Commentary: Linking epistemology and semio-cognitive modeling in visualization

To situate the contributions of these research articles on visualization as an epistemological learning tool, we have employed mathematical, cognitive and functional criteria. Mathematical criteria refer to mathematical content, or more precisely the areas to which they belong: whole numbers (numeracy), algebra, calculus and geometry. They lead us to characterize the “tools” of visualization according to the number of dimensions of the diagrams used in experiments. From a cognitive point of view, visualization should not be confused with a visualization “tool,” which is often called “diagram” and is in fact a semiotic production. To understand how visualization springs from any diagram, we must resort to the notion of figural unity. It results methodologically in the two following criteria and questions: (1) In a given diagram, what are the figural units recognized by the students? (2) What are the mathematically relevant figural units that pupils should recognize? The analysis of difficulties of visualization in mathematical learning and the value of “tools” of visualization depend on the gap between the observations for these two questions. Visualization meets functions that can be quite different from both a cognitive and epistemological point of view. It can fulfill a help function by materializing mathematical relations or transformations in pictures or movements. This function is essential in the early numerical activities in which case the used diagrams are specifically iconic representations. Visualization can also fulfill a heuristic function for solving problems in which case the used diagrams such as graphs and geometrical figures are intrinsically mathematical and are used for the modeling of real problems. Most of the papers in this special issue concern the tools of visualization for whole numbers, their properties, and calculation algorithms. They show the semiotic complexity of classical diagrams assumed as obvious to students. In teaching experiments or case studies they explore new ways to introduce them and make use by students. But they lie within frameworks of a conceptual construction of numbers and meaning of calculation algorithms, which lead to underestimating the importance of the cognitive process specific to mathematical activity. The other papers concern the tools of mathematical visualization at higher levels of teaching. They are based on very simple tasks that develop the ability to see 3D objects by touch of 2D objects or use visual data to reason. They remain short of the crucial problem of graphs and geometrical figures as tools of visualization, or they go beyond that with their presupposition of students' ability to coordinate them with another register of semiotic representation, verbal or algebraic.     

Sur la stabilité thermique des étalons analytiques. X

Résumé Nous avons examiné douze nouveaux corps minéraux et organiques devant servir à faire des liqueurs titrées. La strontiane et le nitrate d'aluminium paraissent d'emploi douteux dans les travaux de précision.

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Summary We have examined twelve inorganic and organic compounds with respect to their use as standard solutions. Strontium oxide and aluminium nitrate appear to be of doubtful value in precise work.

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Zusammenfassung Zwölf weitere anorganische und organische Stoffe wurden auf ihre Eignung als Urtitersubstanzen geprüft. Strontiumoxyd und Aluminiumnitrat eignen sich für exakte Bestimmungen nicht.

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En l'honneur du ProfesseurF. Feigl, pour son 70^e anniversaire.     

Deduction as Reduction, from a Categorical Point of View

Deduction systems and graph transformation systems are compared within a common categorical framework. This comparison results in a proposal for a new deduction method in diagrammatic logics, allowing the deletion of intermediate lemmas.     

Microprojectile velocities in a gas driven launcher

Microprojectile methods of genetic engineering sometimes employ a macroprojectile which launches the microprojectiles when it hits a stopping plate. A study has been made of the relationship between the velocities of the macroprojectile and the microprojectile it launches. Macroprojectile velocities were measured using a beam blanking method and the microprojectile velocities were measured with a laser Doppler anemometer. Particles of tungsten, titanium dioxide and silicon carbide were investigated as microprojectiles. The microprojectile velocity was found to depend not only on the macroprojectile velocity but also on the microprojectile size and material, the bond strength with the macroprojectile and the gas flow that develops ahead of the macroprojectile. On average the microprojectile launch velocity was similar to the macroprojectile velocity. However, some tungsten particles had velocities twice this value. Experimental evidence suggests that these higher velocities were caused by early break-way of particles from the macroprojectile followed by further acceleration by aerodynamic drag arising from the gas flow ahead of the macroprojectile.We are especially grateful for the advice of Dr. M. Gharib on the use of the HSI color system. John Lyons provided expert help in the laboratory and materials for and advice on photography. We thank the staff of the SIO Hydraulics Laboratory for making the wind-wave channel available for our use, and the staff of UCSD library for enabling us to use the Barneyscanner photometer-digitizer. We thank an anonymous reviewer who pointed out a numerical error and improved the clarity of the text.     

Interrelations between charging, structure and electrokinetics of nanometric polyelectrolyte films

Streaming current, surface conductivity and swelling data of poly(acrylic acid) (PAA) and poly(ethylene imine) (PEI) thin films are analyzed on the basis of the theory for diffuse soft interfaces (J.F.L. Duval, R. Zimmermann, A. L. Cordeiro, N. Rein, C. Werner, Langmuir 25 (2009) 10691). Focus is put on ways to unravel the electroosmotic and migration contributions of the measured surface conductivity, which is crucial for appropriate electrokinetic analysis of films carrying high densities of dissociable groups. Results demonstrate that the osmotically-driven swelling of the PAA films with increasing pH is accompanied by an increase in diffuseness for the interphasial polymer segment density distribution. This heterogeneity is particularly marked at low ionic strength with a non-monotonous dependence of the streaming current on pH and the presence of a maximum at pH～6.5. The analysis of the PEI films evidences heterogeneous swelling with lowering pH, i.e. upon protonation of the amine groups. The characteristic decay length in the interphasial PEI segment density distribution is found to be nearly independent of the pH, which is in line with the moderate swelling determined by ellipsometry. A critical discussion is given on the strengths and limitations of electrokinetics/surface conductivity for quantifying the coupled electrohydrodynamic and structural properties of moderately to highly swollen polyelectrolyte thin films.     

Electrostatic interactions between diffuse soft multi-layered (bio)particles: beyond Debye-Hückel approximation and Deryagin formulation

We report a steady-state theory for the evaluation of electrostatic interactions between identical or dissimilar spherical soft multi-layered (bio)particles, e.g. microgels or microorganisms. These generally consist of a rigid core surrounded by concentric ion-permeable layers that may differ in thickness, soft material density, chemical composition and degree of dissociation for the ionogenic groups. The formalism allows the account of diffuse interphases where distributions of ionogenic groups from one layer to the other are position-dependent. The model is valid for any number of ion-permeable layers around the core of the interacting soft particles and covers all limiting situations in terms of nature of interacting particles, i.e. homo- and hetero-interactions between hard, soft or entirely porous colloids. The theory is based on a rigorous numerical solution of the non-linearized Poisson-Boltzmann equation including radial and angular distortions of the electric field distribution within and outside the interacting soft particles in approach. The Gibbs energy of electrostatic interaction is obtained from a general expression derived following the method by Verwey and Overbeek based on appropriate electric double layer charging mechanisms. Original analytical solutions are provided here for cases where interaction takes place between soft multi-layered particles whose size and charge density are in line with Deryagin treatment and Debye-Hückel approximation. These situations include interactions between hard and soft particles, hard plate and soft particle or soft plate and soft particle. The flexibility of the formalism is highlighted by the discussion of few situations which clearly illustrate that electrostatic interaction between multi-layered particles may be partly or predominantly governed by potential distribution within the most internal layers. A major consequence is that both amplitude and sign of Gibbs electrostatic interaction energy may dramatically change depending on the interplay between characteristic Debye length, thickness of ion-permeable layers and their respective protolytic features (e.g. location, magnitude and sign of charge density). This formalism extends a recent model by Ohshima which is strictly limited to interaction between soft mono-shell particles within Deryagin and Debye-Hückel approximations under conditions where ionizable sites are completely dissociated.     

Convexité rationnelle des surfaces lagrangiennes

Sans résuméOblatum 8-VIII-1990