Related papers: A simple and more general approach to Stokes' theo…
This survey revisits classical results in vector calculus and analysis by exploring a generalised perspective on the exterior derivative, interpreting it as a measure of "infinitesimal flux". This viewpoint leads to a higher-dimensional…
We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincar\'e sphere.…
Observer-invariance is regarded as a minimum requirement for an appropriate definition and derived systematically from a spacetime setting, where observer-invariance is a special case of a covariance principle and covered by Ricci-calculus.…
Dividing asks about inconsistency along indiscernible sequences. In order to study the finer structure of simple theories without much dividing, the authors recently introduced shearing, which essentially asks about inconsistency along…
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show…
The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface…
The way a field transforms under rotations determines its statistics--as is easy to see for scalar, Dirac, and vector fields.
We identify points of difference between Invariant Set Theory and standard quantum theory, and show that these lead to noticeable differences in predictions between the two theories. We design a number of experiments to test which of these…
We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel's theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of…
We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated random velocity field. We carry on an expansion in powers of the inverse square…
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes…
We explore the question asking for graphs $G$ for which the total distance decreases, possibly by a fixed constant $k$, upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \v{S}olt\'es' problem…
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in…
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Koml\'os conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.
The generalized Stokes theorem (connecting integrals of dimensions 3 and 4) is formulated in a curved space-time in terms of paths in Minkowski space (forming Path Group). A covariant integral form of the conservation law for the…
Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…
We prove a few cases of a conjecture on the invariance of cohomological support loci under derived equivalence by establishing a concrete connection with the related problem of the invariance of Hodge numbers. We use the main case in order…
A peculiar feature of It\^o's calculus is that it is an integral calculus that gives no explicit derivative with a systematic differentiation theory counterpart, as in elementary calculus. So, can we define a pathwise stochastic derivative…