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We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration...
In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature bounded below. Yau’s gradient estimates for harmonic functions is also obtained on Alexandrov spaces.
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local gradient estimate for positive solution to a simple nonlinear parabolic equation
Let G denote a closed, connected, self adjoint, noncompact subgroup of GL(n,R), and let dR and dL denote respectively the right and left invariant Riemannian metrics defined by the canonical inner pr...
We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same proce...
In this paper, we will obtain some weighted strong type and weak type estimates of Bochner-Riesz operators $T^{{(n-1)}/2}_R$ on the weighted Morrey spaces $L^{p,\kappa}(w)$ for $1\le p<\infty$ and $0...
$W^{2,2}$ Estimates for Solutions to Non-Uniformly Elliptic PDE'S with Measurable Coefficients.
Estimates for the $\partial-$Neumann Operator On Strongly Pseudo-Convex Domain With Lipschitz Boundary.
Estimates for the Green function and Characterization of a Certain Kato Class by the Gauss Semigroup in the Half Space.
The main objective of this paper is to obtain explicit estimates on some integral inequalities on time scale. The obtained inequalities can be used as tools in the study of certain classes of dynamic ...

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