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Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki VII

für 71.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Kniga `Bioinformatika` yavlyaetsya sed`moy v serii. Ona yavlyaetsya pervoy knigoy, v kotoroy sdelan aktsent na rassmotrenii prikladnykh voprosov. Osnovnaya zadacha etoy knigi - poznakomit` chitatelya s geneticheskim fundamentom DNK nanomekhaniki i sootvetstvuyushchimi algoritmicheskimi problemami. V knige sushchestvennoe vnimanie udeleno bazovym algoritmicheskim voprosam raboty s geneticheskimi posledovatel`nostyami. Pri etom rassmatrivayutsya ne tol`ko effektivnye algoritmy, no i vychislitel`no trudnye zadachi. Knigu mozhno rassmatrivat` kak rabochiy material dlya dal`neyshego issledovaniya. ····· 103615377

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki VI

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Kniga `Problema ravenstva, vyvodimost` i vypolnimost` tozhdestv i kvazitozhdestv` yavlyaetsya shestoy v serii pod obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki`. V knige predstavleny rezul`taty po algoritmicheskim voprosam, svyazannym s razreshimost`yu i vychislitel`noy slozhnost`yu problemy ravenstva, razreshimost`yu problemy raspoznavaniya konechnoy baziruemosti, a takzhe problem vyvodimosti i vypolnimosti tozhdestv i kvazitozhdestv. ····· 103615371

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki V

für 71.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Pri glubokom izuchenii algoritmicheskikh problem i metodov ikh resheniya estestvennym obrazom prikhodit ponimanie togo, chto nas okruzhayut stroki dannykh, kombinatornye skhemy. Ikh priroda dostatochno universal`na. Kniga `Otnositel`naya pokryvaemost` i nezavisimo razbivaemye sistemy tozhdestv` yavlyaetsya pyatoy v serii. V knige predstavleny rezul`taty po algoritmicheskim voprosam, svyazannym s nezavisimost`yu sistem tozhdestv algebraicheskikh sistem i raspolozheniem mnogoobraziy v reshetkakh podmnogoobraziy. Rassmatrivayutsya problemy otnositel`noy pokryvaemosti mnogoobraziy i nezavisimoy razbivaemosti sistem tozhdestv. ····· 103615346

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki IV

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Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Kniga `Nezavisimost` sistem tozhdestv` yavlyaetsya chetvertoy v serii. Osnovnoe vnimanie v knige udeleno voprosam, svyazannym s nezavisimost`yu otdel`nykh sistem tozhdestv. Otmetim, chto v polugruppovoy modeli robototekhnicheskogo kompleksa ravenstvo slov v polugruppe sootvetstvuet ekvivalentnosti konfiguratsiy robototekhnicheskogo kompleksa. Sootvetstvenno, tozhdestvo pozvolyaet zadavat` massovuyu ekvivalentnost` konfiguratsiy. Ispol`zovanie tozhdestv daet vozmozhnost` znachitel`no sokrashchat` opisaniya robototekhnicheskikh kompleksov, otodvigaya kombinatornyy vzryv. V etom kontekste issledovanie nezavisimosti sistem tozhdestv daet vazhnyy instrument dlya optimizatsii opisaniy robototekhnicheskikh kompleksov. ····· 103615333

Diffrentsial`nye uravneniya matematicheskoy fiiki

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Kniga posvyashchena rassmotreniyu voprosov, svyazannykh s resheniem zadach matematicheskoy fiziki, vstrechayushchikhsya v inzhenernoy praktike. V ney rassmotreny metody resheniya tekh zadach matematicheskoy fiziki, kotorye svodyatsya k zadacham dlya differentsial`nykh uravneniy s chastnymi proizvodnymi i sovmestno s sootvetstvuyushchimi kraevymi usloviyami obrazuyut matematicheskie modeli rassmatrivaemykh fizicheskikh protsessov. Ispol`zovany traditsionnye materialy, izlagaemye v analogichnykh kursakh, kak-to: vidy differentsial`nykh uravneniy matematicheskoy fiziki (giperbolicheskie, parabolicheskie, ellipticheskie) postanovka kraevykh zadach matematicheskoy fiziki usloviya sushchestvovaniya i edinstvennosti ikh resheniya. Kniga prednaznachena dlya studentov vsekh spetsial`nostey, svyazannykh s elektrotekhnikoy i elektromekhanikoy, elektrosnabzheniem, elektronikoy, elektricheskimi i elektronnymi apparatami, sistemnym analizom, zashchitoy okruzhayushchey sredy i t. p. Mozhet okazat`sya poleznoy i dlya studentov drugikh spetsial`nostey, izuchayushchikh kurs matematicheskoy fiziki, a takzhe aspirantam i inzheneram. ····· 103615328

Algebra

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Izlozhenie kursa algebry, chitavshegosya avtorom v KamGU imeni Vitusa Beringa na protyazhenii ryada let pered Gosudarstvennymi ekzamenami u studentov-matematikov. Ukazany vzaimosvyazi i primeneniya vsekh osnovnykh algebraicheskikh rezul`tatov. Prednaznacheno dlya studentov universitetov, obuchayushchikhsya po fiziko-matematicheskikh spetsial`nostyam, no mozhet byt` polezno dlya uchiteley i uchashchikhsya srednikh shkol, gimnaziy i litseev. ····· 103615322

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki III

für 71.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Pri glubokom izuchenii algoritmicheskikh problem i metodov ikh resheniya estestvennym obrazom prikhodit ponimanie togo, chto nas okruzhayut stroki dannykh, kombinatornye skhemy. Ikh priroda dostatochno universal`na. Kniga `Nezavisimaya baziruemost` mnogoobraziy` yavlyaetsya tret`ey v serii. Osnovnoe vnimanie v knige udeleno voprosam, svyazannym s nezavisimoy baziruemost`yu mnogoobraziy algebraicheskikh sistem. V chastnosti, v knige rassmatrivaetsya problema raspoznavaniya nezavisimoy baziruemosti dlya mnogoobraziy vsekh polugrupp, monoidov i kolets. ····· 103615320

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki II

für 71.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Pri glubokom izuchenii algoritmicheskikh problem i metodov ikh resheniya estestvennym obrazom prikhodit ponimanie togo, chto nas okruzhayut stroki dannykh, kombinatornye skhemy. Ikh priroda dostatochno universal`na. Kniga `Problema opisaniya mnogoobraziy s razreshimoy ekvatsional`noy teoriey` yavlyaetsya vtoroy v serii. Osnovnoe vnimanie v knige udeleno postroeniyu primerov beskonechnykh tsepochek mnogoobraziy kolets i polugrupp, v kotorykh mnogoobraziya s razreshimoy i nerazreshimoy ekvatsional`noy teoriey chereduyutsya. Takie primery yavlyayutsya analogami primerov tsepochek mnogoobraziy, v kotorykh mnogoobraziya s razreshimoy i nerazreshimoy problemoy ravenstva chereduyutsya. V knige takzhe rassmatrivayutsya voprosy, svyazannye s zavisimost`yu razreshimosti ekvatsional`noy teorii mnogoobraziya ot razreshimosti ekvatsional`noy teorii ego pokrytiy. Otmetim, chto znachitel`naya chast` materiala knigi publikuetsya vpervye. ····· 103615287

Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki

für 71.10€ kaufen ···· Rheinberg-Buch.de - Bücher, eBooks, DVD & Blu-ray
Seriya knig s obshchim nazvaniem `Algoritmicheskie problemy algebry, bioinformatiki i robototekhniki` posvyashchena sistematicheskomu izlozheniyu algoritmicheskikh problem algebry, bioinformatiki i robototekhniki, v kotorom za osnovu vzyato nalichie obshchnosti kombinatornykh idey v trekh rassmatrivaemykh oblastyakh. Pri glubokom izuchenii algoritmicheskikh problem i metodov ikh resheniya estestvennym obrazom prikhodit ponimanie togo, chto nas okruzhayut stroki dannykh, kombinatornye skhemy. Ikh priroda dostatochno universal`na. Kniga `Ekvatsional`naya rekursivnost` i granitsy razreshimosti` yavlyaetsya pervoy v serii. Eto pervaya iz shesti knig, posvyashchennykh preimushchestvenno algebraicheskoy problematike. Poetomu v knige znachitel`noe vnimanie udelyaetsya bazovym ponyatiyam, kotorye imeyut vazhnoe znachenie ne tol`ko dlya rezul`tatov dannoy knigi, no i posleduyushchikh. V chastnosti, k etim ponyatiyam sleduet otnesti mashiny Minskogo i slova Murskogo. Kniga nachinaetsya so stat`i `Vvedenie v algoritmicheskie problemy algebry`. Eta stat`ya daet obshchiy obzor naibolee vazhnykh postanovok algoritmicheskikh problem algebry. Ona pomogaet chitatelyu otsenit` mesto rezul`tatov, predstavlennykh v knige, v obshchey kartine issledovaniy po algoritmicheskim problemam algebry. ····· 103615254

Kompleksnaya model` krovenosnoy sistemy cheloveka

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Rol` predskazatel`nogo matematicheskogo modelirovaniya v sovremennoy fiziologii i meditsine trudno pereotsenit`. Etot fakt obuslovlen i ogranichennost`yu vozmozhnostey eksperimental`nykh issledovaniy, i chrezvychaynoy slozhnost`yu protsessov, protekayushchikh v zhivykh organizmakh, i ogromnoy otvetstvennost`yu, svyazannoy s primeneniem novykh metodik dlya lecheniya cheloveka. Takim obrazom, prezhde chem osushchestvlyat` kakie-libo deystviya na praktike, mnogie biologi, mediki, fiziologi, farmatsevty predpochitayut oznakomit`sya s rezul`tatami matematicheskogo modelirovaniya interesuyushchego ikh protsessa. Dannaya rabota posvyashchena izucheniyu tryekh modeley serdechno-sosudistoy sistemy cheloveka, opisyvayushchikh fiziologicheskie i gidrodinamicheskie mekhanizmy regulyatsii etoy sistemy. Nashey tsel`yu yavlyaetsya ob`edinenie ukazannykh modeley na osnove prostykh fizicheskikh zakonov, takikh kak zakon sokhraneniya massy, model` fil`tratsii i dr. V rezul`tate skonstruirovana i realizovana kompleksnaya model` krovenosnoy sistemy, pozvolyayushchaya vosproizvodit` shirokiy spektr sostoyaniy i patologiy. Primenenie kompleksnoy modeli v biologii i meditsine pozvolit detal`no izuchit` razlichnye zabolevaniya krovenosnoy sistemy cheloveka i nayti puti ikh lecheniya. ····· 103615246

Identifikatsiya po otpechatkam pal`tsev

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V dannoy rabote postroena sistema raspoznavaniya otpechatkov pal`tsev, realizuyushchaya algoritmy skanirovaniya papillyarnogo uzora, nakhozhdeniya osnovnykh vidov minyutsiy i sravneniya otpechatkov. Teoreticheskiy razdel sostoit iz dvukh chastey. V pervoy chasti osveshchayutsya osnovnye polozheniya iz teorii raspoznavaniya otpechatkov pal`tsev. Vo vtoroy rassmotreny osnovnye metody identifikatsii. V analiticheskoy chasti rassmotreny adaptivnye fil`try i rezul`taty ikh primeneniya pri razlichnykh usloviyakh. Takzhe v etoy chasti rassmotreny osnovnye sposoby organizatsii dannykh i proveden ikh sravnitel`nyy analiz. V glave, posvyashchennoy realizatsii algoritmov, rassmotreno postroenie konkretnykh protsedur obrabotki izobrazheniy i sravneniya obrazov, privedeny rezul`taty, kharakterizuyushchie rabotu. ····· 103615216

Uchebno-issledovatel`skaya deyatel`nost` uchashchikhsya pri izuchenii drobey

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V knige okharakterizovany teoreticheskie osnovy organizatsii uchebno-issledovatel`skoy deyatel`nosti uchashchikhsya po matematike i privedena sistema uchebno-issledovatel`skikh zadaniy po teme `Drobi i deystviya nad nimi` chast` zadaniy podrobno rassmotrena, drugaya zhe predlozhena dlya samostoyatel`noy raboty. V rabote vydeleny kharakternye priznaki uchebno-issledovatel`skoy deyatel`nosti, raskryty faktory, sposobstvuyushchie aktivizatsii uchashchikhsya v protsesse vypolneniya uchebno-issledovatel`skikh zadaniy, opisany usloviya, sposobstvuyushchie polozhitel`noy motivatsii uchashchikhsya v protsesse vypolneniya uchebno-issledovatel`skikh zadaniy. Raskryty osnovnye didakticheskie funktsii uchebno-issledovatel`skoy deyatel`nosti: otkrytie novykh znaniy, uglublenie izuchaemykh znaniy, sistematizatsiya izuchennykh znaniy, razvitie uchashchikhsya, prevrashchenie uchashchegosya iz ob`ekta obucheniya v sub`ekt poznaniya, obuchenie uchashchikhsya sposobam deyatel`nosti. Kniga budet polezna uchitelyam matematiki i uchashchimsya obshcheobrazovatel`nykh shkol, litseev, gimnaziy, a takzhe studentam, obuchayushchimsya po napravleniyu `Matematika` i prepodavatelyam pedagogicheskikh vuzov. ····· 103615165

Modelirovanie klassicheskoy zadachi Voronogo otyskaniya sovershennykh form

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V predlagaemoy chitatelyam knige rech` idet o klassicheskoy probleme Voronogo otyskanie sovershennykh form, tesno svyazannoy s izvestnoy problemoy Ermita arifmeticheskie minimumy polozhitel`nykh kvadratichnykh form.Eti problemy yavlyayutsya interesnymi i netrivial`nymi zadachami geometricheskoy teorii chisel, kotorymi zanimalis` mnogie matematiki (Ermit, Gauss, Korkin, Zolotarev, Minkovskiy, Voronoy, Venkov, Delone, Ryshkov, Malyshev, Barns, Vladimirov, Skott, Larmout, Stasi, Baranovskiy, Shushbaev, Anzin, Umarov i dr.). Oni poyavilis` i v rabotakh S.L.Soboleva v svyazi s postroeniem reshetchatykh optimal`nykh kubaturnykh formul. Skazannoe svidetel`stvuet ob aktual`nosti problemy Voronogo otyskanie sovershennykh form. ····· 103615157

Vlozheniya konechnykh grupp v periodicheskie gruppy

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Odnoy iz osnovnykh kharakteristik periodicheskoy gruppy yavlyaetsya eye spektr, t.e. mnozhestvo poryadkov eye elementov. Ne menee vazhna informatsiya o konechnykh podgruppakh. Nastoyashchaya rabota posvyashchena issledovaniyu grupp s zadannym spektrom ili s zadannym naborom konechnykh podgrupp. Pri etom metody lokal`nogo analiza konechnykh grupp prisposablivayutsya dlya tseley issledovaniya stroeniya periodicheskikh grupp. Krome togo, ispol`zuyutsya mashinnye vychisleniya dlya ustanovleniya konechnosti nekotorykh konechno opredelyennykh grupp. ····· 103615144

Kompleksnyy analiz

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V knige dany teoreticheskie osnovy postroeniya konformnykh otobrazheniy ploskikh oblastey. Privoditsya dokazatel`stvo teoremy Rimana na baze printsipov maksimuma i kompaktnosti Montelya dlya golomorfnykh funktsiy. Dlya prosteyshikh otobrazheniy otslezhivayutsya preobrazovaniya ortogonal`nykh setok. Teoremy o sootvetstvii granits pri prosteyshikh konformnykh otobrazheniyakh ispol`zuyutsya dlya nakhozhdeniya funktsiy, realizuyushchikh otobrazhenie kruga ili poluploskosti na oblasti s zadannoy granitsey. Daetsya vyvod i ukazany primeneniya formuly Shvartsa-Kristoffelya. Dokazano, chto otobrazhenie kruga na krugovoy mnogougol`nik udovletvoryaet uravneniyu Shvartsa. Rassmatrivayutsya svyazi funktsiy krugovogo treugol`nika s gipergeometricheskoy funktsiey Gaussa. Kniga prednaznachena dlya studentov i aspirantov universitetov. Ona mozhet byt` poleznoy spetsialistam v raznykh oblastyakh nauki, zhelayushchikh oznakomit`sya s osnovnymi polozheniyami teorii konformnykh otobrazheniy. ····· 103615115

Prikladnye aspekty drobnogo ischisleniya

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Kniga posvyashchena izlozheniyu prikladnykh aspektov drobnogo ischisleniya. Rassmatrivayutsya osnovnye ponyatiya matematicheskogo apparata integro-differentsirovaniya drobnogo poryadka, primenenie drobnogo ischisleniya v teorii kolebaniy, nelokal`noy teploprovodnosti i zadache Stefana, a takzhe izlozheny chislennye metody v drobnom ischislenii.Kniga rasschitana dlya spetsialistov zanimayushchikhsya prilozheniem drobnogo ischisleniya v estestvoznanii. ····· 103615111

Topologicheskie svoystva funktsiy na dvukh- i trekhmernykh mnogoobraziyakh

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Poluchennye v rabote rezul`taty polnost`yu reshayut problemu topologicheskoy klassifikatsii funktsiy Morsa na zamknutykh trekhmernykh mnogoobraziyakh, funktsiy na dvumernykh i trekhmernykh mnogoobraziyakh s kraem (m-funktsii) i bolee obshchikh ob`ektov: funktsiy s izolirovannymi kriticheskimi tochkami na zamknutykh poverkhnostyakh, funktsiy s tremya i chetyr`mya kriticheskimi tochkami na trekhmernykh mnogoobraziyakh, zamknutykh 1-form Morsa na zamknutykh poverkhnostyakh, otobrazheniy Uitni zamknutoy poverkhnosti na ploskost` i dr. Effektivnost` postroennykh klassifikatsiy prodemonstrirovana na primerakh podscheta chisla topologicheski ne ekvivalentnykh ob`ektov s zadannymi svoystvami. Postroennye polnye topologicheskie invarianty fakticheski opisyvayut te svoystva dinamicheskikh sistem i funktsiy, kotorye ne izmenyayutsya pri topologicheskikh preobrazovaniyakh (naprimer zamene sistemy koordinat), ne zavisyat ot sposoba izmereniya ili opisanie i t.p. ····· 103615033

Kompleksnyy analiz

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V knige dano sovremennoe postroenie teorii kompleksnogo chisla kak elementa polya, sostavlennogo iz par deystvitel`nykh chisell. Sredi otobrazheniy kompleksnoy ploskosti vydelyayutsya kak ob`ekt glubokogo izucheniya golomorfnye otobrazheniya, imeyushchie mnogochislennye primeneniya v matematike i sostavlyayushchie vazhnuyu chast` analiticheskogo apparata vo mnogikh oblastyakh nauki blagodarya, v chastnosti, integral`nym teoremam. Izlozheny metody vychisleniya integralov, osnovannye na etikh teoremakh. Dokazany osnovnye teoremy o razlozheniyakh tselykh i meromorfnykh funktsiy, o svoystvakh gamma-funktsii Eylera. Issleduyutsya mnogoznachnye funktsii kak odnoznachnye na rimanovykh poverkhnostyakh. Kniga prednaznachena dlya studentov universitetov. Ona mozhet byt` poleznoy spetsialistam v raznykh oblastyakh nauki, zhelayushchikh oznakomit`sya s osnovnymi polozheniyami vvodnoy chasti kompleksnogo analiza. ····· 103614990

Triedinaya obshchaya teoriya differentsial`nogo ischisleniya

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Monografiya posvyashchena novoy teorii differentsial`nogo ischisleniya, organicheski i estestvenno vklyuchayushchey v sebya tri sostavnye chasti: predel`nuyu, bespredel`nuyu i kontinual`nuyu teorii differentsial`nogo ischisleniya. Novaya triedinaya teoriya mnogokratno perekryvaet oblast` primeneniya klassicheskoy teorii blagodarya tomu, chto v otlichie ot klassicheskoy, orientirovannoy isklyuchitel`no na funktsii, avtorskaya teoriya orientirovana i na funktsii, i na prirashcheniya funktsiy, prichyem na prirashcheniya lyubogo poryadka. Predlagaemaya teoriya imeet bezuprechnye teoreticheskie i prakticheskie dokazatel`stva i obosnovaniya. Kniga dostupna shirokoy masse chitateley ot krupneyshikh spetsialistov v oblasti matematicheskogo analiza do srednikh uchenikov srednikh klassov srednikh shkol. ····· 103614978

Gruppy, razlozhimye v svobodnoe proizvedenie

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Rassmatrivayutsya gruppy, yavlyayushchiesya netrivial`nymi svobodnymi proizvedeniyami i proizvedeniyami s ob`edinennoy podgruppoy. Obsuzhdayutsya osobennosti stroeniya grupp, razlozhimykh v takoe proizvedenie, a takzhe pokazyvayutsya primeneniya etikh konstruktsiy. Prednaznacheno dlya nauchnykh rabotnikov, aspirantov i studentov starshikh kursov fiziko-matematicheskikh fakul`tetov, primenyayushchikh i izuchayushchikh teoriyu grupp. Mozhet sluzhit` osnovoy dlya spetsial`nykh kursov i seminarov. ····· 103614942

Zadachi R. Bellmana i D. Knuta i ikh obobshcheniya

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V monografii rassmatrivayutsya obobshcheniya klassicheskoy zadachi o naiskoreyshem vozvedenii v stepen`, t. e. zadachi o nakhozhdenii slozhnosti vozvedeniya v stepen` - minimal`nogo chisla umnozheniy, dostatochnogo dlya vychisleniya po peremennoy zadannoy stepeni etoy peremennoy. Eta zadacha takzhe khorosho izvestna kak zadacha ob additivnykh tsepochkakh. Pomimo postavlennoy v 1963 g. R. Bellmanom zadachi o slozhnosti vychisleniya odnochlena ot mnogikh peremennykh i postavlennoy v 1969 g. D. Knutom zadachi o slozhnosti vychisleniya sistemy stepeney odnoy peremennoy v knige v asimptoticheskoy postanovke issleduyutsya i dal`neyshie obobshcheniya iskhodnoy zadachi. Osnovnoe vnimanie udeleno trem zadacham - zadache o slozhnosti vychisleniya sistem odnochlenov, zadache o slozhnosti vychisleniya sistem tselochislennykh lineynykh form (eta zadacha, kak pravilo, rassmatrivaetsya v additivnoy postanovke) i zadache o slozhnosti vychisleniya sistem elementov svobodnoy abelevoy gruppy. Izuchayutsya obshchie zakonomernosti i razlichiya mezhdu etimi tremya zadachami s tochki zreniya povedeniya slozhnosti. Daetsya obzor izvestnykh rezul`tatov v etoy oblasti, a takzhe predstavlen ryad poluchennykh v poslednee vremya rezul`tatov avtora. ····· 103614936

Chislennyy analiz zadach perenosa zaryada v poluprovodnikovykh ustroystvakh

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V dannoy rabote rassmotrena gidrodinamicheskaya MEP model`, opisyvayushchaya protsess perenosa zaryada v poluprovodnikovykh kremnievykh ustroystvakh submikronnogo razmera. Model` sostoit iz sistemy momentnykh sootnosheniy uravneniya Bol`tsmana i uravneniya Puassona dlya elektricheskogo potentsiala. Chtoby nayti chislennye resheniya smeshannoy kraevoy zadachi dlya uravneniya Puassona, razrabotan i obosnovan novyy vychislitel`nyy algoritm, s pomoshch`yu kotorogo skonstruirovany dva original`nykh effektivnykh podkhoda dlya poiska statsionarnykh resheniy rassmatrivaemoy modeli. Pri ispol`zovanii dannykh podkhodov sozdany algoritmy dlya resheniya neskol`kikh prikladnykh zadach - 1D zadachi o ballisticheskom diode i 2D zadach o perenose zaryada v tranzistorakh MESFET i MOSFET. Na osnove predlozhennykh idey razrabotana universal`naya i udobnaya tekhnologiya konstruirovaniya vychislitel`nykh modeley, kotoraya aprobirovana v prilozheniyakh pri poiske resheniy dvukh zadach. ····· 103614930

Lineynye uravneniya ellipticheskogo tipa

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Issleduetsya razreshimost` zadachi Dirikhle s kvadratichno summiruemoy granichnoy funktsiey dlya obshchego lineynogo ellipticheskogo uravneniya vtorogo poryadka v ogranichennoy oblasti s gladkoy granitsey. Polucheny tochnye (po poryadku rosta) ogranicheniya na rost vblizi granitsy rassmatrivaemoy ogranichennoy oblasti mladshikh koeffitsientov uravneniya pri kotorykh reshenie (esli ono sushchestvuet) obladaet svoystvom (n-1)-mernoy nepreryvnosti, kharakterizuyushchim povedenie resheniya vblizi granitsy oblasti i opisyvayushchee v kakom smysle ono prinimaet svoe granichnoe znachenie. Polucheny neobkhodimye i dostatochnye usloviya sushchestvovaniya (n-1)-merno nepreryvnogo resheniya rassmatrivaemoy zadachi Dirikhle i ustanovleno, chto usloviya razreshimosti izuchaemoy zadachi imeyut vid, analogichnyy usloviyam razreshemosti v obychnoy obobshchennoy postanovke. Dokazano, v chastnosti, chto esli odnorodnaya zadacha (s ravnymi nulyu granichnoy funktsiey i pravoy chast`yu) ne imeet netrivial`nykh resheniy, to dlya vsekh kvadratichno summiruemykh granichnykh funktsiy i vsekh pravykh chastey iz sootvetstvuyushchikh funktsional`nykh prostranstv sushchestvuet (n-1)-merno nepreryvnoe reshenie neodnorodnoy zadachi. ····· 103614924

Zadachi matematicheskoy fiziki

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V posobii rassmotreny osnovnye tipy uravneniy matema-ticheskoy fiziki i fizicheskie zadachi, privodyashchie k uravneniyam v chastnykh proizvodnykh. V otlichie ot osnovnykh uchebnikov izlozhenie soprovozhdaetsya podrobnymi vykladkami analiticheskikh i chislennykh metodov resheniya zadach matematicheskoy fiziki i primerov s ne menee podrobnym ikh resheniem, chto yavlyaetsya odnim iz preimushchestv dannogo posobiya. Imeetsya dostatochnoe kolichestvo uprazhneniy dlya samostoyatel`noy raboty, v tom chisle i s primeneniem EVM. V prilozheniyakh k posobiyu privedeny dlya vsekh reshennykh v kazhdoy glave primerov avtorskie vstavki dokumentov s programmami resheniya i grafikami, kotorye mozhno ispol`zovat` kak obraztsy pri provedenii laboratornykh ili samostoyatel`nykh rabot s primeneniem EVM. Prednaznacheno dlya bakalavrov tekhnicheskikh spetsial`nostey. ····· 103614922

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