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Attempts to throw some light on the sensible use of mathematics in economic theory. Argues that mathematics is a valuable and useful tool which economists should and must apply as long as its use is economically sensible. The dangers of going beyond the “frontier” of what is economically sensible occur when economists depart from the actual (empirical) subject matter because of the applied mathematical instruments, when the underlying value judgements are not, or only insufficiently, taken into consideration, when the recording and measurement of empirical magnitudes as an economic problem is underestimated or is even subordinate under the requirements of the formal language, and when the process of mathematization is considered as a substitute for the process of Verstehen. Concludes that although mathematical reasoning is one way of logical deduction, which secures a style of logical consistency in reasoning, it is a fallacy to believe that mathematical reasoning alone can secure logical, consistent reasoning. Mathematization for the sake of mathematization is useless.

The purpose of this paper is to analyze the aerodynamic improvements obtained in a wing section with a NACA 0018 airfoil manufactured using the fused deposition modeling (FDM) technique with regard to a smooth surface made by milling. The creation of micro-riblets on the surface of the airfoil, due to the deposition of the material layer by layer, improves the general aerodynamic performance of the parts, provided that the riblets are parallel to the flow line. The incidence of the thickness of the thread deposited in each layer – to be the variable on which the geometry of the riblets is based – was studied.

The wing section was designed using 3D software. Three different models were designed by rapid prototyping, using additive and subtractive manufacturing. Two of the profiles were manufactured using FDM varying the thickness of the layer to be able to compare the aerodynamic improvements. The third model was manufactured using a subtractive rapid prototyping machine generating a smooth surface profile. These three models were tested inside the wind tunnel to be able to quantify the aerodynamic efficiency according to the geometry and the riblets size.

The manufacture of an aerodynamic profile using FDM provides, in addition to the lightness and the ability to design parts with complex geometries, an improvement in the aerodynamic efficiency of 10 per cent compared with profiles with a smooth surface.

With the aerodynamic advantage gained through the use of FDM positions, the additive manufacturing serves as an excellent alternative for the manufacture of lightweight aerodynamic parts, with low structural loading and with low Reynolds number (∼5·105). This technological advantage would be applied to the UAV (unmanned aerial vehicle) industry.

The study carried out in this article demonstrates that the use of FDM as a manufacture process of end-used parts that are subject to movement generates an additional advantage that had not been considered. The additive manufacturing allows us to directly manufacture riblets by creating the necessary surface so as to reduce the aerodynamic drag.

The purpose of this study is to look at the multifaceted relationship mechanism between corporate social responsibility (CSR) and organizational performance (OP) via sustainability risk management (SRM) and organizational reputation (OR).

This research connects CSR to OP via SRM and OR. Based on a sample of 325 managers of multinational firms in India, a theoretical model was proposed and analyzed through sequential mediation regressions analysis.

The findings indicate that CSR is positively and appreciably associated with OP. Furthermore, SRM and OR have been found to have a sequentially mediating effect on the interrelationship between CSR and OP. The study recognizes that organizations with a proactive approach to CSR tend to manage sustainability risk more actively, which helps to improve OR and ultimately results in better OP.

The research advances understanding of the triple bottom line and offers a platform for building strategic and successful CSR policies by offering valuable insights on the link between CSR and OP.