Related papers: Integral representation of Skorokhod reflection
We present a novel integral representation for the biharmonic Dirichlet problem. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation…
It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true…
Inspired by the Kruskal-Katona theorem a minimization problem is studied, where the role of the shadow is replaced by the image of the action of the monoid of increasing functions. One of our main results shows that compressed sets are a…
We show that, over a local complete intersection, every possible variety is realized as the cohomological support variety of some module. Moreover, we show that the projective variety of a complete indecomposable maximal Cohen-Macaulay…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
We describe combinatorial aspects of classical resolution of singularities that are free of characteristic and can be applied to singular foliations and vector fields as well as to functions and varieties. In particular, we give a…
We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive…
In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…
It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected…
We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state transform. We derive the expression of the 4d spinfoam vertex for Euclidean and for…
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in…
We study integral representations of random variables with respect to general H\"older continuous processes and with respect to two particular cases; fractional Brownian motion and mixed fractional Brownian motion. We prove that arbitrary…
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…
In this paper we give an algebraic construction of the (active) reflected Dirich- let form. We prove that it is the maximal Silverstein extension whenever the given form does not possess a killing part and we prove that Dirichlet forms need…
In this paper, the strong solutions $ (X, L)$ of multidimensional stochastic differential equations with reflecting boundary and possible anticipating initial random variables is established. The key is to obtain some substitution formula…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
A simple stochastic formulation of the multiple scattering representation solution of the classical linear incoherent trapping problem is presented for a broad audience. A clear connection with the alternative Holstein's solution ansatz is…