The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.
The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.
Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
This volume presents the new objectives of physics on self-organizing systems composed of multi-components, in order to create a new field and establish universal comprehension in physics. The book covers broad topics such as the thermodynamic time asymmetry in both transient and stationary nonequilibrium states, the seriousness of auxiliary conditions in physicochemical processes and biological systems, the quantum-classical and micro-macro interfaces which are familiar in mesoscopic physics, the purification scheme of quantum entanglement, topics on gamma-ray bursts, and the walking mechanism of single molecular motors. Sample Chapter(s). Bio-Physics Manifesto for the Futureof Physics and Biology (570 KB). Contents: Biophysics: Bio-Physics Manifesto OCo For the Future of the Physics and Biology (Y Oono); Single Molecule Force Measurement for Protein Synthesis on the Ribosome (S Uemura); A Rod Probe Reveals Gait of Myosin V (K Shiroguchi); Mechanism of Spontaneous Oscillation Emerging from Collective Molecular Motors (Y Shimamoto and S Ishiwata); Simulated Rotational Diffusion of F o Molecular Motor (H Yamasaki & M Takano); Nonequilibrium Statistical Physics and Related Topics: Thermodynamic Time Asymmetry and Nonequilibrium Statistical Mechanics (P Gaspard); A Measurement-Based Purification Scheme and Decoherence (H Nakazato); Quantum Fluctuation Theorem in the Existence of the Tunneling and the Thermal Activation (T Monnai); Statistical Properties of the Inter-Occurrence Times in the Two-Dimensional Stick-Slip Model of Earthquakes (T Hasumi & Y Aizawa); Second Harmonic Generation and Polarization Microscope Observations of Quantum Relaxor Lithium Doped Potasium Tantalate (H Yokota & Y Uesu); Thermoelectric Properties of Ni-Doped LaRh0 3 (S Shibasaki et al.); Collective Precession of Chiral Liquid Crystals Under Transmembrane Mass Flow (G Watanabe et al.); Interplay of Excitons with Free Carriers in Carrier Tunneling Dynamics (S Lu et al.); Astrophysics as Interdisciplinary Science: New View on Quantum Gravity: Micro-Structure of Spacetime and Origin of the Universe (B L Hu); Colliding Branes and Its Application to String Cosmology (Y Takamizu); One-Loop Corrections to Scalar and Tensor Perturbations During Inflation (Y Urakawa & K Maeda); Variational Calculation for the Equation of State of Nuclear Matter Toward Supernova Simulations (H Kanzawa et al.); Two Strong Radio Bursts at High and Medium Galactic Latitude (S Kida & T Daishido); Effects of QCD Phase Transition on the Ejected Elements from the Envelopes of Compact Stars (Y Yasutake et al.). Readership: Physicists, biologists and material scientists.
A unique tool in imaging diagnosis Due to the complex anatomical structure of the temporal bone, imaging diagnosis requires a very high degree of expertise. This atlas is not only helpful to assess pediatric ear disorders accurately, but also provides a treasure trove to experts. It consists of a pediatric temporal bone imaging atlas followed by case reports of typical pediatric ear diseases. In the first part complete contiguous temporal bone CT sections of an infant and an older child are shown along with a detailed listing of anatomical names of the structures. It further presents developmental changes in size, shape, location and orientation of the primary components of the temporal bone. The second part contains case images in combination with reference illustrations of a healthy child in the same age range allowing the reader to identify the key findings of the disorder with only one reference book at hand. Further images illustrate the posttreatment follow-up. This publication which is translated from the successful Japanese edition (2011) will be essential for otorhinolaryngologists and pediatricians particularly interested in pediatric ear diseases. Its unique layout makes it also a very effective tool for students learning image diagnosis.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.