We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...

Level-crossing sampling refers to a sampling method that generates a sequence of timing samples when a signal crosses a specified set of levels. Conventional sampling techniques more typically rely on producing a sequence of amplitude samples at a specified set of timings. Level-crossing sampling has been considered as a promising alternative to time sampling when it is difficult to implement h...

We address the problem of quantifying the number of samples that can be obtained through a level crossing sampling procedure for applications to mobile systems. We specially investigate the link between the smoothness properties of the signal and the number of samples, both from a theoretical and a numerical point of view.

the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

The mechanism of avoided level crossings in quantum systems is studied. It is traced back to the existence of branch points in the complex plane which influence the properties of resonance states as well as of discrete states. An avoided level crossing of two states causes not only an exchange of the two wave functions but, above all, correlations between them. The correlations play an importan...

In consideration of the safety drivers, we designed a multifunctional intelligent seecurity guarantee integrated system for highway level crossing. Different from existing intersection signs on market, highway-level indicators are based use deep learning and computer vision technology to build convolutional neural network model that can accurately recognize traffic accident images jams in short...