A recent paper in this journal proposed the conversion of conical intersections to avoided crossings by lowering the symmetry with an optical field. The article also claimed that the characters of nonadiabatic transitions caused by avoided crossings and conical intersections are qualitatively different. The present comment shows that this proposal and this claim result from an incorrect appreci...

This paper proves the formulae reg(IJ) ≤ reg(I) + reg(J), reg(I ∩ J) ≤ reg(I) + reg(J) for arbitrary monomial complete intersections I and J , and provides examples showing that these inequalities do not hold for general complete intersections.

Presenting true crossings of adiabatic potential energy surfaces, conical intersections are a paradigm of ultrafast and efficient electronic relaxation dynamics. The same mechanism is shown to apply also for vibrational conical intersections, which may occur when two high-frequency modes (such as OH stretch vibrations) are coupled to low-frequency modes (such as hydrogen bonding modes). By deri...

We study families of volume preserving diffeomorphisms in R(3) that have a pair of hyperbolic fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to elucidate the topology of the intersections and how it changes with the parameters of the system. We show that the "primary intersection" of the stable and unstable manifolds is generically a neat submanifold o...

The yellow signal driver behavior, reflecting the dilemma zone behavior, is analyzed using naturalistic data from digital enforcement cameras. The key variable in the analysis is the entrance time after the yellow onset, and its distribution. This distribution can assist in determining two critical outcomes: the safety outcome related to red-light-running angle accidents, and the efficiency out...

Setting signals at traffic intersections to reduce congestion is one of the most challenging problems in traffic management. To find the optimal control strategy, specific information of the traffic flows passing through intersections, such as vehicle arrival rates (number of vehicles per hour), must be provided in advance. In most control approaches, this parameter is assumed to be a known con...

in this paper we investigate decompositions of submodules in modules over a proufer domain into intersections of quasi-primary and classical quasi-primary submodules. in particular, existence and uniqueness of quasi-primary decompositions in modules over a proufer domain of finite character are proved. proufer domain; primary submodule; quasi-primary submodule; classical quasi-primary; decomposi...

This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent ...

Introduction 2 1. Shimura curves 6 1.1. Modular interpretation 6 1.2. Integral models 13 1.3. Reductions of models 17 1.4. Hecke correspondences 18 1.5. Order R and its level structure 25 2. Heegner points 29 2.1. CM-points 29 2.2. Formal groups 34 2.3. Endomorphisms 37 2.4. Liftings of distinguished points 40 3. Modular forms and L-functions 43 3.1. Modular forms 44 3.2. Newforms on X 49 3.3. ...

Expressways have been constructed in many states as a way to increase mobility without the expense of a full access-controlled or grade-separated facility. In most cases, it was assumed that these segments of highway would produce mobility and safety characteristics similar to other access-controlled facilities. However, recent research has found that there are problems with the safety performa...