
alexandra liyapunov

alexandra mikhailovich liyapunov (αleksandr mikhailovich Lyapunov,; 3 navambar 1918) ack russie ganitshastri, machini aur bhautik vigyaani they. unakaa upnaam vibhinn roop seey latapunov, liyapunov, liaponoff yaa lyapunov key roop mein roman haye. vaha khagolshastri mikhail liyapunov key putra aur piyanovadak aur sangeetkaar sergei liyapunov key bhaai they.
liyapunov koo ack gatishil pranali key sthirata siddhant key vikas key saath-saath ganitiya bhautiki aur sambhaavyata siddhant mein unake kaee yogdaanon key liye jaanaa jaataa haye.
jeevani.
praarambhik jeevan.
liyapunov kaa janm russie samrajya yaroslav mein huaa thaa. unake pitaa mikhail vasilivic liyapunov (1820-1868) demidov lysium dwara niyojit ack khagolshastri they. unake bhaai, sergei liyapunov, ack pratibhashali sangeetkaar aur piyanovadak they. 1863 mein, aim. vee. liyapunov apane vaigyaanik currier seey sevaanivritt hoe gaye aur apane parivaar koo simbersk praant (abb ulyanovsk oblast) mein bolobonov mein apani patni kii sampatti mein sthanantarit curr diyaa. 1868 mein apane pitaa kii mrityu key baad, alexandra liyapunov koo unake chaacha aar. aim. sechenov, shareer vigyaani ivan mikhailovich sechenov key bhaai. apane chaacha key parivaar mein, liyapunov ney apane door key chachere bhaai natalia rafailovna key saath adhyayan kiya, joe 1886 mein unaki patni baneen. 1870 mein, unaki maan apane beton key saath nijhani novgorod chully gaeen, jahan unhone vyayamshala kii teesari kaksha shuru kii. unhone 1876 mein vishishtata key saath vyayamshala seey snaatak kiya.
shiksha.
1876 mein, liyapunov ney sent pietersberg vishvavidyalaya mein bhautik-ganitiya vibhaag mein pravesh kiya, lekin ack maheene key baad unhone vishvavidyalaya key ganit vibhaag mein sthanantaran kiya.
sent pietersberg key ganit key professors mein chebishev aur unake chhaatr alexandra nikolevic korkin aur yegor ivanovic zolotrev they. liyapunov ney yantriki key professor key margadarshan mein apana pahala swatantra vaigyaanik kaary likhaa. key. bobylev. 1880 mein liyapunov koo jalsthirta parr ack kaam key liye ack swarn padak milaa. yeh unake pahale prakaashit vaigyaanik karyon kaa aadhar thaa "ack nishchit roop key paatr mein nihit bhaari drav mein ack bhaari shareer key santulan parr" aur "jalsthaitik dabaav kii kshamata parr". liyapunov ney 1880 mein apana vishvavidyalaya pathyakram bhee puuraa kiya, dou saal baad andree markov ney sent pietersberg vishvavidyalaya seey snaatak kiya thaa. liyapunov ney apane poore jeevan mein markov key saath vaigyaanik sampark banaae rakhaa.
shikshan aur anusandhaan.
liyapunov key shodh mein ack pramukh vishay sambhaavit khagoliya anuprayog key saath ack ghoornan drav dravyamaan kii sthirata thee. iss vishay koo chebishev dwara liyapunov koo unake paraasnaatak shodh prabandh key liye ack vishay key roop mein prastaavit kiya gayaa thaa jise unhone 1884 mein "ghoornan taral padarthon key dirghvrittakar roopon kii sthirata parr" sheershak key saath prastut kiya thaa. 
1885 mein, liyapunov niji hoe gayaa aur kharkiv vishvavidyalaya mein yantriki kii adhyakshata sweekaar karane kaa prastaav rakhaa gayaa, jahan vaha usee varsh gayaa thaa. kharkiv mein praarambhik pravaas key baare mein, smirnov ney liyapunov kii apani jeevani mein likhaa haih
unake chhaatr aur sahayogi, vladmir staclove ney apane pahale vyakhyan koo nimnalikhit tareeke seey yaad kiyaah "ack sunder yuva vyakti, lagbhag anya chhatron kii umr kaa, darshakon key saamane aaya, jahaan puraane deane, professor levakovsky bhee they, jinhen sabhi chhatron dwara sammaanit kiya jaataa thaa. deane key jaane key baad, ack kaampati hui aavaaz vaale yuvak ney gatishil pranaliyon parr ack pathyakram key bajaay, bhautik binduon kii gatishilata parr ack pathyakram vyakhyan denaa shuru curr diyaa. professor delaru key vyakhyanon seey chhatron koo yeh vishay pahale seey hii pataa thaa. lekin liyapunov ney hamein joe sikhaaya vaha merey liye nayaa thaa aur maine iss samagri koo kabhi kissy bhee paathyapustak mein naheen dekhaa thaa. pathyakram key prati sabhi ghrina turant dhool mein uda gaee. usa dinn seey chhaatr liyapunov koo vishesh sammaan denge."
mukhya yogdan prasiddh monograph 'aeye' mein prakaashit kiya gayaa thaa.aim. laipunov, gati kii sthirata kii samanya samasya. 1892. kharkiv ganitiya samaaj, kharkiv, 251पी. (russie mein) '. isake kaaran unaki 1892 kii doctorate thesis "gati kii sthirata kii samanya samasya" bunny. 12 sitambar 1892 koo masco vishvavidyalaya mein nikolai zukowski aur vee. key saath shodh prabandh kaa bachaav kiya gayaa thaa. bee. virodhi key roop mein mlodzivsky. 1908 mein, kharkiv sanskaran kaa french mein anuvaad kiya gayaa aur tolus vishvavidyalaya dwara punah prakaashit kiya gayaah 'samasya samanya dee laa stabilite doo mouvement, paar aim.aeye. liavonoff. anuvaad dou ruse paar aim.edord devox '.
baad key varshon mein.
vigyaan akadami key karyavahak sadasya key saath-saath vishvavidyalaya key anuprayukt ganit key sankaay mein sadharan professor chune jaane key baad, lapunov 1902 mein sent pietersberg laut aae. unake poorv shikshak chebishev kii mrityu key kaaran yeh pada khaali hoe gayaa thaa. koee shikshan daayitva naheen honey key kaaran, isase liyapunov koo apani padhaai parr dhyaan kendrit karane kaa avsar milaa aur vishesh roop seey vaha chebishev kii samasya parr kaam karane mein saksham they, jisake saath unhone apana vaigyaanik currier shuru kiya thaa.
1908 mein unhone rome mein chauthi antarrashtriya ganitiya congress mein bhaag liya. unhone euler key chayanit karyon key prakaashan mein bhee bhaag liyaah way khand 18 aur 19 key sampaadak they.
mrityu.
juuna 1917 key anta taka, liyapunov ney apani patni key saath odessa mein apane bhaai key mahal kii yatra kii. liyapunov kii patni tapedik seey peedit thee isaliye way apane doctor key adesh key anusaar chully gaeen. 31 octuber 1918 koo unaki mrityu hoe gaee. usee dinn, liyapunov ney khud koo sir mein goli maar lii, aur teen dinn baad unaki mrityu hoe gaee. usa samay taka, vaha motiyabind seey andhe hoe rahey they.
kaam karate hain.
liyapunov ney vibhedak samikaranon, sambhaavit siddhant, gatishil pranaliyon aur sambhaavyata siddhant sahit kaee kshetron mein yogdan diyaa. unaki mukhya vyastataaen santulan kii sthirata aur yaantrik pranaliyon kii gati, vishesh roop seey ghoornan drav dravyamaan, aur gurutvaakarshan key prabhaav mein kanon kaa adhyayan theen. ganitiya bhautiki key kshetra mein unake kaam ney lapless key sameekaran kii seema moolya samasya koo maanaa. kshamata key siddhant mein, 1897 seey "dirichlet kii samasya seey judey kuchh prashnon parr" unake kaam ney siddhant key kaee mahatvapurna pahaluon koo spasht kiya. iss kshetra mein unakaa kaam staclove key kaam key saath nikat sambandh mein haye. liyapunov ney kaee mahatvapurna sanniktan vidhiyaan vikasit keen. unake tareeke, jinhen unhone 1899 mein vikasit kiya thaa, samanya vibhedak samikaranon key sett kii sthirata koo paribhaashit karna sambhav banaate hain. unhone ack gatishil pranali kii sthirata kaa aadhunik siddhant banaaya. sambhaavyata key siddhant mein, unhone chebishev aur markov key karyon koo saamaanyikrit kiya, aur apane poorvavartiyon kii tulanaa mein adhik samanya sthitiyon mein kendriya seema pramey koo saabit kiya. pramaan key liye upayog kii gaee visheshta karyon kii vidhi koo baad mein sambhaavyata siddhant mein vyaapak upayog paaya gayaa.
kaee ganitvidon kii tarah, liyapunov ney akele kaam karna pasand kiya aur mukhya roop seey kuchh sahyogiyon aur karibi rishtedaron key saath samvaad kiya. vaha aamtaur parr dair seey kaam karate they, raat mein chaar seey paanch ghante, kabhi-kabhi poori raat. varsh mein ack yaa dou baar way rangmanch jaate they, yaa kissy sangeet karyakram mein jaate they. unake paas kaee chhaatr they. way kaee vishvavidyalayon key maanad sadasya, rome mein akadami key maanad sadasya aur peris mein vigyaan akadami key sambandhit sadasya they.
liyapunov kaa prabhaav mahatvapurna thaa, aur nimnalikhit ganitiya avadhaaranaon kaa naam unake naam parr rakhaa gayaa haih 

