Related papers: Uniformizing complex ODEs and applications
Generalized Halphen systems are solved in terms of functions that uniformize genus zero Riemann surfaces, with automorphism groups that are commensurable with the modular group. Rational maps relating these functions imply subgroup…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We develop a $D-$module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zeros of remainder maps of such long divisions are handled by…
We present a unified approach to holomorphic anomaly equations and some well-known quantum spectral curves. We develop a formalism of abstract quantum field theory based on the diagrammatics of the Deligne-Mumford moduli spaces…
A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…
The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To…
In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit and as 1/N expansions, in the case of…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators,…
Very strong electromagnetic field can be generated in peripheral relativistic heavy ion collisions. This work is devoted to exploring the interplay between the effects of a constant external electric field and confining potential on…
Landmark manifolds consist of a collection of distinct points, and dynamics on this manifold can be used to represent flows, such as solutions of ODEs and flows deforming a shape. We will consider landmark configurations in the Euclidean…
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, such problems are typically tackled…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
We introduce mollifiers in Clifford analysis setting and construct a sequence of $\C^{\infinity}$-functions that approximate a $\gamma$-regular function and a solution to a non homogeneous BVP of an in homogeneous Dirac like operator in…
We show that every bounded hyperconvex Reinhardt domain can be approximated by special polynomial polyhedra defined by homogeneous polynomial mappings. This is achieved by means of approximation of the pluricomplex Green function of the…
We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.
We consider the vector functions in a domain homeomorphic to a spherical layer bounded by twice continuously differentiable surfaces. Additional restrictions are imposed on the domain, which allow to conduct proofs using simple methods. On…
We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…