Conical intersections between electronic potential energy surfaces are paradigmatic for the study of nonadiabatic processes in excited states large molecules. However, since corresponding dynamics occurs on a femtosecond timescale, their investigation remains challenging and requires ultrafast spectroscopy techniques. We demonstrate that trapped Rydberg ions platform to engineer conical simulat...

As a common generalization of matchings and matroid intersection, W.H. Cunningham and J.F. Geelen introduced the notion of path-matchings, then they introduced the more general notion of even factor in weakly symmetric digraphs. Here we give a min-max formula for the maximum cardinality of an even factor. Our proof is purely combinatorial. We also provide a Gallai-Edmonds-type structure theorem...

Last lecture we covered matroid intersection, and defined matroid union. In this lecture we review the definitions of matroid intersection, and then show that the matroid intersection polytope is TDI. This is Chapter 41 in Schrijver’s book. Next we review matroid union, and show that unlike matroid intersection, the union of two matroids is again a matroid. This material is largely contained in...

the class of ads modules with the sip (briefly‎, ‎$sa$-modules) is studied‎. ‎various conditions for a module to be $sa$-module are given‎. ‎it is proved that for a quasi-continuous module $m$‎, ‎$m$ is a uc-module if and only if $m$ is an $sa$-module‎. ‎also‎, ‎it is proved that the direct sum of two $sa$-modules as $r$-modules is an $sa$-module when $r$ is the sum of the annihilators of these...

Some of these curves are considered in a rather incidental way in the writings of Poincare.** However, the full concept of pseudo closed trajectories does not seem to have been discussed explicitly heretofore. We assume that all of the variables in the equations (1) are real, that the functions X and Y are continuous in an open connected region R in the xy-plane, that these functions satisfy Li...

For a set S of n lines labeled from 1 to n, we say that S supports an n-vertex planar graph G if for every labeling from 1 to n of its vertices, G has a straight-line crossing-free drawing with each vertex drawn as a point on its associated line. It is known from previous work [4] that no set of n parallel lines supports all n-vertex planar graphs. We show that intersecting lines, even if they ...

The topological relation is one of the most important spatial relations. Analysis of spatial relation has great practical value. The possible topological relations between 3D simple body objects can be analyzed using 9-intersection model. An algorithm is proposed to analyze the topological relations between body objects. It decomposes the complicated objects into simple objects, so it can get t...

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

We generalize the matroid intersection theorem to distributive supermatroids, a structure that extends the matroid to the partially ordered ground set. Distributive supermatroids are special cases of both supermatroids and greedoids, and they generalize polymatroids. This is the first good characterization proved for the intersection problem of an independence system where the ground set is par...