LEADER 00910nam0-2200325---450- 001 990009638750403321 005 20121026091753.0 010 $a978-1-4516-5447-9 035 $a000963875 035 $aFED01000963875 035 $a(Aleph)000963875FED01 035 $a000963875 100 $a20121024d2012----km-y0itay50------ba 101 0 $aeng 102 $aUS 105 $aa-------001yb 200 1 $aMao$ethe real story$fAlexander V. Pantsov$gwith Steven I. Levine 210 $aNew York$cSimon & Schuster$d2012 215 $axix, 755 p.$cill.$d24 cm 610 0 $aMao, Tse Tung$aBiografia 676 $a951.05092$v22$zita 700 1$aPantsov,$bAlexander V.$0517998 701 1$aLevine,$bSteven I.$0517999 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a990009638750403321 952 $aXIII A 450$b49810$fFSPBC 959 $aFSPBC 996 $aMao$9848305 997 $aUNINA LEADER 00924nam0 22002531i 450 001 UON00398482 005 20231205104645.812 100 $a20111017d1990 |0itac50 ba 101 $aita 102 $aIT 105 $a|||| 1|||| 200 1 $aMedioevo Orientale Europeo$fEnrico Morini 210 $aBologna$cLo Scarabeo Edizioni Scientifiche$d1990 215 $a262 p.$d24 cm. 606 $aCRISTIANESIMO ORIENTALE$3UONC020175$2FI 620 $aIT$dBologna$3UONL000085 700 1$aMORINI$bEnrico$3UONV204648$0459114 712 $aLo Scarabeo$3UONV254597$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00398482 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI BIZANTINO C 0207 $eSI EO 47434 5 0207 996 $aMedioevo orientale europeo$9724110 997 $aUNIOR LEADER 08441nam 22006015 450 001 9910866583403321 005 20240813124825.0 010 $a9789819735778$b(electronic bk.) 010 $z9789819735761 024 7 $a10.1007/978-981-97-3577-8 035 $a(MiAaPQ)EBC31503994 035 $a(Au-PeEL)EBL31503994 035 $a(CKB)32569124700041 035 $a(DE-He213)978-981-97-3577-8 035 $a(EXLCZ)9932569124700041 100 $a20240625d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGuaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems /$fby Xuefeng Liu 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (139 pages) 225 1 $aSpringerBriefs in Mathematics,$x2191-8201 311 08$aPrint version: Liu, Xuefeng Guaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems Singapore : Springer,c2024 9789819735761 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- 1 Introduction to Eigenvalue Problems -- 1.1 Overview of Research on Rigorous Eigenvalue Bounds -- 1.2 Model Eigenvalue Problems -- 1.3 Sobolev Space Settings and Weak Formulation of Eigenvalue Problem -- 1.4 Min-Max Principle and Upper Eigenvalue Bounds -- 1.5 Finite Element Method -- 1.5.1 Mesh for Numerical Examples -- 1.5.2 Approximate Eigenvalue Evaluation -- 2 Explicit Error Estimation for Boundary Value Problems -- 2.1 Poisson's Equation and Its FE Solution -- 2.1.1 Poisson's Equation -- 2.1.2 Finite Element Solution -- 2.2 Interpolation Error Estimation and Several Constants -- 2.2.1 Interpolation Function and Error Estimation -- 2.2.2 Constants in the Trace Theorem -- 2.3 A Priori Error Estimate for Solutions with H2-Regularity -- 2.4 Error Estimate for Solutions Without H2-Regularity -- 2.4.1 Space Settings and Hypercircle in the Prager-Synge Theorem -- 2.4.2 A Posteriori Error Estimation -- 2.4.3 A Priori Error Estimation -- 2.4.4 Numerical Examples -- 2.4.4.1 Square Domain -- 2.4.4.2 L-Shaped Domain -- 2.5 Poisson's Equation with General Settings -- 2.5.1 General Hypercircle Involving c(x) -- 2.5.2 A Priori Error Estimation -- 2.5.3 Computation of ?h and Its Upper Bound -- 2.5.4 Numerical Computation -- 2.6 Error Estimation for Stokes Equations -- 2.6.1 Problem Settings -- 2.6.2 Finite Element Spaces -- 2.6.2.1 Construction of Vh -- 2.6.2.2 Projection Operators -- 2.6.3 Explicit Error Estimation for FE Solutions -- 2.6.3.1 A Posteriori Error Estimation -- 2.6.3.2 A Priori Error Estimation -- 2.6.3.3 Computation of ?h -- 2.6.4 Numerical Computation Results -- 2.6.4.1 A Priori Error Estimation over 3D Domains -- 3 Fundamental Theorem for Explicit Eigenvalue Bounds -- 3.1 Eigenvalue Problem with Positive Definite a(·, ·) -- 3.1.1 Explicit Eigenvalue Bounds. 327 $a3.2 Eigenvalue Problems with Positive Semi-definite a(·,·) -- 3.2.1 Problem Setting and Explicit Eigenvalue Bounds -- 3.3 Evaluation of the Constant in Projection Error Estimation -- 4 Explicit Eigenvalue Bounds for Various Differential Operators -- 4.1 Preparation: Non-conforming FEMs -- 4.1.1 Crouzeix-Raviart FEM -- 4.1.1.1 Interpolation Operator ?hCR -- 4.1.1.2 Interpolation Error Constant CCR(K) -- 4.1.2 Enriched Crouzeix-Raviart FEM -- 4.1.3 Composite Enriched Crouzeix-Raviart FEM -- 4.1.4 Fujino-Morley FEM -- 4.2 Laplacian Eigenvalue Problems -- 4.2.1 Case of c=0 (-?u = ?u) -- 4.2.2 Case of c> -- 0 (-?u + cu = ?u) -- 4.3 Stokes Eigenvalue Problems -- 4.3.1 Weak Formulation of the Stokes Eigenvalue Problem -- 4.3.2 Lower Bounds Using Non-conforming FEMs -- 4.3.3 Lower and Upper Bounds Using Conforming FEMs -- 4.3.4 Numerical Results -- 4.4 Steklov Eigenvalue Problems -- 4.4.1 Lower Bound Using Conforming FEMs -- 4.4.2 Lower Bound Using Non-conforming FEMs -- 4.4.3 Computation Results -- 4.5 Biharmonic Eigenvalue Problems -- 4.5.1 Lower Bounds Using Fujino-Morley FEMs -- 4.5.2 Computation Examples -- 5 Lehmann-Goerisch Method for High-Precision Eigenvalue Bounds -- 5.1 Lehmann-Goerisch Method -- 5.2 Application of the Lehmann-Goerisch Method -- 5.2.1 Dirichlet Eigenvalue Problems -- 5.2.2 Steklov Eigenvalue Problems -- 5.3 Computational Results and Applications -- 5.3.1 Eigenvalue Bounds for Dirichlet Eigenvalues -- 5.3.2 Eigenvalue Bounds for Steklov Eigenvalues -- 6 Guaranteed Eigenfunction Computation -- 6.1 Preliminaries -- 6.1.1 Distance Between Subspaces -- 6.1.2 Eigenspaces for Operators -- 6.2 Algorithm I: Rayleigh Quotient-Based Error Estimation -- 6.3 Algorithm II: Residual-Based Estimation -- 6.3.1 Extension of the Davis-Kahan sin? Theorem to Weakly Formulated Problems -- 6.3.2 Weakly Formulated Residual Error Estimation. 327 $a6.3.3 Direct Estimate of ?a: Another Application of the Davis-Kahan Theorem -- 6.4 Algorithm III: Galerkin Projection-Based Estimation -- 6.4.1 A Priori Error Estimation for FE Solutions of Boundary Value Problems -- 6.4.2 Galerkin Projection-Based Estimate in L2 Norm -- 6.5 Numerical Examples -- 6.5.1 Unit Square Domain -- 6.5.2 L-Shaped Domain -- A Introduction to VFEM Library -- References. 330 $aThis monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential operators. It focuses on deriving explicit lower and upper bounds for eigenvalues, as well as explicit estimations for eigenfunction approximations. Such explicit error estimations rely on the finite element method (FEM) along with a new theory of explicit quantitative error estimation, diverging from traditional studies that primarily focus on qualitative results. To achieve quantitative error estimation, the monograph begins with an extensive analysis of the hypercircle method, that is, the Prager?Synge theorem. It introduces a novel a priori error estimation technique based on the hypercircle method. This facilitates the explicit estimation of Galerkin projection errors for equations such as Poisson's and Stokes', which are crucial for obtaining lower eigenvalue bounds via conforming FEMs. A thorough exploration of the fundamental theory of projection-based explicit lower eigenvalue bounds under a general setting of eigenvalue problems is also offered. This theory is extensively detailed when applied to model eigenvalue problems associated with the Laplace, biharmonic, Stokes, and Steklov differential operators, which are solved by either conforming or non-conforming FEMs. Moreover, there is a detailed discussion on the Lehmann?Goerisch theorem for the purpose of high-precision eigenvalue bounds, showing its relationship with previously established theorems, such as Lehmann?Maehly's method and Kato's bound. The implementation details of this theorem with FEMs, a topic rarely covered in existing literature, are also clarified. Lastly, the monograph introduces three new algorithms to estimate eigenfunction approximation errors, revealing the potency of classical theorems. Algorithm I extends Birkhoff?s result that works for simple eigenvalues to handle clustered eigenvalues, while Algorithm II generalizes the Davis?Kahan theorem, initially designed for strongly formulated eigenvalue problems, to address weakly formulated eigenvalue problems. Algorithm III utilizes the explicit Galerkin projection error estimation to efficiently handle Galerkin projection-based approximations. 410 0$aSpringerBriefs in Mathematics,$x2191-8201 606 $aMathematical analysis 606 $aFunctional analysis 606 $aMathematics$xData processing 606 $aAnalysis 606 $aFunctional Analysis 606 $aComputational Mathematics and Numerical Analysis 615 0$aMathematical analysis. 615 0$aFunctional analysis. 615 0$aMathematics$xData processing. 615 14$aAnalysis. 615 24$aFunctional Analysis. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a512.9436 700 $aLiu$b Xuefeng$f1961-$01771398 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910866583403321 996 $aGuaranteed Computational Methods for Self-Adjoint Differential Eigenvalue Problems$94259490 997 $aUNINA LEADER 04123nam 22005895 450 001 9910731487103321 005 20251008163431.0 010 $a981-9921-50-3 024 7 $a10.1007/978-981-99-2150-8 035 $a(CKB)26946515200041 035 $a(MiAaPQ)EBC30593531 035 $a(Au-PeEL)EBL30593531 035 $a(DE-He213)978-981-99-2150-8 035 $a(PPN)272267058 035 $a(EXLCZ)9926946515200041 100 $a20230613d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTransportation Energy and Dynamics /$fedited by Sunil Kumar Sharma, Ram Krishna Upadhyay, Vikram Kumar, Hardikk Valera 205 $a1st ed. 2023. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2023. 215 $a1 online resource (516 pages) 225 1 $aEnergy, Environment, and Sustainability,$x2522-8374 311 08$a9789819921492 327 $aSustainable Rail Fuel Production from Biomass -- Thermochemical conversion of biomass wastes for biofuel production -- Vibrational Effect on Tribology -- Battery and Fuel Cell Trains: a critical review of activities performed at Florence University -- Automatic speed control of heavy-haulers trains -- A study on the Strength analysis of interior plate for rolling type gangway of urban railroad vehicle -- Safety policies and concerns for transportation of hazardous chemicals by Railway -- Repositioning The Nigerian Rail System For Global Competitiveness: Tackling The Noisome Peculiarities -- Mobile Aerial Ropeways Based On an Autonomous Self-Propelled Chassis: Design and Operation -- Linear Motors for High Speed Rail Transit System : A Sustainable Approach -- Approach to assist in the discovery of railway accident scenarios based on supervised learning -- Futuristic Trends in Automobile Exhaust Mufflers -- Heavy Metals Contaminants Threat to Environment: it's possible treatment -- Operational Greenhouse Gas Emissions of Air, Rail, Road, and Sea Transport Modes in Life Cycle Perspective -- Predicting the Effect on Land Values after Introducing High Speed Rail -- Deploying Machine Learning Models for Predictive Maintenance of high-value assets of Indian Railways -- Combining ITS and Optimization in Public Transit Planning -- Regenerative Braking in Indian Locomotives. 330 $aThis book provides a macro-level understanding of transportation as an industry, through the lens of all the stakeholders that make up the ecosystem. It aids understanding about the transportation ecosystem, its components, challenges, contribution to economic growth, and the interplay between the stakeholders that govern the system. The contents also examine the background and history of transportation, emphasizing the fundamental role and importance the industry plays in companies, society, and the environment in which transportation service is provided. The book also provides an overview of carrier operations, management, technology, and the strategic principles for the successful management of different modes of transportation. This book is of interest to those working in academia, industry, and policy in the areas of transportation. . 410 0$aEnergy, Environment, and Sustainability,$x2522-8374 606 $aTransportation engineering 606 $aTraffic engineering 606 $aSustainability 606 $aTransportation Technology and Traffic Engineering 606 $aSustainability 615 0$aTransportation engineering. 615 0$aTraffic engineering. 615 0$aSustainability. 615 14$aTransportation Technology and Traffic Engineering. 615 24$aSustainability. 676 $a388 700 $aSharma$b Sunil Kumar$01355124 701 $aUpadhyay$b Ram Krishna$01355123 701 $aKumar$b Vikram$01355125 701 $aValera$b Hardikk$01355126 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910731487103321 996 $aTransportation Energy and Dynamics$93394547 997 $aUNINA