Constructing minimal telescopers for rational functions in three discrete variables

We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm is guaranteed by a known existence criterion of telescopers. Our approach has the important feature that it avoids the potentially costly computation of certificates. Computational experiments are also provided so as to illustrate the efficiency of our approach

Probing the phonon surface interaction by wave packet simulation: effect of roughness and morphology

One way to reduce the lattice thermal conductivity of solids is to induce additional phonon surface scattering through nanostructures. However, how phonons interact with boundaries, especially at the atomic level, is not well understood. In this work, we performed two-dimensional atomistic wave packet simulations to investigate the phonon surface interaction. Emphasis has been given to the angular-resolved phonon reflection at smooth, periodically rough, and amorphous surfaces. We found that the acoustic phonon reflection at a smooth surface is not simply specular. Mode conversion can occur after reflection, and the detailed energy distribution after reflection will dependent on surface condition and polarization of incident phonon. At periodically rough surfaces, the reflected wave packet distribution does not follow the well-known Ziman's model, but shows a nonmonotonic dependence on the depth of surface roughness. When an amorphous layer is attached to the surface, the incident wave packet will be absorbed by the amorphous region, and results in quite diffusive reflection. Our results clearly show that the commonly used specular-diffusive model is not enough to describe the phonon reflection at a periodically rough surface, while an amorphous layer can induce strong diffusive reflection. This work provides a careful analysis of phonon reflection at a surface with different morphology, which is important to a better understanding of thermal transport in various nanostructures.Comment: 15pages, 9 figure

The Injury and Therapy of Reactive Oxygen Species in Intracerebral Hemorrhage Looking at Mitochondria

Intracerebral hemorrhage is an emerging major health problem often resulting in death or disability. Reactive oxygen species (ROS) have been identified as one of the major damaging factors in ischemic stroke. However, there is less discussion about ROS in hemorrhage stroke. Metabolic products of hemoglobin, excitatory amino acids, and inflammatory cells are all sources of ROS, and ROS harm the central nervous system through cell death and structural damage, especially disruption of the blood-brain barrier. We have considered the antioxidant system of the CNS itself and the drugs aiming to decrease ROS after ICH, and we find that mitochondria are key players in all of these aspects. Moreover, when the mitochondrial permeability transition pore opens, ROS-induced ROS release, which leads to extensive liberation of ROS and mitochondrial failure, occurs. Therefore, the mitochondrion may be a significant target for elucidating the problem of ROS in ICH; however, additional experimental support is required