04283oam 2200517 450 99641819870331620210505211948.03-030-55849-510.1007/978-3-030-55849-9(CKB)4100000011610338(MiAaPQ)EBC6404813(DE-He213)978-3-030-55849-9(PPN)252507150(EXLCZ)99410000001161033820210505d2020 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierThe generalized Fourier series method bending of elastic plates /Christian Constanda, Dale Doty1st ed. 2020.Cham, Switzerland :Springer,[2020]©20201 online resource (XIII, 254 p. 186 illus., 37 illus. in color.) Developments in Mathematics ;Volume 653-030-55848-7 1. The Mathematical Model -- 2. Generalized Fourier Series -- 3. Interior Dirichlet Problem -- 4. Interior Neumann Problem -- 5. Interior Robin Problem -- 6. Exterior Dirichlet Problem -- 7. Exterior Neumann Problem -- 8. Exterior Robin Problem -- A. Numerical Issues -- B. Numerical Integration -- C. Interior Boundary Value Problem for D[x,y] -- D. Exterior Boundary Value Problems for D^A[X,y] -- E. Numerical Integration of P[x,y] and P^A[x,y] -- References -- Index.This book explains in detail the generalized Fourier series technique for the approximate solution of a mathematical model governed by a linear elliptic partial differential equation or system with constant coefficients. The power, sophistication, and adaptability of the method are illustrated in application to the theory of plates with transverse shear deformation, chosen because of its complexity and special features. In a clear and accessible style, the authors show how the building blocks of the method are developed, and comment on the advantages of this procedure over other numerical approaches. An extensive discussion of the computational algorithms is presented, which encompasses their structure, operation, and accuracy in relation to several appropriately selected examples of classical boundary value problems in both finite and infinite domains. The systematic description of the technique, complemented by explanations of the use of the underlying software, will help the readers create their own codes to find approximate solutions to other similar models. The work is aimed at a diverse readership, including advanced undergraduates, graduate students, general scientific researchers, and engineers. The book strikes a good balance between the theoretical results and the use of appropriate numerical applications. The first chapter gives a detailed presentation of the differential equations of the mathematical model, and of the associated boundary value problems with Dirichlet, Neumann, and Robin conditions. The second chapter presents the fundamentals of generalized Fourier series, and some appropriate techniques for orthonormalizing a complete set of functions in a Hilbert space. Each of the remaining six chapters deals with one of the combinations of domain-type (interior or exterior) and nature of the prescribed conditions on the boundary. The appendices are designed to give insight into some of the computational issues that arise from the use of the numerical methods described in the book. Readers may also want to reference the authors’ other books Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3 and Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.Developments in mathematics ;Volume 65.Fourier seriesMechanicsMathematical analysisFourier series.Mechanics.Mathematical analysis.515.2433Constanda Christian57207Doty DaleCaPaEBRCaPaEBRUtOrBLWBOOK996418198703316The generalized Fourier series method2018982UNISA03680nam 22006975 450 991079921490332120240103163724.09783031475603303147560710.1007/978-3-031-47560-3(CKB)29526975300041(MiAaPQ)EBC31071243(Au-PeEL)EBL31071243(DE-He213)978-3-031-47560-3(OCoLC)1416877148(EXLCZ)992952697530004120240103d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierSynthetic Data Revolutionizing the Industrial Metaverse /by Jimmy Nassif, Joe Tekli, Marc Kamradt1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (186 pages)9783031475597 3031475593 Ch. 1. Welcome to the Age of Industrial Data -- Ch. 2. Industrial Evolution toward the Age of Imagination -- Ch. 3. Background and Technologies -- Ch. 4. How Visual Data is Revolutionizing the Industry World -- Ch. 5. Digital Images – the Bread and Butter of Computer Vision -- Ch. 6. Creating SORDI: the Largest Synthetic Dataset for Industries -- Ch. 7. Towards an Industrial Robot Gym -- Ch. 8. What is Next with SORDI.The book concentrates on the impact of digitalization and digital transformation technologies on the Industry 4.0 and smart factories, how the factory of tomorrow can be designed, built, and run virtually as a digital twin likeness of its real-world counterpart, before the physical structure is actually erected. It highlights the main digitalization technologies that have stimulated the Industry 4.0, how these technologies work and integrate with each other, and how they are shaping the industry of the future. It examines how multimedia data and digital images in particular are being leveraged to create fully virtualized worlds in the form of digital twin factories and fully virtualized industrial assets. It uses BMW Group’s latest SORDI dataset (Synthetic Object Recognition Dataset for Industry), i.e., the largest industrial images dataset to-date and its applications at BMW Group and Idealworks, as one of the main explanatory scenarios throughout the book. It discusses the need of synthetic data to train advanced deep learning computer vision models, and how such datasets will help create the “robot gym” of the future: training robots on synthetic images to prepare them to function in the real world.Artificial intelligenceInternet of thingsMultimedia systemsBig dataComputer networksArtificial IntelligenceInternet of ThingsMultimedia Information SystemsBig DataComputer Communication NetworksArtificial intelligence.Internet of things.Multimedia systems.Big data.Computer networks.Artificial Intelligence.Internet of Things.Multimedia Information Systems.Big Data.Computer Communication Networks.006.3Nassif Jimmy1586272Tekli Joe1586273Kamradt Marc1586274MiAaPQMiAaPQMiAaPQBOOK9910799214903321Synthetic Data3872621UNINA