Related papers: Reflection algebra and functional equations
A metasurface is a surface, tipically a plane, on which a function called phase discontinuity is chosen so that the metasurface produces a desired reflection or refraction job. We derive the equations that the phase discontinuity function…
We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions. In pioneering works of Korepin and Izergin a determinant formula was proposed and…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin…
This paper addresses reflection removal, which is the task of separating reflection components from a captured image and deriving the image with only transmission components. Considering that the existence of the reflection changes the…
We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
A convolution approach leading to an explicit computation of a value of a 4F3 function is outlined. We also investigate about the role of the dilogarithm reflection formula, leading to a remarkable consequence: in some cases, values of 4F3…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.
Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded…
We present a rigorous theoretical framework for designing full-space spatial power dividers using metagratings. In our study, the current restrictions of spatial power dividing platforms such as reflection-only performance, operating at…
The problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions is addressed by considering a particular nonlocal correlation function, called row configuration probability. This correlation…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…