Related papers: New determinants in the 8VSOS model with domain-wa…

We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded $\bar{\partial}$ problem, then the ideal of bounded holomorphic functions vanishing at a point in the domain is finitely generated. We also prove a…

We introduce a new mathematical object, the "fermionant" ${\mathrm{Ferm}}_N(G)$, of type $N$ of an $n \times n$ matrix $G$. It represents certain $n$-point functions involving $N$ species of free fermions. When N=1, the fermionant reduces…

We develop domain theory in constructive univalent foundations without Voevodsky's resizing axioms. In previous work in this direction, we constructed the Scott model of PCF and proved its computational adequacy, based on directed complete…

We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions…

Rewritable nanoelectronics offers new perspectives and potential to both fundamental research and technological applications. Such interest has driven the research focus into conducting domain walls: pseudo 2D conducting channels that can…

We show that nano-scale variations of the order parameter in strongly-correlated systems can induce local spatial regions such as domain walls that exhibit electronic properties representative of a different, but nearby, part of the phase…

This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

We derive an integral expression for the leading-order type I-I-I three-point functions in the $\mathfrak{su}(2) $-sector of $\mathcal{N}=4$ super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the…

In this contribution we first summarize how contour integration methods can be used to derive closed formulae for functional determinants of ordinary differential operators. We then generalize our considerations to partial differential…

The bounded variation seminorm and the Sobolev seminorm on compact manifolds are represented as a limit of fractional Sobolev seminorms. This establishes a characterization of functions of bounded variation and of Sobolev functions on…

Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding…

Yang-Baxter integrable dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models are considered on the torus in their simplest physical regimes. A combination of boundary conditions $(h,v)$ is applied in the horizontal and vertical directions…

In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…

We give a functional characterization of a class of quasi-invariant determinantal processes corresponding to projection kernels in terms of de Branges spaces of entire funcitons.

We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…

We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews's determinant.

The purpose of this paper is to prove optimal estimates for solutions of the Kohn-Laplacian for certain classes of model domains in several complex variables. This will be achieved by applying a type of singular integral operator whose…

Our goal is to find a matrix model with $BMS_3$ constraints built in. These constraints are imposed through Loop equations. We solve them using a free field realisation of the algebra and write down the partition function in eigenvalue…

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…