Related papers: Integral representation results in BVxL^p
Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to…
In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax…
The integral expressions served to decompose vector field into irrotational and divergence-free components represent modern version of the Helmholtz decomposition theorem. These expressions are also widely used to decompose the…
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
Implicit neural representations (INR) have gained significant popularity for signal and image representation for many end-tasks, such as superresolution, 3D modeling, and more. Most INR architectures rely on sinusoidal positional encoding,…
Decomposing a scene into its reflectance and shading is a challenge due to the lack of extensive ground-truth data for real-world scenes. We introduce a novel physics-based approach for intrinsic image decomposition using a pair of visible…
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper. The results are given in terms of $L^p$ integrability of the function and its…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We present a combination of tools which allows for investigation of the coupled orbital and rotational dynamics of two rigid bodies with nearly arbitrary shape and mass distribution, under the influence of their mutual gravitational…
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…
Implicit Neural Representations (INRs) have emerged as a paradigm in knowledge representation, offering exceptional flexibility and performance across a diverse range of applications. INRs leverage multilayer perceptrons (MLPs) to model…
Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…
A model of two-component relativistic fluid is considered, and the thermal nature of coupling between the fluid constituents is outlined. This thermal coupling is responsible for non-ideality of the fluid composite where the components are…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
In Thermal Field Dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall…
A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion coefficient. It is shown that no particularly natural,…