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Hussites

The Hussites (Czech: Husité or Kališníci, "Chalice People"; Latin: Hussitae) were a Czech proto-Protestant Christian movement that followed the teachings of reformer Jan Hus (fl. 1401–1415), a part of the Bohemian Reformation.

After the execution of Hus at the Council of Constance, a series of crusades, civil wars, victories and compromises between various factions with different theological agendas broke out. At the end of the Hussite Wars (1420–1434), the now Catholic-supported Utraquist side came out victorious from conflict with the Taborites and became the dominant Hussite group in Bohemia.

Catholics and Utraquists were given legal equality in Bohemia after the religious peace of Kutná Hora in 1485. Bohemia and Moravia, or what is now the territory of the Czech Republic, remained majority Hussite for two centuries until Roman Catholicism was reimposed by the Holy Roman Emperor following the 1620 Battle of White Mountain during the Thirty Years' War.

The Hussite tradition continues in the Moravian Church, Unity of the Brethren and the refounded Czechoslovak Hussite churches.

History
The Hussite movement began in the Kingdom of Bohemia and quickly spread throughout the remaining Lands of the Bohemian Crown, including Moravia and Silesia. It also made inroads into the northern parts of the Kingdom of Hungary (now Slovakia), but was rejected and gained infamy for the plundering behaviour of the Hussite soldiers. There were also very small temporary communities in Poland-Lithuania and Transylvania which moved to Bohemia after being confronted with religious intolerance. It was a regional movement that failed to expand farther. Hussites emerged as a majority Utraquist movement with a significant Taborite faction, and smaller regional ones that included Adamites, Orebites and Orphans.

Major Hussite theologians included Petr Chelčický, Jerome of Prague. A number of Czech national heroes were Hussite, including Jan Žižka, who led a fierce resistance to five consecutive crusades proclaimed on Hussite Bohemia by the Papacy. Hussites were one of the most important forerunners of the Protestant Reformation. This predominantly religious movement was propelled by social issues and strengthened Czech national awareness.

Hus's death

The Council of Constance lured Jan Hus in with a letter of indemnity, then tried him for heresy and put him to death at the stake on 6 July 1415.

The arrest of Hus in 1414 caused considerable resentment in Czech lands. The authorities of both countries appealed urgently and repeatedly to King Sigismund to release Jan Hus.

When news of his death at the Council of Constance arrived, disturbances broke out, directed primarily against the clergy and especially against the monks. Even the Archbishop narrowly escaped from the effects of this popular anger. The treatment of Hus was felt to be a disgrace inflicted upon the whole country and his death was seen as a criminal act. King Wenceslaus IV., prompted by his grudge against Sigismund, at first gave free vent to his indignation at the course of events in Constance. His wife openly favoured the friends of Hus. Avowed Hussites stood at the head of the government.

A league was formed by certain lords, who pledged themselves to protect the free preaching of the Gospel upon all their possessions and estates and to obey the power of the Bishops only where their orders accorded with the injunctions of the Bible. The university would arbitrate any disputed points. The entire Hussite nobility joined the league. Other than verbal protest of the council's treatment of Hus, there was little evidence of any actions taken by the nobility until 1417. At that point several of the lesser nobility and some barons, signatories of the 1415 protest letter, removed Catholic priests from their parishes, replacing them with priests willing to give communion in both wine and bread. The chalice of wine became the central identifying symbol of the Hussite movement. If the king had joined, its resolutions would have received the sanction of the law; but he refused, and approached the newly formed Roman Catholic League of lords, whose members pledged themselves to support the king, the Catholic Church, and the council. The prospect of a civil war began to emerge.

Prior to becoming pope, Martin V, then known as Cardinal Otto of Colonna had attacked Hus with relentless severity. He energetically resumed the battle against Hus's teaching after the enactments of the Council of Constance. He wished to eradicate completely the doctrine of Hus, for which purpose the co-operation of King Wenceslaus had to be obtained. In 1418, Sigismund succeeded in winning his brother over to the standpoint of the council by pointing out the inevitability of a religious war if the heretics in Bohemia found further protection. Hussite statesmen and army leaders had to leave the country and Roman Catholic priests were reinstated. These measures caused a general commotion which hastened the death of King Wenceslaus by a paralytic stroke in 1419. His heir was Sigismund.

Hussite Wars (1419–1434)

The news of the death of King Wenceslaus in 1419 produced a great commotion among the people of Prague. A revolution swept over the country: churches and monasteries were destroyed, and church property was seized by the Hussite nobility. It was then, and remained till much later, in question whether Bohemia was a hereditary or an elective monarchy, especially as the line through which Sigismund claimed the throne had accepted that the Kingdom of Bohemia was an elective monarchy elected by the nobles, and thus the regent of the kingdom (Čeněk of Wartenberg) also explicitly stated that Sigismund had not been elected as reason for Sigismund's claim to not be accepted. Sigismund could get possession of "his" kingdom only by force of arms. Pope Martin V called upon Catholics of the West to take up arms against the Hussites, declaring a crusade, and twelve years of warfare followed.

The Hussites initially campaigned defensively, but after 1427 they assumed the offensive. Apart from their religious aims, they fought for the national interests of the Czechs. The moderate and radical parties were united, and they not only repelled the attacks of the army of crusaders but crossed the borders into neighboring countries. On March 23, 1430, Joan of Arc dictated a letter that threatened to lead a crusading army against the Hussites unless they returned to the Catholic faith, but her capture by English and Burgundian troops two months later would keep her from carrying out this threat.

Council of Basel and Compacta of Prague
Eventually, the opponents of the Hussites found themselves forced to consider an amicable settlement. The Hussites were sent an invitation to attend the ecumenical Council of Basel on October 15, 1431. The discussions began on 10 January 1432, focusing chiefly on the four articles of Prague. No agreement emerged. After repeated negotiations between the Basel Council and Bohemia, a Bohemian–Moravian state assembly in Prague accepted the "Compactata" of Prague on 30 November 1433. The agreement granted communion in both kinds to all who desired it, but with the understanding that Christ was entirely present in each kind, though on the condition that the rest of the Hussite reforms would no longer be emphasised. Free preaching was granted conditionally: the Church hierarchy had to approve and place priests, and the power of the bishop must be considered. The article which prohibited the secular power of the clergy was almost reversed.

The Taborites refused to conform. The Calixtines united with the Roman Catholics and destroyed the Taborites at the Battle of Lipany on 30 May 1434. From that time, the Taborites lost their importance, though the Hussite movement would continue in Poland for another five years, until the Royalist forces of Poland defeated the Polish Hussites at the Battle of Grotniki. The state assembly of Jihlava in 1436 confirmed the "Compactata" and gave them the sanction of law. This accomplished the reconciliation of Bohemia with Rome and the Western Church, and at last Sigismund obtained possession of the Bohemian crown. His reactionary measures caused a ferment in the whole country, but he died in 1437. The state assembly in Prague rejected Wyclif's doctrine of the Lord's Supper, which was obnoxious to the Utraquists, as heresy in 1444. Most of the Taborites now went over to the party of the Utraquists; the rest joined the "Brothers of the Law of Christ" ("Unitas Fratrum") (see history of the Moravian Church).

Hussite Bohemia, Luther and the Reformation (1434–1618)

In 1462, Pope Pius II declared the "Compacta" null and void, prohibited communion in both kinds, and acknowledged King George of Podebrady as king on condition that he would promise an unconditional harmony with the Roman Church. This he refused, leading to the Bohemian–Hungarian War (1468–1478). His successor, King Vladislaus II, favored the Roman Catholics and proceeded against some zealous clergymen of the Calixtines. The troubles of the Utraquists increased from year to year. In 1485, at the Diet of Kutná Hora, an agreement was made between the Roman Catholics and Utraquists that lasted for thirty-one years. It was only later, at the Diet of 1512, that the equal rights of both religions were permanently established. The appearance of Martin Luther was hailed by the Utraquist clergy, and Luther himself was astonished to find so many points of agreement between the doctrines of Hus and his own. But not all Utraquists approved of the German Reformation; a schism arose among them, and many returned to the Roman doctrine, while other elements had organised the "Unitas Fratrum" already in 1457.

Bohemian Revolt and harsh persecution under the Habsburgs (1618–1918)
Under Emperor Maximilian II, the Bohemian state assembly established the Confessio Bohemica, upon which Lutherans, Reformed, and Bohemian Brethren agreed. From that time forward Hussitism began to die out. After the Battle of White Mountain on 8 November 1620 the Roman Catholic Faith was re-established with vigour, which fundamentally changed the religious conditions of the Czech lands.

Leaders and members of Unitas Fratrum were forced to choose to either leave the many and varied southeastern principalities of what was the Holy Roman Empire (mainly Austria, Hungary, Bohemia, Moravia and parts of Germany and its many states), or to practice their beliefs secretly. As a result, members were forced underground and dispersed across northwestern Europe. The largest remaining communities of the Brethren were located in Lissa (Leszno) in Poland, which had historically strong ties with the Czechs, and in small, isolated groups in Moravia. Some, among them Jan Amos Comenius, fled to western Europe, mainly the Low Countries. A settlement of Hussites in Herrnhut, Saxony, now Germany, in 1722 caused the emergence of the Moravian Church.

Post-Habsburg era and modern times (1918–present)

In 1918, as a result of World War I, the Czech lands regained independence from Austria-Hungary controlled by the Habsburg monarchy as Czechoslovakia (due to Masaryk and Czechoslovak legions with Hussite tradition, in the name of the troops).

Today, the Hussite tradition is represented in the Moravian Church, Unity of the Brethren, and Czechoslovak Hussite Church.

Factions
Hussitism organised itself during the years 1415–1419. Hussites were not a unitary movement, but a diverse one with multiple factions that held different views and opposed each other in the Hussite Wars. From the beginning, there formed two parties, with a smaller number of people withdrawing from both parties around the pacifist Petr Chelčický, whose teachings would form the foundation of the Unitas Fratrum. Hussites can be divided into:

 * Moderate Hussites
 * Prague Hussites
 * Bohemian Hussite nobility
 * Hussites of Žatec and Louny
 * Other Utraquists/Calixtines
 * Radical Hussites
 * Taborites
 * Orebites
 * Adamites
 * Orphans
 * Other Radical Hussites

Moderates
The more conservative Hussites (the moderate party, or Utraquists), who followed Hus more closely, sought to conduct reform while leaving the whole hierarchical and liturgical order of the Church untouched.

Their programme is contained in the Four Articles of Prague, which were written by Jacob of Mies and agreed upon in July 1420, promulgated in the Latin, Czech, and German languages. The full text is about two pages long, but they are often summarized as:

 * Freedom to preach the word of God
 * Celebration of the communion under both kinds (bread and wine to priests and laity alike)
 * Poverty of the clergy and expropriation of church property;
 * Punishment for mortal sins regardless of stature.

The views of the moderate Hussites were widely represented at the university and among the citizens of Prague; they were therefore called the Prague Party, but also Calixtines (Latin calix chalice) or Utraquists (Latin utraque both), because they emphasized the second article of Prague, and the chalice became their emblem.

Radicals
The more radical parties, the Taborites, Orebites and Orphans, identified itself more boldly with the doctrines of John Wycliffe, sharing his passionate hatred of the monastic clergy,  and his desire to return the Church to its supposed condition during the time of the apostles. This required the removal of the existing hierarchy and the secularisation of ecclesiastical possessions. Above all they clung to Wycliffe's doctrine of the Lord's Supper, denying transubstantiation, and this is the principal point by which they are distinguished from the moderate party, the Utraquists.

The radicals preached the "sufficientia legis Christi"—the divine law (i.e. the Bible) is the sole rule and canon for human society, not only in the church, but also in political and civil matters. They rejected therefore, as early as 1416, everything that they believed had no basis in the Bible, such as the veneration of saints and images, fasts, superfluous holidays, the oath, intercession for the dead, auricular Confession, indulgences, the sacraments of Confirmation and the Anointing of the Sick, and chose their own priests.

The radicals had their gathering-places all around the country. Their first armed assault fell on the small town of Ústí, on the river Lužnice, south of Prague (today's Sezimovo Ústí). However, as the place did not prove to be defensible, they settled in the remains of an older town upon a hill not far away and founded a new town, which they named Tábor (a play on words, as "Tábor" not only meant "camp" or "encampment" in Czech, but is also the traditional name of the mountain on which Jesus was expected to return; see Mark 13); hence they were called Táborité (Taborites). They comprised the essential force of the radical Hussites.

Their aim was to destroy the enemies of the law of God, and to defend his kingdom (which had been expected to come in a short time) by the sword. Their end-of-world visions did not come true. In order to preserve their settlement and spread their ideology, they waged bloody wars; in the beginning they observed a strict regime, inflicting the severest punishment equally for murder, as for less severe faults as adultery, perjury and usury, and also tried to apply rigid Biblical standards to the social order of the time. The Taborites usually had the support of the Orebites (later called Orphans), an eastern Bohemian sect of Hussitism based in Hradec Králové.

title: Hussites


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HMS Ark Royal

Five ships of the Royal Navy have borne the name HMS Ark Royal:

 * ENGLISH SHIP Ark Royal, the flagship of the English fleet during the Spanish Armada campaign of 1588
 * HMS Ark Royal (1914), planned as freighter, built as seaplane carrier during the First World War, renamed Pegasus in 1934
 * HMS Ark Royal (91), British aircraft carrier launched in 1937 which participated in the Second World War and was sunk by a U-boat in 1941
 * HMS Ark Royal (R09), an Audacious-class aircraft carrier launched in 1950, decommissioned in 1979
 * HMS Ark Royal (R07), an Invincible-class aircraft carrier, launched in 1981, decommissioned in 2011

Battle honours

 * Armada 1588
 * Cádiz 1596
 * Dardanelles 1915
 * Norway 1940
 * Spartivento 1940
 * Mediterranean 1940–1941
 * Bismarck 1941
 * Malta Convoys 1941
 * Al Faw 2003

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

title: HMS Ark Royal


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Herman of Alaska

Herman of Alaska (Преподобный Ге́рман Аляскинский; c. 1756 – November 15, 1837) was a Russian Orthodox monk and missionary to Alaska, which was then part of Russian America. His gentle approach and ascetic life earned him the love and respect of both the native Alaskans and the Russian colonists. He is considered by many Orthodox Christians to be the patron saint of North America.

Early life
Biographers disagree about Herman's early life. His official biography, which Valaam Monastery published in 1867, said that his pre-monastic name was unknown, but that Herman was born into a merchant's family in Serpukhov, a city in Moscow Governorate. He was said to later become a novice at the Trinity-St. Sergius Hermitage near St. Petersburg before going to Valaam to complete his training and receive full tonsure as a monk. But, modern biographer Sergei Korsun found this account to be based on erroneous information provided by Semyon Yanovsky, an administrator from 1818 through part of 1820 of the Russian-American Company (RAC) in Alaska. He confused Herman's biographical information with that of another monk, Joseph (Telepnev).

Another former RAC Chief Manager, Ferdinand von Wrangel, stated Herman was originally from a prosperous peasant family in the Voronezh Governorate and served in the military. He then entered monastic life as a novice at Sarov Monastery. This concurred with testimony of Archimandrite Theophan (Sokolov), and a letter written by Herman himself. These agree that Herman began his monastic life as a novice at Sarov, and later received the full tonsure at Valaam. A young military clerk named Egor Ivanovich Popov, from the Voronezh Governorate, was tonsured with the name 'Herman' at Valaam in 1782.

All biographers agree that at Valaam, Herman studied under Abbot Nazarius, previously of Sarov Monastery. The abbot had been influenced by the hesychastic tradition of Paisius Velichkovsky. Herman undertook various obediences and was well-liked by the brethren, but wanted a more solitary life. He became a hermit with Abbot Nazarius' blessing. His hermitage, which later became known as "Herman's field" or Germanovo, was two kilometers from the monastery. Metropolitan Gabriel of St. Petersburg offered to ordain Herman to the priesthood and twice offered to send him to lead the Russian Orthodox Mission in China, but he refused, preferring the solitary life and remaining a simple monk. Years after he left for North America, Herman continued to keep in touch with his spiritual home. In a letter to Abbot Nazarius, he wrote, "in my mind I imagine my beloved Valaam, and constantly behold it across the great ocean."

Mission in Alaska

The Russian colonization of the Americas began when Vitus Bering and Aleksei Chirikov discovered Alaska on behalf of the Russian Empire in 1741. The expedition harvested 1,500 sea otter pelts, which Chinese merchants bought for 1,000 rubles each at their trading post near Lake Baikal. This spurred a "fur rush" from 1741 to 1798 in which frontiersmen known as promyshlenniki explored Alaska and the Aleutian Islands. They alternately fought with and intermarried the native peoples.

Grigory Shelikhov, a fur-trader, subjugated the native population of Kodiak Island. With Ivan Golikov, he founded a fur-trading company that eventually received a monopoly from the Imperial government; it became known as the Russian-American Company. Shelikhov founded a school for the natives, and many were converted to Russian Orthodox Christianity.

The Shelikhov-Golikov Company appealed to the Most Holy Synod of the Russian Orthodox Church to provide a priest for the natives. Catherine the Great decided instead to send an entire mission to America. She entrusted the task of recruiting missionaries to Metropolitan Gabriel of St. Petersburg, who sent ten monks from Valaam, including Herman. The missionaries arrived on Kodiak on September 24, 1794.

Herman and the other missionaries encountered a harsh reality at Kodiak that did not correspond to Shelikhov's rosy descriptions. The native Kodiak population, called "Americans" by the Russian settlers, were subject to harsh treatment by the Russian-American Company, which was being overseen by Shelikhov's manager Alexander Baranov. He later became the first governor of the colony.

The men were forced to hunt for sea otter even during harsh weather, and women and children were abused. The monks were also shocked at the widespread alcoholism in the Russian population, and the fact that most of the settlers had taken native mistresses. The monks themselves were not given the supplies that Shelikhov promised them, and had to till the ground with wooden implements.

Despite these difficulties, the monks baptized more than 7,000 natives in the Kodiak region, and set about building a church and monastery. Herman was assigned in the bakery and acted as the mission's steward (ekonom).

The monks became the defenders of the native Kodiak population. Herman was especially noted for his zeal in protecting them from the excessive demands of the RAC, and Baranov disparaged him in a letter as a "hack writer and chatterer." A contemporary historian compares him to Bartolomé de las Casas, the Roman Catholic friar who defended the rights of native South Americans against the Spanish colonists.

After over a decade spent in Alaska, Herman became the head of the mission in 1807, although he was not ordained to the priesthood. The local population loved and respected him, and he had established good relations with Baranov. Herman ran the mission school, where he taught church subjects such as singing and catechism, alongside reading and writing. He also taught agriculture on Spruce Island. But, because he still longed for the life of a hermit, he retired from active duty in the mission and moved to Spruce Island.

Life on Spruce Island
Herman moved to Spruce Island around 1811 to 1817. The island is separated from Kodiak by a mile-wide strait, making it ideal for eremitic life. Herman named his hermitage "New Valaam." He wore simple clothes and slept on a bench covered with a deerskin. When asked how he could bear to be alone in the forest, he replied, "I am not alone. God is here, as God is everywhere."

Despite his solitary life, he soon gained a following. He received many visitors—especially native Aleuts —on Sundays and church feasts. Soon a chapel and guesthouse were built next to his hermitage, and then a school for orphans. Herman had a few disciples, including the Creole orphan Gerasim Ivanovich Zyrianov, a young Aleut woman named Sofia Vlasova, and others.

Entire families moved to the island in order to be closer to the Elder, who helped to sort out their disputes. Herman had a deep love for the native Aleuts: he stood up for them against the excesses of the Russian-American Company, and once during an epidemic, he was the only Russian to visit them, working tirelessly to care for the sick and console the dying. Herman spent the rest of his life on Spruce Island, where he died on November 15, 1837.

Sainthood

On March 11, 1969, the bishops of the Orthodox Church in America (OCA) formally declared their intention to canonize Herman, "as a sublime example of the Holy Life, for our spiritual benefit, inspiration, comfort, and the confirmation of our Faith." On August 9, 1970, Metropolitan Ireney (Bekish) of the OCA along with Archbishop Paul (Olmari) of Finland and other hierarchs and clergy presided over the canonization service, which was held at Holy Resurrection Cathedral on Kodiak Island. His relics were transferred from his grave underneath the Sts. Sergius and Herman of Valaam Chapel (i.e., the Saints Sergius and Herman of Valaam Chapel), on Spruce Island, to the Holy Resurrection Cathedral.

On the same date, the bishops of the Russian Orthodox Church Outside of Russia (ROCOR) also canonized Herman at the Holy Virgin Cathedral ("Joy of All Who Sorrow") in San Francisco. At the all-night vigil, the canon to Herman was read for the first time by Gleb Podmoshensky, one of the founding brothers of the St. Herman of Alaska Serbian Orthodox Brotherhood in 1963. He, Eugene (Seraphim) Rose, and Lawrence Campbell gathered material for the Synod of Bishops in order to support the glorification of Herman, and also helped compose the liturgical service in his honor.

There are several feast days throughout the year on which Saint Herman of Alaska is commemorated. Since there are two different calendars currently in use among various Orthodox churches, two dates are listed: the first date is the date on the traditional Julian Calendar, the second date, after the slash, is the same day on the modern Gregorian Calendar:

 * July 27/August 9—Glorification: This is the anniversary of the joint-glorification (canonization) of Herman of Alaska as a saint in 1970.
 * November 15/28—Repose: This is the anniversary of the actual death of Herman.
 * December 13/26—Repose: Due to an error in record keeping, this was originally thought to be the day of Herman's death, and because of the long-established tradition of celebrating his memory on this day, it has remained a feast day. It is more likely that this is the day he was buried. For those Orthodox Christians who follow the Julian Calendar, this day falls on December 25 of the Gregorian Calendar.
 * Second Sunday after Pentecost:, as one of the saints commemorated on the Synaxis of the Saints of North America—this is a moveable feast of the ecclesiastical year, and the date of its observance will change from year to year.

The major portion of his relics are preserved at Holy Resurrection Cathedral in Kodiak, Alaska, His burial site at the Sts. Sergius and Herman Chapel, Spruce Island, Alaska is an important pilgrimage site. The devout will often take soil from his grave and water from the spring named in his honour.

A portion of his relics are enshrined at the St. Ignatius Chapel at the Antiochan Village in Pennsylvania, a conference and retreat center of the Antiochian Orthodox Christian Archdiocese of North America. He is regarded as one of their patron saints.

In 1963, with the blessing of John Maximovitch, Archbishop of Shanghai and San Francisco, a community of Orthodox booksellers and publishers called the St. Herman of Alaska Brotherhood was formed to publish Orthodox missionary information in English.

One of the founders was Father Seraphim Rose. The Brotherhood did much to advance the cause of Herman's glorification as a saint. Saint Herman's Orthodox Theological Seminary in Kodiak, Alaska is named in his honor, as are numerous parish churches throughout the world.

On Tuesday, August 4, 1970, the 91st Congress of the United States acknowledged the glorification of Herman of Alaska with a speech in the Senate, and his biography was formally entered into the Congressional Record.

In 1993, Patriarch Alexis II visited Kodiak to venerate the relics of Saint Herman. He left as a gift an ornate lampada (oil lamp) which burns constantly over the reliquary. Pilgrims from all over the world are anointed with holy oil from this lampada.

In 2022, Herman was officially added to the Episcopal Church liturgical calendar with a feast day on 15 November.

Finnish Orthodox Espoo Church in Tapiola, Espoo, is dedicated to St. Herman of Alaska.

title: Herman of Alaska


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Hausdorff dimension

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or "rough" sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.

More specifically, the Hausdorff dimension is a dimensional number associated with a metric space, i.e. a set where the distances between all members  are defined. The dimension is drawn from the extended real numbers, $$\overline{\mathbb{R}}$$, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.

In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product space equals n. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=SD. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving—in the Koch and other fractal cases—non-integer dimensions for these objects.

The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski–Bouligand dimension.

Intuition
The intuitive concept of dimension of a geometric object X is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object.

Every space-filling curve hits some points multiple times and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is the greatest integer n such that in every covering of X by small open balls there is at least one point where n + 1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension n = 1.

But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.

The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number N(r) of balls of radius at most r required to cover X completely. When r is very small, N(r) grows polynomially with 1/r. For a sufficiently well-behaved X, the Hausdorff dimension is the unique number d such that N(r) grows as 1/rd as r approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value d is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.

For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes you see around you is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well-documented exceptions where all these dimensions differ.

Formal definition
The formal definition of the Hausdorff dimension is arrived at by defining first the d-dimensional Hausdorff measure, a fractional-dimension analogue of the Lebesgue measure. First, an outer measure is constructed: Let $$X$$ be a metric space. If $$S\subset X$$ and $$d\in [0,\infty)$$,

 * $$H^d_\delta(S)=\inf\left \{\sum_{i=1}^\infty (\operatorname{diam} U_i)^d: \bigcup_{i=1}^\infty U_i\supseteq S, \operatorname{diam} U_i<\delta\right \},$$

where the infimum is taken over all countable covers $$U$$ of $$S$$. The Hausdorff d-dimensional outer measure is then defined as $$\mathcal{H}^d(S)=\lim_{\delta\to 0}H^d_\delta(S)$$, and the restriction of the mapping to measurable sets justifies it as a measure, called the $$d$$-dimensional Hausdorff Measure.

Hausdorff dimension
The Hausdorff dimension $$\dim_{\operatorname{H}}{(X)}$$ of $$X$$ is defined by
 * $$\dim_{\operatorname{H}}{(X)}:=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.$$

This is the same as the supremum of the set of $$d\in [0,\infty)$$ such that the $$d$$-dimensional Hausdorff measure of $$X$$ is infinite (except that when this latter set of numbers $$d$$ is empty the Hausdorff dimension is zero).

Hausdorff content
The $$d$$-dimensional unlimited Hausdorff content of $$S$$ is defined by
 * $$C_H^d(S):= H_\infty^d(S) = \inf\left \{ \sum_{k=1}^\infty (\operatorname{diam} U_k)^d: \bigcup_{k=1}^\infty U_k\supseteq S \right \}$$

In other words, $$C_H^d(S)$$ has the construction of the Hausdorff measure where the covering sets are allowed to have arbitrarily large sizes (Here, we use the standard convention that $\inf\varnothing=\infty$). The Hausdorff measure and the Hausdorff content can both be used to determine the dimension of a set, but if the measure of the set is non-zero, their actual values may disagree.

Examples

 * Countable sets have Hausdorff dimension 0.
 * The Euclidean space $$\R^n$$ has Hausdorff dimension $$n$$, and the circle $$S^1$$ has Hausdorff dimension 1.
 * Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension. For example, the Cantor set, a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3) ≈ 0.63. The Sierpinski triangle is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58. These Hausdorff dimensions are related to the "critical exponent" of the Master theorem for solving recurrence relations in the analysis of algorithms.
 * Space-filling curves like the Peano curve have the same Hausdorff dimension as the space they fill.
 * The trajectory of Brownian motion in dimension 2 and above is conjectured to be Hausdorff dimension 2.
 * Lewis Fry Richardson performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of South Africa to 1.25 for the west coast of Great Britain.

Hausdorff dimension and inductive dimension
Let X be an arbitrary separable metric space. There is a topological notion of inductive dimension for X which is defined recursively. It is always an integer (or +∞) and is denoted dimind(X).

Theorem. Suppose X is non-empty. Then
 * $$ \dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X). $$

Moreover,
 * $$ \inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X), $$

where Y ranges over metric spaces homeomorphic to X. In other words, X and Y have the same underlying set of points and the metric dY of Y is topologically equivalent to dX.

These results were originally established by Edward Szpilrajn (1907–1976), e.g., see Hurewicz and Wallman, Chapter VII.

Hausdorff dimension and Minkowski dimension
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in [0, 1] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.

Hausdorff dimensions and Frostman measures
If there is a measure μ defined on Borel subsets of a metric space X such that μ(X) > 0 and μ(B(x, r)) ≤ rs holds for some constant s > 0 and for every ball B(x, r) in X, then dimHaus(X) ≥ s. A partial converse is provided by Frostman's lemma.

Behaviour under unions and products
If $$X=\bigcup_{i\in I}X_i$$ is a finite or countable union, then

 * $$ \dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).$$

This can be verified directly from the definition.

If X and Y are non-empty metric spaces, then the Hausdorff dimension of their product satisfies

 * $$ \dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).$$

This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when X and Y are Borel subsets of Rn, the Hausdorff dimension of X × Y is bounded from above by the Hausdorff dimension of X plus the upper packing dimension of Y. These facts are discussed in Mattila (1995).

Self-similar sets
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set E is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(E) = E, although the exact definition is given below.

Theorem. Suppose

 * $$ \psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots, m $$

are each a contraction mapping on Rn with contraction constant ri < 1. Then there is a unique non-empty compact set A such that

 * $$ A = \bigcup_{i=1}^m \psi_i (A). $$

The theorem follows from Stefan Banach's contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of Rn with the Hausdorff distance.

The open set condition
To determine the dimension of the self-similar set A (in certain cases), we need a technical condition called the open set condition (OSC) on the sequence of contractions ψi.

There is an open set V with compact closure, such that

 * $$ \bigcup_{i=1}^m\psi_i (V) \subseteq V, $$

where the sets in union on the left are pairwise disjoint.

The open set condition is a separation condition that ensures the images ψi(V) do not overlap "too much".

Theorem. Suppose the open set condition holds and each ψi is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is s where s is the unique solution of

 * $$ \sum_{i=1}^m r_i^s = 1. $$

The contraction coefficient of a similitude is the magnitude of the dilation.

In general, a set E which is carried onto itself by a mapping

 * $$ A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A) $$

is self-similar if and only if the intersections satisfy the following condition:

 * $$ H^s\left(\psi_i(E)\cap \psi_j(E)\right) =0, $$

where s is the Hausdorff dimension of E and Hs denotes s-dimensional Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:

Theorem. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar.

title: Hausdorff dimension


text:
Heckler & Koch

Heckler & Koch GmbH (HK or H&K; ) is a German firearms manufacturer that produces handguns, rifles, submachine guns, and grenade launchers. The company is located in Oberndorf am Neckar, Baden-Württemberg, and also has subsidiaries in the United Kingdom, France, and the United States.

Heckler & Koch was founded in 1949 by former Mauser engineers Edmund Heckler, Theodor Koch, and Alex Seidel, who founded the company out of the shuttered Mauser factory in Oberndorf. The company initially produced machine tool and metal parts until 1956 when, in response to a Bundeswehr contract for a new service rifle, HK developed the Heckler & Koch G3. The success of the G3 rifle prompted HK to transition to the defense industry. HK was briefly owned by Royal Ordnance from 1991 to 2002, and is currently part of the Heckler & Koch Group, comprising Heckler & Koch GmbH, Heckler & Koch Defense, NSAF Ltd., and Heckler & Koch France SAS. The company's motto is "Keine Kompromisse!" (No Compromises!).

History

With the fall of Nazi Germany and the following Allied occupation of Germany, Oberndorf came under French control, and the entire Waffenfabrik Mauser AG factory was dismantled by French occupying forces. All factory records were destroyed on orders of the local French Army commander. In 1948, three former Mauser engineers, Edmund Heckler, Theodor Koch, and Alex Seidel, saved what they could from the factory and used what they salvaged to start a machine tool plant in the vacant factory that became known as the Engineering Office Heckler & Co.

On December 28, 1949, the Engineering Office Heckler & Co. changed its name and was registered officially as Heckler & Koch GmbH. Initially the new company manufactured machine tools, bicycle and sewing machine parts, gauges, and other precision parts.

In 1956, Heckler & Koch responded to the West German government's tender for a new infantry rifle for the Bundeswehr with the proposal of the G3 battle rifle, based on the Spanish CETME Model 58 rifle and developed in cooperation with CETME. The German government awarded Heckler & Koch the tender and in 1959 declared the G3 the standard rifle of the Bundeswehr. Later in 1961, Heckler & Koch developed the 7.62×51mm HK21 general-purpose machine gun, based on the G3.

In 1966, Heckler & Koch introduced the HK54 machine pistol, which eventually launched in 1969 as the MP5 submachine gun. Two years later, the company introduced the HK33 assault rifle, a smaller version of the G3 chambered in 5.56×45mm NATO.

Diversification
In 1974, Heckler & Koch diversified into two more areas, HK Defense and Law Enforcement Technology and HK Hunting and Sports Firearms. Since then HK has designed and manufactured more than 100 different types of firearms and devices for the world's military and law enforcement organizations as well as sports shooters and hunters.

In 1990, Heckler & Koch completed two decades of development of their revolutionary caseless weapon system and produced prototypes of the G11 rifle. The company also produced prototypes of the G41 assault rifle intended for the Bundeswehr. Due to the international political climate at the time (East and West Germany uniting and defense budget cuts) the company was unable to secure funded contracts from the German government to support production of either weapon system and became financially vulnerable. The next year, Heckler & Koch was sold to British Aerospace's Royal Ordnance division.

During 1994 and 1995, the German government awarded Heckler & Koch contracts for producing an updated standard assault rifle and updated standard sidearm for the Bundeswehr. Heckler & Koch developed and produced the Project HK50, a lightweight carbon fiber assault rifle, which became the G36 assault rifle. In addition, Heckler & Koch produced the P8 pistol, derived from its USP handguns produced since 1989. The USP was adopted as the standard sidearm of the Bundeswehr in 1994, and the G36 was adopted as their standard-issue rifle in 1995.

As the result of a 1999 merger between British Aerospace and Marconi Electronic Systems, Heckler & Koch was owned by the resulting BAE Systems; it was contracted to refurbish the British Army's SA80 rifles (which had been built by Royal Ordnance) This contract entailed a modification program to the SA80 series of rifles to address a number of reliability issues with the design. In 2002, BAE Systems restructured and sold Heckler & Koch to a group of private investors, who created the German group holding company HK Beteiligungs GmbH.

In 2003, HK Beteiligungs GmbH's business organization restructured as Heckler & Koch Jagd und Sportwaffen GmbH (HKJS), and its business was separated into the two business areas similar to the 1974 business mission areas: Defense, and Law Enforcement and Sporting Firearms.

In 2004, Heckler & Koch was awarded a major handgun contract for the United States Department of Homeland Security, worth a potential $26.2 million for up to 65,000 handguns. This contract ranks as the single largest handgun procurement contract in U.S. law enforcement history.

HK was contracted by the United States Army to produce the kinetic energy subsystem (see: kinetic projectiles or kinetic energy penetrator) of the Objective Individual Combat Weapon, a planned replacement for the M16 rifle/M203 grenade launcher combination. The OICW was designed to fire 5.56 mm rounds and 25 mm grenades. The kinetic energy component was also developed separately as the XM8, though both the OICW and XM8 are now indefinitely suspended.

Heckler & Koch developed an AR-15/M4 carbine variant, marketed as the HK416. HK replaced the direct impingement system used by the Stoner design on the original M16 with a short-stroke piston operating system. The civilian models are named the MR223 and, in the U.S., the MR556A1.

In 2007, United States Secretary of the Army Pete Geren agreed to hold a "dust chamber" test pitting the M4 against the Heckler & Koch HK416 and XM8, as well as the rival FN SCAR design. The Heckler & Koch XM8 and FN SCAR had the fewest failures in the test, closely followed by the HK416, while the M4 had by far the most. In 2007, the Norwegian Army became the first to field the HK416 as a standard-issue rifle.

HK sells its pistols in the United States to both law enforcement and civilian markets, through its HK USA subsidiary. The company has locations in Virginia, New Hampshire, and Georgia.

Products

Heckler & Koch has produced a variety of firearms including the G3, HK21, MP5, HK4, HK33, HK69, VP70, PSG1, USP, G36, MG4, UMP, MP7, and HK416, which have become some of the most iconic and widely adopted firearms in the world, used by dozens of militaries, police forces, and paramilitaries worldwide. Many of its prototype weapons, including the G11, HK CAWS, XM29 OICW, and XM8, have also become recognizable. HK firearms use blowback operation, short-recoil, roller-delayed blowback, gas-delayed blowback, and short-stroke piston gas operation. HK is responsible for several innovations in firearms, such as the use of polymers in weapon designs, modern polygonal rifling, the feasibility of high-velocity caseless ammunition in prototype service rifles, and integral rails for handgun attachments.

HK naming system

Heckler & Koch products use an internal naming system, consisting of an abbreviation and a two- or three-digit Werknummern designation popularly referred to as the "HK 3-digit system". Each letter and digit is assigned a specific meaning outlined in the convention to make them easier to identify and differentiate by name.

The HK naming convention is not a fixed convention, but rather a guideline, and not all HK products follow it; this is typically done for marketing purposes or quirks in the weapon's development or intended role. For instance, the HK416 does not use a proper abbreviation ("HK" does not mean anything specific), nor does it use proper digits (the HK416 was originally two models, the "HK M4" and "HK M16", that were later amalgamated into the HK416); using the 3-digit system, the standard HK416 would likely be referred to as the G333. Such products tend to have proper internal designations anyway; the HK416 is internally referred to as the HK333.

Abbreviations
Most HK products have a prefix of between one and three letters, corresponding to a word or term in German (though some refer to English terms instead, with no German equivalent). Several were only used for a single model, such as the "Universal" weapons (UMP, UCP, USC, USP). Some abbreviations are used as a suffix to designate specific variants.

Werknummern designations
The Werknummern designation system assigns two or three digits that correspond to the product's technical specifics. These are placed after (or if a suffix, before) the abbreviation, and denote the generation, form factor, and caliber or munition of the weapon.

Date code
The date code is a two-letter combination used to specify the year a weapon was manufactured in. These are not part of the product's name, but are printed for identification directly on the weapon itself. They are only used on handguns.

Heckler & Koch handguns produced at HK's German facilities are marked with "DE", Germany's ISO 3166-1 code. Handguns manufactured in HK facilities outside Germany, or those produced in Germany before 2008, do not have the DE marking.

Trigger group

Heckler & Koch long arms mostly follow a set of shared trigger group standards for selective fire and safety, with corresponding markings and pictograms.

Trafficking
H&K has been accused of shipping small arms to conflict regions such as Bosnia and Nepal, and has licensed its weapons for production by governments with poor human rights records such as Sudan, Thailand and Myanmar. It has been argued that the company effectively evaded EU export restrictions when these licensees sold HK weapons to conflict zones including Indonesia, Sri Lanka and Sierra Leone.

According to the newspaper Stuttgarter Nachrichten (31 August 2011), as well as the state broadcaster ARD, a large stockpile of G36 assault rifles fell into rebel hands during the August 2011 attack on Muammar Gaddafi's compound in Tripoli. It is unclear how many were exported to Libya and by whom.

Illegal arms sales to Mexico
On 11 December 2011, federal, state and local Mexican police officers used battle rifles to fire on Ayotzinapa Rural Teachers' College students and peasant organizations to disperse a blockade on Mexican Federal Highway 95D, resulting in the deaths of students Jorge Alexis Herrera and Gabriel Echeverría de Jesús. According to media reports, 7.62×51mm NATO round casings were found at the scene, matching those used by H&K G3 rifles.

In Iguala and Cocula, corrupt police officers and cartelmen are known to have used H&K G36 rifles during the 2014 Iguala mass kidnapping on 26–27 September 2013. At least six teaching students were murdered by cartelmen and corrupt local police, and 43 others are missing and presumed dead. Other than the six identified persons, no other bodies have been found, and they are believed to have been incinerated.

As a result of efforts by civil society and human rights organizations in Mexico and Germany, H&K and two of its former employees were brought before the Provincial Court of Stuttgart. After ten months of trial, on 21 February 2019, the court convicted them of illegally selling arms to Mexican governmental institutions which failed to acknowledge their due observance of human rights. The two former employees (sales manager Sahlmann and administrative employee Beuter) had been found to have used fraudulent permits in the sale of 4,700 rifles and large quantities of ammunition. H&K was issued a fine of 3.7 million euros, and the two men received suspended sentences of 17 and 22 months. The spokesman of the Presidency of the Republic of Mexico, Jesús Ramírez Cuevas, said that the amount of the fine should go to the victims and their families.

On 30 March 2021, Germany's Federal Court of Justice (BGH) upheld the lower court's decision, finding that H&K employees knowingly falsified information on the nature and destination of arms sold by the company in order to attain federal export licenses.

title: Heckler & Koch


text:
Heckler & Koch MP5

The Heckler & Koch MP5 (Maschinenpistole 5) is a submachine gun developed in the 1960s by German firearms manufacturer Heckler & Koch. It uses a similar modular design to the Heckler & Koch G3, and has over 100 variants and clones, including selective fire, semi-automatic, suppressed, compact, and even marksman variants. The MP5 is one of the most widely used submachine guns in the world, having been adopted by over forty nations and numerous militaries, police forces, intelligence agencies, security organizations, paramilitaries, and non-state actors.

Attempts at replacing the MP5 by Heckler & Koch began in the 1980s, but despite functional prototype weapons having promising performance, a formal successor did not enter commercial production until 1999, when Heckler & Koch developed the UMP. Despite being more expensive however, the MP5 remained the more successful of the two options, owing to its preexisting widespread use, design familiarity, and lower recoil due to its roller-delayed action as opposed to the UMP's straight blowback action.

History
Heckler & Koch, encouraged by the success of the G3 battle rifle in 1959, developed a family of small arms consisting of four types of firearms all based on a common G3 design layout and operating principle. The first type was chambered for 7.62×51mm NATO, the second for 7.62×39mm M43, the third for 5.56×45mm NATO, and the fourth for 9×19mm Parabellum. The MP5 was created for the fourth type as the HK54; under the HK naming system, this categorizes it as a selective fire carbine chambered in a handgun cartridge.

Development began in 1964, and in 1966 the HK54 was adopted by the Bundesgrenzschutz and by Bundeswehr special forces, initially as the MP64, before being redesignated as the MP5. The MP5A1 was introduced in the late 1960s and was the first model to feature the front ring sight and "Slimline" handguard. In 1970, the MP5 and MP5A1 were superseded by the MP5A2 and MP5A3, improvements to the MP5A1 with a fixed stock and retracting stock respectively. In 1974, the MP5SD, an integrally-suppressed variant, was introduced, and in 1976, the MP5K, a redesigned compact variant, was developed per a request for a variant that suited close-quarters combat in South America. In 1977, the original straight magazines were replaced by curved steel magazines. In 1978, the "Tropical" handguard was introduced for the MP5.

In 1980, the MP5 achieved an iconic status during the Iranian Embassy siege, when British Army Special Air Service operatives used MP5s with top-mounted flashlights to assault the embassy and rescue the hostages held inside. Photos of the operation featuring MP5s were widely disseminated in the press and popular media, and drove other military and police units to purchase MP5s as well, quickly making the MP5 widely recognizable and associated with elite counterterrorist units. The MP5 has since become a mainstay in militaries, special forces, and police tactical units across the world, but has gradually been replaced since the late 1990s by rifles, carbines, and personal defense weapons due to changes in armament trends, including growing access to body armor that can stop handgun cartridges.

The MP5 is manufactured under license in several nations including Greece (formerly Hellenic Arms Industry, currently Hellenic Defence Systems), Iran (Defense Industries Organization), Mexico (SEDENA), Pakistan (Pakistan Ordnance Factories), Saudi Arabia, Sudan (Military Industry Corporation), Turkey (MKEK), and the United Kingdom (formerly Royal Ordnance, later moved to Heckler & Koch Great Britain).

Design
The primary version of the MP5 family is the MP5A2, which is a lightweight, air-cooled, selective fire delayed blowback operated 9×19mm Parabellum weapon with a roller-delayed bolt. It fires from a closed bolt (bolt forward) position.

The fixed, free-floating, cold hammer-forged barrel has six right-hand grooves with a 1 in 250 mm (1:10 in) rifling twist rate and is pressed and pinned into the receiver.

Features
The first MP5 models used a double-column straight box magazine, but since 1977, slightly curved steel magazines have been used with a 15-round capacity (weighing 0.12 kg) or a 30-round capacity (0.17 kg empty).

The adjustable iron sights (closed type) consist of a rotating rear diopter drum and a front post installed in a hooded ring. The rear sight is mechanically adjustable for both windage and elevation with the use of a special tool, being adjusted at the factory for firing at 25 m with standard 8 g FMJ 9×19mm NATO ammunition. The rear sight drum provides four apertures of varying diameters used to adjust the diopter system, according to the user's preference and tactical situation. Changing between apertures does not change the point of impact down range.

The MP5 has a hammer firing mechanism. The trigger group is housed inside an interchangeable polymer trigger module (with an integrated pistol grip) and equipped with a three-position fire mode selector that serves as the manual safety toggle. Per HK trigger group standards, most MP5 variants have the option of "SEF" or "Navy" trigger groups, with further alterations based on the availability and type of burst fire; the "SE" and "0-1" trigger groups are only available for semi-automatic and civilian variants. While the "SEF" trigger group's fire selector lever is located on the left-hand side of the trigger, the SEF symbols themselves appear on both sides of the trigger grouping; the "Navy" trigger group, among others, are ambidextrous. The safety/selector is rotated into the various firing settings or safety position by depressing the tail end of the lever. Tactile clicks (stops) are present at each position to provide a positive stop and prevent inadvertent rotation. The "safe" setting disables the trigger by blocking the hammer release with a solid section of the safety axle located inside the trigger housing.

The non-reciprocating cocking handle is located above the handguard and protrudes from the cocking handle tube at approximately a 45° angle. This rigid control is attached to a tubular piece within the cocking lever housing called the cocking lever support, which in turn makes contact with the forward extension of the bolt group. It is not however connected to the bolt carrier and therefore cannot be used as a forward assist to fully seat the bolt group. The cocking handle is held in a forward position by a spring detent located in the front end of the cocking lever support which engages in the cocking lever housing. The lever is locked back by pulling it fully to the rear and rotating it slightly clockwise where it can be hooked into an indent in the cocking lever tube.

Operating mechanism
The bolt rigidly engages the barrel extension—a cylindrical component welded to the receiver into which the barrel is pinned. The delay mechanism is of the same design as that used in the G3 rifle. The two-part bolt consists of a bolt head with rollers and a bolt carrier. The heavier bolt carrier lies up against the bolt head when the weapon is ready to fire and inclined planes on the front locking piece lie between the rollers and force them out into recesses in the barrel extension.

When fired, expanding propellant gases produced from the burning powder in the cartridge exert rearward pressure on the bolt head transferred through the base of the cartridge case as it is propelled out of the chamber. A portion of this force is transmitted through the rollers projecting from the bolt head, which are cammed inward against the inclined flanks of the locking recesses in the barrel extension and to the angled shoulders of the locking piece. The selected angles of the recesses and the incline on the locking piece produce a velocity ratio of about 4:1 between the bolt carrier and the bolt head. This results in a calculated delay, allowing the projectile to exit the barrel and gas pressure to drop to a safe level before the case is extracted from the chamber.

The delay results from the amount of time it takes for enough recoil energy to be transferred through to the bolt carrier in a sufficient quantity for it to be driven to the rear against the force of inertia of the bolt carrier and the forward pressure exerted against the bolt by the recoil spring. As the rollers are forced inward they displace the locking piece and propel the bolt carrier to the rear. The bolt carrier's rearward velocity is four times that of the bolt head since the cartridge remains in the chamber for a short period of time during the initial recoil impulse. After the bolt carrier has travelled rearward 4 mm, the locking piece is withdrawn fully from the bolt head and the rollers are compressed into the bolt head. Only once the locking rollers are fully cammed into the bolt head can the entire bolt group continue its rearward movement in the receiver, breaking the seal in the chamber and continuing the feeding cycle.

Since the 9×19mm Parabellum cartridge is relatively low powered, the bolt does not have an anti-bounce device like the G3, but instead the bolt carrier contains 32.5 g of tungsten granules that prevent the bolt group from bouncing back after impacting the barrel extension. The weapon has a fluted chamber that enhances extraction reliability by bleeding gases backwards into the shallow flutes running along the length of the chamber to prevent the cartridge case from expanding and sticking to the chamber walls (since the bolt is opened under relatively high barrel pressure). A spring extractor is installed inside the bolt head and holds the case securely until it strikes the ejector arm and is thrown out of the ejection port to the right of the receiver. The lever-type ejector is located inside the trigger housing (activated by the movement of the recoiling bolt).

Barrel accessories
Threading is provided at the muzzle to work with certain muzzle devices made by Heckler & Koch, including a slotted flash suppressor, a blank-firing adapter (marked with a red-painted band denoting use with blank ammunition only), a rifle grenade adapter (for use with rifle-style grenades with an inside diameter of 22 mm using a special grenade launching cartridge), and cup-type tear gas rifle grenade adapter. An optional "3-Lug" barrel is also available on some variants for mounting a quick-detachable suppressor.

MP5SD suppressor
The MP5SD's 146 mm barrel has 30 2.5 mm ports drilled forward of the chamber through which escaping gases are diverted to the surrounding sealed tubular casing that is screwed onto threading on the barrel's external surface just prior to the ported segment. The MP5SD's integral suppressor itself is divided into two stages: the initial segment surrounding the ported barrel serves as an expansion chamber for the propellant gases, reducing gas pressure to slow down the acceleration of the projectile. The second decompression stage occupies the remaining length of the suppressor tube and contains a stamped metal helix separator with several compartments which increase the gas volume and decrease its temperature, deflecting the gases as they exit the muzzle, so muffling the exit report. The bullet leaves the muzzle at subsonic velocity, so it does not generate a sonic shock wave in flight. As a result of reducing the barrel's length and venting propellant gases into the suppressor, the bullet's muzzle velocity was lowered anywhere from 16% to 26% (depending on the ammunition used) while maintaining the weapon's automation and reliability.

Receiver
The receiver housing has a proprietary claw-rail mounting system that permits the attachment of a standard Heckler & Koch quick-detachable scope mount (also used with the G3, HK33, and G3SG/1). It can be used to mount daytime optical sights (telescopic 4×24), night sights, reflex sights, and laser sights. The mount features two spring-actuated bolts, positioned along the base of the mount, which exert pressure on the receiver to hold the mount in the same position at all times assuring zero retention. All versions of the quick-detachable scope mount provide a sighting tunnel through the mount so that the shooter can continue to use the fixed iron sights with the scope mount attached to the top of the receiver.

A Picatinny rail adapter can be placed on top that locks into the claw rails. This allows the mounting of STANAG scopes and has a lower profile than the claw-rail system.

Handguard
Standard MP5 variants have the option of two handguards: "Slimline", the original slim checkered metal handguard; and "Tropical", a wider and smoother polymer handguard introduced in 1978.

The MP5SD, MP5K, and SP89 have unique handguards owing to their design differences: the MP5SD handguard is similar to Slimline but larger to fit the integrated suppressor, the MP5K handguard has a built-in foregrip and handstop, and the SP89 handguard is similar to the MP5K's but extended and without the foregrip.

Aftermarket handguards also exist, including newer vented handguards based on the "Tropical" handguard, "dedicated forend" handguards featuring a built-in underbarrel tactical light, and rail integration system-equipped handguards to fit attachments.

MP5

 * HK54
 * Original pre-designation model, introduced in 1964. It has a charcoal-gray phosphated finish rather than the matte-black lacquered finish used on later models. The handguard resembles the "Slimline" handguard but is narrower and has slots along it. Its bolt carrier is longer and heavier than that of the final MP5, and it uses a flip-up "ladder" rear sight similar to that used on early G3 models. It uses straight steel magazines with plastic followers and distinctive "waffle" rib imprints for reinforcement.

 * MP5
 * The basic MP5, based on a modified and improved HK54, introduced in 1966. When first released, it had a gray phosphated finish, "Slimline" handguard, 8.9-inch barrel with "3-Lug" muzzle, and straight waffle magazines. Modernized improvements were introduced in the 1970s: proprietary "claw mount" rails for scope, laser, and flashlight attachments were introduced in 1973; un-ribbed curved magazines with chrome followers were introduced in 1977; the matte-black lacquered finish was introduced for export models also in 1977; and the polymer "Tropical" handguard was introduced in 1978.

 * MP5A1
 * Standard MP5 with no stock and the "SEF" or "Navy" trigger group.

 * MP5A2
 * Standard MP5 with a fixed stock and the "SEF" or "Navy" trigger group.

 * MP5A3
 * Standard MP5 with a retractable stock and the "SEF" or "Navy" trigger group.

 * MP5A4
 * Standard MP5 with a fixed stock, the "Navy 3-Round Burst" trigger group, and a straight pistol grip.

 * MP5A5
 * Standard MP5 with a retractable stock, the "Navy 3-Round Burst" trigger group, and a straight pistol grip.

 * MP5SF
 * Semi-automatic variant of the MP5 intended for the law enforcement and military markets, introduced in 1986 to meet a Federal Bureau of Investigation request for a "9mm semi-automatic carbine". Unlike the HK94, the semi-automatic MP5 variant for the civilian market, the MP5SF retains its standard 8.9-inch barrel. It has two variants: the MP5SFA2 with a fixed stock, and the MP5SFA3 with a retractable stock. It uses the "0-1" trigger group, but since 1991, it has been delivered with select-fire bolt carriers that make it capable of automatic fire if paired with an appropriate trigger group.

 * MP5PT
 * Training variants of the MP5A4 and MP5A5. They are designed to use a plastic 9×19mm round developed by Dynamit Nobel.

 * MP5N
 * Naval variant of the MP5, introduced in 1986 to meet a United States Navy request for a submachine gun effective aboard ships and in low-light conditions. It is essentially an MP5A3 with a retractable stock, "Navy 2-Round Burst" trigger group, tritium illuminated sights, and a custom "3-Lug" muzzle derivative for mounting a stainless steel suppressor produced by Knight's Armament Company (KAC).

 * MP5F
 * Improved French variant of the MP5, introduced in 1999 to meet a French National Gendarmerie request for a suitable standard-issue submachine gun. It is essentially a modified and improved MP5A3, featuring a padded retractable stock, "Navy" trigger group, ambidextrous sling mounts, and internal improvements to handle high-pressure ammunition.

 * MP5 Mid Life Improvement (MLI)
 * Modernized refresh of the MP5, introduced in 2015. It is based on the MP5A5 and features the MP5F's padded retractable stock, triple-rail "Slimline" handguard, "Navy 3-Round Burst" trigger group, quick-release sight mount or sight rail, and a RAL 8000 finish. Compatible components of the MP5 MLI can be switched out and retrofitted with other compatible MP5 variants.

MP5SD
The MP5SD ("SD" meaning Schalldämpfer, German for "sound suppressor") is a variant of the MP5 with an integral suppressor, introduced in 1974. The integral suppressor, built around its 5.7-inch barrel, uses a unique two-stage design that allows it to operate silently in most environments, including when wet, while still remaining reliable. The distinctive size of the integral suppressor gives it a unique handguard design, with a modified charging handle to account for it. The MP5SD has a rate of fire of approximately 700 rounds per minute, and is intended to use standard ammunition, gasses are vented into the suppressor reducing velocities of rounds to sub sonic speeds with the suppressor on at all times, though it can be detached.
 * MP5SD1
 * Standard MP5SD with no stock and the "SEF" or "Navy" trigger group.

 * MP5SD2
 * Standard MP5SD with a fixed stock and the "SEF" or "Navy" trigger group.

 * MP5SD3
 * Standard MP5SD with a retractable stock and the "SEF" or "Navy" trigger group.

 * MP5SD4
 * Standard MP5SD with no stock and the "SEF" or "Navy" trigger group. It is largely similar to the MP5SD1.

 * MP5SD5
 * Standard MP5SD with a fixed stock and the "Navy 3-Round Burst" trigger group.

 * MP5SD6
 * Standard MP5SD with a retractable stock and the "Navy 3-Round Burst" trigger group.

 * MP5SDN-1
 * Naval variant of the MP5SD, with a retractable stock, the "Navy 2-Round Burst" trigger group, and the MP5N's KAC stainless steel suppressor.

 * MP5SDN-2
 * Naval variant of the MP5SD, with a fixed stock, the "Navy 2-Round Burst" trigger group, and the MP5N's KAC stainless steel suppressor.

MP5K
The MP5K ("K" meaning Kurz, German for "short") is a redesigned compact variant of the MP5, introduced in 1976. Developed from the stockless MP5A1, it features a 4.5-inch barrel incompatible with muzzle attachments, an endcap with sling mount instead of a stock, and a unique handguard with a built-in foregrip. Most components of the MP5K are shortened on account of its compact design, including its bolt, receiver, charging handle, cover, and trigger group frame; the lighter bolt gives it a higher rate of fire, at approximately 900 rounds per minute (as opposed to 800 rounds per minute with the regular MP5). Different variants of the MP5K use either unique open iron sights or redesigned fixed iron sights.

 * MP5K Prototype
 * Stockless, cut-down MP5A2 with regular iron sights and an open vertical foregrip, developed in 1976.

 * MP5KA1
 * Standard MP5K with the "SEF" trigger group, smooth upper surface, and small low-profile iron sights.

 * MP5KA4
 * Standard MP5K with the "Navy 3-Round Burst" trigger group and regular iron sights.

 * MP5KA5
 * Standard MP5K with the "Navy 3-Round Burst" trigger group, smooth upper surface, and small low-profile iron sights.

 * MP5K-N
 * Naval variant of the MP5K, with the "Navy" trigger group and a custom "3-Lug" muzzle similar to that of the MP5N.

 * MP5K-PDW
 * "Full-size" variant of the MP5K, introduced in 1991. It is designed to provide the benefits of the MP5K with the size and handling of a regular MP5, and is essentially a regular MP5K with a custom folding stock, "Navy" trigger group, and 5.5-inch barrel with a custom "3-Lug" muzzle similar to that of the MP5N but for a Qual-A-Tec suppressor. Despite its name, the MP5K-PDW is not a personal defense weapon, as it uses a handgun cartridge and not the sub-intermediate cartridges used by actual PDWs; rather, its name is derived from its intended use as a defense firearm for vehicle and aircraft crews.

 * MP5K Operational Briefcase
 * Standard MP5K intended for use with the Spezialkoffer ("Special Case"), a custom briefcase built by Hofbauer GmbH with a modified claw mount for holding the MP5K, a firing port, and a trigger built into the briefcase handgrip, introduced in 1978. Intended for security details in close-range defense or suppressive fire situations, the MP5K Operational Briefcase uses a firing mechanism built into the briefcase to allow the MP5K to fire without taking time to remove it; however, it cannot be reloaded, cleared of obstructions, or emptied of spent shell casings without opening the briefcase and detaching the MP5K.

 * MP5K Special Bag
 * Variant of the MP5K Operational Briefcase introduced around 1978, using a leather suitcase called the Spezialtasche ("Special Bag"). Instead of using the handgrip as a trigger, the Spezialtasche features a hidden opening that allows the user to discreetly reach into the bag and fire the MP5K directly.

 * MP5K Falling Case
 * Variant of the MP5K Operational Briefcase introduced around 1978, using a detachable briefcase called the Zerfallkoffer ("Falling Case"). Instead of allowing the weapon to fire within the case, the Zerfallkoffer's handgrip and claw mount is designed to be quickly detached from the briefcase, "shedding" it and allowing the MP5K to be used normally with a carryhandle. The Zerfallkoffer is also compatible with the MP7.

Rechambered variants
Though the MP5 is normally chambered in 9×19mm Parabellum, two variants and an unreleased kit existed that used different ammunition.

 * MP5/10
 * MP5 chambered in 10mm Auto, introduced in 1992. It features either a fixed or retractable stock, the "Navy 2-Round Burst" trigger group, and the MP5N's custom "3-Lug" muzzle derivative and tritium illuminated sights. It includes a bolt hold-open device, which catches the bolt in its rear position when empty, and is released by pressing a lever on the left side of the receiver. It is fed by a custom 30-round translucent straight magazines. The MP5/10 was discontinued in 2000, but HK still offers support and spare parts.

 * MP5/40
 * MP5 chambered in .40 S&W, introduced in 1992. It has largely the same features and configuration options of the MP5/10, and is fed by similar 30-round translucent straight magazines, but uses the regular "Navy" trigger group (without the burst-fire selection). The MP5/40 was discontinued in 2000, but HK still offers support and spare parts.

 * MP5 .22 LR
 * MP5 chambered in .22 Long Rifle, introduced around 2021. It comes in two variants: the MP5 .22 LR Rifle, which resembles an MP5SD3 with a 16.1-inch barrel hidden by a faux "integral suppressor" barrel shroud; and the MP5 .22 LR Pistol, which resembles an MP5A1 or MP5A3 with an 8.5-inch barrel. Both variants use the "Tropical" handguard and the "0-1" trigger group. Like all civilian market MP5 variants, it is semi-automatic only.

 * MP5 .22 Long Rifle Rechambering Kit
 * Rechambering kit to convert an MP5 to .22 Long Rifle, introduced in the early 1970s and discontinued at an indeterminate point. The kit consisted of a barrel insert, a bolt group, and two 20-round magazines, and was mostly sold to law enforcement agencies for training purposes by easing trainees inexperienced with the MP5 into learning handling techniques and firing practice without the high recoil and cost of 9×19mm rounds. The conversion reduced the MP5's rate of fire to 650 rounds per minute. It was ultimately replaced by the MP5 .22 LR in 2021.

 * MP5 6.5×25mm Rechambering Kit
 * Rechambering kit to convert an MP5 to 6.5×25mm CBJ, which was proposed in the 2000s but never released. It would have allowed an MP5 to be rechambered simply by switching its barrel.

Civilian variants

 * HK94
 * Civilian market variant of the MP5, imported from 1983 to 1989 (with a one-off final order for the California Department of Corrections and Rehabilitation delivered in 1991). It has a 16.54-inch barrel, "0-1" trigger group, push-button magazine release (as opposed to the paddle magazine release on regular MP5s), and a straight pistol grip similar to that on the MP5A4 and MP5A5. It has two variants: the HK94A2 with a fixed stock, and the HK94A3 with a retractable stock. Optional accessories included a handguard-mounted foregrip and a ventilated barrel shroud. The HK94 was particularly popular as a prop in film and television productions of the era, and blank-firing HK94s with "chopped" 8.9-inch barrels and fake automatic conversions were often used as cost-effective MP5 stand-ins well into the 2010s.

 * HK94/SG-1
 * Accurized sharpshooting variant of the HK94, introduced in 1985. It was designed and intended for marksman fire in situations and environments where precise handgun cartridge fire may be needed, such as dense urban areas and indoor environments like prisons. It has a fixed match stock with a rubber buttpad and an adjustable cheekpiece, a folding bipod, a flash hider, and a Leupold 6x telescopic sight. A PSG1-inspired aftermarket trigger pack was also produced, featuring a target pistol grip and match trigger. The HK94/SG-1 did not sell very well due to its niche role and poor performance—it had poor range, penetration, and stopping power, and its Leupold scope was calibrated for .223 Remington and not 9×19mm—and only 50 units were imported to the U.S., primarily to target shooters and firearm collectors.

 * SP89
 * Civilian market variant of the MP5K, imported to the U.S. between 1989 and 1994. To comply with the National Firearms Act, the SP89 features a redesigned handguard that replaces the MP5K's built-in foregrip with an extended barrel shroud. Like all civilian market MP5 variants, it is semi-automatic only.

 * SP5K
 * Modernized SP89 for the American civilian market, imported to the U.S. as a pistol in 2017. It largely resembles the SP89, with a redesigned extended barrel shroud and a top-mounted Picatinny rail for sights. Like all civilian market MP5 variants, it is semi-automatic only.

 * SP5
 * Modernized civilian market variant of the MP5 introduced in 2019, replacing the HK94. It resembles an MP5A2 with an 8.8-inch barrel, MP5K-style threaded adaptor, "Tropical" handguard, "0-1" trigger group, paddle magazine release, fluted chamber, and the buyer's choice of fixed stock, retractable stock, or endcap.

 * SP5K-PDW
 * Modernized civilian market variant of the MP5K introduced in 2019, replacing the SP5K. It resembles an MP5K without its handguard foregrip. Like all civilian market MP5 variants, it is semi-automatic only.

Prototypes
Five prototype firearms based on the MP5 were developed by Heckler & Koch in the 1980s and 1990s, mostly intended as improved variants or potential successors, but were not developed any further.

 * HK54A1
 * Prototype improvement of the HK54, designed for the U.S. Navy Naval Weapons Support Center Crane's (NWSC) Joint Service Small Arms Program (JSSAP) in 1980. It was essentially a refreshed ambidextrous MP5SD with a redesigned retractable stock and compatibility with a 50-round drum magazine. It was designed to be suitable for frogmen and paratroopers in any environment, and was thus also designed to be reliably functional in extreme temperatures and while wearing bulky gloves. HK's proposal for the HK54A1 noted it could be converted to .45 ACP if necessary. An unknown number were produced for testing purposes out of regular MP5 components. The HK54A1 was never properly developed for field use, but it met most JSSAP requirements, drawing the attention of the U.S. government and leading to the development of the SMG I and SMG II.

 * SMG I
 * Prototype derived from the HK54A1, first developed for the JSSAP between 1982 and 1983. It was intended to spawn a "family" of modular all-purpose submachine guns. Unique for HK, the SMG I used a simple blowback operation with separate lower and upper receivers and an easy-to-remove 5.8-inch barrel with an integral suppressor. It had a boxy body with a retractable stock and a diagonal foregrip. A mechanical and hydraulic buffer in the backplate and a timing device in the stock reduced its rate of fire to a manageable 500 rounds per minute, roughly half that of the HK54A1. The rear iron sight, resembling that of the HK21E, allowed for adjustments based on wind, ammunition type, and sight elevation, and also featured indents to assist with close-range point shooting. The trigger included an add-on to be used with bulkier gloves such as mittens. Only 20 handmade examples were produced. The SMG I was tested by NWSC Crane in 1984 and proved promising, but several minor issues prompted the development of the SMG II.

 * SMG II
 * Prototype derived from the SMG I, developed around 1985. It has a largely identical design but addresses the issues reported by NWSC Crane. Its combination of the MP5, MP5SD, and MP5K was made more clear: analogous to the MP5 by default, the addition of a custom suppressor made it akin to the MP5SD, and the removal of the suppressor and retractable stock converted it into an MP5K-like automatic pistol. The three-round burst fire setting returned from the HK54A1. Several components were made from plastic to reduce weight, while the over-engineered rear sight was abandoned for a simpler MP5-style sight. Uniquely, the SMG II had a gas cylinder in the handguard with a gas relief valve on the receiver, used to control round velocity and thus also sound: the "L" setting reduced the propellant gases to fire rounds below the speed of sound—and thus without the usual crack of supersonic projectiles—for almost silent suppressed fire, while the "H" setting used all available gas to fire rounds at full velocity for reliable unsuppressed fire. Other internal changes were made to reduce cost and simplify production and maintenance, but otherwise the SMG II was largely just an improvement of the SMG I. Like the SMG I, only 20 handmade examples were produced for testing by NWSC Crane. While the SMG II again proved promising, it was ultimately abandoned, not for budgetary or technical concerns, but simply due to the success of the regular MP5 and its derivatives, which were already popular enough with the U.S. Navy and all other potential customers to make a replacement unnecessary; HK ultimately developed the MP5N for the U.S. Navy instead. Allegedly, between 60 and 80 additional SMG IIs were secretly commissioned for an unidentified U.S. government agency, possibly a member of the U.S. Intelligence Community, where they were favored by their users, but the lack of spare parts and the gradual move to higher-caliber firearms for close-quarters combat led to all of them being retired and melted down for disposal some time around 1999. Technical knowledge from the SMG II and the concept of a universal submachine gun were later repurposed for the MP2000 prototype and the UMP.

 * MP5 PIP
 * Prototype developed around the late 1980s and early 1990s. Very little is known about the MP5 PIP or why it was developed, but it had a boxier body resembling the later UMP, a shorter diagonal magazine, and the "flipper" charging handle later used on the G36. Only one non-functional wooden mockup was produced.

 * MP2000
 * Prototype derived from the SMG II, developed in the 1990s. It somewhat resembled the SMG II and featured a propellant gas-based round velocity silencing system similar to that of the SMG II. It was presumably an attempted revival of the SMG II concept to replace the MP5 for the 21st century. It is an immediate predecessor of the UMP, which was ultimately marketed as such.

Clone manufacturers

 * 🇨🇳 China: Norinco manufactures unlicensed copies of the MP5A4 as the NR-08 and NR-08A, and the MP5A5 as the CS/LS3.
 * 🇬🇷 Greece: Hellenic Defence Systems manufactures the MP5 under license.
 * 🇮🇳 India: Indian Ordnance Factory manufactures unlicensed copies of the MP5A3 as the OFB Anamika 9mm.
 * 🇮🇷 Iran: DIO manufactures the MP5A3 under license as the Tondar, and the MP5K as the Tondar Light.
 * 🇲🇽 Mexico: SEDENA manufactures the MP5 under license.
 * 🇵🇰 Pakistan: Pakistan Ordnance Factories manufactures the MP5 under license as the MP5P, POF4, and POF-5.
 * 🇸🇦 Saudi Arabia: Military Industries Corporation manufactures the MP5 under license.
 * 🇸🇩 Sudan: Military Industry Corporation manufactures the MP5A3 as the Tihraga, itself a clone of the DIO Tondar.
 * 🇨🇭 Switzerland: Brügger & Thomet manufactures the MP5 under license.
 * 🇹🇷 Turkey: MKEK manufactures the MP5 with different trigger groups: E (Safe), T (Semi-Auto) and S (Full Auto).
 * 🇬🇧 United Kingdom: Royal Small Arms Factory manufactures the MP5 under license.
 * 🇺🇸 United States: PTR Industries, Zenith Firearms, Dakota Tactical, and Century International Arms manufacture semi-automatic clones of the MP5 that are legally classified as pistols. In 2007, Professional Arms demonstrated the MK5, an MP5 clone that could be rechambered between 9×19mm, .45 ACP, and .40 S&W.

Former users

 * : Used by Diensteinheit IX.

title: Heckler & Koch MP5


text:
Henry Middleton

Henry Middleton (1717 – June 13, 1784) was an American politician and planter from South Carolina. A member of the colonial legislature, during the American Revolution he attended the First Continental Congress and served as that body's president for four days in 1774 after the passage of the Continental Association, which he signed. He left the Second Continental Congress before it declared independence. Back in South Carolina, he served as president of the provincial congress and senator in the newly created state government. After his capture by the British in 1780, he accepted defeat and returned to the status of a British subject until the end of the war.

Early life
Henry Middleton was born in 1717 on the family plantation, "The Oaks", near Charleston, Province of South Carolina. He was the second son of Susan (née Amory) Middleton (1690-1722) and Arthur Middleton (1681–1737), a wealthy planter who had served as an acting governor of South Carolina. His grandfather, Edward Middleton, emigrated from England via Barbados. He was educated in England before returning to South Carolina to inherit his father's plantation. He became one of the largest landowners in the colony, owning 50000 acre and about 800 slaves.

Public career
Middleton served in a variety of public offices in South Carolina. He was a justice of the peace and a member of the Commons House of Assembly, where he was elected speaker in 1747, 1754, and 1755. He was a member of provincial council but resigned in 1770 in opposition to British policy.

In 1774, at the outset of the American Revolution, Middleton was selected as a delegate to the Continental Congress. He served as that body's president during the last few days of the First Continental Congress, following the departure of Peyton Randolph. Middleton opposed declaring independence from Great Britain and resigned from the Second Continental Congress in February 1776 when more radical delegates began pushing for independence. He was succeeded in Congress by his son Arthur who was more radical than his father and became a signer of the Declaration of Independence.

After Middleton's return to South Carolina, he was elected president of the provincial congress and, beginning on November 16, 1775, served on the council of safety. In 1776, he and his son Arthur helped frame a temporary state constitution. In 1779, he became a state senator in the new government.

When Charleston was captured by the British at the Siege of Charleston in 1780, Middleton accepted defeat and status as a British subject. This reversal apparently did not damage his reputation in the long run, because of his previous support of the Revolution, and he did not suffer the fate of having his estates confiscated, as many Loyalists did after the war.

Personal life
In 1741, Middleton was married to Mary Baker Williams (1721–1761), the daughter of John Williams, an early South Carolina planter who began building what is today known as Middleton Place around 1730. Together, Henry and Mary were the parents of five sons and seven daughters, seven of whom survived to adulthood, including:

 * Arthur Middleton (1742–1787), a signer of the Declaration of Independence who married Mary Izard (1747–1814).
 * Henrietta Middleton (1750–1792), who married Governor Edward Rutledge.
 * Thomas Middleton (1753–1797), who married Anne Manigault.
 * Hester Middleton (1754–1789), who married Charles Drayton.
 * Sarah Middleton (1756–1784), who married Charles Cotesworth Pinckney.
 * Mary Middleton (1757-1825), who married Peter Smith.
 * Susannah Middleton (1760–1834), who married Continental Congressman John Parker.

After his wife's death in 1761, Middleton would go on to marry twice more. His second marriage was to Maria Henrietta Bull (1722–1772), daughter of William Bull Sr., the lieutenant governor of South Carolina, in 1762. His second wife's sister, Charlotta (née Bull) Drayton, was the mother of Continental Congressman William Henry Drayton, and her brother, William Bull II, served as governor of South Carolina before leaving the colony in 1782 when British troops were evacuated at the end of the War.

After his second wife's death in 1772, he married for the third time, although it was her fourth marriage, to Lady Mary McKenzie, the daughter of George Mackenzie, 3rd Earl of Cromartie, in 1776. Among Lady Mary's brothers were John Mackenzie, Lord MacLeod and George Mackenzie. Her father was a Scottish nobleman who followed Charles Edward Stuart, the Jacobite Pretender. The Earl of Cromartie was tried and sentenced to death, but he obtained a conditional pardon although his peerage was forfeited.

Middleton died on June 13, 1784, in Charleston. He was buried at Goosecreek Churchyard, St. James Parish, Berkeley County, South Carolina.

Descendants
His grandson, also named Henry (1770–1846), had a long career in politics. He was governor of South Carolina (1810–1812), U.S. Representative (1815–1819), and the minister to Russia (1820–1830). Henry had fourteen children, including Williams Middleton and Edward Middleton.

title: Henry Middleton