Related papers: Nullity bounds for certain Hamiltonian delay equat…
We establish the existence of solutions to the following semilinear Neumann problem for fractional Laplacian and critical exponent: \begin{align*}\left\{\begin{array}{l l} { (-\Delta)^{s}u+ \lambda u= \abs{u}^{p-1}u } & \text{in $ \Omega,$…
We show that the actions and indexes of fixed points of a Hamiltonian diffeomorphism with finitely many periodic points must satisfy certain relations, provided that the quantum cohomology of the ambient manifold meets an algebraic…
We exactly solve a quantum Fermi accelerator model consisting of a time-independent non-Hermitian Hamiltonian with time-dependent Dirichlet boundary conditions. A Hilbert space for such systems can be defined in two equivalent ways, either…
We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $\delta$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike…
We obtain bounded for all $t$ solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on $(-L,L)$, with $L \rightarrow \infty$. We derive a priori estimates for the Dirichlet problems,…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…
We consider N-body problems with homogeneous potential $1/r^{2\kappa}$ where $\kappa\in(0,1)$, including the Newtonian case ($\kappa=1/2$). Given $R>0$ and $T>0$, we find a uniform upper bound for the minimal action of paths binding in time…
This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the timelike boundary $\cal B$ orthogonally. The expressions for the action and Hamiltonian…
An abstract framework guaranteeing the continuous differentiability of local value functions on $H^1(\Omega)$ associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm…
A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…
Our principal aim in the present article is to establish a uniform hybrid bound for individual values on the critical line of Hecke $L$-functions associated with cusp forms over the full modular group. This is rendered in the statement that…
Following the classical result of long-time asymptotic convergence towards the Gaussian kernel that holds true for integrable solutions of the Heat Equation posed in the Euclidean Space $\mathbb{R}^n$, we examine the question of long-time…
We describe a variational approach to a notion of Hamiltonian delay equations. Our delay Hamiltonians are of product form. We consider several examples. For closed symplectically aspherical symplectic manifolds $(M,\omega)$ we prove that…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
Our main goal is the comparative study of singularities of solutions to the systems of first order quasilinear PDEs and their perturbations containing higher derivatives. The study is focused on the subclass of Hamiltonian PDEs with one…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
The dynamics of a class of nonsymmetric gravitational theories is presented in Hamiltonian form. The derivation begins with the first-order action, treating the generalized connection coefficients as the canonical coordinates and the…
In this paper, we study the sufficient conditions for the existence of solutions of first-order Hamiltonian stochastic impulsive differential equations under Dirichlet boundary value conditions. By using the variational method, we first…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found.…