相关论文: Geography as a Science of the Earth's Surface Foun…

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of…

Most modern theoretical considerations of the physical world suggest that nature is: (1) field-theoretic, (2) smooth, (3) local, (4) gauged, (5) containing fermions, and (6) non-perturbative. Tautologous as this may sound to experts, it is…

This chapter provides an overview of the basic concepts foundational to atmospheric physics and chemistry. We discuss the retention of atmospheres against thermal evaporation and the global energy balance of planets. We present simple…

Topos theory occupies a singular place in contemporary mathematics: born from Grothendieck's algebraic geometry, it has emerged as a unifying language for geometry, topology, algebra, and logic. This book offers a progressive introduction…

Geography scholarship currently includes interdisciplinary approaches and theories and reflects shifts in research methodologies. Since the spatial turn in geographical thought and the emergence of geo-web technologies, geography…

The Earth's surface is composed of a staggering diversity of particulate-fluid mixtures: dry to wet, dilute to dense, colloidal to granular, and attractive to repulsive particles. This material variety is matched by the range of relevant…

Neutral surfaces, along which most of the mixing in the ocean occurs, are notoriously difficult objects: they do not exist as well-defined surfaces, and as such can only be approximated. In a hypothetical ocean where neutral surfaces are…

The origins of life stands among the great open scientific questions of our time. While a number of proposals exist for possible starting points in the pathway from non-living to living matter, these have so far not achieved states of…

This paper explores how a pluralist view can arise in a natural way out of the day-to-day practice of modern set theory. By contrast, the widely accepted orthodox view is that there is an ultimate universe of sets $V$, and it is in this…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is…

The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is…

We study the statistical underpinnings of life. We question some common assumptions about the thermodynamics of life and illustrate how, contrary to widespread belief, even in a closed system entropy growth can accompany an increase in…

How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may…

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…

In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…

Understanding how AI will represent and reason about geography should be a key concern for all of us, as the broader public increasingly interacts with spaces and places through these systems. Similarly, in line with the nature of…

This treatise concerns shapes in the sense of constellations of points with various automorphisms quotiented out: continuous translations, rotations and dilations, and also discrete mirror image identification and labelling…

There are anthropic reasons to suspect that life in more than three spatial dimensions is not possible, and if the same could be said of fewer than three, then one would have an anthropic argument for why we experience precisely three large…

The space-time geometry is considered to be a physical geometry, i.e. a geometry described completely by the world function. All geometrical concepts and geometric objects are taken from the proper Euclidean geometry. They are expressed via…