相关论文: Numerical Bifurcation Analysis of the Conformal Me…

We prove the existence of a $C^{1,1}$ conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to $-1$ plus terms of order $e^{-2r}$ where $r$ is the distance from any fixed compact set. This metric has…

The secant method, as an important approach for solving nonlinear equations, is introduced in nearly all numerical analysis textbooks. However, most textbooks only briefly address the Q-order of convergence of this method, with few…

The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…

This paper presents the Hausdorff measure of noncompactness (MNC) within the framework of the generalized Hahn sequence space. By applying the MNC, we explore the existence of solutions for nonlinear Caputo fractional differential equations…

The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…

The supersymmetric reformulation of physical observables in the Chalker-Coddington model (CC) for the plateau transition in the integer quantum Hall effect leads to a reformulation of its critical properties in terms of a 2D non-compact…

Conformal prediction is a framework for uncertainty quantification that constructs prediction sets for previously unseen data, guaranteeing coverage of the true label with a specified probability. However, the efficiency of these prediction…

We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the…

Block-coordinate descent (BCD) is a popular framework for large-scale regularized optimization problems with block-separable structure. Existing methods have several limitations. They often assume that subproblems can be solved exactly at…

This paper provides a formal econometric framework behind the newly developed difference-in-discontinuities design (DiDC). Despite its increasing use in applied research, there are currently limited studies of its properties. We formalize…

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and…

In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and…

Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments, and provides systematic…

In 1992, motivated by Riemann mapping theorem, Escobar considered a version of Yamabe problem on manifolds of dimension n greater than 2 with boundary. The problem consists in finding a conformal metric such that the scalar curvature is…

The aim of this paper is to highlight a hitherto unknown computational aspect of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's system T have been introduced ([2,9,12]), and it was shown in [26] that the…

In this paper we study variational inequalities in a real Hilbert space, which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $C$. We assume that the set $C$ can be outerly…

Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction…

Conformal prediction is a distribution-free and model-agnostic uncertainty-quantification method that provides finite-sample prediction intervals with guaranteed coverage. In this work, for the first time, we apply conformal-prediction to…

We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…