A potential theory for the k-curvature equation

In this paper, we introduce a potential theory for the k-curvature equation, which can also be seen as a PDE approach to curvature measures. We assign a measure to a bounded, upper semicontinuous function which is strictly subharmonic with respect to the k-curvature operator, and establish the weak continuity of the measure

A Model of Two-Way Selection System for Human Behavior

We propose a model of two-way selection system. It appears in the processes like choosing a mate between men and women, making contracts between job hunters and recruiters, and trading between buyers and sellers. In this paper, we propose a model of two-way selection system, and present its analytic solution for the expectation of successful matching total and the regular pattern that the matching rate trends toward an inverse proportion to either the ratio between the two sides or the ratio of the state total to the smaller people number. The proposed model is verified by empirical data of the matchmaking fairs. Results indicate that the model well predicts this typical real-world two- way selection behavior to the bounded error extent, thus it is helpful for understanding the dynamics mechanism of the real-world two-way selection system.Comment: 8 pages, 4 figure

The Fundamental and Application of Surface Heat Flux Estimation by Inverse Method in Cryogen Spray Cooling

Surface heat flux is an important parameter in various industrial applications, which is often estimated based on measured temperature by solving inverse heat conduction problem (IHCP). In this chapter, the available IHCP methods including sequential function specification (SFS), transfer function (TF) and Duhamel’s theorem were compared, taking the example of surface heat flux estimation during spray cooling. The Duhamel’s theorem was improved to solve 1D multi-layer ICHP. Considering the significant nonuniformity of heat transfer, the 2D filter solution method was proposed to estimate surface heat flux for 2D multi-layer mediums. The maximum heat flux calculated by the 1D method was underestimated by 60% than that calculated by 2D filter solution, indicating that the lateral heat transfer cannot be ignored. The cooling performances based on 2D filter solution demonstrated that substituting the environment friendly R1234yf for R134a can remarkably reduce global warming potential to <1, but its cooling capacity is insufficient. The effective heat flux of R1234yf can be enhanced by 18.8% by reducing the nozzle diameter and decreasing the back pressure, providing the theoretical basis for the clinical potential substitution of R1234yf with low global warming potential (GWP) for commercial R134a with high GWP in laser dermatology

A construction of imprimitive symmetric graphs which are not multicovers of their quotients

This paper gives a sufficient and necessary condition for the existence of an (X, s)-arc-transitive imprimitive graph which is not a multicover of a given quotient graph.Comment: 16 pages with 1 figure, Published in Discrete Math 201