Homotopy Analysis Method for the First Order Fuzzy Volterra-Fredholm Integro-differential Equations

A fuzzy Volterra-Fredholm integro-differential equation (FVFIDE) in a parametric case is converted to its related crisp case. We use homotopy analysis method to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the FVFIDE. This paper discusses existence and uniqueness results and convergence of the proposed method.

Algorithmic complexity of shape grammar implementation

Computer-based shape grammar implementations aim to support creative design exploration by automating rule-application. This paper reviews existing shape grammar implementations in terms of their algorithmic complexity, extends the definition of shape grammars with sets of transformations for rule application, categorizes (parametric and non-parametric) sets of transformations, and analyses these categories in terms of the resulting algorithmic complexity. Specifically, it describes how different sets of transformations admit different numbers of targets (i.e., potential inputs) for rule application. In the non-parametric case, this number is quadratic or cubic, while in the parametric case, it can be non-polynomial, depending on the size of the target shape. The analysis thus yields lower bounds for the algorithmic complexity of shape grammar implementations that hold independently of the employed algorithm or data structure. Based on these bounds, we propose novel matching algorithms for non-parametric and parametric shape grammar implementation and analyze their complexity. The results provide guidance for future, general-purpose shape grammar implementations for design exploration.

Parametric Study of Heat Insulation in Case of Plate Heat Exchangers

Contribution is aimed on lost heat of plate heat exchangers to surrounding environment. Heat losses to vicinity are insignificant relative to transferred heat flow in the plate heat exchangers. This small part of the lost heat is demonstrated in parametric case study of plate heat exchanger, where is the lost part of heat energy lower than 0.50 % in ordinary cases.