in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

Experimental determination of solubility and ternary phase diagram of chiral compound are of tedious and time consuming tasks, and in many cases, there is not enough experimental data for different enantiomeric compositions to access the experimental ternary phase diagram. Using thermodynamic models with predictive capability, having less dependency on experimental data, affords a great advanta...

Constructing phase diagram and its subsequent quality lines for lean gas condensate reservoirs is always crucial and challenging topic in reservoir fluid studies. Due to small amounts of liquid drop-outs in lean gas condensates at reservoir conditions, full experimental tracking of phase diagram and its relevant quality lines is almost impossible for lean gas condensates.On the other hand, ...

The protein tubulin is found in every cell of every living organism (with the exception of bacteria ) [1]. In the presence of guanosine-tri-phosphate (GTP) and magnesium ions (Mg +), tubulin-GTP complexes form [2] and aggregate [3] into long, hollow cylinders called microtu bules. Microtubules are about 25 nm in outer diameter, incorporate 1625 tubulin dimers per micrometer of their length [4] ...