相关论文: Vanishing Cycles and the Inverse Problem of Potent…

A nonnegative function on the vertices of an infinite graph G which vanishes at a distinguished vertex o, has Laplacian 1 at o, and is harmonic at all other vertices is called a potential. We survey basic properties of potentials in…

The Newtonian Potential is computed exactly in a theory that is fundamentally Non Commutative in the space-time coordinates. When the dispersion for the distribution of the source is minimal (i.e. it is equal to the non commutative…

We show that a central $1/r^n$ singular potential (with $n\geq 2$) is renormalized by a one-parameter square-well counterterm; low-energy observables are made independent of the square-well width by adjusting the square-well strength. We…

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…

Little is known about the global structure of the basins of attraction of Newton's method in two or more complex variables. We make the first steps by focusing on the specific Newton mapping to solve for the common roots of $P(x,y) =…

We consider the nonlocal Cahn-Hilliard equation with singular (logarithmic) potential and constant mobility in three-dimensional bounded domains and we establish the validity of the instantaneous strict separation property. This means that…

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…

This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…

The problem of a particle of mass m in the field of the inverse square potential is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate…

This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…

For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This…

Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime…

Let $D\subset \R^n$, $n\geq 3,$ be a bounded domain with a $C^{\infty}$ boundary $S$, $L=-\nabla^2+q(x)$ be a selfadjoint operator defined in $H=L^2(D)$ by the Neumann boundary condition, $\theta(x,y,\lambda)$ be its spectral function,…

Let f be a transcendental entire function that omits a complex value a. We show that for every simply connected region D that does not contain a the full preimage of D is disconnected. We conjecture that the same holds if one only assumes…

The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we…

This is Part 1 of two papers where we develop the basic potential theory of elliptic operators on posssibly singular almost minimzers using their hyperbolic unfoldings. We can establish surprisingly robust boundary Harnack inequalities…

We discuss the nonlocal nature of quantum mechanics and the link with relativistic quantum mechanics such as formulated by quantum field theory. We use here a nonlocal quantum field theory (NLQFT) which is finite, satisfies Poincar\'e…

We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…