Related papers: Geophysical modelling with Colombeau functions: Mi…
The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space.…
This paper is a tutorial that demonstrates various methods from the Colombeau theory of generalized functions in the context of semilinear wave equations. The Colombeau generalized functions constitute differential algebras that contain the…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
We introduce here the two-fractal model of earthquake dynamics. As the fractured surfaces have self-affine properties, we consider the solid-solid interface of the earth's crust and the tectonic plate below as fractal surfaces. The overlap…
Scale invariance property in the global geometry of Earth may lead to a coupled interactive behaviour between various components of the climate system. One of the most interesting correlations exists between spatial statistics of the global…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…
Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster…
We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this…
We have previously proposed a study of arrangements of small circles which also surround regions in the plane realized as the images of natural real algebraic maps yielding Morse-Bott functions by projections. Among studies of arrangements,…
Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can…
The purpose of this paper is to provide a set of sufficient conditions so that the normalized form of the Fox-Wright functions have certain geometric properties like close-to-convexity, univalency, convexity and starlikeness inside the unit…
Coupling of rupture processes in solids with waves also propagating in fluids is a prominent phenomenon arising during tectonic earthquakes. It is executed here in a single `monolithic' model which can asymptotically capture both damageable…
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
In distribution theory the pullback of a general distribution by a $C^{\infty}$-function is well-defined whenever the normal bundle of the $C^{\infty}$-function does not intersect the wavefront set of the distribution. However, the…
Remarkable global correlations exist between geometrical features of terrestrial surface on the Earth, current mean sea level and its geological internal processes whose origins have remained an essential goal in the Earth sciences.…
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring…
In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution…