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A unique history of crime revealed through the key numbers associated with famous murders.

Crime --- Symbolism of numbers. --- History.

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Success in business. --- Success. --- Law of large numbers.

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This book contains part of the results of a research project funded by Colciencias and executed by the research group Grupo de Investigación en Matemáticas Uninorte (Colombia), and contains details of properties, which are satis ed by certain spaces of vector value functions and distributions de ned on the n dimensional torus. In particular, the text addresses an introductory study of the toroidal Besov spaces, which appear in many applications to partial di erential equations with periodic conditions and in harmonic analysis. This work can be very useful for undergraduate and graduate students in Mathematics as well as for researchers interested in the topics mentioned above.

Vector analysis. --- Análisis vectorial. --- Algebra, Universal --- Mathematics --- Numbers, Complex --- Quaternions --- Spinor analysis --- Vector algebra

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This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis. Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied. Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required.

Diophantine equations. --- Algebraic fields. --- Bases (Linear topological spaces) --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra

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Biodiversity. --- Biodiversity --- Biological diversification --- Biological diversity --- Biotic diversity --- Diversification, Biological --- Diversity, Biological --- Biology --- Biocomplexity --- Ecological heterogeneity --- Numbers of species