquim Agostinho' (avenue) leads to the centre the Santa Cruz Beach.
 * In France, on the 14th curve of the Alpe d'Huez, a bronze bust (1.70 m high, 70 cm wide and weighing 70 kg), mounted on a granite pedestal three feet high, commemorates his stage victory in 1979.
 * In 2000 the journalists of A Bola selected Agostinho as the 4th most important Portuguese Sportsman of the 20th Century, behind Eusébio (1st), Carlos Lopes (2nd) and Rosa Mota (3rd).
 * In 1984 Agostinho was made an Officer of the Order of Prince Henry the Navigator, by then President of Portugal Ramalho Eanes.

Major results
Sources:

 * 1968
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * 2nd Overall Volta a Portugal

 * 1969
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * 1st Trofeo Baracchi (with Herman Van Springel)
 * 1st Stage 4b Tour de Luxembourg (ITT)
 * 5th Overall À travers Lausanne
 * 5th Grand Prix des Nations
 * 7th Overall Volta a Portugal
 * 8th Overall Tour de France
 * 1st Stages 5 & 14

 * 1970
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * 1st Overall Volta a Portugal
 * 1st Stages 8a, 14a, 14b (ITT) & 16b
 * 1st Stage 1a Setmana Catalana de Ciclisme
 * 3rd Overall Escalada a Montjuïc
 * 3rd Overall Trophée d'Europe de la Montagne
 * 6th Overall Vuelta a Mallorca

 * 1971
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * 1st Overall Volta a Portugal
 * 1st Stages 1, 2a, 4b, 7b, 11a, 12, 13a, 16b (ITT)
 * 1st Overall GP de Sintra
 * 1st Stages 1a & 1b
 * 3rd Overall À travers Lausanne
 * 5th Overall Tour de France
 * 6th Baden-Baden

 * 1972
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * 1st Overall Volta a Portugal
 * 1st Stages 8, 10, 13, 17 & 24 (ITT)
 * 1st Overall GP de Sintra
 * 1st Stage 2
 * 5th Overall Tour de Suisse
 * 1st Stages 3 (ITT) & 8b (ITT)
 * 8th Overall Tour de France

 * 1973
 * National Road Championships
 * 1st MaillotPortugal.PNG Time trial
 * 1st MaillotPortugal.PNG Road race
 * Volta a Portugal
 * 1st Prologue & Stages 3b, 5, 9a (ITT), 10, 11b, 15
 * 5th Overall GP du Midi-Libre
 * 5th Subida a Arrate
 * 6th Overall Vuelta a España
 * 8th Overall Tour de France
 * 1st Stage 16b (ITT)

 * 1974
 * 2nd Overall Vuelta a España
 * 1st Stages 14 & 19b (ITT)
 * 3rd Overall Setmana Catalana de Ciclisme
 * 6th Overall Tour de France
 * 7th Overall GP du Midi-Libre

 * 1975
 * 3rd Overall Tour de l'Aude

 * 1976
 * 3rd Overall Tour of the Basque Country
 * 3rd Overall Volta a la Comunitat Valenciana
 * 3rd Overall Escalada a Montjuïc
 * 6th Overall Setmana Catalana de Ciclisme
 * 7th Overall Vuelta a España
 * 1st Stage 6 (ITT)
 * Held after Stages 6-8 & 15-16

 * 1977
 * 1st Stage 18 Tour de France
 * Vuelta a los Valles Mineros
 * 1st Stages 3a & 3b
 * 4th Overall Critérium du Dauphiné Libéré
 * 4th Overall Setmana Catalana de Ciclisme
 * 7th Overall Volta a la Comunitat Valenciana

 * 1978
 * 3rd Overall Tour de France
 * 3rd Overall Tour de Corse

 * 1979
 * 2nd Overall GP du Midi-Libre
 * 1st Stage 2
 * 3rd Overall Tour de France
 * 1st Stage 17
 * 6th Overall Critérium du Dauphiné Libéré

 * 1980
 * 2nd Overall GP du Midi-Libre
 * 3rd Overall Critérium du Dauphiné Libéré
 * 3rd Overall 4 Jours de Dunkerque
 * 3rd Overall Escalada a Montjuïc
 * 3rd Overall Tour de Corse
 * 3rd Bordeaux–Paris
 * 4th GP Eddy Merckx
 * 5th Overall Tour de France

 * 1981
 * 2nd Overall Critérium du Dauphiné Libéré
 * 5th Overall Tour de Romandie

 * 1984
 * 1st Stage 3 Volta ao Algarve

title: Joaquim Agostinho


text:
Irreducible representation

In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation $$(\rho, V)$$ or irrep of an algebraic structure $$A$$ is a nonzero representation that has no proper nontrivial subrepresentation $$(\rho|_W,W)$$, with $$W \subset V$$ closed under the action of $$\{ \rho(a) : a\in A \}$$.

Every finite-dimensional unitary representation on a Hilbert space $$V$$ is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible.

History
Group representation theory was generalized by Richard Brauer from the 1940s to give modular representation theory, in which the matrix operators act on a vector space over a field $$K$$ of arbitrary characteristic, rather than a vector space over the field of real numbers or over the field of complex numbers. The structure analogous to an irreducible representation in the resulting theory is a simple module.

Overview
Let $$\rho$$ be a representation i.e. a homomorphism $$\rho: G \to GL(V)$$ of a group $$G$$ where $$V$$ is a vector space over a field $$F$$. If we pick a basis $$B$$ for $$V$$, $$\rho$$ can be thought of as a function (a homomorphism) from a group into a set of invertible matrices and in this context is called a matrix representation. However, it simplifies things greatly if we think of the space $$V$$ without a basis.

A linear subspace $$W\subset V$$ is called $$G$$-invariant if $$\rho(g)w\in W$$ for all $$g\in G$$ and all $$ w\in W$$. The co-restriction of $$\rho$$ to the general linear group of a $$G$$-invariant subspace $$W\subset V$$ is known as a subrepresentation. A representation $$\rho: G \to GL(V)$$ is said to be irreducible if it has only trivial subrepresentations (all representations can form a subrepresentation with the trivial $$G$$-invariant subspaces, e.g. the whole vector space $$V$$, and {0}). If there is a proper nontrivial invariant subspace, $$\rho$$ is said to be reducible.

Notation and terminology of group representations
Group elements can be represented by matrices, although the term "represented" has a specific and precise meaning in this context. A representation of a group is a mapping from the group elements to the general linear group of matrices. As notation, let $a, b, c, ...$ denote elements of a group $G$ with group product signified without any symbol, so $ab$ is the group product of $a$ and $b$ and is also an element of $G$, and let representations be indicated by $D$. The representation of a is written as

 * $$D(a) = \begin{pmatrix}

D(a)_{11} & D(a)_{12} & \cdots & D(a)_{1n} \\ D(a)_{21} & D(a)_{22} & \cdots & D(a)_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ D(a)_{n1} & D(a)_{n2} & \cdots & D(a)_{nn} \\ \end{pmatrix}$$

By definition of group representations, the representation of a group product is translated into matrix multiplication of the representations:

 * $$D(ab) = D(a)D(b) $$

If $e$ is the identity element of the group (so that $ae = ea = a$, etc.), then $D(e)$ is an identity matrix, or identically a block matrix of identity matrices, since we must have

 * $$D(ea) = D(ae) = D(a)D(e) = D(e)D(a) = D(a)$$

and similarly for all other group elements. The last two statements correspond to the requirement that $D$ is a group homomorphism.

Reducible and irreducible representations
A representation is reducible if it contains a nontrivial G-invariant subspace, that is to say, all the matrices $$D(a)$$ can be put in upper triangular block form by the same invertible matrix $$P$$. In other words, if there is a similarity transformation:
 * $$ D'(a) \equiv P^{-1} D(a) P,$$

which maps every matrix in the representation into the same pattern upper triangular blocks. Every ordered sequence minor block is a group subrepresentation. That is to say, if the representation is, for example, of dimension 2, then we have: $$D'(a) = P^{-1} D(a) P = \begin{pmatrix} D^{(11)}(a) & D^{(12)}(a) \\ 0 & D^{(22)}(a) \end{pmatrix}, $$

where $$D^{(11)}(a)$$ is a nontrivial subrepresentation. If we are able to find a matrix $$P $$ that makes $$D^{(12)}(a) = 0$$ as well, then $$D(a)$$ is not only reducible but also decomposable.

Notice: Even if a representation is reducible, its matrix representation may still not be the upper triangular block form. It will only have this form if we choose a suitable basis, which can be obtained by applying the matrix $$P^{-1}$$ above to the standard basis.

Decomposable and indecomposable representations
A representation is decomposable if all the matrices $$D(a)$$ can be put in block-diagonal form by the same invertible matrix $$P$$. In other words, if there is a similarity transformation:

 * $$ D'(a) \equiv P^{-1} D(a) P,$$

which diagonalizes every matrix in the representation into the same pattern of diagonal blocks. Each such block is then a group subrepresentation independent from the others. The representations $D(a)$ and $D′(a)$ are said to be equivalent representations. The (k-dimensional, say) representation can be decomposed into a direct sum of $k > 1$ matrices:

 * $$D'(a) = P^{-1} D(a) P = \begin{pmatrix}

D^{(1)}(a) & 0 & \cdots & 0 \\ 0 & D^{(2)}(a) & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & D^{(k)}(a) \\ \end{pmatrix} = D^{(1)}(a) \oplus D^{(2)}(a) \oplus \cdots \oplus D^{(k)}(a),$$

so $D(a)$ is decomposable, and it is customary to label the decomposed matrices by a superscript in brackets, as in $D^{(n)}(a)$ for $n = 1, 2, ..., k$, although some authors just write the numerical label without parentheses.

The dimension of $D(a)$ is the sum of the dimensions of the blocks:

 * $$\dim[D(a)] = \dim[D^{(1)}(a)] + \dim[D^{(2)}(a)] + \cdots + \dim[D^{(k)}(a)].$$

If this is not possible, i.e. $k = 1$, then the representation is indecomposable.

Notice: Even if a representation is decomposable, its matrix representation may not be the diagonal block form. It will only have this form if we choose a suitable basis, which can be obtained by applying the matrix $$P^{-1}$$ above to the standard basis.

Connection between irreducible representation and indecomposable representation
An irreducible representation is by nature an indecomposable one. However, the converse may fail.

But under some conditions, we do have an indecomposable representation being an irreducible representation.

 * When group $$G$$ is finite, and it has a representation over field $$\Complex$$, then an indecomposable representation is an irreducible representation.
 * When group $$G$$ is finite, and it has a representation over field $$K$$, if we have $$char(K)\nmid |G|$$, then an indecomposable representation is an irreducible representation.

Trivial representation
All groups $$G$$ have a one-dimensional, irreducible trivial representation by mapping all group elements to the identity transformation.

One-dimensional representation
Any one-dimensional representation is irreducible since it has no proper nontrivial invariant subspaces.

Irreducible complex representations
The irreducible complex representations of a finite group G can be characterized using results from character theory. In particular, all complex representations decompose as a direct sum of irreps, and the number of irreps of $$G$$ is equal to the number of conjugacy classes of $$G$$.

 * The irreducible complex representations of $$\Z / n\Z$$ are exactly given by the maps $$1 \mapsto \gamma$$, where $$\gamma$$ is an $$n$$th root of unity.
 * Let $$V$$ be an $$n$$-dimensional complex representation of $$S_n$$ with basis $$\{v_i\}^n_{i=1}$$. Then $$V$$ decomposes as a direct sum of the irreps $$V_\text{triv} = \Complex \left ( \sum^n_{i=1} v_i \right )$$ and the orthogonal subspace given by $$V_\text{std} = \left \{ \sum^n_{i=1} a_i v_i : a_i \in \Complex, \sum^n_{i=1} a_i = 0 \right \}.$$ The former irrep is one-dimensional and isomorphic to the trivial representation of $$S_n$$. The latter is $$n-1$$ dimensional and is known as the standard representation of $$S_n$$.
 * Let $$G$$ be a group. The regular representation of $$G$$ is the free complex vector space on the basis $$\{e_g\}_{g \in G}$$ with the group action $$g \cdot e_{g'} = e_{gg'}$$, denoted $$\Complex G.$$ All irreducible representations of $$G$$ appear in the decomposition of $$\Complex G$$ as a direct sum of irreps.

Example of an irreducible representation over $F_{p}$

 * Let $$G$$ be a $$p$$ group and $$V = \mathbb{F}_p^{n}$$ be a finite dimensional irreducible representation of G over $$\mathbb{F}_p$$. By Orbit-stabilizer theorem, the orbit of every $$V$$ element acted by the $$p$$ group $$G$$ has size being power of $$p$$. Since the sizes of all these orbits sum up to the size of $$G$$, and $$0 \in V$$ is in a size 1 orbit only containing itself, there must be other orbits of size 1 for the sum to match. That is, there exists some $$v\in V$$ such that $$gv = v$$ for all $$g \in G$$. This forces every irreducible representation of a  $$p$$ group over $$ \mathbb{F}_p$$ to be one dimensional.

Applications in theoretical physics and chemistry
In quantum physics and quantum chemistry, each set of degenerate eigenstates of the Hamiltonian operator comprises a vector space $V$ for a representation of the symmetry group of the Hamiltonian, a "multiplet", best studied through reduction to its irreducible parts. Identifying the irreducible representations therefore allows one to label the states, predict how they will split under perturbations; or transition to other states in $V$. Thus, in quantum mechanics, irreducible representations of the symmetry group of the system partially or completely label the energy levels of the system, allowing the selection rules to be determined.

Lorentz group
The irreps of $D(K)$ and $D(J)$, where $J$ is the generator of rotations and $K$ the generator of boosts, can be used to build to spin representations of the Lorentz group, because they are related to the spin matrices of quantum mechanics. This allows them to derive relativistic wave equations.

Associative algebras

 * Simple module
 * Indecomposable module
 * Representation of an associative algebra

Lie groups

 * Representation theory of Lie algebras
 * Representation theory of SU(2)
 * Representation theory of SL2(R)
 * Representation theory of the Galilean group
 * Representation theory of diffeomorphism groups
 * Representation theory of the Poincaré group
 * Theorem of the highest weight

Books

 *
 *

title: Irreducible representation


text:
Talk:Artesia, New Mexico

Annexations to the City of Artesia 1982-2007
PLAT INDEX BOOK PAGE BOOK PAGE BOOK PAGE FILING                                     FORMER   RESTR COV ORDINANCE CAB SLIDE PG       SUBDIVISION NAME        S- T- R   DATE                  DESCRIPTION          -EXEMPTN -DISC STMT -VACATION A   93  1 ANNEXATION, ARTESIA            32 17 26  6/09/1982 ST RDS 229&357,SECS TWPS 16 &17RG26                   212   539 A  113  1 ANNEXATION, ARTESIA            23 17 25 11/15/1982 JAYCEES PARK, SECS TWP 17 RGS 25&26                   217   713 A  114  1 ANNEXATION, ARTESIA             2 17 26 11/15/1982 WATER PLANT,SR357, SECS TWP 17 RG26                   217   716 A  115  1 ANNEXATION, ARTESIA             2 17 25 11/15/1982 AIRPORT, R/W MAIN ST, 1711.55 ACRES                   217   719 A  141  1 ANNEXATION, ARTESIA             7 17 26  7/07/1983 PT S2SW4SW4 SEC 7-17-26                               225   310 A  194  1 ANNEXATION, ARTESIA             7 17 26  2/21/1985 GOOD SAMARITAN CTR, NE4NE4 7-17-26 A  218  1 ANNEXATION, ARTESIA             7 17 26  1/15/1986 PT N2NW4 SEC 7-17-26                                  258   594 A  219  1 ANNEXATION, ARTESIA             6 17 25  1/15/1986 LOMA VISTA #1, 2 & 3 PT SEC 6-17-25                   258   594 A  228  1 ANNEXATION, ARTESIA            12 17 25  7/31/1986 PT TRS 5 & 9 SE4 SEC 12-17-25                         267   845 A  235  1 ANNEXATION, ARTESIA            12 17 25  1/16/1987 SE4SE4 SEC 12-17-25                                   273  1082 A  401  1 ANNEXATION, ARTESIA            19 17 26  5/15/1996 PT BLKS 6, 10 PLAINS PARK 1   54  1 ANNEXATION, ARTESIA             9 17 26 10/31/1989 SE4SW4 SEC 9-17-26                                     56   192 1   60  2 ANNEXATION, ARTESIA             7 17 26  9/16/1971 PT N2S2SE4 SEC 7-17-26              7    43 1  116  1 ANNEXATION, ARTESIA            18 17 26  6/21/1965 PT SEC 18-17-26                     6    11 1  117  1 ANNEXATION, ARTESIA             7 17 26 10/26/1965 PT SEC 13-17-25, PT SECS 7 & 28-2   6    14 1  117  2 ANNEXATION, ARTESIA            13 17 25  9/08/1965 PT SW4NE4 SEC 13-17-25              6    14            51   540 1  118  1 ANNEXATION, ARTESIA             8 17 26  8/26/1965 PT SPENCER #2 10TH & 13TH           6    13            51   391 1  118  2 ANNEXATION, ARTESIA            20 17 26  6/30/1965 HERMOSA DR & US 285, PT 20-17-26    6    12 1  162  2 ANNEXATION, ARTESIA             6 17 26  5/17/1988 PT SEC 6-17-26                                         21   161 1  321  2 ANNEXATION, ARTESIA            17 17 26  7/22/1947 BLKS 4 & 5 ROSELAWN SE4 17-17-26    3   240 2   51  3 ANNEXATION, ARTESIA            19 17 26  2/24/1967 PT NE4NE4 SEC 19-17-26              6    41 2   57  1 ANNEXATION, ARTESIA             7 17 26  4/20/1966 13TH,10TH-GILCHRIST-CANNON7&8-17-   6    23 2  168  3 ANNEXATION, ARTESIA             7 17 26 11/15/2000 PT SE4SW4 SEC 7-17-26 3   61  1 ANNEXATION, ARTESIA            12 17 25  2/07/2002 PT N2SE4 SEC 12-17-25 3   94  1 ANNEXATION, ARTESIA            20 17 26  5/13/2002 PT SECS 16, 17, 20, 21-17-26 3  164  1 ANNEXATION, ARTESIA             7 17 26  8/30/2002 TR 2 RAYMOND R SMITH                                  469   474 3  222  1 ANNEXATION, ARTESIA            19 17 26  3/03/2003 PT NW4NW4 SEC 19-17-26 CHURCH OF JESUS CHRIST OF LATTER    S 3   239  1 ANNEXATION, ARTESIA            24 17 25  4/17/2003 JC PARK, PT N2N2SE4, S2S2NE4, S2SE4NW4 SEC 24-17-25 3  342  1 ANNEXATION, ARTESIA             7 17 26  1/26/2004 PT SEC 7-17-26                                        537   469 3  423  1 ANNEXATION, ARTESIA            32 16 26  8/17/2004 PT SE4 SEC 32-16-26                                   562  1022 3  448  1 ANNEXATION, ARTESIA            18 17 26 10/01/2004 PT SW4 SEC 18-17-26                                   568   214 3  465  1 ANNEXATION, ARTESIA             7 17 26 11/23/2004 PT SW4 SEC 7-17-26 3  607  1 ANNEXATION, ARTESIA            33 16 26 10/24/2005 N2SE4 SEC 32 & NW4SW4 SEC 33-16-26 ORD                616   585 RECORDED IN BK 616 PG 585 10-24-0 3  649  1 ANNEXATION, ARTESIA             6 17 26 12/23/2005 LTS 5, 6, SE4NW4, NE4SW4 SEC 6-17-26,                 623  1163 MYCO INDUSTRIES ET AL 3  734  1 ANNEXATION, ARTESIA             7 17 26  7/12/2006 PT SW4SW4 7-17-26, BREWER                             652   552 3  747  1 ANNEXATION, ARTESIA            20 17 26  8/08/2006 PT BLKS 3-9 ARTESIA ESTATES                           656   424 3  788  1 ANNEXATION, ARTESIA            33 16 26 12/01/2006 PT E2SW4 33-16-26, TRANSFER STATION 4  900  2 ANNEXATION, ARTESIA            33 16 26  7/10/2007 TR 1 FRED R GARCIA TRACTS REPLAT                      701   553 --Bejnar (talk) 19:40, 30 June 2014 (UTC)

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title: Talk:Artesia, New Mexico