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This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.
Research & information: general --- Mathematics & science --- fractional derivative --- generalized Mittag-Leffler kernel (GMLK) --- Legendre polynomials --- Legendre spectral collocation method --- dynamical systems --- random time change --- inverse subordinator --- asymptotic behavior --- Mittag–Leffler function --- data fitting --- magnetization --- magnetic fluids --- Gamma function --- Psi function --- Pochhammer symbol --- hypergeometric function 2F1 --- generalized hypergeometric functions tFu --- Gauss’s summation theorem for 2F1(1) --- Kummer’s summation theorem for 2F1(−1) --- generalized Kummer’s summation theorem for 2F1(−1) --- Stirling numbers of the first kind --- Hilfer–Hadamard fractional derivative --- Riemann–Liouville fractional derivative --- Caputo fractional derivative --- fractional differential equations --- inclusions --- nonlocal boundary conditions --- existence and uniqueness --- fixed point --- gamma function --- Beta function --- Mittag-Leffler function --- Generalized Mittag-Leffler functions --- generalized hypergeometric function --- Fox–Wright function --- recurrence relations --- Riemann–Liouville fractional calculus operators --- (α, h-m)-p-convex function --- Fejér–Hadamard inequality --- extended generalized fractional integrals --- Mittag–Leffler functions --- initial value problems --- Laplace transform --- exact solution --- Chebyshev inequality --- Pólya-Szegö inequality --- fractional integral operators --- Wright function --- Srivastava’s polynomials --- fractional calculus operators --- Lavoie–Trottier integral formula --- Oberhettinger integral formula --- fractional partial differential equation --- boundary value problem --- separation of variables --- Mittag-Leffler --- Abel-Gontscharoff Green’s function --- Hermite-Hadamard inequalities --- convex function --- κ-Riemann-Liouville fractional integral --- Dirichlet averages --- B-splines --- dirichlet splines --- Riemann–Liouville fractional integrals --- hypergeometric functions of one and several variables --- generalized Mittag-Leffler type function --- Srivastava–Daoust generalized Lauricella hypergeometric function --- fractional calculus --- Hermite–Hadamard inequality --- Fox H function --- subordinator and inverse stable subordinator --- Lamperti law --- order statistic --- n/a --- Gauss's summation theorem for 2F1(1) --- Kummer's summation theorem for 2F1(−1) --- generalized Kummer's summation theorem for 2F1(−1) --- Hilfer-Hadamard fractional derivative --- Riemann-Liouville fractional derivative --- Fox-Wright function --- Riemann-Liouville fractional calculus operators --- Fejér-Hadamard inequality --- Mittag-Leffler functions --- Pólya-Szegö inequality --- Srivastava's polynomials --- Lavoie-Trottier integral formula --- Abel-Gontscharoff Green's function --- Riemann-Liouville fractional integrals --- Srivastava-Daoust generalized Lauricella hypergeometric function --- Hermite-Hadamard inequality
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Changes of past and present environment of Slovenia are discussed in nine papers, which were written by 21 authors, coming from 14 research organisations. Our aim is to increase multidisciplinary communication and cooperation between Slovenian researchers, working in the fields of palaeoecology and ecology. Research topics include: archaeozoology, biology, ecology, geoarchaeology, palynology, nature protection, dendrochronology, archaeobotany, geochemistry, Karst research and geography. V knjigi je predstavljenih devet prispevkov, ki obravnavajo spremembe nekdanjega in današnjega okolja v Sloveniji. Pri nastajanju knjige je sodelovalo 21 avtorjev, ki prihajajo iz 14 različnih raziskovalnih organizacij. Naš cilj je okrepiti komunikacijo in sodelovanje med slovenskimi raziskovalci, ki se ukvarjamo s paleoekološkimi in ekološkimi raziskavami, zato teme prispevkov prihajajo iz na videz zelo različnih, a med seboj povezanih raziskovalnih področij kot so: arheozoologija, biologija, ekologija, geoarheologija, palinologija, varstvo okolja, dendrokronologija, arheobotanika, geokemija, krasoslovje in geografija.
algae --- animal remains (archaeology) --- biodiversity --- cave sediments --- collective volume --- dendrochronology --- geomorphology --- Gulf of Trieste --- karst (geology) --- land use --- Ljubljansko barje --- paleobotany --- paleoclimatology --- paleoecology --- palynology --- phytocenology --- sinkholes --- stratigraphy --- taphonomy --- White Carniola --- alge --- Bela krajina --- biološka raznovrstnost --- dendrokronologija --- fitocenologija --- geomorfologija --- jamski sedimenti --- kras (geologija) --- paleobotanika --- paleoekologija --- paleoklimatologija --- palinologija --- raba tal --- stratigrafija --- tafonomija --- Tržaški zaliv --- vrtače --- zborniki --- živalski ostanki (arheologija)
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Fouilles archéologiques --- Antiquités préhistoriques --- Paléontologie --- Slovénie --- Antiquités. --- Biodiversity --- Climatic changes --- Paleoecology --- Palaeoecology --- Ecology --- Paleobiology --- Changes, Climatic --- Climate change --- Climate changes --- Climate variations --- Climatic change --- Climatic fluctuations --- Climatic variations --- Global climate changes --- Global climatic changes --- Climatology --- Climate change mitigation --- Teleconnections (Climatology) --- Biological diversification --- Biological diversity --- Biotic diversity --- Diversification, Biological --- Diversity, Biological --- Biology --- Biocomplexity --- Ecological heterogeneity --- Numbers of species --- Environmental aspects --- Slovenia --- Antiquities. --- Changes in climate --- Climate change science --- Global environmental change
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[Environmental Archaeology and Palaeoecology:Palynology, Archaeobotany and Archaeozoology]Plant and animal remains, which are found on archaeological sites and in lake/marsh sediments, are a good source of information about past economy, environment, food procurement, and the adaptation of people to changeable environmental conditions in various archaeological time periods. However, all these data need to be collected and interpreted. With the first manual presenting palynology, archaeobotany and archaeozoology fields of research in Slovenian language, this task should be more easily achievable. Rastlinski in živalski ostanki, ki jih najdemo na arheoloških najdiščih ter v močvirskih in jezerskih sedimentih, so dober vir podatkov o načinu življenja, gospodarstvu, prehranskih navadah, nekdanjem okolju in prilagoditvi človeka nanj v različnih obdobjih. Vendar pa je treba znati te podatke pravilno zbrati in »prebrati«. S prvo celovito predstavitvijo področja delovanja palinologije, arheobotanike in arheozoologije v slovenskem jeziku bo to odslej lažje.Knjiga je razdeljena na dva dela. Prvi, splošni del je posvečen teoretični predstavitvi palinologije, arheobotanike in arheozoologije. Orisu osnovnih vrst rastlinskih in živalskih najdb ter razmer, v kakršnih se odlagajo in ohranjajo v sedimentu, sledi predstavitev poglavitnih raziskovalnih metod in najpomembnejših interpretativnih okvirjev. V drugem delu je na kratko povzetih več primerov uporabe okoljske arheologije pri obravnavi različnih arheološko pomembnih problematik, s poudarkom na pomenu primerne izbire osnovnih metod dela.
Plant remains (Archaeology) --- Animal remains (Archaeology) --- Palynology. --- Excavations (Archaeology) --- Archaeological digs --- Archaeological excavations --- Digs (Archaeology) --- Excavation sites (Archaeology) --- Ruins --- Sites, Excavation (Archaeology) --- Archaeology --- Pollen --- Pollen analysis --- Botany --- Paleobotany --- Pollen, Fossil --- Plant spores --- Plant spores, Fossil --- Archaeozoology --- Zooarchaeology --- Zoology in archaeology --- Bones --- Animal paleopathology --- Archaeobotanical assemblages --- Archaeobotanical material --- Archaeobotanical remains --- Archaeobotany --- Archaeological plant remains --- Archaeology, Botanical --- Assemblages, Archaeobotanical --- Botanical archaeology --- Botany in archaeology --- Material, Archaeobotanical --- Phytoarchaeology --- Remains, Archaeobotanical --- Remains, Plant (Archaeology) --- Remains, Vegetal (Archaeology) --- Vegetal remains (Archaeology) --- Anthracology --- Analysis --- Methodology --- Slovenia --- Environmental archaeology --- animal remains (archaelogy) --- archaelogy --- archaeological remains --- archaeological research --- human environment --- paleobotany --- paleoecology --- paleozoology --- palynology --- plant remains (archaeology) --- arheologija --- arheološke ostaline --- arheološke raziskave --- človekovo okolje --- paleobotanika --- paleoekologija --- paleozoologija --- palinologija --- rastlinski ostanki (arheologija) --- živalski ostanki (arheologija) --- animal remains (archaeology) --- archaeology
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