相关论文: The Shadowing Properties Of Nonautonomous Dynamica…

We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function $N_L(E)$, the number of bound states of the operator $L = \Delta+V$ in $\R^d$ below $-E$. Here $V$ is a bounded potential behaving asymptotically…

A successful method to describe the asymptotic behavior of various deterministic and stochastic processes such as asymptotically autonomous differential equations or stochastic approximation processes is to relate it to an appropriately…

The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show…

Let $M$ be a closed smooth Riemannian manifold $M$, and let $f:M\to M$ be a diffeomorphism. Herein, we demonstrate that (i) if $f$ has the $C^1$ robustly inverse shadowing property on the chain recurrent set $\mathcal{CR}(f)$, then…

This is the second of two papers that study the asymptotic structure of space-times with a non-negative cosmological constant $\Lambda$. This paper deals with the case $\Lambda >0$. Our approach is founded on the `tidal energies' built with…

The problem of existence of spacelike hypersurfaces with constant mean curvature in asymptotically flat spacetimes is considered for a class of asymptotically Schwarzschild spacetimes satisfying an interior condition. Using a barrier…

We describe an algorithm for constructing N-body realizations of equilibrium spherical systems. A general form for the mass density rho(r) is used, making it possible to represent most of the popular density profiles found in the…

The non-relativistic self-gravitating gas in thermal equilibrium in the presence of a positive cosmological constant Lambda (dark energy) is investigated. The dark energy introduces a force pushing outward all particles with strength…

We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two. We find a one-dimensional pseudopotential that…

We investigate the shadow cast by a regular black hole in scalar-tensor-vector mOdified gravity theory. This black hole differs from a Schwarzschild-Kerr black hole by the dimensionless parameter $\beta$. The size of the shadow depends on…

We investigate symmetry properties of positive solutions for fully nonlinear uniformly elliptic systems, such as $$ F_i \,(x,Du_i,D^2u_i) +f_i \,(x,u_1, \ldots , u_n,Du_i)=0, \;\; 1 \leq i \leq n, $$ in a bounded domain $\Omega$ in…

We investigate the spectral properties of the Dirichlet Laplacian on large finite metric balls within irregular infinite graphs of quadratic volume growth. We consider an exhaustion $G_n = B_{R_n}(x_0)$ and the spectral zeta value $Z_n(1) =…

In this paper, we investigate stochastic heat equation with sublinear diffusion coefficients. By assuming certain concavity of the diffusion coefficient, we establish non-trivial moment upper bounds and almost sure spatial asymptotic…

This work investigates observational properties, namely the shadow and photon ring structure, of emission profiles originating near compact objects. In particular, we consider a distorted and deformed compact object characterised by two…

Let $G\subset \O(n)$ be a group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of G. Consider a symmetric, classical…

Asymptotic boundedness is a crucial property of Distributed Set-Membership Filtering (DSMFing) that prevents the unbounded growth of the set estimates caused by the wrapping effect. However, this important property remains…

A result of Simonovits and S\'os states that for any fixed graph $H$ and any $\epsilon > 0$ there exists $\delta > 0$ such that if $G$ is an $n$-vertex graph with the property that every $S \subseteq V(G)$ contains $p^{e(H)} |S|^{v(H)} \pm…

We analytically investigate the shadows cast by rotating black holes in the asymptotically safe gravity (ASG) by deriving complete null geodesics and observables using the Hamilton-Jacobi equation and Carter separable method. It turns out…

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: 1. X is in the C1-interior of the set of expansive divergence-free vector…

The pseudomode method for open quantum systems, also known as the mesoscopic leads approach, consists in replacing a structured environment by a set of auxiliary "pseudomodes" subject to local damping that approximate the environment's…