Verification and Inversion of Isoparametric Transformations

In this note we consider isoparametric and blended finite elementsand provide simple algebraic and/or geometric conditions thathave to be satisfied if the transformation on to a referenceelement is one—one. It is shown that the well-known "quarter-point"condition is a special case of one of the necessary conditionsbut it is only sufficient in exceptional cases. Equivalent necessaryconditions for three-dimensional tetrahedron and brick elementsare developed. Cubic and higher-order elements are also includedin more general conditions derived from blending function approximations.     

A REACTION–DIFFUSION EQUATION MODELING THE INVASION OF THE ARGENTINE ANT POPULATION,LINEPITHEMA HUMILE,AT JASPER RIDGE BIOLOGICAL PRESERVE

Abstract A continuous reaction–diffusion model is developed for the invasive Argentine ant population within a preserve in northern California. The model is a second‐order partial differential equation incorporating a logistic growth term. The dispersal distance traveled during the reproductive process of budding is used to estimate the diffusion coefficient. The model has two homogeneous steady states, one occurring at the propagation front where the Argentine ant population does not yet exist and one occurring where the population has reached carrying capacity. The traveling wave solutions of the model depict the population density for a given time and location. Using current research, parameter values for the model are estimated and a traveling wave solution for the average parameter values is numerically demonstrated.     

THE EFFECT OF A CHALCOGENAPYRYLIUM DYE WITH AND WITHOUT PHOTOLYSIS ON MITOCHONDRIAL FUNCTION IN NORMAL AND TUMOR CELLS

A chalcogenapyrylium dye 8b, which is under investigation for the photodynamic therapy of malignant gliomas (brain tumors), was evaluated for inhibition of mitochondrial function both before and after exposure to laser light of 800 nm. Neoplastic and normal cells forced to use mitochondrial substrates were killed by the light-activation of intracellular 8b as well as exposure to classic mitochondrial inhibitors, rotenone and sodium azide. Correspondingly, cells in glucose-rich media showed little decrease in viability due to the photolysis of intracellular 8b or the presence of mitochondrial toxins. The toxicity of 8b without light activation was found to be the same regardless of the cell's energy source. Measurement of cellular ATP generated during treatment also showed the photolysis of intracellular 8b to be more inhibitory towards mitochondrial function than the unactivated parent compound. We conclude that the chalcogenapyrylium dyes localize to the mitochondrion and that photoactivation results in mitochondrial injury.     

Mixture network autoregressive model with application on students’successes

We propose a mixture network regression model which considers both response variables and the node-specific random vector depend on the time.In order to estimate and compare the impacts of various connections on a response variable simultaneously,we extend it into p different types of connections.An ordinary least square estimators of the effects of different types of connections on a response variable is derived with its asymptotic property.Simulation studies demonstrate the effectiveness of our proposed method in the estimation of the mixture autoregressive model.In the end,a real data illustration on the students’GPA is discussed.