Related papers: Combinatorial solutions to the reflection equation
We study the convergence of the method of reflections for the Stokes equations in domains perforated by countably many spherical particles with boundary conditions typical for the suspension of rigid particles. We prove that a relaxed…
Neutron reflectometry analysis is an inherently ill-posed, which is to say that there are many possible solutions which agree equally well with the measured data. This leads to the application of model-dependent analysis, where information…
The theory of specular X-ray reflectivity from a rough interface based upon the reflection function method (RFM) is proposed. The RFM transforms the second order differential equation for the wave amplitude into the non-linear first order…
We list solutions of the graded reflection equation associated with the fundamental vector representation of the quantum supergroup of GL-type.
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
The current article is a short survey on the theory of Hecke algebras, and in particular Kazhdan-Lusztig theory, and on the theory of symplectic reflection algebras, and in particular rational Cherednik algebras. The emphasis is on the…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We express the defining relations of the $q$-deformed Minkowski space algebra as well as that of the corresponding derivatives and differentials in the form of reflection equations. This formulation encompasses the covariance properties…
Skew braces are one of the main algebraic tools controlling the structure of a non-degenerate bijective set-theoretic solution of the Yang-Baxter equation. The aim of this paper is to study model-theoretically tame skew braces, with…
In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…
This paper is devoted to the study of reflected Stochastic Differential Equations when the constraint is not on the paths of the solution but acts on the law of the solution. These reflected equations have been introduced recently by…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we…
We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
We study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some…
We construct an extended Hubbard model with open boundaries from a $R$-matrix based on the $U_q[Osp(2|2)]$ superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open…
We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the…