OpenLLM-France/wikimedia huggingface dataset:
# Hautus lemma

In control theory and in particular when studying the properties of a linear time-invariant system in state space form, the Hautus lemma (after Malo L. J. Hautus), also commonly known as the Popov-Belevitch-Hautus test or PBH test, can prove to be a powerful tool.
A special case of this result appeared first in 1963 in a paper by Elmer G. Gilbert, and was later expanded to the current PBH test with contributions by Vasile M. Popov in 1966, Vitold Belevitch in 1968, and Malo Hautus in 1969, who emphasized its applicability in proving results for linear time-invariant systems.

## Statement

There exist multiple forms of the lemma:

### Hautus Lemma for controllability

The Hautus lemma for controllability says that given a square matrix $\mathbf {A} \in M_{n}(\Re )$ and a $\mathbf {B} \in M_{n\times m}(\Re )$ the following are equivalent:
* The pair $(\mathbf {A} ,\mathbf {B} )$ is controllable
* For all $\lambda \in \mathbb {C}$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ,\mathbf {B} ]=n$
* For all $\lambda \in \mathbb {C}$ that are eigenvalues of $\mathbf {A}$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ,\mathbf {B} ]=n$

### Hautus Lemma for stabilizability

The Hautus lemma for stabilizability says that given a square matrix $\mathbf {A} \in M_{n}(\Re )$ and a $\mathbf {B} \in M_{n\times m}(\Re )$ the following are equivalent:
* The pair $(\mathbf {A} ,\mathbf {B} )$ is stabilizable
* For all $\lambda \in \mathbb {C}$ that are eigenvalues of $\mathbf {A}$ and for which $\Re (\lambda )\geq 0$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ,\mathbf {B} ]=n$

### Hautus Lemma for observability

The Hautus lemma for observability says that given a square matrix $\mathbf {A} \in M_{n}(\Re )$ and a $\mathbf {C} \in M_{m\times n}(\Re )$ the following are equivalent:
* The pair $(\mathbf {A} ,\mathbf {C} )$ is observable.
* For all $\lambda \in \mathbb {C}$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ;\mathbf {C} ]=n$
* For all $\lambda \in \mathbb {C}$ that are eigenvalues of $\mathbf {A}$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ;\mathbf {C} ]=n$

### Hautus Lemma for detectability

The Hautus lemma for detectability says that given a square matrix $\mathbf {A} \in M_{n}(\Re )$ and a $\mathbf {C} \in M_{m\times n}(\Re )$ the following are equivalent:
* The pair $(\mathbf {A} ,\mathbf {C} )$ is detectable
* For all $\lambda \in \mathbb {C}$ that are eigenvalues of $\mathbf {A}$ and for which $\Re (\lambda )\geq 0$ it holds that $\operatorname {rank} [\lambda \mathbf {I} -\mathbf {A} ;\mathbf {C} ]=n$
# Moqilan

Moqilan (Persian: مقيلان, also Romanized as Moqīlān, Maghīlān, and Magīlān) is a village in Zohan Rural District, Zohan District, Zirkuh County, South Khorasan Province, Iran. At the 2006 census, its population was 242, in 78 families.
# Nelidovo

Nelidovo (Russian: Нелидово) is the name of several inhabited localities in Russia.

## Rural localities

* Nelidovo, Ivanovo Oblast, a village in Zavolzhsky District of Ivanovo Oblast
* Nelidovo, Chukhlomsky District, Kostroma Oblast, a village in Nozhkinskoye Settlement of Chukhlomsky District of Kostroma Oblast
* Nelidovo, Krasnoselsky District, Kostroma Oblast, a village in Borovikovskoye Settlement of Krasnoselsky District of Kostroma Oblast
* Nelidovo, Moscow Oblast, a village in Chismenskoye Rural Settlement of Volokolamsky District of Moscow Oblast
* Nelidovo, Kalininsky District, Tver Oblast, a village in Verkhnevolzhskoye Rural Settlement of Kalininsky District of Tver Oblast
* Nelidovo, Sokolsky District, Vologda Oblast, a village in Vorobyevsky Selsoviet of Sokolsky District of Vologda Oblast
* Nelidovo, Vologodsky District, Vologda Oblast, a village in Raboche-Krestyansky Selsoviet of Vologodsky District of Vologda Oblast
# Kotuy

The Kotuy (Russian: Котуй) is a river in Krasnoyarsk Krai, Russia. It is one of the two rivers that form the Khatanga; the other one being the Kheta.
The Kotuy is 1,409 kilometres (876 mi) long, and the area of its basin is 176,000 square kilometres (68,000 sq mi). It freezes up in late September or early October and breaks up in late May or early June.

## Course

The Kotuy has its source in the Putorana Mountains and flows north, cutting from the south across the western side of the Anabar Plateau. After leaving the plateau area it flows northwestwards until the confluence with the Kheta to form the Khatanga, a little distance upstream from Khatanga town.
Its main tributaries are the Moyero, the Tukalan, the Eriyechka, the Changada, and the Kotuykan, which has its source in the highest part of the Anabar Plateau. Lake Yessey is part of the river basin.
# Sazman-i Nasr

Sazman-i Nasr (Persian: سازمان نصر, lit. 'Organization of Victory') was a Hazara militant group, opposed to the leftist Afghan government during the 1980s. After the Revolutionary Council of Islamic Unity of Afghanistan, Al-Nasr was the elite militant group. The organisation included many young men educated in Kabul, including Shia clergymen, and received support from the Khomeini government. It was a part of the Tehran Eight political constellation after 1987.
# Kachin National Congress

The Kachin National Congress (Burmese: ကချင်အမျိုးသားများ ကွန်ဂရက်; KNC) was a political party in Burma.

## History

Allied with the Anti-Fascist People's Freedom League, the party won seven seats in the Chamber of Deputies in the 1951–52 elections. It was reduced to just two seats in the 1956 elections, but won three seats in the 1960 elections. It allied with the Stable AFPFL in the same year.
Following the restoration of multi-party democracy in the 1980s, a new Kachin National Congress was formed. It nominated five candidates for the 1990 general elections, but failed to win a seat.
# Dobrovolsky, Altai Krai

Dobrovolsky (Russian: Добровольский) is a rural locality (a settlement) in Aleksandrovsky Selsoviet, Suyetsky District, Altai Krai, Russia. The population was 10 as of 2013. There is 1 street.

## Geography

Dobrovolsky is located 19 km southeast of Verkh-Suyetka (the district's administrative centre) by road. Aleksandrovka and Ukrainsky are the nearest rural localities.
# Teshio Mountains

The Teshio Mountains (天塩山地 Teshio-sanchi) are a mountain range of Hokkaidō, Japan.

## Mountains

* Mount Pisshiri
* Mount Santō
# Sparrowpit

Sparrowpit is a small village between Chapel-en-le-Frith and Peak Forest in the High Peak area of the Peak District, Derbyshire, England.
The name is derived from 'spar row pit' from the fluorspar mines.
The village has an active community, including a methodist chapel and village hall.
It is situated at a crossroads where the main road (A623) takes a right-angled bend at the Wanted Inn. From this junction, one minor road takes a different and hillier route to Chapel-en-le-Frith, and another heads for Mam Tor and Castleton by way of the Winnats Pass.
The watershed between rivers running east into the North Sea and west into the Irish Sea runs almost exactly through the village.
# Coeur d'Alene Mountains

The Coeur d'Alene Mountains are the northwesternmost portion of the Bitterroot Range, part of the Rocky Mountains, located in northern Idaho and westernmost Montana in the Western United States.
The mountain range spans an area of 2,590 square miles (6,708 km$^2$) and its two highest peaks are the 7,352-foot (2,241 m) Cherry Peak and the 6,837-foot (2,084 m) Patricks Knob.
The range is named after the Coeur d'Alene Tribe.
Several decent-sized roadless areas exist in the Montana portion of the Coeur d'Alenes. Around 43,000 acres (17,000 ha) of roadless country centered on 5,980-foot (1,823 m) Mount Bushnell, south of Thompson Falls, provides good habitat for deer, elk, and mountain lion. This area is/was densely forested with lodgepole pine generated from the Great Fire of 1910. Thirty miles (48 km) of trails provide good hiking opportunities in this roadless area. Talus slopes, grassy parks in the highest reaches, and boggy creek bottoms characterize the landscape here in addition to the forests. Lush riparian areas are home to the Coeur d'Alene salamander and tailed frog.
Just east of the Mount Bushnell area are approximately 40,000 acres (16,000 ha) of roadless land centered on Cherry Peak, highest in the Coeur d'Alenes. Vertical relief exceeds 4,500 feet (1,372 m) in less than two miles (3.2 km) from the Clark Fork River to this area's highest peaks. Several tiny alpine lakes are hidden in cirque basins on Eddy Mountain. Subalpine fir and devil's club are commonly found.
Another 18,000 acres (7,300 ha) are roadless around Patrick's Knob. This area contains thick forests of Douglas-fir and larch in the west and scattered trees in the east; a large and commonly seen herd of bighorn sheep winters here. An old bootlegger's cabin is located on Fourteen Mile Creek.
# Hum, Bugojno

Hum (Serbian: Хум) is a village in the municipality of Bugojno, Bosnia and Herzegovina.

## Demographics

According to the 2013 census, its population was 48, all Bosniaks.
# Knockmealdown Mountains

The Knockmealdown Mountains (Irish: Sléibhte Chnoc Mhaoldomhnaigh) are a mountain range located on the border of counties Tipperary and Waterford in Ireland, running east and west between the two counties. The highest peak of the range is Knockmealdown, in County Waterford. On the western side of the summit, the range is crossed by a high pass called ‘The Vee’ through which runs the old mail coach road from Lismore to Clogheen.
The mountains were formerly known as Sliabh gCua, sometimes anglicized 'Slieve Gua' or 'Slieve Goe'.

## Mountain peaks

List of peaks in the Knockmealdown Mountains ordered by height:
* Knockmealdown, Cnoc Mhaoldomhnaigh (794 m)
* Knockmoylan, Cnoc Maoláin (768 m)
* Knocknafallia, Cnoc na Faille (668 m)
* Sugarloaf Hill, Cnoc na gCloch (663 m)
* Knocknagnauv, Cnoc na gCnámh (655 m)
* Knockshanahullion, Cnoc Seanchuillinn (652 m)
* Knocknalougha, Cnoc na Loiche (630 m)
* Knockmeal, An Cnoc Maol (560 m)
* Crohan West, An Cruachán (521 m)
* Farbreaga, An Fear Bréige (518 m)

## Wildlife

This mountain range is an important breeding ground for two endangered species, the red grouse and the hen harrier; cuckoo, nightjar, crossbill, buzzard and grasshopper warbler can also be seen.
# Vukov sabor

Vukov sabor (Serbian: Вуков сабор, romanized: Vukov sabor), also known as Vuk's Convocation or Vuk's Fair, is the oldest and most massive cultural event in Serbia. It was named after the reformer of the Serbian language Vuk Karadžić. The central program is traditionally held in September in Vuk's birthplace Tršić, near Loznica. Part of the program is realized in Loznica, Belgrade and the nearby Tronoša Monastery.
The manifestation was registered in the National Registrar of Intangible Cultural Heritage of Serbia on June 18, 2012.

## History

The first Vukov sabor was held in 1933 and, in following years, Vukov sabor wasn't held only in 1941 and 1944 due to World War II.
| # | Year | Dates | Central manifestation orator |
| 1 | 1933 | 17 September 1933 | |
| 2 | 1934 | | |
| 3 | 1935 | | |
| 4 | 1936 | | |
| 5 | 1937 | | |
| 6 | 1938 | | |
| 7 | 1939 | | |
| 8 | 1940 | | |
| | 1941 | — | — |
| 9 | 1942 | | |
| 10 | 1943 | | |
| | 1944 | — | — |
| 75 | 2008 | | Radovan Beli Marković |
| 76 | 2009 | September 14–20, 2009 (2009-09-14 – 2009-09-20) | Zoran Hamović |
| 77 | 2010 | September 13–19, 2010 (2010-09-13 – 2010-09-19) | Nebojša Bradić |
| 78 | 2011 | September 12–18, 2011 (2011-09-12 – 2011-09-18) | Angela Richter |
| 79 | 2012 | September 10–16, 2012 (2012-09-10 – 2012-09-16) | Ranko Risojević |
| 80 | 2013 | September 9–15, 2013 (2013-09-09 – 2013-09-15) | Dušan Kovačević |
| 81 | 2014 | September 8–14, 2014 (2014-09-08 – 2014-09-14) | Dragan Stanić |
| 82 | 2015 | September 14–20, 2015 (2015-09-14 – 2015-09-20) | Boško Suvajdžić |
| 83 | 2016 | September 12–18, 2016 (2016-09-12 – 2016-09-18) | Svetislav Božić |
| 84 | 2017 | September 11–17, 2017 (2017-09-11 – 2017-09-17) | Aleksandar Vučić |
| 85 | 2018 | September 10–16, 2018 (2018-09-10 – 2018-09-16) | Veljko Brborić |
| 86 | 2019 | September 9–15, 2019 (2019-09-09 – 2019-09-15) | Emir Kusturica |
| 87 | 2020 | September 14–20, 2020 (2020-09-14 – 2020-09-20) | Janko Vujinović |
| 88 | 2021 | September 13–19, 2021 (2021-09-13 – 2021-09-19) | Aleksandar Milanović |

## Organizers

Organizers of Vukov sabor are Vuk Karadžić Cultural Center, the city of Loznica, and Serbian Ministry of Culture and Information.
# Nikolay Maksyuta

Nikolay Kirillovich Maksyuta (Russian: Николай Кириллович Максюта; 26 May 1947 – 1 November 2020) was a Russian politician who was governor of Volgograd Oblast from 1997–2010. In 1996 he won the election for governor. He won his last re-election in 2004, and left office at the end of 2009.
On 1 November 2020, Maksyuta died from COVID-19 in a Moscow hospital. His wife had also died from COVID-19 on 8 October 2020.

## Family

Maksyuta was married. He had a son and daughter.
# People's Socialist Party of Montenegro

The People Socialist Party of Montenegro (Serbian: Народна социјалистичка странка Црне Горе, НСС ЦГ, romanized: Narodna socijalistička stranka Crne Gore, NSS CG) was an opposition political party in Montenegro within the Serbian List due to its support of political union of Montenegro with Serbia, holding 1 seat (represented by MP Emilo Labudović) in the Assembly of the Republic of Montenegro. Its de facto honorary head was Momir Bulatović and the last de jure acting leader was Novo Vujošević.
The party was formed in 2001 from dissidents of the Socialist People's Party of Montenegro under Momir Bulatovic that lost the election for the new party leadership at the party's 2nd Congress to the pro-democratic, pro-European wing of Predrag Bulatović. SNP CG was previously controlled by Momir's leadership since its creation when Momir's wing left the Democratic Party of Socialists of Montenegro in 1998. In late 2001, SNP CG crumbled again with its founders quickly withdrawing from politics, abandoning Momir.
In 2002 NSS led a "Patriotic Coalition for Yugoslavia" with the Serbian Radical Party of Vojislav Šešelj and the Yugoslav Left that failed to enter the parliament not surpassing the threshold.
In 2006 NSS formed a permanent coalition with parties committed to union with Serbia, which included the Serbian People's Party together with the Party of Serb Radicals, Democratic Party of Unity, Socialist Party of Yugoslavia and several non-governmental organizations such as the Serbian People's Council of Montenegro and Academic Alternative, known as the "Serbian List". It received one seat of the 12 that SL won of the total 81-seat Parliament of Montenegro.
In January 2009, it merged into New Serb Democracy.

## Election results
### Parliament

| Election | Votes | % | Seats | Coalition | Status |
| 2001 | 10,702 | 2.9% | 0 / 75 | – | extra-parliamentary |
| 2002 | 9,911 | 2.8% | 0 / 75 | PKJ | extra-parliamentary |
| 2006 | 49,730 | 14.6% | 1 / 81 | SL | opposition |
# Danila Alistratov

Danila Viktorovich Alistratov (Russian: Данила Викторович Алистратов; born October 30, 1990) is a Russian ice hockey goaltender. He has played for Traktor Chelyabinsk and is currently on a try-out contract with the Manchester Monarchs of the ECHL

## Career statistics
### Regular season

| Season | Team | League | GP | W | L | OTL | MIN | GA | SO | GAA | SV% |
| 2007–08 | Traktor Chelyabinsk | RSL | 18 | — | — | — | — | — | — | 3.29 | — |
| 2008–09 | Traktor Chelyabinsk | KHL | 39 | 17 | 16 | 3 | 2068 | 94 | 2 | 2.73 | .894 |
| 2009–10 | Traktor Chelyabinsk | KHL | 40 | 13 | 17 | 4 | 2063 | 105 | 2 | 3.05 | .897 |
| 2010–11 | Traktor Chelyabinsk | KHL | 23 | 7 | 9 | 7 | 1103 | 60 | 1 | 2.61 | .889 |
| KHL Totals | KHL Totals | KHL Totals | 102 | 37 | 42 | 14 | 5234 | 259 | 5 | 2.80 | .893 |

### Playoffs

| Season | Team | League | GP | W | L | MIN | GA | SO | GAA | SV% |
| 2007–08 | Traktor Chelyabinsk | RSL | 3 | — | — | — | — | — | 5.04 | — |
| 2008–09 | Traktor Chelyabinsk | KHL | 3 | 0 | 3 | 128 | 9 | 0 | 4.22 | .866 |
| 2009–10 | Traktor Chelyabinsk | KHL | 3 | 1 | 1 | 146 | 6 | 0 | 2.46 | .919 |
| KHL Totals | KHL Totals | KHL Totals | 6 | 1 | 4 | 274 | 15 | 0 | 3.28 | .893 |

### International

| Year | Team | Event | GP | W | L | T | MIN | GA | SO | GAA | SV% |
| 2008 | Russia | WJC18 | 3 | 2 | 1 | 0 | 144 | 7 | 0 | 2.91 | .870 |
| 2009 | Russia | WJC | 3 | 2 | 1 | 0 | 137 | 7 | 0 | 3.05 | .829 |
| Junior int'l totals | Junior int'l totals | Junior int'l totals | 6 | 4 | 2 | 0 | 281 | 14 | 0 | 2.98 | .850 |
# Dawei Township

Dawei Township (Burmese: ထားဝယ်မြို့နယ်) is a township of Dawei District in the Taninthayi Division of Myanmar. The principal town is Dawei.

## 2014 demographics

The 2014 Myanmar Census reported that Dawei Township had a population of 125,605. The population density was 29.4 people per km$^2$. The census reported that the median age was 28.5 years, and a sex ratio of 92 males per 100 females. There were 45,753 households; the mean household size was 4.6.

## Attractions

* Shwedaungza Pagoda, Peinnetaw Ward
* Shin Mokhti Buddha, Shin Mokhti Village
* Shinbinkayu Pagoda, Kanyon Ward
* Shin-u-aw Pagoda, Peinnetaw Ward
* Shindatwe Pagoda, Maungmeshaung Village
* Shwethalyaung Buddha, Kanaingda Village
# Baitush Sharaf Adarsha Kamil Madrasah

Baitush Sharaf Adarsha Kamil Madrasah (Arabic: مدرسة الكاملة بيت الشرف; Bengali: বায়তুশ শরফ আদর্শ কামিল মাদ্রাসা)) is a religious educational institution and alia madrasah in Bangladesh. The madrasah was founded in 1982 by Shah Sufi Abdul Jabbar. The madrasah is located in Dhanialapara area under Double Mooring Thana of Chittagong city. This madrasah secured the first rank in the departmental level in the Dakhil examination held under Madrasa Education Board in 2019.

## History

Baitush Sharaf Madrasah initially started with only five classes. Later, by 1994, the madrasah was gradually raised to Kamil level. Lessons are ongoing in science and humanities at Dakhil and Alim levels. Fazil and Kamil joined Islami University, Bangladesh in 2006 for their higher education. Then in the session 2016-17 in 2016 under Islamic Arabic University honors course in two subjects was introduced. The two subjects are Al-Quran and Islamic Studies and Al-Hadith.

## Infrastructure

The madrasah consists of two L-shaped five-storied buildings for administrative activities and teaching. There is also a five-storey dormitory building for residential students. Which is known as Hafez Abdur Rahim Hostel.

### Library management

The madrasah has a library on the second floor of the academic building. Also, the madrasah campus has a library of 'Baitush Sharaf Islamic Research Centre'.

### Residential system

The madrasah has hostels. Which is known as Hafez Abdur Rahim Hostel. About 350 students are staying in it.
# Darreh Dun, Chaharmahal and Bakhtiari

Darreh Dun (Persian: دره دون, also Romanized as Darreh Dūn) is a village in Miankuh Rural District, Miankuh District, Ardal County, Chaharmahal and Bakhtiari Province, Iran. At the 2006 census, its population was 172, in 37 families. The village is populated by Lurs.
# Sarab-e Dowkal

Sarab-e Dowkal (Persian: سراب دوكل, also Romanized as Sarāb-e Dowkāl, Sarāb Do Kal, Sarāb Dukāl, and Sarāb-e Do Kal; also known as Sarab Dogol) is a village in Sis Rural District, Bolbanabad District, Dehgolan County, Kurdistan Province, Iran. At the 2006 census, its population was 136, in 32 families. The village is populated by Kurds.
# Sari Qayeh, Malekan

Sari Qayeh (Persian: ساري قيه, also Romanized as Sārī Qayeh and Sārīqayeh) is a village in Gavdul-e Sharqi Rural District, in the Central District of Malekan County, East Azerbaijan Province, Iran. At the 2006 census, its population was 183, in 40 families.
# HMCS Trinity (MCB 157)

HMCS Trinity (hull number MCB 157) was a Bay-class minesweeper that was constructed for the Royal Canadian Navy during the Cold War. Entering service in 1954, the minesweeper was paid off in 1958 and transferred to the Turkish Navy. Renamed Terme, the ship remained in service until 1991.

## Design and description

The Bay class were designed and ordered as replacements for the Second World War-era minesweepers that the Royal Canadian Navy operated at the time. Similar to the Ton-class minesweeper, they were constructed of wood planking and aluminum framing.
Displacing 390 long tons (400 t) standard at 412 long tons (419 t) at deep load, the minesweepers were 152 ft (46 m) long with a beam of 28 ft (8.5 m) and a draught of 8 ft (2.4 m). They had a complement of 38 officers and ratings.
The Bay-class minesweepers were powered by two GM 12-cylinder diesel engines driving two shafts creating 2,400 brake horsepower (1,800 kW). This gave the ships a maximum speed of 16 knots (30 km/h; 18 mph) and a range of 3,290 nautical miles (6,090 km; 3,790 mi) at 12 knots (22 km/h; 14 mph). The ships were armed with one 40 mm Bofors gun and were equipped with minesweeping gear.

## Operational history

The ship's keel was laid down on 31 January 1952 by George T. Davie & Sons. Ltd at their yard in Lauzon, Quebec. Named for a bay located in Newfoundland, Trinity was launched on 31 July 1953. The ship was commissioned on 16 June 1954. The ship joined the First Canadian Minesweeping Squadron upon commissioning. The squadron sailed to the Caribbean Sea in April 1955 for a training cruise, making several port visits. In May 1956, the First Canadian Minesweeping Squadron deployed as part of the NATO minesweeping exercise Minex Sweep Clear One in the western Atlantic.
The ship remained in service with the Royal Canadian Navy until being paid off on 21 August 1957. The ship was transferred to the Turkish Navy as part of the NATO Mutual Aid Agreement on 31 March 1958. Renamed Terme by the Turkish Navy, the vessel sailed for Turkey on 19 May 1958. The ship remained in service until 1991.
# Ajay Singh Kilak

Ajay Singh Kilak is an Indian politician currently serving as a member of the 16th Rajasthan Assembly, representing the Degana Assembly constituency as a member of the Bharatiya Janata Party.

## Political career

Following the 2023 Rajasthan Legislative Assembly election, he was elected as an MLA from the Degana Assembly constituency. He defeated Indian National Congress (INC) candidate Vijaypal Mirdha with 7,755 votes.
From 2008 to 2018, he was MLA from Degana Assembly constituency.
# Akçegedik, Kurtalan

Akçegedik (Kurdish: Ziqeyf) is a village in the Kurtalan District of Siirt Province in Turkey. The village is populated by Kurds and had a population of 201 in 2021.
# Mir Qaleh

Mir Qaleh (Persian: ميرقلعه, also Romanized as Mīr Qal‘eh) is a village in Dibaj Rural District, Lotfabad District, Dargaz County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 177, in 56 families.