PolyAgent/wiki_arabic_en_parallel_20231101 huggingface dataset:
ماريو براندنبيرغ

ماريو براندنبيرغ هو سياسي ألماني، ولد في 3 أكتوبر 1983 في باد بيرغتسابرن في ألمانيا. نشط حزبياً في الحزب الديمقراطي الحر. في الانتخابات الفيدرالية الألمانية 2017، انتخب عضو في البوندستاغ الألماني عن دائرة وقد انضم خلال البوندستاغ الألماني التاسع عشر (24 أكتوبر 2017 – ) للكتلة البرلمانية .
مراجع
أعضاء البوندستاغ من ولاية راينلند بالاتينات
أعضاء بوندستاغ 2017–2021
أعضاء بوندستاغ 2021–2025
سياسيون ألمان في القرن 21
ساسة الحزب الديمقراطي الحر (ألمانيا)
مواليد 1983
خرمال أنداماني

خرمال أنداماني هو من النباتات يتبع الخرمال من ال الأبنوسية.
انظر أيضًا
الخرمال
مراجع
أشجار بورنيو
خرمال
نباتات وصفت في 1870
نباتات جزر أندمان
Slovakia national rugby union team

Slovakia national rugby union team
The Slovakia national rugby union team has yet to qualify for a Rugby World Cup. They are currently affiliated to FIRA-AER, but not yet to World Rugby.
History
Slovakia played their first match in 2006 against the Principality of Monaco and lost 0-6. However, the points went to them after it was discovered that Monaco had used ineligible players.
In 2009, they withdrew from European competition for financial reasons, after having been unable to secure sponsorship. However, they returned to European competition in 2010, playing in the 2010–12 European Nations Cup Third Division.
The new dynamic has been supported by the city of Bratislava and the Government of Slovakia.
Record
Overall
See also
Rugby union in Slovakia
Czechoslovakia national rugby union team
References
External links
Official site
Slovakia on rugbydata.com
Statistics on rugbyinternational.net
Teams in European Nations Cup (rugby union)
European national rugby union teams
Rugby union in Slovakia
Rugby union
Braulio Vázquez

Braulio Vázquez
Braulio Jesús Vázquez Benítez (born 14 March 1972), simply known as Braulio, is a Spanish football manager and former player who played as a forward. He is the current sporting director of CA Osasuna.
Career
As a player, Braulio's career consisted mostly of Segunda División B appearances. His professional inputs included two La Liga matches for Deportivo de La Coruña, aside from a two-season spell with Portuguese Primeira Liga side S.C. Farense and one year with CP Mérida in Segunda División.
After retiring, Braulio worked as a manager for Soneira SD and Laracha CF before joining Valencia CF as a technical secretary. He subsequently moved to the sporting director position at the latter club in 2010, later working under the same role at Real Valladolid and CA Osasuna.
Personal life
Braulio's son Jesús is also a footballer. A left back, he was a Valencia youth graduate.
References
External links
1972 births
Living people
Footballers from Pontevedra
Spanish men's footballers
Men's association football forwards
La Liga players
Segunda División players
Segunda División B players
Tercera División players
Deportivo Fabril players
Deportivo de La Coruña players
CP Mérida footballers
CD Castellón footballers
Zamora CF footballers
Novelda CF players
CD Lugo players
Bergantiños FC players
Primeira Liga players
S.C. Farense players
Spanish expatriate men's footballers
Spanish expatriate sportspeople in Portugal
Expatriate men's footballers in Portugal
Spanish football managers
CA Osasuna non-playing staff
Raoul Peeters

Raoul Peeters (born 1 January 1947) is a Belgian former football player and manager.
References
1947 births
Living people
Belgian men's footballers
Belgian football managers
K.R.C. Mechelen managers
K. Berchem Sport managers
K.V. Oostende managers
K.S.V. Roeselare managers
Men's association football players not categorized by position
Mabel Fuller Blodgett

Mabel Fuller Blodgett (1869 – 1959) was a novelist and writer of children's books.
Biography
Born on April 10, 1869, as Mabel Louise Fuller in Bangor, Maine, she was the daughter of Ransom Burritt Fuller and Louise White. Her father became the president of two insurance companies in Boston. She graduated from the Sacred Heart Convent at Elmhurst in Providence, Rhode Island, and wrote her first novel At the Queen’s Mercy (1897) at the age of 19. Her subsequent works include:
The Aspen Shade: A Romance (1889)
Fairy Tales with illustrations by Ethel Reed (Boston, 1896)
A Mother's Prayer (1900)
The Giant's Ruby and Other Fairy Tales (1903)
When Christmas Came Too Early (1912)
The Strange Story of Mr. Dog and Mr. Bear (1915)
Peasblossom: The Adventures of the Pine Tree Fairy and Others (1917)
The Magic Slippers (1917)
She also published a non-fiction work, The Life and Letters of Richard Ashley Blodgett, First Lieutenant United States Air Service in 1919. Richard Blodgett was her son, and he was killed in action during World War I (1918).
Blodgett was living with her husband, attorney Edward E. Blodgett, in Brookline, Massachusetts by 1897, when Richard was born. She is buried in Mount Auburn Cemetery in Cambridge, Massachusetts.
References
External links
1869 births
1959 deaths
19th-century American novelists
20th-century American novelists
American women novelists
Writers from Bangor, Maine
Writers from Brookline, Massachusetts
Writers from Providence, Rhode Island
Novelists from Massachusetts
20th-century American women writers
19th-century American women writers
Novelists from Maine
Adelina Zagidullina

Adelina Zagidullina
Adelina Rustemovna Zagidullina (born 13 January 1993) is a Russian right-handed foil fencer of Tatar origin. She is the two-time team European champion, two-time team world champion and 2021 team Olympic champion. Zagidullina has been married to her coach Egor Popov since 2007. She is a Russian Armed Forces athlete, and her clubs are the Central Sports Army Club [RUS], and the Ufa Fencing Sports School of Olympic Reserve [RUS].
Medal record
Olympic Games
World Championship
European Championship
Grand Prix
World Cup
References
External links
(archive)
Adelina Zagidullina at the Russian Fencing Federation (in English) (archive)
1993 births
Living people
Russian female foil fencers
Volga Tatars
Tatar sportspeople
Tatar people of Russia
Sportspeople from Ufa
European Games gold medalists for Russia
European Games bronze medalists for Russia
European Games medalists in fencing
Fencers at the 2015 European Games
Olympic fencers for Russia
Fencers at the 2020 Summer Olympics
Medalists at the 2020 Summer Olympics
Olympic gold medalists for the Russian Olympic Committee athletes
Olympic medalists in fencing
21st-century Russian women
21st-century Russian military personnel
Katsunori Hirai

Katsunori Hirai
is a professional Japanese professional baseball pitcher for the Saitama Seibu Lions of Nippon Professional Baseball (NPB). Hirai was selected in the 5th round in the 2016 Nippon Professional Baseball draft. In the 2019 NPB season, Hirai appeared in 81 games, breaking the Pacific League Record for most games pitched, previously held by Kazuhisa Inao.
References
External links
NPB.com
1991 births
Living people
Baseball people from Aichi Prefecture
Japanese baseball players
Nippon Professional Baseball pitchers
Saitama Seibu Lions players
People from Ichinomiya, Aichi
فاينل فانتسي 9

فاينل فانتسي 9 هي لعبة فيديو تقمص الأدوار من إنتاج شركة سكوير لألعاب الفيديو على سوني بلاي ستيشن. صدرت اللعبة في عام 2000، وهي التاسعة في سلسلة فاينل فانتسي وآخر لعبة يتم إصدارها أولا على الجيل الأول من نظام بلاي ستيشن. وأعيد إصدارها في عام 2010، ضمن بي إس ون كلاسيكس على شبكة بلاي ستيشن. قدمت اللعبة ميزات جديدة إلى السلسلة مثل "الوقت النشط"، ونظام المعدات والمهارات.
تركز القصة على على الحرب بين الدول. ويتحكم اللاعب بلص شاب يدعى زيدان ترايبال، وينضم مع الآخرين لهزيمة الملكة بران من ألكساندريا، وهي المسؤولة عن بدء الحرب. إلا أن الحبكة تتغير عندما تدرك الشخصيات أن بران تعمل مع شخص أكثر خطرا يدعى كوجا.
تم تطوير اللعبة التاسعة جنبا إلى جنب مع الثامنة، ولكن المصممين اتخذوا نهجا مختلفا بالعودة إلى نمط ألعاب فاينل فانتسي الأولى الأكثر تقليدية. ونتيجة لذلك، تأثر اللعبة التاسعة بشكل ملحوظ بالأصلية، وبها إشارات إلى ألعاب أخرى في هذه السلسلة. لقيت اللعبة إشادة من النقاد وهي تحمل أعلى نتيجة على موقع ميتاكريتيك بين ألعاب فاينل فانتسي. حققت اللعبة نجاحا تجاريا، وبيع منها 5.30 مليون وحدة في جميع أنحاء العالم من قبل 31 مارس 2003.
أعلنت سكوير انيكس في 31 ديسمبر 2015 أن فاينل فانتسي 9 سيتم تعزيز وإعادة إصدارها على ويندوز والهواتف الذكية (آي أو إس وأندرويد).
روابط خارجية
مراجع
أعمال وجودية
ألعاب آي أو إس
ألعاب أندرويد
ألعاب إكس بوكس ون
ألعاب بلاي ستيشن
ألعاب بلاي ستيشن 3
ألعاب بلاي ستيشن 4
ألعاب سوني إنتراكتيف إنترتينمنت
ألعاب فاينل فانتسي
ألعاب فيديو 2000
ألعاب فيديو تحوي شخصيات مؤنسة
ألعاب فيديو تقع أحداثها على كواكب خياليون
ألعاب فيديو تقمص الأدوار
ألعاب فيديو ذات عوالم متوازية
ألعاب فيديو سجلها نوبوؤو أويماتسو
ألعاب فيديو فردية وجماعية
ألعاب فيديو مطورة في الولايات المتحدة
ألعاب فيديو مناهضة للحرب
ألعاب نينتندو سويتش
ألعاب ويندوز
ألعاب يونيتي
المناطيد في الخيال
حائزون على جائزة أكاديمية الفنون والعلوم التفاعلية
دائرة مارميلادي

دائرة مارميلادي هي إحدى الدوائر الخمس في إدارة أرتيبونيت في هايتي. تتبعها بلديتان. يبلغ عدد سكانها 120,193 نسمة حسب احصائيات أغسطس 2003، رمزها البريدي بالرقم 45.
تتكون الدائرة من البلديات التالية:
سانت ميشيل دي اتالايا
مارميلادي
مراجع
أرتيبونيت (إدارة)
دوائر هايتي
الشيخ سيدي بيمول

الشيخ سيدي بيمول فرقة موسيقية جزائرية تاسست في 1992 في باريس تؤدي الأغنية القبائلية والشعبي وأغاني التراث المدافعة عن القضية الأمازيغية.
نجاحاتها
حققت الكثير من النجاحات خصوصا في باريس واوساط الشباب القبائلي.
فرق موسيقية
فرق موسيقية أسست في 1992
فرق موسيقية جزائرية
فرق موسيقية فرنسية من إيل دو فرانس
قبائليون
مغنون قبائليون
Maqluba

Maqluba or Maqlooba is a traditional Iraqi, Lebanese, Palestinian, Jordanian, and Syrian dish served throughout the Levant. It consists of meat, rice, and fried vegetables placed in a pot which is flipped upside down when served, hence the name maqluba, which translates literally as "upside-down." The dish goes back centuries and is found in the Kitab al-Tabikh, a collection of 13th-century recipes.
Ingredients
Maqluba can include a variety of vegetables, such as fried tomatoes, potatoes, cauliflower, and eggplant, accompanied by either chicken or lamb. The most common are cauliflower and eggplant. All the ingredients are carefully placed in the pot in layers, so that when the pot is inverted for serving, the dish looks like a layer cake.
Maqluba is typically garnished with pine nuts and chopped fresh parsley. It sometimes served with salad and fresh yogurt, and is often prepared for feasts and large gatherings.
Since the unsuccessful coup attempt in Turkey, in 2016, the dish is seen as a "Gulenist delicacy". It is assessed as strong evidence of membership of the Gülen movement.
See also
Arab cuisine
Egyptian cuisine
Israeli cuisine
Jordanian cuisine
List of casserole dishes
Macaroni Hamin
Palestinian cuisine
References
External links
Maqluba (Upside-Down Chicken and Rice)
Arab cuisine
Jordanian cuisine
Palestinian cuisine
Iraqi cuisine
Levantine cuisine
Lebanese cuisine
Mediterranean cuisine
Israeli cuisine
Syrian cuisine
Rice dishes
أبو القاسم الشاهد

أبو القاسم الشاهد
وهو الشيخ أبو القاسم الشاهد سليمان بن محمد بن أحمد ابن أبي أيوب محمد بن إسماعيل بن سليمان بن يحيى بن هلال مولى الخليفة الأموي عمر بن عبد العزيز، ولـد عام 298هـ/ 910م، وكان في علم الحديث ثقة عدلاً مقبولاُ.
وسمع الحديث ورواه عن: محمد بن سليمان الباغندي، وعبد الله ابن محمد البغوي، وأبي بكر ابن داود، وعبد الحميد بن محمد بن درستويه، وعبد الله بن أحمد بن سعيد الجصاص، وأحمد بن الحسن المعروف بـدبيس المقريء.
روى عنه: الأزهري، والحسن بن محمد الخلال، وأبو الفرج الطناجيري، وعبد العزيز بن علي الأزجي، وأبو طالب محمد بن علي البيضاوي. كان أبو القاسم من الثقات، وقال عنه محمد ابن أبي الفوارس: (كان سليمان بن محمد بن أحمد ابن أبي أيوب، من أهل بيت الشهادة والثقة، وكان في الحديث ثقة جميل الأمر).
وفاته
توفي في بغداد يوم الأربعاء لخمس ليال بقين من شهر ربيع الآخر عام 378هـ/ 988م، ودفن يوم الخميس في مقبرة الخيزران ببغداد.
مصادر
أشخاص من بغداد
علماء حديث من العراق
مواليد 298 هـ
مواليد 910
وفيات 378 هـ
وفيات 988
مدفونون في مقبرة الخيزران
آنكي ب. مولدر باكر

آنكي ب. مولدر باكر
أنتجي بيتسك «آنكي» مولدر باكر (من مواليد 7 أبريل 1940) هي مؤرخة في جامعة جرونينجن وهي متخصصة في منصب النساء خلال العصور الوسطى. تكتب بشكل رئيسي باللغة الهولندية.
منشورات مختارة باللغة الإنجليزية
• الاختراع من [سينتلينس], [روتّلدج], 2002. ISBN 0415267595
• رؤية ومعرفة: نساء والتعلم في أوروبا قرون وسطى, 1200-1550, [بربولس], 2004. (نساء القرون الوسطى: النصوص والسياقات) ISBN 2503514480
• حياة المراسيس: صعود التراجع الحضري في أوروبا في العصور الوسطى، (ميرا هيرسبينك شولز، مترجم)، مطبعة جامعة بنسلفانيا، فيلادلفيا، 2005. ردمك 978-0-8122-3852-5
• النساء والخبرات في الكتابة اللاحقة للقرون الوسطى: قراءة كتاب الحياة، بالجريف ماكميلان، 2009. ردمك 9780230602878
المراجع
Lives of the Anchoresses The Rise of the Urban Recluse in Medieval Europe. University of Pennsylvania Press. 24 October 2015.
BOOK REVIEWS: HOUSE OF HERMITS. Hermitary, 2006. Retrieved 24 October 2015.
Women and Experience in Later Medieval Writing. Palgrave Macmillan. Retrieved 24 October 2015.
أشخاص على قيد الحياة
جامعة خرونينغن
كاتبات هولنديات في القرن 20
كاتبات هولنديات في القرن 21
مواليد 1940
مؤرخات
الفوقانية (أوفوس)

الفوقانية (أوفوس)
الفوقانية هي إحدى مشيخات المملكة المغربية، تتبع جغرافيا لإقليم الرشيدية وإداريًا لأوفوس. يقدر عدد سكانها بـ 7460 نسمة حسب الإحصاء الرسمي للسكان والسكنى لسنة 2004.
مراجع
انظر أيضا
قائمة مدن المغرب
أماكن مأهولة في أوفوس
Bahraini Super Cup

Bahraini Super Cup
The Bahraini Super Cup is the curtain raiser to the Bahrain football season.
Previous winners
1995 : Al-MuharraqSC
2003 : Al-Ahli 2-1 Al-Muharraq SC
2004 : Al-Shabab 2-1 Busaiteen
2005 : Al-Muharraq SC 1-0 Al-Shabab
2006 : Al-Muharraq SC 3-2 Al-Najma
2007 : Al-Najma 3-2 Al-Riffa SC
2008 : Al-Najma 1-0 Busaiteen Club
2013 : Al-Muharraq SC 2-1 Busaiteen Club
2014 : East Riffa SCC 1-1 (6-5 penalty kicks) Al-Riffa SC
2015 : Hidd SCC 1-1 (6-5 penalty kicks) Al-Muharraq SC
2016 : Hidd SCC 1-0 Al-Muharraq SC
2017 : Manama SC 1-1 (4-2 penalty kicks) Malkiya SCC
2018 : Muharraq SC 2-2 (4-3 penalty kicks) Al-Najma SCC
2019 : Riffa SC 1-1 (5-3 penalty kicks) Manama SC
2020 :
2021 : Riffa SC 1-1 (4-3 penalty kicks) East Riffa SCC
2022 : Al-Khaldiya SC 2-0 Riffa SC
Top-Performing Clubs
References
Bahrain - List of Cup Winners (RSSSF)
Super
National association football supercups
Martínez, Ávila

Martínez, Ávila
Martínez is a municipality in the province of Ávila, Castile and León, Spain. It had 162 inhabitants in 2010.
References
Municipalities in the Province of Ávila
ستيفن بيواتر

ستيفن بيواتر (7 يونيو 1981 بمانشستر في المملكة المتحدة - ) هو لاعب كرة قدم بريطاني في مركز حراسة المرمى. شارك مع منتخب إنجلترا تحت 21 سنة لكرة القدم. أما مع النوادي، فقد لعب مع إيبسويتش تاون وديربي كاونتي وشيفيلد وينزداي وكارديف سيتي وكوفنتري سيتي ونادي دونكاستر روفرز ونادي غيلينغهام ونادي ميلوول وهال سيتي ووست هام يونايتد ووولفرهامبتون واندررز ونادي كيرلا بلاستيرز ونادي بيرتن ألبيون ونادي روتشديل وويكمب وندررز.
مراجع
وصلات خارجية
أشخاص على قيد الحياة
حراس مرمى كرة قدم رجالية
لاعبو الدوري الإنجليزي الممتاز
لاعبو إيبسويتش تاون
لاعبو دوري الدرجة الأولى الإنجليزي
لاعبو ديربي كاونتي
لاعبو شيفيلد وينزداي
لاعبو كرة قدم إنجليز
لاعبو كرة قدم رجالية إنجليز
لاعبو كرة قدم من أولدهام
لاعبو كرة قدم من داربيشير
لاعبو كوفتري سيتي
لاعبو منتخب إنجلترا تحت 21 سنة لكرة القدم
لاعبو منتخب إنجلترا لكرة القدم للشباب
لاعبو نادي بيرتن ألبيون
لاعبو نادي دونكاستر روفرز
لاعبو نادي روتشدیل
لاعبو نادي غيلينغهام
لاعبو نادي كارديف سيتي
لاعبو نادي ميلوول
لاعبو هال سيتي
لاعبو وست هام يونايتد
لاعبو وولفرهامبتون واندررز
لاعبو ويكمب وندررز
مواليد 1981
Justin Thompson (soccer)

Justin Thompson (soccer)
Justin Thompson (born January 9, 1981 in Prince Rupert, British Columbia) is a Canadian retired soccer defender who played professionally in the United States, Canada and England. He was a member of the Canada U-20 men's national soccer team at the 2001 FIFA World Youth Championship.
Career
College
Thompson played college soccer for Fairfield University in Fairfield, Connecticut from 2001 to 2003, where he captained the Stags during his final two years. In 2002, the NSCAA selected him as a Regional All-American.
Professional
Thompson started his career with Bury in England, and spent the next few years bouncing backward and forward from the UK to North America across the summer and winter seasons, from Vancouver Whitecaps to Hornchurch to Virginia Beach Mariners to Worcester City. In two seasons with Worcester City, Thompson made 73 league appearances. In total, he made 97 appearances in all competitions. Thompson joined USL First Division side Portland Timbers in April 2007. On 3 December 2008, he returned to the Vancouver Whitecaps. On 31 March 2010, Thompson played his first game for West Van FC in the Imperial Cup.
International
Thompson was a member of Canada's U-18, U-20 and U-23 National Teams. In 2001, he was a member of the Canadian U-20 team which finished first in Group A at the 2001 CONCACAF Under-20 Qualification Tournament to qualify for the 2001 FIFA World Youth Championship in Argentina. Thompson made his Canadian Olympic (U-23) team debut in May 2002 and earned six caps with the team in 2004 Olympic qualifying matches.
Personal
Justin founded the ACT Sports Group in 2003 where he is involved in a number of soccer-related activities, including the organization of team tours from North America to Europe and the designing and overseeing of soccer camps in the UK, as well as the coordination of international professional player transfers. Thompson graduated with a B.S. in Finance from the Fairfield University Dolan School of Business.
References
External links
Portland Timbers bio
ACT-SPORTSGROUP
FIFA: Justin Thompson
1981 births
Living people
Bury F.C. players
Expatriate men's footballers in England
Canadian expatriate sportspeople in the United States
Canadian men's soccer players
Canadian expatriate men's soccer players
Fairfield Stags men's soccer players
Fairfield University Dolan School of Business alumni
Men's association football defenders
Hornchurch F.C. players
Portland Timbers (2001–2010) players
USL First Division players
Vancouver Whitecaps (1986–2010) players
Virginia Beach Mariners players
Worcester City F.C. players
People from Prince Rupert, British Columbia
Canada men's youth international soccer players
Canada men's under-23 international soccer players
Canadian expatriate sportspeople in England
Fadlu Davids

Fadlu Davids
Fadluraghman "Fadlu" Davids (born 21 May 1981 in Cape Town, Western Cape) is a retired South African football (soccer) striker who last played for Premier Soccer League club Maritzburg United. He was twice the highest goalscorer in the South African National First Division.
Since his retirement in 2012 Davids has served as assistant coach to Ernst Middendorp at Maritzburg United. When Middendorp left Martizburg United in 2016, Davids was named interim coach of Maritzburg for a third time in his career. His brother, Maahier Davids, was named as his assistant.
Upon the arrival of Roger De Sá, Davids resumed his position as Maritzburg's assistant coach. However, only seven games later, he reclaimed his position as interim coach after De Sá's resignation. Davids was caretaker for the rest of the 2016–17 South African Premier Division. On 1 July, Maritzburg United announced that Fadlu Davids would be the permanent coach after a very good performance as caretaker; he was in charge for the final nine games of the season, winning four, drawing three and losing two. Davids first full season as a coach was a success united were 4 points away from going to the 2018–19 CAF Confederation Cup and they also lost in the finals of the 2017–18 Nedbank Cup which was their last chance to qualify for the CAF tournament. Davids team played 15 league games and only won once, and on 24 December, Maritzburg United sacked Davids. Davids returned to be an assistant coach, this time for Orlando Pirates F.C., and has been in that position since 15 January 2019.
Davids has gained a reputation for promoting younger players after creating first team opportunities for the likes of Siphesihle Ndlovu‚ Bandile Shandu and Mlondi Dlamini, all of whom started out as ball boys.
Joined Maritzburg United: 2007
Previous clubs: Silver Stars; Vasco Da Gama; Manning Rangers; Santos Cape Town; Chernomorets Burgas, Bulgaria; Avendale Athletico, Mother City
References
1981 births
Living people
Soccer players from Cape Town
South African people of Malay descent
South African men's soccer players
Men's association football forwards
Platinum Stars F.C. players
Santos F.C. (South Africa) players
Maritzburg United F.C. players
Manning Rangers F.C. players
Jeans's theorem

Jeans's theorem
In astrophysics and statistical mechanics, Jeans's theorem, named after James Jeans, states that any steady-state solution of the collisionless Boltzmann equation depends on the phase space coordinates only through integrals of motion in the given potential, and conversely any function of the integrals is a steady-state solution.
Jeans's theorem is most often discussed in the context of potentials characterized by three, global integrals. In such potentials, all of the orbits are regular, i.e. non-chaotic; the Kepler potential is one example. In generic potentials, some orbits respect only one or two integrals and the corresponding motion is chaotic. Jeans's theorem can be generalized to such potentials as follows:
The phase-space density of a stationary stellar system is constant within every well-connected region.
A well-connected region is one that cannot be decomposed into two finite regions such that all trajectories lie, for all time, in either one or the other. Invariant tori of regular orbits are such regions, but so are the more complex parts of phase space associated with chaotic trajectories. Integrability of the motion is therefore not required for a steady state.
Mathematical description
Consider the collisionless Boltzmann equation for the distribution function
Consider the Lagrangian approach to the particle's motion in which case, the required equations are
Let the solutions of these equations be
where s are the integration constants. Let us assume that from the above set, we are able to solve , that is to say, we are able to find
Now consider an arbitrary function of 's,
Then this function is the solution of the collisionless Boltzmann equation, as can be verified by substituting this function into the collisionless Boltzmann equation to find
This proves the theorem.
A trivial set of integration constants are the initial location and the initial velocities of the particle. In this case, any function
is a solution of the collisionless Boltzmann equation.
See also
Jeans equations
References
Astrophysics
Dave Wright (baseball)

Dave Wright (baseball)
David William Wright (August 27, 1875 – January 18, 1946) was a professional baseball pitcher. He appeared in two games in Major League Baseball, one for the Pittsburgh Pirates in 1895 and one for the Chicago Colts in 1897.
Sources
Major League Baseball pitchers
Pittsburgh Pirates players
Chicago Colts players
New Castle (minor league baseball) players
Twin Cities Hustlers players
Columbus Buckeyes (minor league) players
Columbus Senators players
Minneapolis Millers (baseball) players
Baseball players from Ohio
19th-century baseball players
People from Dennison, Ohio
1875 births
1946 deaths