This book outlines an integrative framework for business-model innovation in the paradigm of the Internet of Things. It elaborates several tools and methodologies for the quantitative, qualitative, analytical and effectual evaluation, and analyzes their applicability and efficiency for several phases of the business-model innovation process. As such, it provides guidance to managers, decision-makers and entrepreneurs on how to systematically employ the business-model concept with the aim of achieving sustainable competitive advantages. For researchers the book introduces cases and examples for successful business-model innovation and presents an integrated approach to the methods and tools applied.

The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V - E + F =2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

The Calculus of Friendship is the story of an extraordinary connection between a teacher and a student, as chronicled through more than thirty years of letters between them. What makes their relationship unique is that it is based almost entirely on a shared love of calculus. For them, calculus is more than a branch of mathematics; it is a game they love playing together, a constant when all else is in flux. The teacher goes from the prime of his career to retirement, competes in whitewater kayaking at the international level, and loses a son. The student matures from high school math whiz to Ivy League professor, suffers the sudden death of a parent, and blunders into a marriage destined to fail. Yet through it all they take refuge in the haven of calculus--until a day comes when calculus is no longer enough. Like calculus itself, The Calculus of Friendship is an exploration of change. It's about the transformation that takes place in a student's heart, as he and his teacher reverse roles, as they age, as they are buffeted by life itself. Written by a renowned teacher and communicator of mathematics, The Calculus of Friendship is warm, intimate, and deeply moving. The most inspiring ideas of calculus, differential equations, and chaos theory are explained through metaphors, images, and anecdotes in a way that all readers will find beautiful, and even poignant. Math enthusiasts, from high school students to professionals, will delight in the offbeat problems and lucid explanations in the letters. For anyone whose life has been changed by a mentor, The Calculus of Friendship will be an unforgettable journey.

Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena—chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular Lévy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.

Quantum Mechanics is a fundamental scientific discipline. At the same time, it is viewed as being very difficult. This book attempts to present the Theory of Quanta as a scientific discipline which has emerged naturally from experiment, making use of general concepts of the Classical Mechanics and enlarging their nature and applicability. According to the historical development, the first natural way of introducing the quantum-mechanical concepts is the matricial theory, followed by the very useful approach of the undulatory theory. The core of the Theory of Quanta is the quasi-classical theory, described at large in the book. The book does not circumvent the so-called philosophical problems of the Quantum Mechanics. 1) Ch. 1, Beginnings, includes all the experimental, preliminary indications of the necessity of a new theory. The usual textbooks say little about this aspect. In particular, Double Slit and Particle and Waves sections are completely new. 2) Ch. 2, Classical Mechanics, is seldom included in the usual textbooks. In addition, it is formulated here on the basis of the Hamilton-Jacobi equation, though rarely used, it is the direct way of passing from the Classical Mechanics to the Theory of Quanta. The Lenz vector in the central field is emphasized, the only way to deduce the hydrogen atom by using the Matricial Theory, a fundamental result. 3) Ch. 3, Quantum Mechanics, is the exposition of the matricial method. This is the core of the Theory of Quanta, which exhibits the basic ingredients. The Matricial theory is not included today in textbooks, which prefer the Wave Mechanics (Schrodinger equation). It is shown here the direct way to Schrodinger equation from the Matricial Theory. This chapter is written from the little-known book by Born and Jordan, Matricial Mechanics (cited there). 4) Chs. 4 to 8 are standard, technical subjects, with many novelties: Coulomb degeneracy, adiabatic hypothesis, second quantization and many-body theories (the latter is never included in textbooks). 5) Ch. 9, Quasi-Classical Quantum Mechanics, is completely new. In particular, the Tunneling, the Chemical Reactivity, Adiabatic Transitions, Reflexion above Barrier (with many applications, to ionization, for instance) are described in detail. Also, in this chapter the "philosophical" problems of the Theory of Quanta are discussed. The Quasi-Classical Mechanics is the most interesting subject in the Theory of Quanta. 6) Ch. 10, Scattering, includes a completely new formulation. Usually, the scattering theory is presented in a very fastidious way. There is a much simpler way, leading directly to results, which is present in this chapter. The clue to the scattering theory is the solution of the Helmholtz equation, usually overlooked. 7) Finally, Ch. 11 includes the much discussed problem of Measurement. The most advanced result in this direction belongs to Pauli (in his book on Quantum Mechanics). The result is still unsatisfactory. A more direct description of the measurement is given here, based on the very quantum-mechanical principles. The results are perfectly convincing, and, of course, new. 8) It is indeed hard to believe that something new can be said about the Theory of Quanta. A great impediment in understanding the Quantum Mechanics is because there are too many books published on the subject. The subject was distorted in all imaginable ways, every author trying to be original. I hope that I have succeeded to be as close as possible to the original meaning of the subject, without being too original.