Tools for computational differentiation transform a program that computes a numerical function F(x) into a related program that computes F ′(x) (the derivative of F). This paper describes how techniques similar to those used in computational-differentiation tools can be used to implement other program transformations—in particular, a variety of transformations for computational divided differen...

From the time levulinic acid was listed as one of top-12 building blocks for sugars-high value compounds conversion, interest in this compound increased. As part its possible production route, definition viable separation schemes appears paramount importance overall development exploitation. Hybrid sequences where liquid-liquid extraction is followed by distillation were considered proving how ...

• A feasible path-based procedure allows to bypass the simulation failures due non-ideal thermodynamics or complex optimization algorithms. The proposed use a shortcut design provided by ProSimPlus® process simulator initialize algorithm coupled with rigorous simulations. Although “non-optimal”, DWC obtained via fulfills expectations both from an economic and environmental point of view respect...

Dividing-wall columns (DWCs) are intensified processes that have attracted industrial and academic attention due to the reduction in operating installation costs compared traditional distillation systems. Several methodologies available for design of DWCs. Most them consist three parts: an analysis variables; structural (topology); optimization resulting preliminary design. This paper aims stud...

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

Under general conditions, the equation g(x, y) = 0 implicitly defines y locally as a function of x. In this short note we study the combinatorial structure underlying a recently discovered formula for the divided differences of y expressed in terms of bivariate divided differences of g, by analyzing the number of terms an in this formula. The main result describes six equivalent characterizatio...