Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

The micro staring hyperspectral imager can simultaneously acquire two spatial and one spectral images, and only record the external orientation elements of the entire hyperspectral image rather than the external orientation elements of each frame of the image, which avoids the geometric instability during scanning, effectively solves the problem of large geometric deformation of the small line scanning hyperspectral imager, and is suitable for the small UAV load platform with unstable attitude. At present, most of the research focuses on the radio-metric correction method of line scan hyperspectral imager. The application time of staring hyperspectral imager is short, and there is no mature data processing re-search at home and abroad, which hinders the application of UAV micro staring hyperspectral imaging system. In this paper, the calibration method of the linearity and variability of the radiation response of the micro staring hyperspectral imager on the UAV is studied, and the effectiveness of this method is quantitatively evaluated. The results show that the hyperspectral image has obvious vignetting effect and strip phenomenon before the correction of radiation response variability. After the correction, the radiation response variation coefficient of pixels in different bands decreases significantly, and the vignetting effect and image strip decrease significantly. In this paper, a multi-target radiometric calibration method is proposed, and the accuracy of radiometric calibration is verified by comparing the calibrated hyperspectral image spectrum with the measured ground object spectrum of the ground spectrometer. The results show that the calibration results of the multi-target radiometric calibration method show better results, especially for the near-infrared band, and the difference with the surface reflectance measured by the spectrometer is small.

The present research is on the propagation of Rayleigh waves in a homogenous thermoelastic solid half-space by considering the compact form of six different theories of thermoelasticity. The medium is subjected to an insulated boundary surface that is free from normal stress, tangential stress, and a temperature gradient normal to the surface. After developing a mathematical model, a dispersion equation is obtained with irrational terms. To apply the algebraic method, this equation must be converted into a rational polynomial equation. From this, only those roots are filtered out, which has satisfied both of the above equations for the propagation of waves decaying with depth. With the help of these roots, different characteristics are computed numerically, like phase velocity, attenuation coefficient, and path of particles. Various particular cases are compared graphically by using phase velocity and attenuation coefficient. The elliptic path of surface particles in Rayleigh wave propagation is also presented for the different theories using physical constants of copper material for different depths and thermal conductivity.

Digital labor, as a new theoretical form of "audience commodity theory" in the digital media era, represents a new form of production and labor. This paper explores the unique features of digital labor in labor form, labor products and labor time, and combining Marx's theory, it further reveals the alienation and exploitation of human social relations, emotional value and social class in the process of digital labor, and finally makes suggestions on the unequal relationship between platform and workers in the process of digital labor.

Fruits are a source of vitamins. Mango is one of the abundantly nutritional fruits. Vitamin B9, or folic acid, is one of the important vital amines due to its role in preventing neural deficiency. Several beneficial micro-organisms are used for the synthesis of folic acid. In this study, Lactobacillus acidophilus, Leuconostoc mesenteroides, Streptococcus thermophilus, and Saccharomyces cerevisiae were used. Saccharomyces cerevisiae synthesized folic acid as compared to other organisms. There were five different concentrations of mango pulp that were analyzed for folic acid synthesis (5%, 10%, 15%, 20%, and 30%). The initial concentration of pulp was 133.37 mg kg⁻¹, but after fermentation with four micro-organisms it got reduced. As compared to the other three organisms, Saccharomyces cerevisiae synthesizes 17.15 mg kg⁻¹, 30.14 mg kg⁻¹, 28.62 mg kg⁻¹, 21.70 mg kg⁻¹, and 21.78 mg kg⁻¹, respectively, at different pulp concentrations of 5%, 10%, 15, 20%, and 30%. Vitamin C increased to 320 mg as compared to the control, and there was no significant difference between the four micro-organisms. Antioxidants also showed positive results at different concentrations of pulp. There was an increase in titratable acidity and a decrease in pH recorded for the 24 h fermentation period. In this variety, the color of mango pulp slightly changes to yellow shades due to the breakdown of pigments, so this effects the *b value in between the pulp concentrations. Data supports the enrichment of folic acid, which will further support the utilization of beneficial micro-organisms in food beverages.