LEADER 01541cam0-22003731i-450 001 990005113320403321 005 20250311105925.0 010 $a90-04-04488-4$bVol. 3 035 $a000511332 100 $a19990604g19641976km-y0itay50------ba 101 0 $aeng$agre 102 $aNL 105 $ay-------001yy 200 1 $aEpigraphica 210 $aLeiden$cE. J. Brill$d1964-1976 215 $a3 v.$d20 cm 225 1 $aTextus minores$v31$v41$v47 327 1 $a1.: Texts on the economic history of the greek world / by H. W. Pleket. - 1964$a2.: Texts on the social history of the greek world / by H. W. Pleket. - 1969$a3.: Texts on bankers, banking and credit in the greek world / by R. Bogaert. - 1976 700 1$aPleket,$bHenri Willy$0187090 701 1$aBogaert,$bRaymond$0187149 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990005113320403321 952 $aP2B-100-EPIGR.(1)-1964$bIst.St.Ant.gr.rom. 666$fFLFBC$mBRAU-28956 952 $aP2B-100-EPIGR.(1)-1964 bis$bBibl. 38358$fFLFBC$mBRAU-28960 952 $aOPUSC. 44 (043)$bBibl. 44311$fFLFBC$mBRAU-28959 952 $aP2B-100-EPIGR.(2)-1969 bis$bIst.St.Ant.gr.rom. 667$fFLFBC$mBRAU-28957 952 $aOPUSC. 44 (031)$bIst.St.Ant.gr.rom. 2631$fFLFBC$mBRAU-28958 952 $aOPUSC. 44 (032)$bBibl. 51253$fFLFBC$mBRAU-28961 952 $aP2B-100-EPIGR.(3)-1976 ter$bIst.St.Ant.gr.rom. 4502$fFLFBC$mBRAU-38674 952 $aP2B-100-EPIGR.(3)-1976 quater$bpapir 625$fFLFBC 959 $aFLFBC 996 $aEpigraphica$9534198 997 $aUNINA LEADER 03328nam 22006495 450 001 9911016078703321 005 20250720130223.0 010 $a981-9627-24-9 024 7 $a10.1007/978-981-96-2724-0 035 $a(MiAaPQ)EBC32226719 035 $a(Au-PeEL)EBL32226719 035 $a(CKB)39672119900041 035 $a(DE-He213)978-981-96-2724-0 035 $a(EXLCZ)9939672119900041 100 $a20250720d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aData Science and Applications $eProceedings of ICDSA 2024, Volume 1 /$fedited by Satyasai Jagannath Nanda, Rajendra Prasad Yadav, Amir H. Gandomi, Mukesh Saraswat 205 $a1st ed. 2025. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2025. 215 $a1 online resource (656 pages) 225 1 $aLecture Notes in Networks and Systems,$x2367-3389 ;$v1263 311 08$a981-9627-23-0 327 $aBrain Tumor Classification using Gabor Transform and ANN Classifier -- Leveraging Sentiment Analysis for Enhanced Educational Video Recommendations on YouTube-Easyfy -- V2SL: The speech to sign language translator -- Soft Computing Techniques Approaches in Battery Management System: A Review -- Survey on the Pivotal Role of Artificial Intelligence and Machine Learning in Shaping the Future of 6th Generation (6G) Communications. 330 $aThis book gathers outstanding papers presented at the 5th International Conference on Data Science and Applications (ICDSA 2024), organized by Soft Computing Research Society (SCRS) and Malaviya National Institute of Technology Jaipur, India, from July 17 to 19, 2024. The book is divided into four volumes, and it covers theoretical and empirical developments in various areas of big data analytics, big data technologies, decision tree learning, wireless communication, wireless sensor networking, bioinformatics and systems, artificial neural networks, deep learning, genetic algorithms, data mining, fuzzy logic, optimization algorithms, image processing, computational intelligence in civil engineering, and creative computing. 410 0$aLecture Notes in Networks and Systems,$x2367-3389 ;$v1263 606 $aComputational intelligence 606 $aData mining 606 $aCooperating objects (Computer systems) 606 $aInternet of things 606 $aComputational Intelligence 606 $aData Mining and Knowledge Discovery 606 $aCyber-Physical Systems 606 $aInternet of Things 615 0$aComputational intelligence. 615 0$aData mining. 615 0$aCooperating objects (Computer systems) 615 0$aInternet of things. 615 14$aComputational Intelligence. 615 24$aData Mining and Knowledge Discovery. 615 24$aCyber-Physical Systems. 615 24$aInternet of Things. 676 $a006.3 700 $aNanda$b Satyasai Jagannath$01431767 701 $aYadav$b Rajendra Prasad$01588635 701 $aGandomi$b Amir H$01588636 701 $aSaraswat$b Mukesh$01373695 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911016078703321 996 $aData Science and Applications$93882660 997 $aUNINA LEADER 08634nam 22006615 450 001 9910866583403321 005 20251215143851.0 010 $a9789819735778$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 606 $aEspais vectorials$2thub 606 $aAnālisi funcional$2thub 608 $aLlibres electrōnics$2thub 615 0$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. 615 7$aEspais vectorials 615 7$aAnālisi funcional 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