The uncertain premium principle based on the distortion function

In this paper, we discuss the premium principle in uncertain environment. First, the net premium principle for uncertain risks is presented within the framework of uncertainty theory. With the help of distortion function, a new uncertain premium principle is derived from the uncertain net premium. Some properties of uncertain distortion premium principle are proved. Furthermore, a sufficient and necessary condition that an uncertain premium principle is an uncertain distortion premium principle has been characterized. Finally, some examples are given to illustrate the calculations of the uncertain distortion premium.     

Chromatographic determination of some biomarkers of liver cirrhosis and hepatocellular carcinoma in Egyptian patients

Metabolomics has been shown to be an effective tool for disease diagnosis, biomarker screening and characterization of biological pathways. A total of 140 subjects were included in this study; urine metabolomes of patients with liver cirrhosis (LC, n = 40), patients with hepatocellular carcinoma (HCC; n = 55) and healthy male subjects (n = 45) as a control group were studied. Gas chromatography/mass spectrometry‐based urine metabolomics profiles were investigated for all participants. Diagnostic models were constructed with a combination of marker metabolites, using principal components analysis and receiver operator characteristic curves. A total of 57 peaks could be auto‐identified of which 13 marker metabolites (glycine, serine, threonine, proline, urea, phosphate, pyrimidine, arabinose, xylitol, hippuric acid, citric acid, xylonic acid and glycerol) were responsible for the separation of HCC group from healthy subjects. Also, eight markers metabolites (glycine, serine, threonine, proline, citric acid, urea, xylitol and arabinose) showed significant differences between the LC group and healthy subjects. No significant difference was detected between HCC and LC groups regarding all these metabolites. Metabolomic profile using GC–MS established an optimized diagnostic model to discriminate between HCC patients and healthy subjects; also it could be useful for diagnosis of LC patients. However, it failed to differentiate between HCC and LC patients.     

Equilibrium analysis for a mass-conserving model in presence of cavitation

We study the existence of equilibrium positions for the load problem in Lubrication Theory. The problem consists of two surfaces in relative motion separated by a small distance filled by a lubricant. The system is described by the modified Reynolds equation (Elrod–Adams model) which describes the behavior of the lubricant and an extra integral equation given the balance of forces. The balance of forces allows to obtain the unknown position of the surfaces, defined with one degree of freedom.     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.     

Prediction of the Frontier Electronic States in a Finite Single-wall Carbon Nanotube

A theoretical model is summarized into the shorter vector principle. It is used to predict the topological structure of wave function and the oscillation rule of energy gap in various types of finite carbon nanotubes (CNTs). The theoretical model indicates that the characteristics of the electronic states only depend on the nanotube size and its symmetry along the shorter vector direction. In this direction, the wave functions of the original 3m (or 3m/2) periodicity are also suitable for armchair, chiral and zigzag finite CNTs with the C2 (Cs), C1 and Cn point groups, respectively. Energy gaps present the oscillation with 3m (or 3m/2) or odd-even n. The first principle calculations for some prototype systems are performed. The results are consistent with the theoretical model.