Mathematics and cross-curricular activities: Bridges exist for crossing them

The paper presents some thoughts on the relations of mathematics teaching and learning and the cross-curricular activities. Some Spantsh examples are reviewed and some insights for future actions are given.     

On convex triangle functions

We prove that the strongest (largest convex) solution of the functional inequality $$\tau \left( {\frac{{F + G}}{2},\frac{{H + K}}{2}} \right) \le \frac{{\tau (F,H) + \tau (G,K)}}{2},$$ whereF, G, H andK are arbitrary distribution functions, is the triangle function τ(F, G)(x) = Max(F(x) +G(x) ? 1, 0).     

On a functional equation based upon a result of Gaspard Monge

We present and solve completely a functional equation motivated by a classical result of Gaspard Monge.     

Some functional equations in the space of uniform distribution functions

In this paper various functional equations which arise in the study of binary operations on the set of uniform probability distribution functions are considered and solved.     

Subcooled flow boiling of R-134a in vertical channels of small diameter

Subcooled flow boiling heat transfer for refrigerant R-134a in vertical cylindrical tubes with 0.83, 1.22 and 1.70 mm internal diameter was experimentally investigated. The effects of the heat flux, q″ = 1–26 kW/m², mass flux, G = 300–700 kg/m² s, inlet subcooling, ΔT_sub,i = 5–15 °C, system pressure, P = 7.70–10.17 bar, and channel diameter, D, on the subcooled boiling heat transfer were explored in detail. The results are presented in the form of boiling curves and heat transfer coefficients. The boiling curves evidenced the existence of hysteresis when increasing the heat flux until the onset of nucleate boiling, ONB. The wall superheat at ONB was found to be essentially higher than that predicted with correlations for larger tubes. An increase of the mass flux leads, for early subcooled boiling, to an increase in the heat transfer coefficient. However, for fully developed subcooled boiling, increases of the mass flux only result in a slight improvement of the heat transfer. Higher inlet subcooling, higher system pressure and smaller channel diameter lead to better boiling heat transfer. Experimental heat transfer coefficients are compared to predictions from classical correlations available in the literature. None of them predicts the experimental data for all tested conditions.     

One-Step Synthesis of 4-Alkoxy-1-Ethoxycarbonylmethylazetidin-2-ones

Stereoselective one-step synthesis of 4-alkoxy-1-ethoxycarbonylmethylazetidin-2-ones from acid chlorides and N-ethoxycarbonylmethylimidates.     

Characterization of some topological semigroups whose level curves are homothetic

We characterize all non-strict Archimedeant-norms whose level curves are homothetic.     

A synthesis of multidimensional judgements consistent with linear transformations

Summary We give a characterization of the weighted arithmetic mean onR ⁿ by solving a functional equation motivated by a problem of synthesizing multidimensional judgements consistent with nonsingular linear transformations.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.