Related papers: Integral representation results in BVxL^p
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
We derive an integral representation for Herglotz-Nevanlinna functions in two variables which provides a complete characterization of this class in terms of a real number, two non-negative numbers and a positive measure satisfying certain…
Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…
Within the framework of thermofield dynamics, we construct a thermalized coherent thermal state, which is a general type of the coherent state with the thermal effects and can be presumably produced experimentally. The wavefunction and the…
In the present article the reduced integral representation of partitions in terms of harmonic products has been derived first by using hypergeometry and the new concept of fractional sum and secondly by studying the Fourier series of the…
This paper presents a rigorous treatment of the concept of extensivity in equilibrium thermodynamics from a geometric point of view. This is achieved by endowing the manifold of equilibrium states of a system with a smooth atlas that is…
We obtain the reflected entropy for bipartite states in a class of $(1+1)$-dimensional Galilean conformal field theories ($GCFT_{1+1}$) through a replica technique. Furthermore we compare our results with the entanglement wedge cross…
We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case…
The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a $\Gamma$-convergence result for a smaller class of functionals.
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
This document attempts to clarify potential confusion regarding electrostatics calculations, specifically in the context of biomolecular structure and specifically as regards the units typically used to contour/visualize isopotential…
In many cases the correct theoretical description of flexoelectricity requires the consideration of the finite size of a body and is reduced to the solution of boundary problems for partial differential equations. Generally speaking, in…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we…
In this paper we achieve some $\Gamma$-compactness results for suitable classes of integral functionals depending on a given family of Lipschitz vector fields, with respect to both the strong $L^p-$topology and the strong…
Multimodal in-context learning (ICL) equips Large Vision-language Models (LVLMs) with the ability to adapt to new tasks via multiple user-provided demonstrations, without requiring any model parameter updates. However, its effectiveness is…
The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
This work deals with the homogenization of functionals with linear growth in the context of $\mathcal{A}$-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the…