相关论文: Elie Cartan's geometrical vision or how to avoid e…

We propose the notion of $E_{2}$-quasi-exact solvability and apply this idea to find explicit solutions to the eigenvalue problem for a non-Hermitian Hamiltonian system depending on two parameters. The model considered reduces to the…

We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal approaches within a unifying framework. First, we establish a…

Pure advection of a conservative scalar is relevant to several applications including two-phase flow. Successful numerical schemes must capture the sharp interface between the phases while maintaining a smooth (wrinkle-free) interfacial…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

Let $E/\mathbb{Q}_p$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$-adic images of $E$ using tools from $p$-adic Hodge theory via a careful analysis of the…

We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

It is becoming more important to subtract renormalons efficiently from perturbative calculations, in order to achieve high precision QCD calculations. We propose a new framework ``Dual Space Approach" for renormalon separation, which…

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…

Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…

Let M be a manifold and g a Lie algebra acting on M. Differential forms Omega(M) carry a natural action of Lie derivatives L(x) and contractions I(x) of fundamental vector fields for x \in g. Contractions (anti-) commute with each other,…

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…

In a higher-order modified teleparallel theory cosmological we present analytical cosmological solutions. In particular we determine forms of the unknown potential which drives the scalar field such that the field equations form a Liouville…

We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method for second-order elliptic problems. Our method is obtained by inserting the $L^2$-orthogonal projection onto the approximate space for a numerical trace into all…

We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…

The linearization problem by use of the Cartan equivalence method for scalar third-order ODEs via point transformations was solved partially in [1,2]. In order to solve this problem completely, the Cartan equivalence method is applied to…

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…

This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…

In this paper we combine a flexible covariant formulation of the shallow water equations with the semi-implicit numerical scheme developed over the years by Casulli and collaborators. After adopting an orthogonal, but non-orthonormal,…

We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In…