Format: Hardback, 227 pages, height x width: 235x155 mm, 47 Illustrations, color;
45 Illustrations, black and white; XVII, 227 p. 92 illus., 47 illus. in color., 1 Hardback
Series: PNLDE Subseries in Control 99
Pub. Date: 02-Apr-2022
ISBN-13: 9783030930141
Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
Introduction.- Boundary Control.- Decentralized Control.- Distributed Control.- Lagrangian Control.- Hamilton-Jacobi Equations.- Appendix A: Balance Laws with Boundary.- Conservation Laws on Networks.
Format: Hardback, 229 pages, height x width: 235x155 mm, weight: 580 g,
10 Illustrations, black and white; XI, 229 p. 10 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 369
Pub. Date: 25-Jan-2022
ISBN-13: 9789811641725
Gaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91.
Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solution. His arguments on the conjecture and proof theory in general have had great influence on the later developments of mathematical logic, philosophy of mathematics, and applications of mathematical logic to theoretical computer science.
Takeuti's work ranged over the whole spectrum of mathematical logic, including set theory, computability theory, Boolean valued analysis, fuzzy logic, bounded arithmetic, and theoretical computer science. He wrote many monographs and textbooks both in English and in Japanese, and his monumental monograph Proof Theory, published in 1975, has long been a standard reference of proof theory. He had a wide range of interests covering virtually all areas of mathematics and extending to physics. His publications include many Japanese books for students and general readers about mathematical logic, mathematics in general, and connections between mathematics and physics, as well as many essays for Japanese science magazines.
This volume is a collection of papers based on the Symposium on Advances in Mathematical Logic 2018. The symposium was held September 18?20, 2018, at Kobe University, Japan, and was dedicated to the memory of Professor Gaisi Takeuti.
S. Fuchino and A. Ottenbreit Ottenbreit Maschio Rodrigues, Reflection principles, generic large cardinals, and the Continuum Problem.- D. Ikegami and N. Trang, On supercompactness of 1.- S. Iwata, Interpolation properties for Sacchetti's logics.- T. Kurahashi, Rosser provability and the second incompleteness theorem.- H. Kurokawa, On Takeuti's early view of the concept of set.- Yo Matsubara and T. Usuba, On Countable Stationary Towers.- M. Ozawa, Reforming Takeuti's Quantum Set Theory to Satisfy De Morgan's Laws.- T. Usuba, Choiceless Lowenheim-Skolem property and uniform definability of grounds.- M. Yasugi, Y. Tsujii, T. Mori, Irrational-based computability of functions.- M. Yasugi, "Gaisi Takeuti's finitist standpoint" and its mathematical embodiment.- Y. Yoshinobu, Properness under closed forcing.
Format: Hardback, 200 pages, height x width: 235x155 mm,
5 Tables, color; 5 Illustrations, color; X, 200 p. 5 illus. in color.
Series: Mathematical Physics Studies
Pub. Date: 28-Apr-2022
ISBN-13: 9783030949983
This book is based on the analysis of canonical commutation relations (CCRs) and their possible deformations. In light of the recent interest on PT-quantum mechanics, the author presents a special deformed version of the CCRs, and discusses the consequences of this deformation both from a mathematical side, and for its possible applications to physics. These include the analysis of several non self-adjoint Hamiltonians, a novel view to the position and momentum operators, and a general approach to compute path integrals and transition probabilities using the so-called bi-coherent states. The book is meant for researchers and is also suited for advanced students. It can be used as a gentle introduction to some delicate aspects in functional analysis and in quantum mechanics for non self-adjoint observables.
Introduction.- Bosons and Pseudo-Bosons.- Other Ladder Operators.- Our Way to the BCH Formula.- Bi-coherent States.- Examples of Bi-coherent States.- Weak Pseudo-Bosons and Related Bi-coherent States.- An Application to Transition Probability.- Conclusions.- Appendix.
Format: Hardback, 434 pages, height x width: 235x155 mm, 103 Illustrations, color;
11 Illustrations, black and white; XXII, 434 p. 114 illus., 103 illus. in color., 1 Hardback
Pub. Date: 03-May-2022
ISBN-13: 9783030951566
This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications
Part I: Linear Dynamical Systems: B. Joseph, The rational interpolation problem: Grassmannian and Loewner-matrix approaches.- B. Jean-Paul, The conditioning of a linear barycentric rational interpolant.- D. Zlatko, Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation.- E. Mark, Pseudospectra of Loewner Matrix Pencils.- R. Paolo, A Loewner matrix approach to the identification of linear time-varying systems.- V. D. Paul, Linear System Matrices of Rational Transfer Functions.- Part II: Nonlinear Dynamical Systems: C. Xingang, Interpolation-based Model Order Reduction for Quadratic-Bilinear Systems and H2 Optimal Approximation.- C. Sridhar, An Adaptive Sampling Approach for the reduced basis method.- K. Boris, Balanced Truncation Model Reduction for Lifted Nonlinear Systems.- L. Sanda, Modeling the buck converter from measurements of its Harmonic Transfer Function.- P. Mihaly, Model reduction and realization theory of linear switched systems.- Part III: Structured Dynamical Systems: F. F. Damasceno, Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros.- M. Volker, Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems.- P. D. Igor, Data-Driven Identification of Rayleigh-Damped Second-Order Systems.- S. Tatjana, Balanced truncation model reduction for 3D linear magneto-quasistatic field problems.- Van der S. Arjan, Structure-preserving model reduction of physical network systems.- Part IV: Model Reduction for Control: B. Tobias, H2-gap model reduction for stabilizable and detactable systems.- H. Matthias, Reduced Order Model Hessian Approximations in Newton Methods for Optimal Control.- P.-V. Charles, Interpolation-based irrational model control design and stabilty analysis.- Part V: Applications: D. Clifford, Oscillations in Biology: G. Eduardo, Model-Order Reduction for Coupled Flow and Linear Thermal-Poroplasticity with Applications to Unconventional Reservoirs.- I. Roxana, Challenges in model reduction for real-time simulation of traction chain systems.- N. Masaaki, Sparse Representation for Sampled-data Hinf Filter.- S. Eduardo, Analysis of a reduced model of epithelial-mesenchymal fate determination in cancer metastasis as a singularly-perturbed monotone system
Format: Paperback / softback, 324 pages, height x width: 235x155 mm, XVIII, 324 p
Series: Lecture Notes in Mathematics 2300
Pub. Date: 29-Mar-2022
ISBN-13: 9783030944995
This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis?Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi?Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.</div><div><br></div><div>The theory of periodic monopoles of GCK type has applications to Yang?Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.</div><div><br></div><div>This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.
Introduction.- Preliminaries.- Formal difference modules and good parabolic structure.- Filtered bundles.- Basic examples of monopoles around infinity.- Asymptotic behaviour of periodic monopoles around infinity.- The filtered bundles associated with periodic monopoles.- Global periodic monopoles of rank one.- Global periodic monopoles and filtered difference modules.- Appendix.