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1. |
Record Nr. |
UNIORUON00022877 |
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Autore |
SHIBA Yoshinobu |
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Titolo |
Commerce and society in Sung China / Yoshinobu Shiba |
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Pubbl/distr/stampa |
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Ann Arbor, : Center for Chinese Studies The University of Michigan, 1970 iv, 228 p. ; 23 cm |
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Classificazione |
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Soggetti |
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COMMERCIO - CINA - DINASTIA SUNG (960-1279) |
CINA - SOCIETA' - DINASTIA SUNG (960-1279) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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2. |
Record Nr. |
UNINA9910254280703321 |
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Autore |
Lapidus Michel L |
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Titolo |
Fractal zeta functions and fractal drums : higher-dimensional theory of complex dimensions / / by Michel L. Lapidus, Goran Radunović, Darko Žubrinić |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
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ISBN |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (XL, 655 p. 55 illus., 10 illus. in color.) |
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Collana |
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Springer Monographs in Mathematics, , 1439-7382 |
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Disciplina |
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Soggetti |
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Number theory |
Measure theory |
Mathematical physics |
Number Theory |
Measure and Integration |
Mathematical Physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and indexes. |
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Nota di contenuto |
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Overview -- Preface -- List of Figures -- Key Words -- Selected Key Results -- Glossary -- 1. Introduction -- 2 Distance and Tube Zeta Functions -- 3. Applications of Distance and Tube Zeta Functions -- 4. Relative Fractal Drums and Their Complex Dimensions -- 5.Fractal Tube Formulas and Complex Dimensions -- 6. Classification of Fractal Sets and Concluding Comments -- Appendix A. Tame Dirchlet-Type Integrals -- Appendix B. Local Distance Zeta Functions -- Appendix C. Distance Zeta Functions and Principal Complex Dimensions of RFDs -- Acknowledgements -- Bibliography -- Author Index -- Subject Index. . |
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Sommario/riassunto |
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This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field. |
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3. |
Record Nr. |
UNINA9910484702003321 |
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Autore |
Borisyuk Alla |
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Titolo |
Tutorials in Mathematical Biosciences I : Mathematical Neuroscience / / by Alla Borisyuk, G. Bard Ermentrout, Avner Friedman, David H. Terman |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2005 |
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ISBN |
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Edizione |
[1st ed. 2005.] |
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Descrizione fisica |
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1 online resource (IX,170 p.) |
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Collana |
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Mathematical Biosciences Subseries, , 2524-6771 ; ; 1860 |
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Disciplina |
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Soggetti |
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Biomathematics |
Differential equations |
Differential equations, Partial |
Computer science - Mathematics |
Neurobiology |
Bioinformatics |
Computational biology |
Mathematical and Computational Biology |
Ordinary Differential Equations |
Partial Differential Equations |
Computational Mathematics and Numerical Analysis |
Computer Appl. in Life Sciences |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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Preface -- A. Friedman: Introduction to Neurons -- D. Terman: An Introduction to Dynamical Systems and Neuronal Dynamics -- B. Ermentrout: Neural Oscillators -- A. Borisyuk: Physiology and Mathematical Modeling of the Auditory System. |
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Sommario/riassunto |
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This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. |
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Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems. |
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