A touch of mathematics: coming to our senses by observing the visually impaired

During the last three decades, the impact of visualization processes on the teaching and learning of mathematics has been extensively researched. However, considerably less work has been devoted to haptic processes. In this paper, we describe and analyze the role of haptic processes from data collected in mathematics lessons taught in a school for blind students. The analysis builds upon studies from perception and also from teaching experiences in order to examine the teacher’s and the students’ hand movements and metaphors when handling solids of revolution and communicating verbally with each other about their insights. We highlight the powerful combination of the visual and the haptic components of their interactions for the conceptualization of mathematical experiences, and we also note the critical role mathematical language plays in supporting the teaching–learning processes in this context. Finally, we consider important educational implications not only for blind people, but for all students and teachers of mathematics.     

1,2,4,5‐Tetrazines vs. Carboxylic Acid Dimers: Molecular Chemistry vs. Supramolecular Chemistry

The structures of six new tetrazines have been determined and their molecular packing has been compared to the supermolecular architecture observed in related carboxylic acid dimers. In the tetrazines, covalent N? N bonds are considered to replace the intermolecular O? H???O hydrogen bonds of the carboxylic acids. In the systems investigated, it is apparent that, in the majority of cases, the covalent six‐membered ring of the tetrazine is an appropriate replacement for the carboxylic acid synthon. This apparent interplay between molecular and supramolecular units may have applications in the crystal engineering of new materials.     

Rhodium(I) carbonyl complexes with α-diimine ligands containing amino or hydroxy substituents

-Diimines, RN:C(R)C(R):NR(LL) derived from glyoxal, GLL (R=H) abbreviated as GAA (R= R=4-dimethylaminophenyl) or GHA (R= R=4-hydroxyphenyl), and derived from biacetyl, BLL (R=Me) abbreviated as BDH (R=R= NH₂), BOH (R=NH₂, R=OH) react with carbonylrhodium(I) compounds to give different products depending on the imino substituents in the ligand and/or the solvent employed. The reaction of -diimines bearing amino groups, such as GAA or BDH with [RhCl(CO)₂]₂ in acetone yields binuclear [RhCl(CO)₂]₂(-LL) while in CH₂Cl₂ ionic [Rh- (CO)₂(LL)]⁺[RhCl₂(CO)₂]^– species are obtained. In acetone [RhCl(CO)₂]₂(-GAA) exists as an equilibrium mixture between two different neutral binuclear species; [Rh(CO)₂(BDH)]⁺ exists as a mixture of two species containing chelate or monodentate bonded diimine respectively. GAA or BDH react in situ with [RhCl(CO)(C₂H₄)]₂ in benzene to yield tetracoordinated monocarbonylated [RhCl(CO)(LL)] compounds. -Diimines (LL) bearing hydroxy groups, such as GHA or BOH react with [RhCl(CO)₂]₂ or [RhCl(CO)(C₂H₄)]₂ to give pentacoordinated dicarbonylated [RhCl(CO)₂(LL)] compounds.     

Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow

The behavior of short glass fiber–polypropylene suspensions in extensional flow was investigated using three different commercial instruments: the SER wind-up drums geometry (Extensional Rheology System) with a strain-controlled rotational rheometer, a Meissner-type rheometer (RME), and the Rheotens. Results from uniaxial tensile testing have been compared with data previously obtained using a planar slit die with a hyperbolic entrance. The effect of three initial fiber orientations was investigated: planar random, fully aligned in the stretching flow direction and perpendicular to it. The elongational viscosity increased with fiber content and was larger for fibers initially oriented in the stretching direction. The behavior at low elongational rates showed differences among the various experimental setups, which are partly explained by preshearing history and nonhomogenous strain rates. However, at moderate and high rates, the results are comparable, and the behavior is strain thinning. Finally, a new constitutive equation for fibers suspended into a fluid obeying the Carreau model is used to predict the elongational viscosity, and the predictions are in good agreement with the experimental data.     

A furan ring expansion approach to the synthesis of novel pyridazino-psoralen derivatives

A convenient preparation of the parent tetrahydrobenzodifuran 2 was developed from resorcinol. The oxidation of one or both furan rings of this key intermediate was accomplished with DDQ and the resulting benzodifuran was subsequently reacted with 3,6-dimethoxycarbonyl-1,2,4,5-tetrazine to afford the expected pyridazino-psoralen derivative in good yield. This simple method allowed the efficient preparation of a pyridazino-psoralen derivative with a formyl group at C-7, which was introduced by directed ortho-lithiation in the intermediate 2. An aminoalkyl side-chain was also introduced to the tetracyclic skeleton through the aldehyde functionality in a reductive amination process, which was accompanied by an unprecedented reduction of the pyridazine ring.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Matrix‐free thin‐layer chromatography/laser desorption ionization mass spectrometry for facile separation and identification of medicinal alkaloids

Quaternary protoberberine alkaloids belong to a pharmaceutically important class of isoquinoline alkaloids associated with bactericidal, fungicidal, insecticidal and antiviral activities. As traditional medicine gains wider acceptance, quick and robust analytical methods for the screening and analysis of plants containing these compounds attract considerable interest. Thin‐layer chromatography (TLC) combined with matrix‐assisted laser desorption/ionization mass spectrometry (MALDI‐MS) is a powerful technique but suffers from dilution of the TLC bands resulting in decreased sensitivity and masking of signals in the low‐mass region both due to addition of matrix. This study integrates for the first time conventional silica gel TLC and laser desorption ionization mass spectrometry (LDI‐MS) thus eliminating the need for any external matrix. Successful separation of berberine (R_f = 0.56) and palmatine (R_f = 0.46) from Berberis barandana including their identification by MS are demonstrated. Furthermore, a robust electrospray ionization (ESI)‐MS method utilizing residual sample from TLC for quantification of berberine applying selected reaction monitoring and standard addition method is presented. The amount of berberine in the plant root prepared for the study was determined to be 0.70% (w/w). Copyright © 2009 John Wiley & Sons, Ltd.     

A graphical characterization of the efficient set for?convex multiobjective problems

In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective problem is derived. This characterization takes into account the relative position of the gradients of the objective functions and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective problems is derived, which consists of solving a single linear optimization problem.     

Isothermal crystallization kinetics and spherulitic morphology of poly(4‐hydroxybutyric acid‐alt‐glycolic acid)

Isothermal crystallization behavior of a new regular polyester constituted by glycolic acid and 4‐hydroxybutyric acid units is studied by means of differential scanning calorimetry and hot‐stage optical microscopy. A wide range of crystallization conditions were experimentally accessible, allowing various morphological features to be observed and accurate estimates made of characteristic growth parameters, including radial growth and nucleation rates. Three‐dimensional spherulitic growth from heterogeneous nuclei is deduced from the Avrami analysis, whereas optical micrographs reveal two different spherulitic textures that agree with the existence of two crystallization regimes. These can be well distinguished from the breaks observed in the Lauritzen and Hoffman plots when the linear crystal growth rate or the overall crystallization rate is considered. Ringed and nonringed spherulites with negative and positive birefringence, respectively, can be obtained depending on crystallization conditions and regimes. The studied polyester shows rather complex melting behavior which is interpreted in terms of a recrystallization process involving the two different kinds of spherulites. This study allows polymorphism to be discounted. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2640–2653, 2007