04435nam 2200649 450 991082270620332120220819043419.00-8218-8228-7(CKB)3240000000070072(EBL)3113291(SSID)ssj0000629465(PQKBManifestationID)11394956(PQKBTitleCode)TC0000629465(PQKBWorkID)10731696(PQKB)10679548(MiAaPQ)EBC3113291(RPAM)16741796(PPN)197108792(EXLCZ)99324000000007007220110419h20112011 uy| 0engur|n|---|||||txtccrSymmetries and related topics in differential and difference equations Jairo Charris Seminar 2009, Symmetries of Differential and Difference Equations, Escuela de Matemáticas, Universidad Sergio Arboleda, Bogotá, Colombia /David Blázquez-Sanz, Juan J. Morales-Ruiz, Jesús Rodríguez Lombardero, editorsProvidence, Rhode Island :American Mathematical Society ;[Bogotá, Colombia] :Instituto de Matemáticas y sus Aplicaciones,[2011]©20111 online resource (178 p.)Contemporary mathematics,5490271-4132Description based upon print version of record.0-8218-6872-1 Includes bibliographical references.Contents -- Jairo Charris, The mathematician, The seminar -- Preface -- A reduction method for higher order variational equations of Hamiltonian systems -- A survey on integration of parabolic equations by reducing them to the heat equation -- 1. Introduction -- 2. Reduction by transformation (1.2) -- 3. Applications of Theorem 2.1 -- 4. Reduction by general equivalence transformation -- References -- Weil jets, Lie correspondences and applications -- Introduction -- 1. Jets of submanifolds -- 2. Lie correspondences between jet spaces -- 3. Prolongations and correspondences. -- 4. Characteristics, singular vector fields and correspondences -- 5. Symmetries and Lie correspondences -- 6. Projections, transversality and the process of reduction by symmetries -- Acknowledgments -- References -- Some applications of summability: An illustrated survey -- The structure of time and inertial forces in Lagrangian mechanics -- Introduction -- 0. Notations and definitions -- 1. Structure of a second order differential equation relative to a metric -- 2. Newton-Lagrange mechanics of a free system -- 3. Constrained systems -- 4. The class of time and the calculus of variations -- 5. Time constraints -- 6. Modification caused by a time constraint in a free system -- 7. Linear constraints depending on time -- 8. Reference frames and inertial forces -- Acknowledgements. -- References -- Differential invariant algebras -- 1. Introduction. -- 2. Moving Frames and Differential Invariants. -- 3. Equivariant Moving Frames. -- 4. Recurrence. -- 5. Generating Invariants. -- 6. Differential Invariant Algebras of Pseudo-Groups. -- References -- The Stokes phenomenon for linear q-difference equations -- 1. Introduction -- 2. Some background -- 3. Some examples around the q-Euler equation -- References -- Finite Hamiltonian systems on phase space.Contemporary mathematics,5490271-4132Symmetry (Mathematics)CongressesDifference equationsCongressesDifferential-algebraic equationsCongressesSymmetry (Mathematics)Difference equationsDifferential-algebraic equations515/.3535A3034M1517B4535C0570A0537J0522F0535A3053A0439A13mscCharris Castañeda Jairo A.Blázquez-Sanz David1980-Morales Ruiz Juan J(Juan José),1953-Lombardero Jesús Rodríguez1961-American Mathematical Society,Universidad Sergio Arboleda.Instituto de Matemáticas y sus Aplicaciones,Jairo Charris SeminarMiAaPQMiAaPQMiAaPQBOOK9910822706203321Symmetries and related topics in differential and difference equations760869UNINA04938nam 22006615 450 991043326030332120251113190603.03-030-64743-910.1007/978-3-030-64743-8(CKB)4100000011728400(DE-He213)978-3-030-64743-8(MiAaPQ)EBC6460926(PPN)253252822(MiAaPQ)EBC29092680(EXLCZ)99410000001172840020210120d2020 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrier21st Century Challenges in Chemical Crystallography I History and Technical Developments /edited by D. Michael P. Mingos, Paul R. Raithby1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (IX, 278 p. 69 illus., 46 illus. in color.)Structure and Bonding,1616-8550 ;185Includes index.3-030-64742-0 The Early History of X-ray Crystallography -- Recent developments in refinement and analysis of X-ray crystal structures -- Leading edge chemical crystallography service provision and its impact on crystallographic data science in the 21st century -- Crystallographic analysis of crystals under high pressure conditions -- Watching Photochemistry Happen: Recent Developments in Dynamic Single-crystal X-ray Diffraction Studies -- Time Resolved Single Crystal X-ray Crystallography. .This volume summarises recent developments and possible future directions for small molecule X-ray crystallography. It reviews specific areas of crystallography which are rapidly developing and places them in a historical context. The interdisciplinary nature of the technique is emphasised throughout. It introduces and describes the chemical crystallographic and synchrotron facilities which have been at the cutting edge of the subject in recent decades. The introduction of new computer-based algorithms has proved to be very influential and stimulated and accelerated the growth of new areas of science. The challenges which will arise from the acquisition of ever larger databases are considered and the potential impact of artificial intelligence techniques stressed. Recent advances in the refinement and analysis of X-ray crystal structures are highlighted. In addition the recent developments in time resolved single crystal X-ray crystallography are discussed. Recent years have demonstrated how this technique has provided important mechanistic information on solid-state reactions and complements information from traditional spectroscopic measurements. The volume highlights how the prospect of being able to routinely “watch” chemical processes as they occur provides an exciting possibility for the future. Recent advances in X-ray sources and detectors that have also contributed to the possibility of dynamic single-crystal X-ray diffraction methods are presented. The coupling of crystallography and quantum chemical calculations provides detailed information about electron distributions in crystals and has resulted in a more detailed understanding of chemical bonding. The volume will be of interest to chemists and crystallographers with an interest in the synthesis, characterisation and physical and catalytic properties of solid-state materials. Postgraduate students entering the field will benefit from a historicalintroduction to the subject and a description of those techniques which are currently used. Since X-ray crystallography is used so widely in modern chemistry it will serve to alert senior chemists to those developments which will become routine in coming decades. It will also be of interest to the broad community of computational chemists who study chemical systems.Structure and Bonding,1616-8550 ;185Analytical chemistryCrystallographyChemistry, Physical and theoreticalChemistry, OrganicAnalytical ChemistryCrystallography and Scattering MethodsTheoretical ChemistryOrganic ChemistryAnalytical chemistry.Crystallography.Chemistry, Physical and theoretical.Chemistry, Organic.Analytical Chemistry.Crystallography and Scattering Methods.Theoretical Chemistry.Organic Chemistry.016.54532548.3Mingos D. M. P.1944-Raithby P. R(Paul R.),MiAaPQMiAaPQMiAaPQBOOK991043326030332121st century challenges in chemical crystallography. I2537921UNINA