Sources providing information about the value of a variable may not be totally reliable. In such a case, it is common in uncertainty theories to take account of this unreliability by a so-called discounting rule. A few discounting rules have been proposed in the framework of imprecise probability theory, but one of the drawback of those rules is that they do not preserve interesting properties ...

A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily high-order convergence. The quadratures result from alterations to the trapezoidal rule, in which a small number of nodes and weights at the ends of the integration interval are repla...

In this paper, stability and error estimates for time discretizations of linear semilinear parabolic equations by the two-step backward differentiation formula (BDF2) method with variable step-sizes are derived. An affirmative answer is provided to question: whether upper bound step-size ratios $l^{\infty }(0,T;H)$ -stability BDF2 identical zero-stability. The }(0,T;V)$ also established under m...

This work aimed to investigate the distribution characteristics of low-frequency magnetic flux leakage (LF-MFL) field defect on oil and gas pipelines in electromagnetic detection technique (LFET). Taking four types crack defects (rectangular, semicircular, trapezoidal, V-shaped grooves) with equal lengths, widths different bottom shapes into consideration, specific mathematical model LF-MFL was...

In this work, a reverse trapezoidal cross-section channel shape for single flow PEM fuel cell was examined with computational fluid dynamic (CFD) method. ANSYS Fluent applied to solve electrochemical reactions, potential fields, mass, species, and energy transport equations. Species mass ratio, temperature distribution relative humidity were obtained the as well i-V power density plots. The res...