The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.

In this paper, spherical gold nanoparticles (AuNPs), rod-shape AuNPs and triangular AuNPs were synthesized using CTAB as the coating reagent, and their bactericidal properties against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) were studied. By the plate count method and turbidity method, the minimum bactericidal concentrations (MBC) and the minimum bacteriostasis concentrations (MIC) to the two kinds of bacteria were determined. The MIC of rod-shape AuNPs, triangular AuNPs and spherical AuNPs to E. coli were 0.65 μg/mL, 3.71 μg/mL, 21.21 μg/mL, and MBC were 1.30 μg/mL, 11.09 μg/mL, 21.21 μg/mL, respectively. The MIC to S. aureus were 0.26 μg/mL, 0.56 μg/mL, 2.65 μg/mL, while MBC were 0.52 μg/mL, 1.11 μg/mL, 2.65 μg/mL, respectively. The results showed that the bactericidal effect of rod-shape AuNPs on E. coli and S. aureus was higher than that of the other two forms, and the bactericidal effect of three different forms of AuNPs on S. aureus was better than that on E. coli.

Tidal sea level variations in the Mediterranean basin, although altered and amplified by resonance phenomena in confined sub-basins (e.g., Adriatic Sea), are generally confined within 0.5 meters and exceptionally up to 1.5 meters. Here we explore the possibility of retrieving sea level measurements using data from GNSS antennas on duty for ground motion monitoring and analyze the spectral outcomes of such distinctive measurements. We estimate one year of GNSS data collected on the Mediterranean coasts in order to get reliable sea level data from all publicly available data and compare it with collocated tide gauges. A total of eleven stations were suitable for interferometric analysis (as of 2021), and all were able to supply centimeter-level sea level estimates. The spectra in the tidal frequency windows are remarkably similar to tide gauge data. We find that the O₁ and M₂ diurnal and semidiurnal tides and MK₃, MS₄ shallow sea water tides may be disturbed by aliasing effects.

Infrared thermal imaging technology is another new branch for medical imaging after traditional medical imaging technologies such as X-ray, ultrasound and magnetic resonance (MRI). It has the advantages of noninvasive, nondestructive, simple and fast. Its application can radiate multiple clinical departments. This paper mainly expounds the principle, influencing factors of medical infrared thermography and its application in radiation protection and other medical fields.