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Bounds on isolated scattering number
Get PDFThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas depending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
References
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Characteristic polynomials of simple ordinary abelian varieties over finite fields
No full texthttp://dx.doi.org/10.1017/S000497271200033
The alternative Kirchhoff approximation in elastodynamics with applications in ultrasonic nondestructive testing
No full textThe Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.
doi:10.1017/S144618112000003
The paradox of enrichment, spatial heterogeneity, community effects and the phenomenon of apparent disappearance in the marine bacteriophage dynamics
No full textIn aquatic microbial systems, high magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance ("apparent disappearance'') are relatively common. The authors suggest that, in order to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind, or external factors of any other nature, and can be caused by internal factors, and in particular by bacteria-phage interaction. Specifically, the authors suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, the authors consider a reasonably simple mathematical model of bacteria-phage interaction based on the model suggested by Edoardo Beretta and Yang Kuang, which assumes neither periodic forcing, nor action of other external factors. The model admits a loss of stability via Andronov-Hopf bifurcation and exhibits dynamics which is able to explains the phenomenon. These properties of the model are especially distinctive for spatially non-homogeneous biosystems as well as biosystem with some sorts of cooperation or community effects.
doi:10.1017/S144618112000008
Distribution-free confidence intervals for functions of quantiles
No full texthttp://dx.doi.org/10.1017/S000497271200033
The generalised weighted composition operators on Bergman spaces induced by doubling weights
No full texthttp://dx.doi.org/10.1017/S000497271200033
Interaction of a singular surface with a strong shock in the interstellar gas clouds
No full textWe investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.
doi:10.1017/S144618112100032
