Bubble column reactors are used in a wide variety of applications such as multiphase bioreactors, catalytic slurry reactors, and absorption processes. The superficial gas velocity-gas holdup relationship and transition point are two important parameters for characterizing the hydrodynamics of a bubble column reactor. In this study, systematic investigation of a nitrogen - water - glass bead...

Shape modeling using planar cubic algebraic curves calls for computing the real inflection points of these curves since inflection points represents important shape feature. A real inflection point is also required for transforming projectively a planar cubic algebraic curve to the normal form, in order to facilitate further analysis of the curve. However, the naive method for computing the inf...

Using slope enclosures may provide sharper bounds for the range of a function than using enclosures of the derivative. Hence, slope enclosures may be useful in verifying the assumptions for existence tests or in algorithms for global optimization. Previous papers by Kolev and Ratz show how to compute slope enclosures for convex and concave functions. In this paper, we generalize these formulas ...

— A point P on a smooth hypersurface X of degree d in PN is called a star point if and only if the intersection of X with the embedded tangent space TP (X) is a cone with vertex P . This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in P3. We generalize results on the configuration space of total inflection points on plane curv...

We explore a feasible model that combines near-inflection point small-field slow roll inflationary scenario driven by single scalar inflaton with the production of non-thermal vector-like fermionic dark matter, χ, during reheating era. For scenario, we consider two separate polynomial forms potential; one is symmetric about origin, and other not. fix coefficients potentials satisfying current P...

We investigate the effect of cooperative interactions on the asymmetric exclusion process, which causes the particle velocity to be an increasing function of the density. Within a hydrodynamic theory, initial density upsteps and downsteps can evolve into: (a) shock waves, (b) continuous compression or rarefaction waves, or (c) a mixture of shocks and continuous waves. These unusual phenomena ar...