01323nam0 2200301 i 450 SUN010435920191106094920.4528-94-017-8621-80.00N978-94-017-8622-520151221d2014 |0engc50 baengNL|||| |||||*Computational experiment approach to advanced secondary mathematics curriculumSergei AbramovichDordrecht : Springer, 2014XV325 p.ill. ; 24 cmPubblicazione in formato elettronico001SUN01043572001 *Mathematics Education in the Digital Era3210 BerlinSpringer2013-.97UxxEducational material and media and educational technology in mathematics education [MSC 2020]MFSUNC028607NLDordrechtSUNL000068Abramovich, SergeiSUNV081400721174SpringerSUNV000178650ITSOL20201012RICAhttp://dx.doi.org/10.1007/978-94-017-8622-5SUN0104359BIBLIOTECA CENTRO DI SERVIZIO SBA15CONS SBA EBOOK 4326 15EB 4326 20191106 Computational experiment approach to advanced secondary mathematics curriculum1410009UNICAMPANIA05197nam 22009135 450 991098338590332120251031124241.09789819795390981979539710.1007/978-981-97-9539-0(MiAaPQ)EBC31897888(Au-PeEL)EBL31897888(CKB)37465303000041(DE-He213)978-981-97-9539-0(OCoLC)1500771322(EXLCZ)993746530300004120250206d2025 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLocalization Approaches in Strongly Indefinite Problems /by Yanheng Ding, Tian Xu1st ed. 2025.Singapore :Springer Nature Singapore :Imprint: Springer,2025.1 online resource (598 pages)Series in Contemporary Mathematics,2364-0103 ;69789819795383 9819795389 Chapter 1. Variational Problems —– A Brief Retrospective -- Chapter 2. Strongly Indefinite Problems —– Examples and Motivations -- Chapter 3. Localized Energy Estimates for Strongly Indefinite Functionals -- Chapter 4. Semiclassical Standing Waves of Nonlinear Dirac Equations -- Chapter 5. Effect of External Potentials in a Coupled System Reaction-Diffusion -- Chapter 6. The Spinorial Brezis-Nirenberg Problem -- Chapter 7. Isometrically Embedded Sphere with Prescribed Mean Curvature -- Chapter 8. Further Problems with Strongly Indefinite Structures.Several important problems arising in Physics, Differential Geometry and other topics lead to consider semilinear variational equations of strongly indefinite type and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments and non-degenerate structure, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. This book discusses some new abstract methods together with their applications to several localization problems, whose common feature is to involve semilinear partial differential equations with a strongly indefinite structure. This book deals with a variety of partial differential equations, including nonlinear Dirac equation from quantum physics (which is of first order), coupled system of multi-component incongruent diffusion and spinorial Yamabe type equations on spin manifolds. The unified framework in this book covers not only the existence of solutions to these PDEs problems, but also asymptotic behaviors of these solutions. In particular, the results for the nonlinear Dirac equations show several concentration behaviors of semiclassical standing waves under the effect of external potentials and the results for the spinorial Yamabe type equations show the existence of conformal embeddings of the 2-sphere into Euclidean 3-space with prescribed mean curvature. This book will be appealing to a variety of audiences including researchers, postdocs, and advanced graduate students who are interested in strongly indefinite problems.Series in Contemporary Mathematics,2364-0103 ;6Differential equationsGlobal analysis (Mathematics)Manifolds (Mathematics)Mathematical optimizationCalculus of variationsGeometry, DifferentialQuantum theoryDifferential EquationsGlobal Analysis and Analysis on ManifoldsCalculus of Variations and OptimizationDifferential GeometryQuantum PhysicsEquacions diferencialsthubAnàlisi global (Matemàtica)thubOptimització matemàticathubCàlcul de variacionsthubGeometria diferencialthubTeoria quànticathubLlibres electrònicsthubDifferential equations.Global analysis (Mathematics)Manifolds (Mathematics)Mathematical optimization.Calculus of variations.Geometry, Differential.Quantum theory.Differential Equations.Global Analysis and Analysis on Manifolds.Calculus of Variations and Optimization.Differential Geometry.Quantum Physics.Equacions diferencialsAnàlisi global (Matemàtica)Optimització matemàticaCàlcul de variacionsGeometria diferencialTeoria quàntica515.35Ding Yanheng1784409Xu Tian1784410MiAaPQMiAaPQMiAaPQBOOK9910983385903321Localization Approaches in Strongly Indefinite Problems4316032UNINA