06674nam 22017655 450 991015474470332120230808192420.01-4008-8243-510.1515/9781400882434(CKB)3710000000631344(SSID)ssj0001651276(PQKBManifestationID)16425629(PQKBTitleCode)TC0001651276(PQKBWorkID)14512364(PQKB)10492814(MiAaPQ)EBC4738723(DE-B1597)467977(OCoLC)979633762(DE-B1597)9781400882434(EXLCZ)99371000000063134420190708d2016 fg engurcnu||||||||txtccrExponential Sums and Differential Equations. (AM-124), Volume 124 /Nicholas M. KatzPrinceton, NJ : Princeton University Press, [2016]©19911 online resource (445 pages) illustrationsAnnals of Mathematics Studies ;305Bibliographic Level Mode of Issuance: Monograph0-691-08599-4 0-691-08598-6 Includes bibliographical references.Frontmatter -- Contents -- Introduction -- CHAPTER 1. Results from Representation Theory -- CHAPTER 2. D.E.'s and D-modules -- CHAPTER 3. The Generalized Hypergeometric Equation -- CHAPTER 4. Detailed Analysis of the Exceptional Cases -- CHAPTER 5. Convolution of D-modules -- CHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics -- CHAPTER 7. The ℓ- adic Theory -- CHAPTER 8. ℓ-adic Hypergeometrics -- CHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics -- CHAPTER 10. ℓ -adic Exceptional Cases -- CHAPTER 11. Reductive Tannakian Categories -- CHAPTER 12. Fourier Universality -- CHAPTER 13. Stratifications and Convolution -- CHAPTER 14. The Fundamental Comparison Theorems -- ReferencesThis book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.Annals of mathematics studies ;no. 124.Exponential sumsDifferential equationsAdjoint representation.Algebraic geometry.Algebraic integer.Algebraically closed field.Automorphism.Base change.Bernard Dwork.Big O notation.Bijection.Calculation.Characteristic polynomial.Codimension.Coefficient.Cohomology.Comparison theorem.Complex manifold.Conjugacy class.Connected component (graph theory).Convolution.Determinant.Diagram (category theory).Differential Galois theory.Differential equation.Dimension (vector space).Dimension.Direct sum.Divisor.Eigenvalues and eigenvectors.Endomorphism.Equation.Euler characteristic.Existential quantification.Exponential sum.Fiber bundle.Field of fractions.Finite field.Formal power series.Fourier transform.Fundamental group.Fundamental representation.Galois extension.Galois group.Gauss sum.Generic point.Group theory.Homomorphism.Hypergeometric function.Identity component.Identity element.Integer.Irreducibility (mathematics).Irreducible representation.Isogeny.Isomorphism class.L-function.Laurent polynomial.Lie algebra.Logarithm.Mathematical induction.Matrix coefficient.Maximal compact subgroup.Maximal torus.Mellin transform.Monic polynomial.Monodromy theorem.Monodromy.Monomial.Natural number.Normal subgroup.P-adic number.Permutation.Polynomial.Prime number.Pullback.Quotient group.Reductive group.Regular singular point.Representation theory.Ring homomorphism.Root of unity.Scientific notation.Set (mathematics).Sheaf (mathematics).Special case.Subcategory.Subgroup.Subring.Subset.Summation.Surjective function.Symmetric group.Tensor product.Theorem.Theory.Three-dimensional space (mathematics).Torsor (algebraic geometry).Trichotomy (mathematics).Unitarian trick.Unitary group.Variable (mathematics).Exponential sums.Differential equations.512/.73Katz Nicholas M., 59374DE-B1597DE-B1597BOOK9910154744703321Exponential Sums and Differential Equations. (AM-124), Volume 1242839523UNINA06740nam 22004815 450 991030027830332120251116195356.03-319-68841-310.1007/978-3-319-68841-1(CKB)4100000002892062(MiAaPQ)EBC5327232(DE-He213)978-3-319-68841-1(PPN)225552965(EXLCZ)99410000000289206220180319d2018 u| 0engurcnu||||||||rdacontentrdamediardacarrierAdvanced Procedures for Pain Management A Step-by-Step Atlas /edited by Sudhir Diwan, Timothy R Deer1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (595 pages) illustrations3-319-68839-1 Includes bibliographical references at the end of each chapters and index.Section I: Advanced Spinal Interventions -- 1. Advanced Spinal Mapping: An Interventional Continuum for Axial, Radicular, and Dorsal Root Ganglion–Related Pain -- 2. MILD: Percutaneous Lumbar Decompression -- 3. Superion: An Indirect Lumbar Decompression -- 4. Minimally Invasive Discectomy: Transforaminal Approach -- 5. Minimally Invasive Percutaneous Endoscopic Discectomy: Transdiscal Approach -- 6. Minimally Invasive Facet Fusion -- 7. Vertebral Augmentation: Vertebroplasty and Kyphoplasty -- Section II: Advanced Neuromodulation -- 8. Neuromodulation: Mechanisms of Action -- 9. Anatomy of Neuromodulatory Targets: Central Nervous System and the Periphery -- 10. Neuromodulation: Optimizing Surgical Outcomes and Risk Reduction -- 11. Extracranial Peripheral Nerve and Peripheral Nerve Field Stimulation for Headache: Trialing -- 12. Extracranial Peripheral Nerve Field and Peripheral Nerve Stimulation for Headache: Permanent Implant -- 13. Intracranial Neuromodulation: Deep Brain Stimulation for Pain -- 14. Spinal Cord Stimulation, Cervical: Trialing -- 15. Spinal Cord Stimulation: Thoracic and Lumbar—Trial -- 16. Spinal Cord Stimulation—Hybrid Lead Array: Epidural and Peripheral Nerve Field Stimulation Trialv -- 17. Hybrid Neuromodulation -- 18. Permanent Percutaneous Spinal Cord Stimulator Implantation: Cervical/Lumbar -- 19. Spinal Cord Stimulation for Chronic Abdominal Pain -- 20. Spinal Cord Stimulation: Pelvic Pain -- 21. Truncal Stimulation Trial and Implant -- 22. Peripheral Nerve Stimulation for the Painful Extremity -- 23. Advanced Neuromodulation Techniques: Dorsal Root Ganglion Stimulation -- 24. High-Frequency Stimulation -- 25. Burst Stimulation: An Innovative Waveform Strategy for Spinal Cord Stimulation -- 26. Novel Waveforms -- 27. Transcutaneous Vagus Nerve Stimulation: Novel Treatment Strategies -- 28. Sacral Stimulation for Pelvic Pain -- 29. Intrathecal Drug Delivery: Pharmacokinetics and Dynamics -- 30. Patient Selection for Drug Delivery System Implantation -- 31. Intrathecal Drug Delivery: Medication Selection -- 32. Intrathecal Drug Delivery: Trialing -- 33. Intrathecal Drug Delivery: Implantation -- 34. Intrathecal Drug Delivery Maintenance: Refill and Programming -- 35. Intrathecal Drug Delivery Maintenance: Catheter Evaluation -- 36. Intrathecal Drug Delivery: Innovation -- Section III: Advanced Regenerative Medicine -- 37. History of Regenerative Medicine -- 38. Platelet-Rich Plasma -- 39. Alpha-2-Macroglobulin: Protease Inhibitor Treatment (PRP Variant) -- 40. Bone Marrow Derived Stem Cells and their Application in Pain Medicine -- 41. Adipose-Derived Stromal Stem Cells -- 42. Intradiscal Biologic Treatments: Allogeneic Stem Cells -- 43. Intradiscal Biologic Treatments: Intra-annular Fibrin Disc Sealant -- 44. Amniotic Tissue -- 45. Platelet-Rich Plasma (PRP): Procedural Techniques for Musculoskeletal Injuries -- 46. Technical Aspects of Regenerative Injection Therapy -- 47. Platelet-Rich Plasma Therapy: An Overview. .Edited by Sudhir Diwan, a former Director of Pain Medicine fellowship program at Ivy League Weill Cornell Medical College, and Timothy R. Deer, an internationally renowned expert in neuromodulation and minimally invasive spinal procedures, this atlas covers advanced procedures that normal residency and fellowship programs may not cover. It consolidates information pain fellows usually amass by traveling throughout the country to various specialized weekend courses. Advanced Procedures for Interventional Pain Management: A Step-by-Step Atlas is for physicians that know the fundamentals of pain medicine and want to push their knowledge further. Through easy-to-digest bullet points, extensive diagrams, hundreds of figures, and expanded legends beneath each illustration, this compendium covers techniques such as fluoroscopic guidance and radiation safety, endoscopic transforaminal discectomy, endoscopic direct-percutaneous discectomy, transforaminal myelogram, percutaneous facet fusion, percutaneous sacroplasty, vertebral augmentations, percutaneous tumor ablation, percutaneous spinal fusion, minimally invasive spinal decompression (MILD), Interspinous Spacer Placement and advanced neuroaugmentation techniques like high frequency stimulation and DRG stimulation. This book also has a dedicated section on Regenerative Medicine with chapters on platelet rich plasma, stem cell therapy, and intradiscal regenerative therapy. Each chapter has a strict chapter format that includes the indications and contraindications for each procedure, a list of equipment and drugs, a step-by-step illustration-focused how-to, a list of possible post-procedural complications, and bullet-pointed clinical pearls and pitfalls. Within each chapter the authors will also cover the variations of each procedure due to different equipment. This book is ideal for pain medicine fellows, spine surgeons, and interventional pain physicians who want access to the best minds and specialized procedures in a single package.Pain medicineNervous systemSurgeryPain Medicinehttps://scigraph.springernature.com/ontologies/product-market-codes/H47003Neurosurgeryhttps://scigraph.springernature.com/ontologies/product-market-codes/H39000Pain medicine.Nervous systemSurgery.Pain Medicine.Neurosurgery.616.0472Diwan Sudhiredthttp://id.loc.gov/vocabulary/relators/edtDeer Timothy R.edthttp://id.loc.gov/vocabulary/relators/edtBOOK9910300278303321Advanced Procedures for Pain Management1742359UNINA