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Surface mapping plays an important role in geometric processing. They induce both area and angular distortions. If the angular distortion is bounded, the mapping is called a {\it quasi-conformal} map. Many surface maps in our physical world…

Numerical Analysis · Mathematics 2024-07-29 W. Zeng , L. M. Lui , F. Luo , J. S. Liu , T. F. Chan , S. T. Yau , X. F. Gu

The Heisenberg hierarchy and its Hamiltonian structure are derived respectively by virtue of the zero curvature equation and the trace identity. With the help of the Lax matrix we introduce an algebraic curve $\mathcal{K}_{n}$ of arithmetic…

Mathematical Physics · Physics 2014-05-06 Xianguo Geng , Zhu Li , Liang Guan

Given a curve defined over an algebraically closed field which is complete with respect to a nontrivial valuation, we study its tropical Jacobian. This is done by first tropicalizing the curve, and then computing the Jacobian of the…

Algebraic Geometry · Mathematics 2017-01-13 Barbara Bolognese , Madeline Brandt , Lynn Chua

Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T-matrix equations are solved numerically in the real-time domain. The single-particle…

Strongly Correlated Electrons · Physics 2009-10-31 P. E. Kornilovitch , Bumsoo Kyung

We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…

Analysis of PDEs · Mathematics 2017-08-31 Taiga Kumagai

The semidiscretization of a sound soft scattering problem modelled by the wave equation is analyzed. The spatial treatment is done by integral equation methods. Two temporal discretizations based on Runge-Kutta convolution quadrature are…

Numerical Analysis · Mathematics 2024-07-25 Jens Markus Melenk , Alexander Rieder

A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…

Algebraic Geometry · Mathematics 2025-10-30 Alessandro Oneto , Nick Vannieuwenhoven

We study the asymptotic behavior of solutions of the two dimensional incompressible Euler equations in the exterior of a curve when the curve shrinks to a point. This work links two previous results: [Iftimie, Lopes Filho and Nussenzveig…

Analysis of PDEs · Mathematics 2011-02-07 Christophe Lacave

The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \in \mathbb{C}^{2n\times 2n}$ with a…

Numerical Analysis · Mathematics 2018-01-04 Zhen-Chen Guo , Eric King-Wah Chu , Wen-Wei Lin

We prove that every locally finite, quasi-transitive graph with a thick end whose cycle space is generated by cycles of bounded length contains the full-grid as an asymptotic minor and as a diverging minor. This in particular includes all…

Combinatorics · Mathematics 2025-10-23 Sandra Albrechtsen , Matthias Hamann

We apply the circle method to obtain an asymptotic formula for the number of integral points on a certain sliced cubic hypersurface related to the Segre cubic. Unusually, the major and minor arc integrals in this application are both…

Number Theory · Mathematics 2019-11-13 Joerg Bruedern , Trevor D. Wooley

Watanabe's theta graph diffeomorphism, constructed using Watanabe's clasper surgery construction which turns trivalent graphs in 4-manifolds into parameterized families of diffeomorphisms of 4-manifolds, is a diffeomorphism of $S^4$…

Geometric Topology · Mathematics 2025-11-26 David T. Gay

Thurston maps are branched self-coverings of the sphere whose critical points have finite forward orbits. We give combinatorial and algebraic characterizations of Thurston maps that are isotopic to expanding maps as "Levy-free" maps and as…

Dynamical Systems · Mathematics 2016-10-11 Laurent Bartholdi , Dzmitry Dudko

This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…

Statistics Theory · Mathematics 2023-09-07 Yinan Shen , Dong Xia

This article is concerned with the existence of solution to the stochastic Degasperis-Procesi equation on $\mathbb{R}$ with an infinite dimensional multiplicative noise and integrable initial data. Writing the equation as a system composed…

Probability · Mathematics 2024-09-05 Nikolai V. Chemetov , Fernanda Cipriano

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…

Graphics · Computer Science 2026-03-04 Yue Ruan , Albert Chern , Tzu-Mao Li , Kartic Subr , Amir Vaxman

B\"acklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear…

Differential Geometry · Mathematics 2007-05-23 Tim Hoffmann

The precise asymptotic behaviour of the solutions to the twodimensional curvature equation $\Delta u=k(z) e^{2 u}$ with $e^{2 u} \in L^1$ for bounded nonnegative curvature functions $-k(z)$ near isolated singularities is obtained.

Analysis of PDEs · Mathematics 2015-05-13 Daniela Kraus , Oliver Roth

This is a review article on a tropical geometric realization of the ultradiscrete periodic Toda lattice (UD-pTL). Time evolution of the UD-pTL is translated into an addition on the Picard group of its spectral curve, which is a tropical…

Exactly Solvable and Integrable Systems · Physics 2018-02-06 Atsushi Nobe

We study the geodesic problem on the group of diffeomorphism of a domain M$\subset$Rd, equipped with the H(div) metric. The geodesic equations coincide with the Camassa-Holm equation when d=1, and represent one of its possible…

Analysis of PDEs · Mathematics 2020-01-08 Thomas Gallouët , Andrea Natale , François-Xavier Vialard