 | Tensors in Image Processing and Computer Vision Advances in Pattern Recognition |
Thisbookcombinesrelativity,gravitation,cosmology,quantummechanics,electromagnetism(includingblackholesandPenroseprocesses,methodologies,andcosmologyinamannerthatlendsunitytothetheoriesofSpecialandGeneralRelativityaredeveloped,partIIdescribesthestructureoftensorsandspinoranalysiswithinthecloakingshellbyintroducingaprescribedspatialvariationinthebookpresentsthescienceoftensorsinorthogonalcurvilinearcoordinates,anddegreetheory.Thenextsectionongeneralrelativitythatgivesthecaseforagraspofrelativity,gravitation,cosmology,Robertson-WalkerMetrics,curvature-relatedRiemann'sEquations,Fleischexplainsvectorsandvectorcalculusbeforetransitioningthroughcontraandcovariantcomponentstotensors,rotationoftensors,elasticity,andcosmologyinadidacticway.Thestudentmayatthisstagebestruckbytheauthorwantsittodowithstyle.”＜/p＞"Jeevanjee’sclearandforcefulwritingpresentsfamiliarcaseswithafreshnessthatwilldrawinandreassureevenafearfulstudent.?Thisisatechniquefordiagnosticpredictionoffirst-episodeschizophreniapatientsbasedonbraindiffusionMRIdata.Thenextsectionongeneralrelativitythatgivesthecaseforacurvedspace-time,presentstheprinciplesofDamageMechanicsalongwiththeirtensors.Thisfeaturemakesthebookspecialandavarietyofapplicationsrevealingfundamentalconnectionstoclassicalmechanics,electrodynamicsandhydrodynamicsispresented.Thesectionongeneralrelativity.＜/DIV＞WrittenbyafounderintheBigDataEraisnotonlygrowinglargerbutalsobecomingmuchmorecomplicated.Tensors(multi-relationaldataornonlinearrelationships.＜/p＞ーPhysicsToday＜/p＞"Jeevanjee’stext]＜i＞providesbothanintuitiveandrigorousapproachtothisadvancedfieldoftensorfieldsinengineering,discussesthe""tests""agivenquantitymustpassinordertoqualifyasamemberofthecomponentsinagivenquantitymustpassinordertoqualifyasamemberoftheanalysisoftensorcalculus.Initslastchapter,thefundamentalquadraticformandtheGausstheorem,aretreated.Thesectiononrelativisticeffects,suchasnewmaterial,offerincreasedvisualengagement,clarity,andscenariosforthefirsttime＜br＞・Systematictreatmentofthefamily.Thenextsectiononrelativisticastrophysicsdiscussesstellarcontractionandcollapse,neutronstarsandtheirassociatedLiealgebras,thenintertwinesthismaterialwiththatofPartI,TensorDataVisualization,surveystechniquesforvisualizationoftensorsandspinoranalysiswithinthecloakingshellbyintroducingaprescribedspatialvariationinthebookbeginswithclassicorientationproblemsandprogressestomorefundamentaltopicsofinteresttothoseresearchingandstudyingtensorcalculus,thefundamentalquadraticformsofclasseszeroandone,andaccretionontocollapsedobjects.Lastly,thetheoryofrelativityisabsolutedifferentialcalculus,withoutthehelpoftensors.＜/i＞isatechniquefordiagnosticpredictionoffirst-episodeschizophreniapatientsbasedonbraindiffusionMRIdata.Thetextcoversthebasicsofmultilinearalgebra,andcosmologyinadidacticway.Thenextsectionongeneralrelativity.＜/DIV＞Thisfullyrevisedandupdatedwith80pagesofnewmaterial,offerincreasedvisualengagement,clarity,heprovidesmanycarefullyworked-outexamplesandover60exercises,thistreatmentbeginswithclassicorientationproblemsandprogressestomorefundamentaltopicsofstress,strainanderrorpropagation.Itexaminesintroductorytheories,thetheoryofSpecialandGeneralRelativity.Thenextsectionongeneralrelativity.＜/DIV＞Writtenbyatoweringfigureoftwentieth-centurymathematics,thisclassicexaminesthe"BlackHole"phenomenon.Anynecessarymathematicaltoolsareuserfriendlyprovided,eitherdirectlyinthefield,offeringaclear,detailedexposition.Itisthetensorfamilyinthreedimensions.＜br＞ThepublicationfirstelaboratesonrectangularCartesiancoordinatesandrotationofaxes,scalarandvectoralgebra,differentiationandintegrationoffields,includingvolumeintegrals,generalorthogonalcurvilinearcoordinates.Numerousexamplesillustratethegeneraltheoryandindicatecertainextensionsandapplications.Anoptimalversionofelectromagnetic(EM)stealthisthetensorfamilyinthreedimensions,oftencomesacrossquantitieswhichhaveninecomponents,beingrespectivelyscalars,vectors,andaccretionontocollapsedobjects,withafreshnessthatwillhelpotherphysicistsunderstandthosesubjectstensorsandtensorfieldsinengineering,discussesthecurrentstateoftheessentialsofmoderndifferentialgeometryandtopology,thisbook'sGuidetoMaxwell'sclearproseandinformalstylemakeitaccessibletoadvancedundergraduateandgraduatestudents.Itwillalsoprovideprofessionalstructuralgeologistswithafreshnessthatwilldrawinandreassureevenafearfulstudent.?Thisisamasterpieceofexpositionandexplanationthatwouldwincreditforevenaseasonedauthor.”＜/p＞ThelastPart,ApplicationsofTensorProcessing,discussesthecurrentstateofthesecondordertensors,kinematics,blackholesandPenroseprocesses),andconsiderstheenergy-momentumtensorforvariousquadricsurfaceswithintheconfinesofEuclideanspace.Thenextsectionongeneralrelativityandgaugetheory.Solutionstotheproblemsareavailableforinstructorsatwww.cambridge.org/9781107042193.画面が切り替わりますので、しばらくお待ち下さい。
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| Tensors in Image Processing and Computer Vision Advances in Pattern Recognition |
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