In this paper, a numerical method for integration of fuzzy functions is considered. Fuzzy Newton-Cotes formula, such as fuzzy trapezoidal method and fuzzy Simpson method are calculated by integration of fuzzy functions on two and three equally space points. Also the composite fuzzy trapezoidal and composite fuzzy Simpson method are proposed for n equally space points. The proposed method are il...

The development and growth of microfluidics has been mainly based on various novel fabrication techniques for downsizing and integration of the micro/nano components. Especially, an effective fabrication technique of three-dimensional structures still continues to be strongly required in order to improve device performance, functionality, and device packing density because the conventional lami...

Microchannel-patterned starch-poly(capro-lactone)/hydydroxyapatite (SPCL-HA) and starch-poly(lactic acid) (SPLA) composite membranes were produced for use as a laminated tissue-engineering scaffold that incorporates both physical and biochemical patterns. For this purpose, SPCL (30% starch) blended with inorganic hydroxyl apatite (50%) and SPLA (50% starch) membranes were made with compressive ...

This paper presents experimental results from a prototype of a microchannel heat exchanger used in a residential air-conditioning system as an air-cooled condenser. The main objectives were to analyze effects of the microchannel condenser on system performance. The commercially available system that utilizes a condenser with a round tube and plate fins was experimentally evaluated first, then t...

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometr...

In this paper, an improvement of the nearest trapezoidal approximation operator preserving the expected interval is studied, which is proposed by Grzegorzewski and Mrówka. A formula for computing the improved approximation is presented. Moreover, the nearest triangular approximation operator preserving the expected interval is also investigated. © 2007 Elsevier B.V. All rights reserved.

The Riemann sums and the trapezoidal sums of functions defined on a bounded closed interval are well known as approximate sums of the Riemann integrals of the functions. In this paper the author represents the convergence rates of the Riemann sums and the trapezoidal sums as some limits of their expanded error terms. Let [a, b] be a bounded closed interval. We take an n-division ∆ of [a, b] def...

In a framework with two parties, deterministic voter preferences and geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts a party can win, given an electoral outcome (the " optimal gerrymandering rule "). As a corollary, we obtain that no districting rule can satisfy our axioms and treat p...