Related papers: Metric Currents and Alberti representations
Neural networks with PDEs embedded in their loss functions (physics-informed neural networks) are employed as a function approximators to find solutions to the Ricci flow (a curvature based evolution) of Riemannian metrics. A general method…
Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…
We prove some basic results about irreducible components of varieties of modules for an arbitrary finitely generated associative algebra. Our work generalizes results of Kac and Schofield on representations of quivers, but our methods are…
We clearly characterize the relation between real and complex Wiener-Ito integrals. Given a complex multiple Wiener-Ito integral, we get explicit expressions for two kernels of its real and imaginary parts. Conversely, consider a…
In the framework of the Einstein-Maxwell-aether-axion theory we consider the self-consistent model based on the concept of a two-level control, which is carried out by the dynamic aether over the behavior of the axionically active…
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity…
We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
Several mathematical formulae are used nowadays in order to compute a magnetic torque. We demonstrate that its more general expression is the vectorial product of the current density with the vector potential. We associate this Larmor's…
We develop an algebro-geometric formulation for neural networks in machine learning using the moduli space of framed quiver representations. We find natural Hermitian metrics on the universal bundles over the moduli which are compatible…
We present a mechanical model of a quasi-elastic body (aether) which reproduces Maxwell's equations with charges and currents. Major criticism against mechanical models of electrodynamics is that any presence of charges in the known models…
We construct a moduli space of polarised manifolds which admit a constant scalar curvature K\"ahler metric. We show that this space admits a natural K\"ahler metric.
We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution of the adjoint problem, we show that error indicators in the…
We generalize the DeWitt-Virasoro (DWV) construction of arXiv:0912.3987 [hep-th] to tensor representations of higher ranks. A rank-$n$ tensor state, which is by itself coordinate invariant, is expanded in terms of position eigenstates that…
We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz…
The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major influencing factors relevant to the direct and…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…
Choosing an encoding over binary strings for input/output to/by a Turing Machine is usually straightforward and/or inessential for discrete data (like graphs), but delicate -- heavily affecting computability and even more computational…
A wire that conducts an electric current will give rise to circular magnetic field (the \O{}rsted magnetic field), which can be calculated using the Maxwell-Ampere equation. For wires with diameters in the macroscopic scale, the…
We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exact count in the case when the quiver is of…