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.

Spectroscopic constants for the ground and low-lying excited electronic states of the Ga2 molecule have been studied using MRSDCI and MRCPA methods with an extensive basis set of Gaussian-type functions. In this study, we are going to present spectroscopic constants and potential energy curves for the ground Pu and the excited Sg , Sg , Pu, Dg, …2†Sg and Su states, in which electron correlation...

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...

Carotenoid spheroidene (SPO) functions for photoprotection in the photosynthetic reaction centers (RCs) and effectively dissipates its triplet excitation energy. Sensitized cis-to-trans isomerization was proposed as a possible mechanism for a singlet-triplet energy crossing for the 15,15'-cis-SPO; however, it has been questioned recently. To understand the dissipative photoprotective mechanism ...

Double resonance level crossing detection cannot normally be used to record transitions between the quadrupole Zeeman levels. Neither can it be used if the quadrupole resonance frequency is larger than the pro ton N M R frequency in high field. A simple variation of the level crossing experiment is demonstrated which allows energy to be efficiently transferred f rom quadrupole to proton system ...

Due to the presence of the chiral anomaly sphalerons with Chern-Simons number a half (CS=1/2) are the only static configurations that allow for a fermion level crossing in the two-dimensional Abelian-Higgs model with massless fermions, i.e. in the absence of Yukawa interactions. In the presence of fermion-Higgs interactions we demonstrate the existence of zero energy solutions to the one-dimens...

We discuss the non-Abelian artificial magnetic monopoles associated with n-level energy crossing in quantum systems. found that hidden symmetries reveal themselves as observables such spin, hypercharge, and other physical degrees of freedom. illustrated our results on concrete examples two three energy-level crossings. Our findings can be helpful for modeling various phenomena systems SU(N) top...

– We consider the inverse Landau-Zener problem which consists in finding the energy-sweep functions W (t) ≡ ε1(t) − ε2(t) resulting in the required time dependences of the level populations for a two-level system crossing the resonance one or more times during the sweep. We find sweep functions of particular forms that let manipulate the system in a required way, including complete switching fr...

In this paper, various temporal features (i.e., zero crossing rate and short-time energy) and spectral features (spectral flux and spectral centroid) have been derived from the Teager energy operator (TEO) profile of the speech waveform. The efficacy of these features has been analyzed for the classification of normal and dysphonic voices by comparing their performance with the features derived...

We consider the generalization of the Kramers escape over a barrier problem to the case of a long chain molecule. The problem involves the motion of a chain molecule of N segments across a region where the free energy per segment is higher, so that it has to cross a barrier. We consider the limit where the length of the molecule is much larger than the width of the barrier. The width is taken t...