We introduce a sublevel Moment-SOS hierarchy where each SDP relaxation can be viewed as an intermediate (or interpolation) between the d-th and \((d+1)\)-th order relaxations of (dense or sparse version). With flexible choice determining size (level) number (depth) subsets in relaxation, one is able to obtain different improvements compared based on machine memory capacity. In particular, we pr...

We consider an oscillatory integral operator with Loomis—Whitney multilinear form. The phase is real analytic in a neighborhood of the origin ℝd and satisfies nondegeneracy condition related to its Newton polyhedron. Maximal decay obtained for this certain cases, depending on polyhedron given Lebesgue exponents. Our estimates imply volumes sublevel sets such functions are small relative product...

An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of the values on its vertices. The resulting acyclic partial matching may be used to construct a reduced filtered complex with the same multidimensional persisten...

We investigate the excitation of atomic levels in a high-voltage discharge gap by studying the spectrum of the 2p-3d transitions of Li I atoms flowing in the gap. The Stark splitting of this transition, due to the gap electric field, enables resolving the lines originating from different magnetic sublevels of the 3d level. We show that the atomic level populations are dominated by excitations d...

Retention of orbital alignment during near-resonant energy transfer collisions of rare-gas projectiles with excited alkaline-earth-metal atoms is explored theoretically for scattering of Xe from Rydberg states of Ca. For such collisions, conventional interpretations of alignment phenomena, which are based on potential curves for a transient molecule thought to form during the collision, are not...

Seeking the convex hull of an object (or point set) is a very fundamental problem arising from various tasks. In this work, we propose variational approach based on level-set representation for hulls 2-dimensional objects. This method can adapt to exact and inexact problems. addition, compute multiple simultaneously. model, characterized by zero sublevel-set function. For case, require be conta...