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In this article, we will study plane curves of a certain degree d with three or four total inflection points. In particular, we will study their image in the moduli spaces. Also a result on curves with five total inflection points is included.
In this paper we prove three different types of the so-called many-particle Hardy inequalities. One of them is a ‘classical type’ which is valid in any dimension d ≠ 2. The second type deals with 2-dimensional magnetic Dirichlet forms, where every particle is supplied with a solenoid....
We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation (PDE) Δ u =4 e 2 u and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with prescribed critical points and specified boundary...
A long-standing conjecture for the linear Schrödinger equation states that 1/4 of the derivative in L 2 , in the sense of Sobolev spaces, suffices in any dimension for the solution to that equation to converge almost everywhere to the initial datum as the time goes to zero. This is only known to...
The main result in the above-mentioned paper, namely the existence and uniqueness theorem for host algebras, is wrong.
An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on flags, with adjacent flags lying in different orbits. In this paper, we describe a method for constructing finite chiral n -polytopes, by seeking particular normal subgroups of the...
Suppose that 𝔥 is a complex Hilbert space and that (𝔥) denotes the bounded linear operators on 𝔥. In this paper we show that if ⊆ (𝔥) is an abelian algebra with elements that admit representations under which they have a spanning set of eigenvectors, and if has the property that...
We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve graph of a compact orientable surface. We use this to...
The concept of generalised species of structures between small categories and, correspondingly, that of generalised analytic functor between presheaf categories are introduced. An operation of substitution for generalised species, which is the counterpart to the composition of generalised...
We define the odd affine Temperley–Lieb algebra (OATLA) to be the category defined by planar diagrams in an annulus with an odd number of marked points on each boundary connected in pairs by disjoint strings and a modulus δ . This algebra is the odd part of the annularization of the...
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