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We will prove existence results for some three-point boundary value problems by applying a Gronwall inequality. Then, we establish the existence of at least one positive solution for a three-point boundary value problem where the nonlinearity involves the first derivative.
Existence of positive solutions for second order differential equations arising from chemical reactor theory
In this paper, we study second-order differential equations that represent the steady state model in an adiabatic tubular chemical reactor. Theoretical results on existence and range of positive solutions are proved by applying a fixed point theorem. At the mean time, numerical solutions are obtained by computer programming. Results from mathematical analysis are compared with the numerical solutions.
In this paper, an economic epidemiological model with vaccination is studied. The stability of the endemic steady-state is analyzed and some bifurcation properties of the system are investigated. It is established that the system exhibits saddle-point and period-doubling bifurcations when adult susceptible individuals are vaccinated. Furthermore, it is shown that susceptible individuals also have the tendency of opting for more number of contacts even if the vaccine is inefficacious and thus causes the disease endemic to increase in the long run. Results from sensitivity analysis with specific disease parameters are also presented. Finally, it is shown that the qualitative behaviour of the system is affected by contact levels.
Coalition attack is nowadays one of the most common type of attacks in the industry of online advertising. In this paper, we attempt to mitigate the problem of frauds by proposing a hybrid framework that detects the coalition attacks based on multiple metrics. We also articulate the theoretical basis for these metrics to be integrated into the hybrid framework. Furthermore, we instance the framework with two metrics and develop a detection system that identifies the coalition attacks from two distinguish perspectives.
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