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Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic…
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…
This article is composed of two parts; In the first part (Sec. 1), the ultra-large-scale electronic structure theory is reviewed for (i) its fundamental numerical algorithm and (ii) its role in nano-material science. The second part (Sec.…
An introduction to the physics of heavy fermion compounds is presented, attempting to highlight the conceptual developments and emphasize the mysteries and open questions that persist in this active field of research.
The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out…
These lecture notes provide an introduction to logarithmic geometry with a view towards recent applications in the desingularization theory.
This is the second of three papers I will present as an application of the Basic Unit System concept, a complex mathematical unit presented in The Basic Unit System concept and The Principle of Synergy. In this case this Bus concept is used…
These lecture notes give an introduction to the theory of interacting particle systems. The main subjects are the construction using generators and graphical representations, the mean field limit, stochastic order, duality, and the relation…
Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…
We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict demands of reason that we first introduce. We follow the historical…
We present an original undergraduate level compilation for the physics of electromechanical systems with special attention to power flow. An approach based on energy considerations is presented that is specially suited to compute the…
The field nature of spin in the framework of the field electromagnetic particle concept is considered. A mathematical character of the fine structure constant is discussed. Three topologically different field models for charged particle…
The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.
This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of…