Simple distillation columns with ideal vapor-liquid equilibrium may display multiple steady-state solutions. Two fundamentally different sources for the multiplicity are presented. Both bring about the unexpected result that increasing reflux makes separation worse in the top part of the column. It corresponds to an unstable operating point. The first type of multiplicity is found for columns w...

nowadays the position of the renewable energy is so important because of the environment pollution and the limitation of fossil fuels in the world. energy can be generated more and more by the renewable sources, but the fossil fuels are non-renewable. one of the most important renewable sources is the wind energy. the wind energy is an appropriate alternative source of fossil fuel. the replacem...

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

According to the pseudo-ideal mixing assumption employed in practically all chemical transport models, organic aerosol components from different sources interact with each other in a single solution, independent of their composition. This critical assumption greatly affects modeled organic aerosol concentrations, but there is little direct experimental evidence to support it. A main experimenta...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

study of the potential fields at different altitudes, constituting a multiscale field is a class of interpretative methods which are used to approximate depth and geometry of sources. interpretation of potential fields by this class of methods is mainly based on the recognition that the gravity or magnetic fields, generated by ideal sources (point mass, line of mass, sheet and contact) are homo...