Cognitive-learning theories hold a unique place in history: they explore the depths of the mind from the perspective of process. This paper discusses the history of cognitive-learning theories and how they grew to shape the way one perceives, organizes, stores, and retrieves information. The paper, after providing a definition and synopsis of cognitive theory and its basic concepts, turns to th...

This paper opens a new chapter in the study of planar tilings by introducing conformal tilings. These are similar to traditional tilings in that they realize abstract patterns of combinatorial polygons as concrete patterns of geometric shapes, the tiles. In the conformal case, however, these geometric tiles carry prescribed conformal rather than prescribed euclidean structure. The authors devel...

Intriguing questions from the early history of quantum theory (QT) raise serious doubts about the accepted theory of black body radiation. (The Planck theory builds on the apparently flawed Rayleigh-Jeans approach.) Furthermore, the validity of the theory of diffraction, the basis of the wave theory of radiation and matter, seems uncertain. Together, these raise fundamental questions about the ...

Sociologists frequently invoke the concept of form when analyzing organizations, collective action, art, music, culture and other phenomena. Nonetheless, the form concept has not received careful theoretical analysis, either generally or in specific context. Using the tools of formal logic, set theory, and algebra, we propose a language for defining social forms that is suÆciently general to in...

As known, to finish this book, you may not need to get it at once in a day. Doing the activities along the day may make you feel so bored. If you try to force reading, you may prefer to do other entertaining activities. But, one of concepts we want you to have this book is that it will not make you feel bored. Feeling bored when reading will be only unless you don't like the book. foundations o...

The starting point of the paper presented are the well-known defuzzification procedures on the one hand and approaches to axiomatize the concept of defuzzification, on the other hand. We present a new attempt to build up an axiomatic foundation for defuzzification theory using the theory of groups and the theory of partially ordered sets, and in particular, the theory of GALOIS connections.

We initiate a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of Berkovich. In this paper, we give a thorough development of φ-modules over a relative Robba ring associated to a perfect Banach ring of characteristic p, including the relationship between these objects and étale Zp-local systems an...

We establish the conditions that must be satisfied for the mathematical operations of linear algebra and calculus to be applicable. The mathematical foundations of the social sciences including economic theory, utility theory, and game theory, depend on these conditions which have not been correctly identified in the classical literature.