Mathematical modeling of pressurized system behaviour with entrapped air

The presence of entrapped air in pressurized hydraulic systems is considered a critical condition for the infrastructure security, due to the transient pressure enhancement related with its dynamic behaviour, similar to non-linear spring action. A mathematical model for the assessment of hydraulic transients resulting from rapid pressurizations, under referred condition is presented. Water movement was modeled through the elastic column theory considering a moving liquid boundary and the entrapped air pocket as lumped gas mass, where the acoustic effects are negligible. The method of characteristics was used to obtain the numerical solution of the liquid flow. The resulting model is applied to an experimental set-up having entrapped air in the top of a vertical pipe section and the numerical results are analyzed.

A model to forecast financial failure, in non financial galician SMES

We are concerned with providing more empirical evidence on forecast failure, developing forecast models, and examining the impact of events such as audit reports. A joint consideration of classic financial ratios and relevant external indicators leads us to build a basic prediction model focused in non-financial Galician SMEs. Explanatory variables are relevant financial indicators from the viewpoint of the financial logic and financial failure theory. The paper explores three mathematical models: discriminant analysis, Logit, and linear multivariate regression. We conclude that, even though they both offer high explanatory and predictive abilities, Logit and MDA models should be used and interpreted jointly.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.