Mathematical model of aerobic stabilization of old landfills

A short-term aerobic stabilization of digested waste in the final methane phase was studied. The effect of aeration rate on the reduction of leachate parameters and on the rate of CO₂ production and O₂ assimilation was investigated. Experimental simulation of aerobic landfill stabilization was carried out using lysimeters. When testing the effect of aeration rate on the reduction of leachate indices (BOD₅, COD, N-NH₄⁺), it was reported that the most significant reduction was obtained at the highest rate of aeration and the smallest reduction of leachate indices was attained not at the lowest but at medium aeration rates. Both the rate of CO₂ production and the O₂ assimilation reached their highest values in the lysimeters aerated at a high rate of aeration. The proposed mathematical model which consists of a system of five differential equations describing CO₂ production, O₂ assimilation and the changes of organic carbon content in the leachate correspond well with the experimental data.     

Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks

Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity conditions. We extend these arguments to discrete mass functions and their associated measures using the concept that the mass function can be embedded in a joint density function with continuous arguments. We give two different conditions, monotonicity and convergence on the unit sphere, both of which can make the discrete function embeddable. Our results are then applied to the preferential attachment network model, and we conclude that the joint mass function of in- and out-degree is embeddable and thus regularly varying.     

Polyvinyl alcohol-borate hydrogel containing Prussian blue for surface decontamination

A polyvinyl alcohol (PVA)-borate hydrogel-based strippable surface decontaminant containing an ammonium salt and Prussian blue (PB) was developed for the removal of ¹³⁷Cs from various surfaces. This surface decontaminant can be easily prepared by the simple mixing of commercially available materials, such as PVA, borax, NH₄Cl and PB, in water, and the decontaminant can be peeled off surfaces due to its high elastic property after surface decontamination. The hydrogel displayed an effective removal performance for Cs from painted cement, aluminum, stainless steel, and cement surfaces and a potential for reusability. Therefore, the PB/PVA-borate hydrogel has good potential as a new surface decontaminant.     

Possible acceleration of cosmic rays in a rotating system: Uehling-Uhlenbeck model

We illustrate the possible acceleration of cosmic rays passing through a kind of amplification channel (via diffusion modes of propagating plane-wave fronts) induced by a rotating system. Our analysis is mainly based on the quantum discrete kinetic model (considering a discrete Uehling-Uhlenbeck collision term), which has been used to study the propagation of plane (e.g., acoustic) waves in a system of rotating gases.     

Limit averages of continuous functions under the action of cellular automata

We consider averages of continuous functions under the action of cellular automata, which were proposed by Boyle, Lind and Rudolph in 1988. It is proved that, at non-shift-periodic points, the averages converge point-wisely to the integration with respect to the uniform Bernoulli measure.     

An Integrated Version of Varadhan’s Asymptotics for Lower-Order Perturbations of Strong Local Dirichlet Forms

The studies of J. A. Ramírez, Hino–Ramírez, and Ariyoshi–Hino showed that an integrated version of Varadhan’s asymptotics holds for Markovian semigroups associated with arbitrary strong local symmetric Dirichlet forms. In this paper, we consider non-symmetric bilinear forms that are the sum of strong local symmetric Dirichlet forms and lower-order perturbed terms. We give sufficient conditions for the associated semigroups to have asymptotics of the same type.     

A broad view of queueing theory through one issue

This is an overview and appreciation of the contributions to this special issue.