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In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…

Probability · Mathematics 2020-01-28 James Thompson

We establish the existence of at least two solutions of the {\it Prandtl-Batchelor} like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable and hence the usual…

Analysis of PDEs · Mathematics 2023-06-23 Debajyoti Choudhuri , Dušan D. Repovš

In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data.…

Analysis of PDEs · Mathematics 2024-01-05 Minh-Phuong Tran , Thanh-Nhan Nguyen

Generically, a fully measured elasticity tensor has no material symmetry. For single crystals with a cubic lattice, or for the aeronautics turbine blades superalloys such as Nickelbased CMSX-4, cubic symmetry is nevertheless expected. It is…

Optimization and Control · Mathematics 2022-03-29 Perla Azzi , Rodrigue Desmorat , Boris Kolev , Fabien Priziac

In this note we consider the Steiner tree problem under Bilu-Linial stability. We give strong geometric structural properties that need to be satisfied by stable instances. We then make use of, and strengthen, these geometric properties to…

Data Structures and Algorithms · Computer Science 2021-09-29 James Freitag , Neshat Mohammadi , Aditya Potukuchi , Lev Reyzin

In this paper we derive topological and number theoretical consequences of the rigidity of elliptic genera, which are special modular forms associated to each compact almost complex manifold. In particular, on the geometry side, we prove…

Algebraic Topology · Mathematics 2020-01-31 Kathrin Bringmann , Alexander Caviedes Castro , Silvia Sabatini , Markus Schwagenscheidt

We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner…

Metric Geometry · Mathematics 2011-11-11 Marcus Brazil , Charl Ras , Doreen Thomas

We consider the variant of a stochastic parabolic Ginzburg-Landau equation that allows for the formation of point defects of the solution. The noise in the equation is multiplicative of the gradient type. We show that the family of the…

Probability · Mathematics 2016-11-22 Olga Chugreeva , Christof Melcher

We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear isotropic elliptic equations on compact Riemannian manifolds, depending only on dimension and a lower bound for the…

Differential Geometry · Mathematics 2019-05-07 Ben Andrews , Changwei Xiong

We study a generalization of the Steiner tree problem, where we are given a weighted network $G$ together with a collection of $k$ subsets of its vertices and a root $r$. We wish to construct a minimum cost network such that the network…

Data Structures and Algorithms · Computer Science 2017-07-12 Guru Guruganesh , Jennifer Iglesias , R. Ravi , Laura Sanità

The Directed Steiner Tree (DST) problem is defined on a directed graph $G=(V,E)$, where we are given a designated root vertex $r$ and a set of $k$ terminals $K \subseteq V \setminus {r}$. The goal is to find a minimum-cost subgraph that…

Data Structures and Algorithms · Computer Science 2025-10-13 Bundit Laekhanukit

As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…

High Energy Physics - Theory · Physics 2014-11-18 V. V. Mangazeev , Yu. G. Stroganov

In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path…

Data Structures and Algorithms · Computer Science 2022-11-10 Stephan Held , Yannik Kyle Dustin Spitzley

The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…

Data Structures and Algorithms · Computer Science 2023-08-16 Cristina G. Fernandes , Carla N. Lintzmayer , Phablo F. S. Moura

In this paper we first employ the energetic variational method to derive a micro-macro model for compressible polymeric fluids. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear Fokker-Planck…

Analysis of PDEs · Mathematics 2017-06-28 Ning Jiang , Yanan Liu , Teng-Fei Zhang

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees.This notion arises in numerical approximations of…

Metric Geometry · Mathematics 2020-02-25 Charl Ras , Konrad J. Swanepoel , Doreen Thomas

We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application…

Analysis of PDEs · Mathematics 2012-11-09 Yann Brenier

In this paper we obtain $C^{1,\theta}$-estimates on the distance of inertial manifolds for dynamical systems generated by evolutionary parabolic type equations. We consider the situation where the systems are defined in different phase…

Analysis of PDEs · Mathematics 2017-04-12 José M. Arrieta , Esperanza Santamaría

The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…

Computational Geometry · Computer Science 2023-12-01 T-H. Hubert Chan , Gramoz Goranci , Shaofeng H. -C. Jiang , Bo Wang , Quan Xue

The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…

Data Structures and Algorithms · Computer Science 2025-03-07 Stephan Held , Edgar Perner