Published in Journal of Mathematical Chemistry
on a basic element, vertex degree, of topological graphs, insights are obtained on the structural features hidden in the degree distributions (DD) of saturated hydrocarbons. The investigation shows that the cyclicity and branching features are mainly coded by the different mathematical characteristics of the degree distributions. Surprisingly, the ...
Published in Qualitative Theory of Dynamical Systems
We investigate the bifurcation of small-amplitude limit cycles in generalized Liénard equations. We use the simplicity of the Liénard family, to illustrate the advantages of the approach based on Bautin ideals. Essentially, this Bautin ideal is generated by the so-called Lyapunov quantities, that are computed for generalized Liénard equations and u...
Published in Journal of Optimization Theory and Applications
Rockafellar has shown that the subdifferentials of convex functions are always cyclically monotone operators. Moreover, maximal cyclically monotone operators are necessarily operators of this type, since one can construct explicitly a convex function, which turns out to be unique up to a constant, whose subdifferential gives back the operator. This...
This paper argues for an implementation of cyclicity through a natural economy condition, the Earliness Principle (EP), which requires a feature to be eliminated as early as possible. EP predicts that the search space for feature checking should increase throughout the derivation with the growth of the phrase marker. This prediction is shown to be ...
Published in Veterinary Research Communications
Published in Mathematical Geology
Common variogram models, such as spherical or exponential functions, increase monotonically with increasing lag distance. On the other hand, a hole-effect variogram typically exhibits sinusoidal waves that form peaks and troughs, thereby conveying the cyclicity of the underlying phenomenon. In order to incorporate this cyclicity into a stochastic s...
Published in Mathematical Geology
Variograms calculated from binary variables, such as from two lithologies, tend to show sinusoidal forms with decreasing amplitudes for increasing lag distances. This cyclicity is observed often when analyzing drill-hole data for rock sequences with alternating lithologies, and the variograms are thus labeled “hole-effect variograms.” Such variogra...
Published in Russian Journal of Ecology
Analysis of the reproductive dynamics ofCalliptamus italicus during the past 100 years confirmed the dependence of locust invasions on the 11-year cycles of solar activity, which was previously known for other gregarious locusts. Over a considerable part of the species range, the onset of mass reproduction is promoted by a hot and droughty spring a...
Published in Science in China Series A: Mathematics
New conditions for a planar homoclinic loop to have cyclicity two under multiple parameter perturbations have been obtained. As an application it is proved that a homoclinic loop of a nongeneric cubic Hamiltonian has cyclicity two under arbitrary quadratic perturbations.
Published in Chinese Science Bulletin
The conjectureE(k)⩽k is proved to be true if and only ifk=1, 2, 3, whereE(k) is the cyclicity of condimensionk generic elementary polycycles. It is also proved that the cyclicity of any codimension 3 ensembles except ensembles with “lips” is ⩽6. By the way, the methods usually used in the study of cyclicity of polycycles such as derivation division...
