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Fundamental assumptions which form the basis of models for large-scale structure in the Universe are sketched in light of a Lagrangian description of inhomogeneities. This description is introduced for Newtonian self-gravitating flows. On…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We present the error analysis of Lagrange interpolation on triangles. A new \textit{a priori} error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity…
We study the symplectic geometry of derived intersections of Lagrangian morphisms. In particular, we show that for a functional $f : X \rightarrow \mathbb{A}_k^1$, the derived critical locus has a natural Lagrangian fibration…
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
Consider three-dimensional fractional MHD equations in an exterior domain with the Dirichlet boundary condition assumed. Asymptotic behaviours of weak solutions to the three-dimensional exterior fractional MHD equations are studied. $L^2$…
We prove interior weighted Hessian estimates in Orlicz spaces for nondivergence type elliptic equations with a lower order term which involves a nonnegative potential satisfying a reverse H\"older type condition.
A framework is developed in which one can write down the constraint equations on a three--dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract…
We formulate higher order variations of a Lagrangian in the geometric framework of jet prolongations of fibered manifolds. Our formalism applies to Lagrangians which depend on an arbitrary number of independent and dependent variables,…
Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasi-nonlinear stage well. We present a third-order perturbative equation for Lagrangian perturbation with pressure in both the longitudinal and…
We use spectral decimation to provide formulae for computing the harmonic gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These formulae are given in terms of special functions that are defined as infinite products.
In this paper we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of…
Let $(X,\alpha)$ be a K\"ahler manifold of dimension n, and let $[\omega] \in H^{1,1}(X,\mathbb{R})$. We study the problem of specifying the Lagrangian phase of $\omega$ with respect to $\alpha$, which is described by the nonlinear elliptic…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
Lagrangian perturbation theory for cosmological fluid describes structure formation in the quasi-nonlinear stage well. In a previous paper, we presented a third-order perturbative equation for Lagrangian perturbation with pressure. There we…
We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to…
After an introduction to the phases of QCD at high density and zero temperature, we introduce the effective lagrangian for the CFL phase and discuss the perturbative evaluation of its parameters
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…