A generalization and short proof of a theorem of Hano on affine vector fields

We prove that a bounded affine vector field on a complete Finsler manifold is a Killing vector field. This generalizes the analogous result of Hano for Riemannian manifolds. Even though our result is more general, the proof is significantly simpler.Comment: 3 page

Determining Sonication Effect on <i>E. coli</i> in Liquid Egg, Egg Yolk and Albumen and Inspecting Structural Property Changes by Near-Infrared Spectra

In this study, liquid egg, albumen, and egg yolk were artificially inoculated with E. coli. Ultrasound equipment (20/40 kHz, 180/300 W; 30/45/60 min) with a circulation cooling system was used to lower the colony forming units (CFU) of E. coli samples. Frequency, absorbed power, energy dose, and duration of sonication showed a significant impact on E. coli with 0.5 log CFU/mL in albumen, 0.7 log CFU/mL in yolk and 0.5 log CFU/mL decrease at 40 kHz and 6.9 W absorbed power level. Significant linear correlation (p E. coli. The results showed that sonication can be a useful tool as a supplementary method to reduce the number of microorganism in egg products. With near-infrared (NIR) spectra analysis we were able to detect the structural changes of the egg samples, due to ultrasonic treatment. Principal component analysis (PCA) showed that sonication can alter C–H, C–N, –OH and N–H bonds in egg. The aquagrams showed that sonication can alter the properties of H2O structure in egg products. The observed data showed that the absorbance of free water (1412 nm), water molecules with one (1440 nm), two (1462 nm), three (1472 nm) and four (1488 nm) hydrogen bonds, water solvation shell (1452 nm) and strongly bonded water (1512 nm) of the egg samples have been changed during ultrasonic treatment