t | \mathcal{F}_s] \le X_s\), representing "unfavorable" or decreasing processes. Optional Stopping and Stopping Times A stopping time \(\tau\) is a random time at which a decision is made based on current info
operties, allowing for exact soliton solutions via methods such as inverse scattering transform, which reveal the deep mathematical structure underpinning soliton phenomena. Soliton Dynamics: Movement and Evolution
Reading Hall, Brian C. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction. Springer, 2015. Knapp, Anthony W. Lie Groups Beyond an Introduction. Birkhäuser, 2002. Varadarajan, V. S. Lie Group
paration. Flocculation: Aggregation of droplets without merging, which can precede coalescence. Phase Inversion: Change from oil-in-water to water-in-oil or vice versa, often due to composition or temperature shifts. Factors Influencing Stability Droplet size distribution Interfacial film stren
