PolyAgent/wiki_arabic_en_parallel_20231101 huggingface dataset:
Wadi al-Qura

Wadi al-Qura is a wadi north of Medina in Saudi Arabia, mentioned in early Islamic sources. It was located on the main trade road between the Hejaz and Syria. This valley is also called Imam-e-Mubeen (open way) Quran (al-Hijar).
The wadi is tentatively identified with the modern Wadi al-'Ula region. The meaning of the name, "Valley of Villages", suggests the area contained several villages. The 10th-century geographer Istakhri noted it was one of the most populous and agriculturally productive areas of Arabia. The 9th-century historian Ibn al-Kalbi described it as highly fertile and dotted with villages throughout.
The wadi is referenced in many early Islamic texts. Several military expeditions took place there during the time of the Islamic Prophet Muhammad. These include:
the Expedition of Zaid ibn Haritha (Wadi al-Qura), where Muhammad sent Zayd ibn Haritha to survey the area and to monitor the movements of the enemies of Muhammad,
the Second Expedition of Wadi al-Qura which Muhammad ordered to raid the inhabitants of Wadi al-Qura for revenge, because a number of Muslims were killed when they tried to raid the inhabitants previously, but failed.
During the end of Muhammad's era the Third Expedition of Wadi al Qura was ordered, with the purpose of attacking the Jews of Wadi al-Qura to conquer their land
Recent discoveries of Geonic responsa have shown that there was a Jewish presence in Wadi al-Qura as late as the 11th century CE, and that they maintained correspondence with Rabbi Sherira Gaon and Rabbi Hai Gaon.
See also
List of expeditions of Muhammad
References
History of Saudi Arabia
Valleys of Saudi Arabia
إبراهيم القطان (توضيح)

إبراهيم القطان (توضيح)
إبراهيم القطان، أديب وقاضي وسفير ووزير أردني سابق.
إبراهيم القطان، ممثل كويتي.
صفحات توضيح أشخاص
Jovan Miladinović

Jovan Miladinović (30 January 1939 – 11 September 1982), commonly known as Zoran, was an association football player. He was born and died in Belgrade.
During his club career he played for FK Partizan and 1. FC Nürnberg. He earned 17 caps for the Yugoslavia national team and participated in the 1960 European Nations' Cup.
His entire coaching career was tied to FK Partizan, where he worked as assistant to various head coaches and filled in at the head position during two separate stints that lasted a few months. He was married and had two children.
References
External links
1939 births
1982 deaths
Serbian men's footballers
Yugoslav men's footballers
Yugoslavia men's international footballers
1960 European Nations' Cup players
Olympic footballers for Yugoslavia
Footballers at the 1964 Summer Olympics
FK Partizan players
1. FC Nürnberg players
Yugoslav First League players
Bundesliga players
Yugoslav expatriate men's footballers
Expatriate men's footballers in West Germany
Expatriate men's footballers in Germany
Footballers from Belgrade
Serbian football managers
Yugoslav football managers
FK Partizan managers
Alcohol-related deaths in Yugoslavia
Men's association football midfielders
Seyyed Maan

Seyyed Maan (also Romanized as Seyyed Ma‘an) is a village in Elhayi Rural District, in the Central District of Ahvaz County, Khuzestan Province, Iran. At the 2006 census, its population was 198, in 27 families.
References
Populated places in Ahvaz County
مؤسسة ياسر عرفات

مؤسسة ياسر عرفات هي منظمة غير ربحية مُستقلة فلسطينية أنشئت بموجب مرسوم رئاسي عام 2007 للحفاظ على تراث ياسر عرفات وللإبقاء على ذكراه خالده يٌشرف عليها مجلس أمناء ويُديرها مجلس إدارة. يُعد الصندوق القومي الفلسطيني مرجعيتها الإدارية والمالية منذ 17 سبتمبر 2015. وفقًا للنظام الداخلي الأساسي، تُعد العاصمة الفلسطينية القدس المقر الدائم للمؤسسة، ويُعد مقرها في مدينة رام الله مؤقتًا. للمؤسسة مكتب في مدينة غزة.
تمنح المؤسسة جائزة ياسر عرفات للإنجاز السنوية منذ عام 2007 لتشجيع الإبداع والأعمال الجادة والمتميزة في مجالات العمل الوطني أو الثقافي أو الاجتماعي أو الاقتصادي أو العلمي أو الأكاديمي. كما تُنظم العديد من مخيمات ياسر عرفات السنوية.
التاريخ
يُعد ياسر عرفات شخصًا بارزًا في تاريخ القضية الفلسطينية، حيث شارك في تأسيس حركة التحرير الوطني الفلسطيني، وكان رئيسًا لمنظمة التحرير الفلسطينية، ورئيسًا لدولة فلسطين (بما فيه السلطة الوطنية الفلسطينية).
في 24 مارس 2007، أصدر رئيس السلطة الوطنية الفلسطينية محمود عباس المرسوم رقم (5) وجاء في المادة الأولى:
في 25 مارس 2007، شُكلت لجنة تأسيسية مؤقتة ضمت ناصر القدوة، وانتصار الوزير، ورفيق الحسيني، ورمزي خوري، ومحمد مصطفى، وعلي مهنا وعلام الأحمد لتنفيذ أحكام مرسوم إنشاء المؤسسة خلال 6 شهور. مُددت فترتها في 1 أكتوبر 2007 حتى 25 مارس 2008.
في 6 أبريل 2008، عُدل مرسوم إنشاء المؤسسة.
في 12 يوليو 2012، نشرت المؤسسة على موقعها الرسمي مجموعة من التقارير الطبية حول الحالة المرضية لياسر عرفات.
متحف ياسر عرفات
في 30 أغسطس 2018، قرر الرئيس الفلسطيني محمود عباس، وقرر حفظه في متحف ياسر عرفات.
المراجع
وصلات خارجية
النظام الداخلي الأساسي للمؤسسة
أماكن سميت نسبة لياسر عرفات
تأسيسات سنة 2007 في فلسطين
منظمات مقرها في رام الله
منظمات غير ربحية مقرها في فلسطين
مؤسسات منظمة التحرير الفلسطينية
هاينريش جيرهارد كوهن

هاينريش جيرهارد كوهن (و. 1904 – 1994 م) هو فيزيائي من المملكة المتحدة . شارك في مشروع مانهاتن .وكان عضواً في الجمعية الملكية .
جوائز
حصل على جوائز منها:
(1967).
مراجع
أشخاص مرتبطون بمشروع مانهاتن
ألمان مهاجرون في المملكة المتحدة
خريجو جامعة غوتنغن
زملاء الجمعية الملكية
زملاء كلية باليول بجامعة أوكسفورد
فيزيائيون بريطانيون
مواليد 1904
مواليد في فروتسواف
وفيات 1994
وفيات في أكسفورد
توم براون (لاعب كرة قدم)

توم براون (لاعب كرة قدم)
توم براون (26 أكتوبر 1919 في المملكة المتحدة - 1 مايو 2000) هو لاعب كرة قدم بريطاني (وحمل سابقاً جنسية المملكة المتحدة لبريطانيا العظمى وأيرلندا) في مركز حراسة المرمى. لعب مع إيبسويتش تاون وبري تاون.
مراجع
وصلات خارجية
لاعبو كرة قدم رجالية إسكتلنديون
حراس مرمى كرة قدم رجالية
أفراد عسكريون إسكتلنديون
رياضيون من جنوب أيرشاير
شخصيات الجيش البريطاني في الحرب العالمية الثانية
لاعبو اتحاد إسكتلندا لكرة القدم للناشئين
لاعبو إيبسويتش تاون
لاعبو بري تاون
لاعبو دوري الدرجة الأولى الإنجليزي
لاعبو كرة قدم إسكتلنديون
لاعبو كرة قدم من جنوب أيرشاير
مواليد 1919
وفيات 2000
كراب ماتس

كراب ماتس هو أحد جبال سلسلة جبال الألب غلاروس وجزء من القمة الأم رينغيلزبيش يقع في كانتون غراوبوندن، سويسرا. يبلغ ارتفاع الجبل حوالي 2947 متر، بينما يبلغ ارتفاع نتوء الجبل 97 متر.
انظر أيضًا
قائمة جبال سويسرا
مراجع
جبال الألب
جبال سويسرا
جبال غراوبوندن
جبال في سويسرا يتجاوز ارتفاعها 2000 متر
إثيل فوينيتش

إثيل فوينيتش (11 مايو 1864 في جمهورية أيرلندا - 27 يوليو 1960، نيويورك في الولايات المتحدة)؛ ملحنة، كاتِبة وروائية بريطانية.
روابط خارجية
المصادر
أشخاص من مقاطعة كورك
روائيات أيرلنديات
روائيات بريطانيات
روائيون أيرلنديون في القرن 19
روائيون أيرلنديون في القرن 20
روائيون بريطانيون في القرن 19
روائيون بريطانيون في القرن 20
كاتبات أيرلنديات في القرن 19
كاتبات أيرلنديات في القرن 20
كتاب أيرلنديون في القرن 19
كتاب من مقاطعة كورك
كتاب وكاتبات أيرلنديون في القرن 20
ملحنات أيرلنديات
ملحنون أيرلنديون
ملحنون أيرلنديون في القرن 19
ملحنون أيرلنديون في القرن 20
ملحنون وملحنات بريطانيون
مواليد 1864
ناشطون سياسيون
ناشطون سياسيون أيرلنديون
ناشطون سياسيون بريطانيون
وفيات 1960
US Ouakam

US Ouakam
Union Sportive Ouakam (estimate Wolof form: Wakaam), abbreviation: USO is a Senegalese football club based in Dakar in the subdivision of Ouakam in the west of the city close to Cap Vert.
They play in the top division in Senegalese football. Their home stadium is Stade Demba Diop.
History
The club was founded in the 1951 by el Hadji Moussa Diagne in the last decade of French rule in Senegal.
After independence, Ouakam was becoming one of the top clubs in Senegal in the 1960s. Ouakam was suspended in the 1962-63 season and played in the second tier competition for some time which was the lowest level in Senegal before returning to top flight competition again. The last time Ouakam played in second tier competitions was in 2003.
Ouakam win their first cup title in 1964, their second in 1989 and their recent in 2006. Ouakam won their only championship title in 2011.
In the 2017 season, Ouakam started 6th for the 2016-17 season, they climbed to 7th at the 7th round and dropped to 13th at the 12th round and remained for four weeks, slowly, their positions risen to 12th at the 16th round, 11th at the 18th round, 10th a round later and would finish 8th place with 32 points, the club had 7 wins which was the same as Stade Mbour, Ouakam had 11 draws, more than that club. Together with Stade Mbour, they scored 22 goals which was the 12th least ahead of US Gorée and conceded 24 goals which was the third least, that was also the same as Niarry Tally.
Ouakam appeared at the continentals after winning their second cup title in 1990 at the Winners' Cup and advanced up to the quarterfinals where they lost to Nigeria's BCC Lions. They came back for the second and last time in 2007 and lost to Burkina Faso's Étoile Filante. After winning their only championship title, they made their only appearance at the 2012 CAF Champions League and challenged Brikama United and lost the Senegambian match in the preliminaries.
Logo
Its logo color has a crested shield with a wave below the middle of the shield, on top is coloured red and white on the bottom. On top has a shark and on the bottom right the club's name in its acronym and year of its foundation.
Its other logo has a white circle with a thin red rim with a shark on top and the club name's acronym on the bottom.
Honours
Senegal Premier League: 1
2011.
Senegal FA Cup: 3
1964, 1989, 2006.
League and cup history
Performance in CAF competitions
National level
References
External links
Football clubs in Senegal
Football clubs in Dakar
Ligue 1 (Senegal) clubs
Sports clubs and teams in Dakar
1951 establishments in Senegal
Nemophila maculata

Nemophila maculata, commonly known as fivespot, is a species of flowering plant in the borage family (Boraginaceae).
Distribution
The wildflower is found on slopes in elevations between . The plant is endemic to California. It is most common in the Sierra Nevada, Sacramento Valley, and the California Coast Ranges in the San Francisco Bay Area.
It is found in several plant communities, including valley grassland, foothill woodland, and pine and fir forest.
Description
Nemophila maculata is an annual herb that flowers in the spring. The leaves are up to 3 centimeters long and 1.5 wide, and are divided into several smooth or toothed lobes.
The flowers are bowl-shaped, white with dark veins and dots. The lobe tips are purple-spotted. The corolla is 1 to 2 centimeters long and up to 5 centimeters wide. The flowers' spots, giving the common name fivespot, attracts its primary pollinators, which are solitary bees. Male and female bees feed on the nectar and females collect pollen to feed their larvae.
The seeds are greenish-brown and are smooth or shallowly pitted. The fruit produces up to 12 seeds. The entire fruiting and seed cycle begins in spring and ends in the summer.
Cultivation
Nemophila maculata is sown as an annual ornamental plant in traditional, native plant, and pollinator/wildlife gardens. It grows in loose, evenly moist, and well-drained soils. It requires full sun to part shade and will self seed in optimum growth conditions.
References
External links
Calflora Database: Nemophila maculata (baby blue eyes)
Jepson Flora Project (1993): Nemophila maculata
Nemophila maculata — UC Photos gallery
maculata
Endemic flora of California
Flora of the Sierra Nevada (United States)
Natural history of the California chaparral and woodlands
Natural history of the California Coast Ranges
Natural history of the San Francisco Bay Area
Garden plants of North America
Flora without expected TNC conservation status
مقاطعة تشامبرز (تكساس)

مقاطعة تشامبرز (تكساس)
مقاطعة تشامبرز هي إحدى المقاطعات في ولاية تكساس، الولايات المتحدة الأمريكية، يبلغ عدد سكانها 35,096 نسمة طبقا لإحصاء عام 2010 .
مراجع
أماكن مأهولة أسست في 1858
تأسيسات سنة 1858 في تكساس
مقاطعات ولاية تكساس
هيوستن الكبرى
مقاطعة شامبيرس (تكساس)
Molla Sarab

Molla Sarab (also Romanized as Mollā Sarāb) is a village in Gavdul-e Gharbi Rural District, in the Central District of Malekan County, East Azerbaijan Province, Iran. At the 2006 census, its population was 912, in 195 families.
References
Populated places in Malekan County
European Practice Assessment

European Practice Assessment
The European Practice Assessment is a pan-European development for quality management in primary health care. The scaffolding is a set of indicators, that EPA instrument enables
general practitioners to compare and to improve the organisation and management of their practices. It is based on an extended review of the international
literature on assessment models for primary care, with special attention
to the Dutch model of practice visits.
Aims
EPA's key aspects of activity are the development and validation of a set of indicators and tools describing the organisational aspects of primary care practices. It was initiated in EQuiP, and the first set of indicators was developed through an international study by the EQuiP countries (2001–2004). Since 2005 it will be evaluated every three years.
The intention of the EPA instrument as a quality management system is to allow management and organization of medical practices to be measured and evaluated at regional, national and international levels with an educational approach.
History
Based on the TOPAS research project, the continuous development of EPA instruments started 2001. In autumn 2003 EPA as an instrument came into operation in nine countries.
Within a framework of an |international project the idea of an indicator-based instrument proved to give internationally valid, reliable and feasible
results for quality improvement in primary health care.
The following nine countries took part in the study and the further development: Belgium, France, Germany, Great Britain, the Netherlands, Switzerland, Slovenia, Austria and Israel.
Practice
encouraged several organisations to establish the European Practice Assessment model as an offer for high quality practice management on a national base. From six European countries leading institutes with experience in research in quality of primary health care and practice visits collaborate in the European Practice Assessment project:
Belgium: Flemish Institute of General Practice WWVH, Antwerp
France: ANAES, Paris
Germany: AQUA-Institute on Applied Quality Improvement and Research in Health Care, Göttingen
Netherlands: Centre for Quality of Care Research WOK, University of Nijmegen/University Maastricht
Switzerland: swisspep Institute for Quality and Research in Health Care, Gümlingen
UK: Department of General Practice, University of Wales College of Medicine, Cardiff
National Primary Care Research and Development Centre NPCRDC, Manchester
See also
EFQM European Foundation for Quality Management
ISO 9000 The standards for Quality Management Systems from the International Organization for Standardization
References
Primary care
Health care quality
عمرة بنت وائلة

عمرة بنت وائلة
عَمرة أبنةُ وائِلَة الغامدي،امرأة جاهلية، زوجة عبد شمس بن عبد مناف توأم جد النبي محمد هاشم بن عبد مناف، وهي جدة أمية بن أبي الصلت أمّ أمّه قال الزبيري: «وعبدَ العُزَّى بن عبد شمس ؛ ورُقَيةَ بنت عبد شمس ، وأمُّهما : عمرة بنت وائلة ابن الدُّؤل»
نسبها
هي عَمرة بنت وائِلَة بن الدَّؤل بن سَعدِ مَنَاة بن عَمرو وهو (غامد) بن كَعب (الجد الأصغر لأزد شنوءة) وهو كعب بن الحارث بن كعب بن عبد الله بن مالك بن نصر (شنوءة) بن الأزد
أبنائها
عبد العُزَّى بن عبد شمس
رُقَيةَ بنت عبد شمس
المراجع
جاهليات
عرب في القرن 5
سنة الولادة غير معروفة
سنة الوفاة غير معروفة
Beni Suef Cultural Palace fire

Beni Suef Cultural Palace fire
The Beni Suef Cultural Palace fire occurred in Beni Suef, Egypt, on September 5, 2005, and killed 46 people.
The Cultural Palace was overcrowded at the occasion of the Amateur Theatre Festival when a burning candle lit paper scenery on the stage and started a conflagration. A stampede erupted towards a single exit. Fire extinguishing equipment was locked in a distant room, and fire engines and ambulances arrived late and unprepared People died both from burns and in the stampede.
In the aftermath the Minister of Culture, Farouk Hosni, resigned, a move that was later revoked by President Hosni Mubarak. In May 2006 eight cultural bureaucrats were convicted for negligence and received ten-year prison sentences.
The fire drastically affected the theatrical community of Egypt who had come to the Cultural Palace on that day for the festival. September 5 has been named the National Day of Theatre in remembrance.
References
External links
Who is to blame for the Beni Suef theatre tragedy? Retrieved on 2008-08-29
Beni Suef
2005 disasters in Africa
Fires in Egypt
2005 in Egypt
2000s fires in Africa
2005 fires
Theatre fires
September 2005 events in Africa
ميلان ألبريشت

ميلان ألبريشت (مواليد ) هو لاعب كرة قدم. يلعب مع منتخب تشيكوسلوفاكيا لكرة القدم. سبق له أن لعب في كأس العالم لكرة القدم مع منتخب بلاده.
روابط خارجية
مراجع
لاعبو كرة قدم رجالية سلوفاكيون
مهاجمو كرة قدم رجالية
أشخاص على قيد الحياة
رياضيون من ترنتشين
لاعبو بانيك أوسترافا
لاعبو دوكلا بانسكا بيستريتسا
لاعبو كأس العالم 1970
لاعبو كرة قدم تشيكوسلوفاكيون
لاعبو كرة قدم سلوفاكيون
لاعبو منتخب تشيكوسلوفاكيا لكرة القدم
لاعبو منتخب تشيكوسلوفاكيا لكرة القدم للشباب
مدربو كرة قدم سلوفاكيون
مدربو نادي ترنتشين
مواليد 1950
لاعبو كرة قدم من ترنتشين
لين موريس (موسيقية)

لين موريس (موسيقية)
لين موريس هي موسيقية أمريكية، ولدت في 8 أكتوبر 1948.
مراجع
وصلات خارجية
أشخاص من لاميسا
مغنون وكتاب أغاني كنتري أمريكيون
مغنيات كانتري أمريكيات
مواليد 1948
موسيقيو بلوغراس أمريكيون
موسيقيو كانتري من تكساس
خوان بابلو رودريغيز

خوان بابلو رودريغيز (7 أغسطس 1979 بسابوبان في المكسيك - ) هو لاعب كرة قدم مكسيكي في مركز الوسط. شارك مع منتخب المكسيك تحت 20 سنة لكرة القدم ومنتخب المكسيك لكرة القدم. أما مع النوادي، فقد لعب مع ريال مدريد وسانتوس لاغونا ونادي أطلس ونادي تيكوس ونادي غوادالاخارا و.
مسيرته الكروية
لعب خوان بابلو رودريغيز خلال مسيرته الاحترافية مع 5 أندية في أربعة وعشرون موسمًا وسجل خلالها 98 هدفًا ضمن 594 مباراة. حيث فاز في موسم واحد بالكأس وفي أربعة مواسم بالدوري.
خاض خوان بابلو رودريغيز مسيرته مع نادي أطلس في موسم 1996–97 في المرة الأولى ليلعب معه سبعة مواسم ثم في موسم 2014–15 لمدة موسم واحد، مشاركًا طوالها في 177 مباراة سجل خلالها 45 هدفًا. ثم انتقل إلى نادي تيكوس في موسم 2003–04 واستمر معه طيلة ثلاثة مواسم، حيث شارك في 98 مباراة سجل خلالها 11 هدفًا. لينتقل بعدها إلى نادي سانتوس لاغونا في موسم 2006–07 ليلعب معه تسعة مواسم، مشاركًا في 241 مباراة سجل خلالها 30 هدف. ثم انتقل إلى في موسم 2015–16 واستمر معه طيلة ثلاثة مواسم، مشاركًا في 65 مباراة سجل خلالها 12 هدفًا.
مراجع
وصلات خارجية
لاعبو كرة قدم رجالية مكسيكيون
لاعبو وسط كرة قدم رجالية
أشخاص من سابوبان (خاليسكو)
لاعبو الدوري المكسيكي الممتاز
لاعبو سانتوس لاغونا
لاعبو كأس القارات 2001
لاعبو كأس القارات 2005
لاعبو كأس الكونكاكاف الذهبية 2003
لاعبو كرة قدم مكسيكيون
لاعبو كرة قدم من ولاية خاليسكو
لاعبو كوبا أمريكا 2001
لاعبو منتخب المكسيك تحت 20 سنة لكرة القدم
لاعبو منتخب المكسيك لكرة القدم
لاعبو مونيركاس موريليا
لاعبو نادي أطلس
لاعبو نادي تيكوس
لاعبو نادي غوادالاخارا
لاعبون فائزون بالكأس الذهبية الكونكاكاف
مواليد 1979
Classic Lorient Agglomération

Classic Lorient Agglomération
The Classic Lorient Agglomération is an elite professional women's road bicycle race held in Plouay, France.
The race was first organized since 2002 as Grand Prix de Plouay – Bretagne, on the day of the men's race and on the same circuit. The race consists of four 26.9 km laps and two 13.9 km laps, totalling 135.4 km.
The race was part of the UCI Women's Road World Cup until 2015. In 2016, the race became part of the new UCI Women's World Tour. In 2022, the race rebranded as Classic Lorient Agglomération.
Route
The course is known for its high rate of attrition, with riders rapidly dropping out of contention. The first climb starts almost immediately as the race goes over the Côte du Lézot, a one-kilometre climb with an average gradient of 6%. Next is a six-kilometre ascent up to the Chapelle Sainte-Anne des Bois marking the halfway point of the lap. After a flat section, the race addresses the Côte de Ty Marrec, which has a maximum gradient of 10%. The riders will have to tackle this 26.9 kilometre loop 4 times, before entering a last shortened 13.9 kilometre version of the loop, taking the riders over the Côte du Lézot and the Côte de Ty Marrec. The run-in to the finish is slightly downhill. The race is often won by the best sprinter of the climbers.
Winners
Multiple winners
Wins per country
External links
Official site
References
Recurring sporting events established in 2002
2002 establishments in France
Cycle races in France
UCI Women's Road World Cup
Women's road bicycle races
UCI Women's World Tour races
David Andersson (speed skater)

David Andersson (speed skater)
David Andersson (born 23 February 1994) is a Swedish speed skater.
Andersson competed at the 2014 Winter Olympics for Sweden. In the 1000 metres and the 1500 metres he finished 38th overall.
As of September 2014, Andersson's best performance at the World Single Distance Championships is 23rd, in the 2013 1500 metres.
Andersson made his World Cup debut in November 2012. As of September 2014, Andersson's top World Cup finish is 4th in a 1500m B race at Kolomna in 2012–13. His best overall finish in the World Cup is 37th, in the 1500 metres in 2012–13.
References
1994 births
Swedish male speed skaters
Speed skaters at the 2014 Winter Olympics
Olympic speed skaters for Sweden
People from Vänersborg Municipality
Living people
Sportspeople from Västra Götaland County
21st-century Swedish people
Hilbert's eleventh problem

Hilbert's eleventh problem is one of David Hilbert's list of open mathematical problems posed at the Second International Congress of Mathematicians in Paris in 1900. A furthering of the theory of quadratic forms, he stated the problem as follows:
Our present knowledge of the theory of quadratic number fields puts us in a position to attack successfully the theory of quadratic forms with any number of variables and with any algebraic numerical coefficients. This leads in particular to the interesting problem: to solve a given quadratic equation with algebraic numerical coefficients in any number of variables by integral or fractional numbers belonging to the algebraic realm of rationality determined by the coefficients.
As stated by Kaplansky, "The 11th Problem is simply this: classify quadratic forms over algebraic number fields." This is exactly what Minkowski did for quadratic form with fractional coefficients. A quadratic form (not quadratic equation) is any polynomial in which each term has variables appearing exactly twice. The general form of such an equation is ax2 + bxy + cy2. (All coefficients must be whole numbers.)
A given quadratic form is said to represent a natural number if substituting specific numbers for the variables gives the number. Gauss and those who followed found that if we change variables in certain ways, the new quadratic form represented the same natural numbers as the old, but in a different, more easily interpreted form. He used this theory of equivalent quadratic forms to prove number theory results. Lagrange, for example, had shown that any natural number can be expressed as the sum of four squares. Gauss proved this using his theory of equivalence relations by showing that the quadratic represents all natural numbers. As mentioned earlier, Minkowski created and proved a similar theory for quadratic forms that had fractions as coefficients. Hilbert's eleventh problem asks for a similar theory. That is, a mode of classification so we can tell if one form is equivalent to another, but in the case where coefficients can be algebraic numbers. Helmut Hasse's accomplished this in a proof using his local-global principle and the fact that the theory is relatively simple for p-adic systems in October 1920. He published his work in 1923 and 1924. See Hasse principle, Hasse–Minkowski theorem. The local-global principle says that a general result about a rational number or even all rational numbers can often be established by verifying that the result holds true for each of the p-adic number systems.
There is also more recent work on Hilbert's eleventh problem studying when an integer can be represented by a quadratic form. An example is the work of Cogdell, Piatetski-Shapiro and Sarnak.
See also
Hilbert's problems
Notes
References
Yandell, Benjamin H. The Honors Class: Hilbert's Problems and Their Solvers. Natik: K Peters. Print.
11
Quadratic forms