Mathematics: a means of collaboration between industry and university

This paper is divided into two distinct but connected parts. In the first one we look for the best approach to the Mathematics teaching of the future engineer. This approach should have an eminently pragmatic character and should be directed towards teaching engineers to know and manage Mathematics at a tool. In the second part we illustrate how a collaboration with industry can be obtained from this kind of teaching.

Finally the conditions and consequences which should produce this cooperation are analysed, and some particular examples are mentioned.     

pH‐Dependent Chloride Transport by Pseudopeptidic Cages for the Selective Killing of Cancer Cells in Acidic Microenvironments

Acidic microenvironments in solid tumors are a hallmark of cancer. Inspired by that, we designed a family of pseudopeptidic cage‐like anionophores displaying pH‐dependent activity. When protonated, they efficiently bind chloride anions. They also transport chloride through lipid bilayers, with their anionophoric properties improving at acidic pH, suggesting an H⁺/Cl^? symport mechanism. NMR studies in DPC micelles demonstrate that the cages bind chloride within the lipid phase. The chloride affinity and the chloride‐exchange rate with the aqueous bulk solution are improved when the pH is lowered. This increases cytotoxicity towards lung adenocarcinoma cells at the pH of the microenvironment of a solid tumor. These properties depend on the nature of the amino‐acid side chains of the cages, which modulate their lipophilicity and interactions with the cell membrane. This paves the way towards using pH as a parameter to control the selectivity of cytotoxic ionophores as anticancer drugs.     

High-pressure synthesis and structural behavior of sodium orthonitrate Na3NO4

Sodium orthonitrate (Na₃NO₄) is an unusual phase containing the first example of isolated tetrahedrally bonded NO₄³⁻ groups. This compound was obtained originally by heating together mixtures of Na₂O and NaNO₃ for periods extending up to >14 days in evacuated chambers. Considering the negative volume change between reactants and products, it was inferred that a high-pressure synthesis route might favor the formation of the Na₃NO₄ compound. We found that the recovered sample is likely to be a high-pressure polymorph, containing NO₄³⁻ groups as evidenced by Raman spectroscopy. The high-pressure behavior of Na₃NO₄ was studied using Raman spectroscopy and synchrotron X-ray diffraction in a diamond anvil cell above 60 GPa. We found no evidence for major structural transformations, even following laser heating experiments carried out at high pressure, although broadening of the Raman peaks could indicate the onset of disordering at higher pressure.     

The N- and C-terminal domains of parathyroid hormone-related protein affect differently the osteogenic and adipogenic potential of human mesenchymal stem cells

Parathyroid hormone-related protein (PTHrP) is synthesized by diverse tissues, and its processing produces several fragments, each with apparently distinct autocrine and paracrine bioactivities. In bone, PTHrP appears to modulate bone formation in part through promoting osteoblast differentiation. The putative effect of PTH-like and PTH-unrelated fragments of PTHrP on human mesenchymal stem cell (MSCs) is not well known. Human MSCs were treated with PTHrP (1-36) or PTHrP (107-139) or both (each at 10 nM) in osteogenic or adipogenic medium, from the start or after 6 days of exposure to the corresponding medium, and the expression of several osteoblastogenic and adipogenic markers was analyzed. PTHrP (1-36) inhibited adipogenesis in MSCs and favoured the expression of osteogenic early markers. The opposite was observed with treatment of MSCs with PTHrP (107-139). Moreover, inhibition of the adipogenic differentiation by PTHrP (1-36) prevailed in the presence of PTHrP (107-139). The PTH/PTHrP type 1 receptor (PTH1R) gene expression was maximum in the earlier and later stages of osteogenesis and adipogenesis, respectively. While PTHrP (107-139) did not modify the PTH1R overexpression during adipogenesis, PTHrP (1-36) did inhibit it; an effect which was partially affected by PTHrP (7-34), a PTH1R antagonist, at 1 µM. These findings demonstrate that both PTHrP domains can exert varying effects on human MSCs differentiation. PTHrP (107-139) showed a tendency to favor adipogenesis, while PTHrP (1-36) induced a mild osteogenic effect in these cells, and inhibited their adipocytic commitment. This further supports the potential anabolic action of the latter peptide in humans.     

Direct estimate for positive linear operators in polynomial weighted spaces

We present direct theorems for some sequences of positive linear operators in weighted spaces. The results, given in terms of some Ditzian–Totik moduli of smoothness, include estimations in norms and Becker type estimations.     

Materials for spintronic: Room temperature ferromagnetism in Zn–Mn–O interfaces

In this paper we study the room temperature ferromagnetism reported on Mn-doped ZnO and ascribed to spin polarization of conduction electrons. We experimentally show that the ferromagnetic behaviour is associated to the coexistence of Mn³⁺ and Mn⁺⁴ in MnO₂ grains where diffusion of Zn promotes the Mn⁴⁺→Mn³⁺ reduction. Potential uses of this material in spintronic devices are analysed.     

An application to the MKZ-operators of generalized convexity on ECT-systems

We analyze some relations between classical convexities and some generalized convexities. The results are applied to obtain some new shape preserving properties of the Meyer-König and Zeller operators.     

The first total syntheses of (±)-Preussomerins K and L using 2-arylacetal anion technology

The first syntheses of newly isolated members of the Preussomerin family, Preussomerins K and L, are reported. Key steps include the functionalisation of a 2-arylacetal anion, one-pot Friedel-Crafts cyclisation-deprotection and reductive opening of epoxides.     

A conflict between sequential rationality and consistency principles

It is shown that no solution concept that selects sequentially rational (perfect, proper, persistent, or members of some stable set of) equilibria satisfies the following consistency property. Suppose that in every solution of the game G, player i's action is a, and denote by G ^a the game in which player i is restricted to choose a. Then some player j≠i has an action c that is used with positive probability in both some solution of G and some solution of G ^a. This result illustrates a conflict between a mild consistency condition and sequential rationality. Received: January 2001/Final version: April 2002