Advances in Mathematics Research. Volume 26

Albert R. Baswell (Editor)

Series: Advances in Mathematics Research
BISAC: MAT027000




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In Advances in Mathematics Research. Volume 26, the opening chapter aims to show the importance of mathematical means associated with the role of Pythagorean musical tradition in mathematical and architectural contexts up to the Renaissance.

The following chapter proposes a formalism which enables us to separate fields of investigation from the epistemological questions in philosophy and to consider models as parts of hierarchical model families.

Continuity of the modulus and phase degrees-of-freedom of molecular electronic states is commented upon in the next section, and the resultant entropy/information descriptors of electronic states, combining the probability and current contributions, are applied to classical issues in chemical-reactivity theory.

Additionally, the authors study the categorical generalizations of the Möbius function emphasizing the geometric meaning of these constructions, and discuss the relations between the various approaches.

The final chapter introduces the PWP method as a technique for measuring indirect influences in complex networks. (Imprint: Nova)


Chapter 1. Mathematical Means in Music and Architecture up to the Renaissance
(Oscar João Abdounur, and Tânia Baier, IME, University of São Paulo, SP, Brazil, and others)

Chapter 2. Epistemology and Mathematical Modeling - Formalizing the Modeling Process in Natural Sciences
(Janina Dierkes, Cordula Reisch, and Dirk Langemann, TU Braunschweig, Inst. Computational Mathematics, Braunschweig, Germany)

Chapter 3. On Entropy/Information Description of Reactivity Phenomena
(Roman F. Nalewajski, Department of Theoretical Chemistry, Jagiellonian University, Cracow, Poland)

Chapter 4. On the Categorification of the Mobius Function
(Rafael Diaz, Escuela de Matematicas, Universidad Nacional de Columbia, Sede Medellin, Colombia)

Chapter 5. On the Stability of the PWP Method
(Rafael Diaz, and Angelica Vargas, Escuela de Matematicas, Universidad Nacional de Columbia, Sede Medellin, Columbia, and others)


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