Related papers: Discounted Gottschalk-Hedlund theorem
In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing…
Gateway will represent a primary logistic infrastructure in cislunar space. The identification of efficient orbit transfers capable of connecting Earth, Moon, and Gateway paves the way for enabling refurbishment, servicing, and utilization…
The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems from recent models in biology and phylogenetics, where…
Commutative $d$-torsion $K$-theory is a variant of topological $K$-theory constructed from commuting unitary matrices of order dividing $d$. Such matrices appear as solutions of linear constraint systems that play a role in the study of…
We prove the existence of quasi-periodic, small amplitude, solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities we also obtain the linear stability of the…
A growing body of applied mathematics literature in recent years has focussed on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
This work extends weak KAM theory to the case of a nonsmooth Lagrangian satisfying a superlinear growth condition. Using the solution of a weak KAM equation that is a stationary Hamilton-Jacobi equation and the proximal aiming method, we…
We propose a proximal algorithm for minimizing objective functions consisting of three summands: the composition of a nonsmooth function with a linear operator, another nonsmooth function, each of the nonsmooth summands depending on an…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…
In this paper, we consider a time independent $C^2$ Hamiltonian, sa\-tisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the…
We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that the action has a dense orbit, and demonstrate two novel…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of…
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…
For a reduced hyperplane arrangement we prove the analytic Twisted Logarithmic Comparison Theorem, subject to mild combinatorial arithmetic conditions on the weights defining the twist. This gives a quasi-isomorphism between the twisted…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…