Related papers: Reflection algebra and functional equations
Inverse transformation optics is introduced, and used to calculate the reflection at the boundary of a transformation medium under consideration. The transformation medium for a practical device is obtained from a two-dimensional (2D)…
We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to L\'evy subordinators, and provide explicit sufficient conditions that both ensure convergence and characterize the law of the…
We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for…
We use holomorphic factorization to find the partition functions of an abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that…
Five simple guidelines are proposed to compute the generating function for the nonnegative integer solutions of a system of linear inequalities. In contrast to other approaches, the emphasis is on deriving recurrences. We show how to use…
We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…
We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time,…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour…
One of the main virtues of trees is to represent formal solutions of various functional equations which can be cast in the form of fixed point problems. Basic examples include differential equations and functional (Lagrange) inversion in…
The computation of the partition function in certain quantum field theories, such as those of the Argyres-Douglas or Minahan-Nemeschansky type, is problematic due to the lack of a Lagrangian description. In this paper, we use the…
Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\A$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
The graded reflection equation is investigated for the $U_{q}[sl(r|2m)^{(2)}]$ vertex model. We have found four classes of diagonal solutions and twelve classes of non-diagonal ones. The number of free parameters for some solutions depends…
This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…