theory of martingales mathematics and its applicat 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 Apr 28, 2026 Read more →
solitons properties dynamics interactions applicat 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 Jan 3, 2026 Read more →
lie groups lie algebras and some of their applicat 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 Mar 18, 2026 Read more →
emulsions formation stability industrial applicat 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 Jan 14, 2026 Read more →
