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.     

Variation Operators for Semigroups and Riesz Transforms on BMO in the Schrödinger Setting

In this paper we prove that the variation operators of the heat semigroup and the truncations of Riesz transforms associated to the Schrödinger operator are bounded on a suitable BMO type space.     

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.     

Synthesis and crosslinking of polyethers that have mesogenic cores and propargyl groups

We modified poly(epichlorohydrin) (PECH) with biphenyl carboxylic and naphthalene carboxylic acid derivatives which contains propargyloxy moieties. The linear polymers were characterized by NMR and IR spectroscopy, elemental analysis, DSC and TGA. We obtained only one side chain liquid crystalline. A smectic A mesophase of this biphenyl derivative was identified by DSC, light polarized optical microscopy and X‐ray diffraction. Thermal crosslinking of the aryl propargyl ether group via sigmatropic rearrangement took place while the material was in the isotropic phase. Partially curing this reactive liquid crystalline polymer resulted in the formation of an anisotropic elastomer when the curing was radically initiated in the range of mesophase stability. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3883–3892, 2002     

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     

Electrochemical Immunosensor for the Determination of Total Ghrelin Hormone in Saliva

An electrochemical immunosensor for ghrelin (GHRL) determination in saliva is reported. Anti‐GHRL was immobilized onto Protein G‐magnetic beads and a competitive immunoassay involving biotinylated GHRL and alkaline phosphatase‐streptavidin was implemented. Once conjugate was magnetically captured on a screen‐printed carbon electrode, GHRL quantization was accomplished by DPV of 1‐naphtol formed upon addition of 1‐naphtyl phosphate. A linear range between 10^?3 and 10³ ng/mL GHRL, and a LOD of 7 pg/mL, much smaller than those from commercial ELISA kits, were found. The usefulness of the immunosensor was demonstrated by analyzing human saliva spiked with GHRL at 0.01, 0.1, 1 and 10 ng/mL.     

On the structure of the automorphism group of certain automorphic loop

Automorphic loops, or A-loops, are loops in which all inner mappings are automorphisms. We investigated A-loops arising from a Lie algebra and describe their automorphism group. Also, we identify and describe their inner mapping group.     

Thermal stability studies on clay nanocomposites prepared from a degradable poly(ester amide) constituted by glycolic acid and 6-aminohexanoic acid

An intercalated nanocomposite of the organically modified montmorillonite Cloisite C25A and a degradable poly(ester amide) based on glycolic acid and 6-aminohexanoic acid units (poly(glc-alt-amh)) was prepared using a twin-screw co-rotating extruder. The non-isothermal degradation kinetics was investigated by thermogravimetric analysis (TG and DTG) in the temperature range of 50–600 °C at five heating rates (2, 5, 10, 20 and 40 °C/min) and compared with the neat polymer. Significant differences were found since the nanocomposite showed three degradation steps instead of the two decomposition processes detected in the pristine sample. The onset mass loss temperature decreased in the nanocomposite due to the presence of the organo-modifier compound, but the presence of the silicate layers significantly decreased the degradation rate at the last stages of decomposition. Kinetic analysis was performed using the Kissinger method and the isoconversional (Kissinger–Akahira–Sunose and Friedman) methods. The true kinetic triplets (E, A, f(α)) were determined for the first two steps of degradation through the Coats–Redfern and the Invariant Kinetic Parameters methods. The results clearly indicated that the presence of the organo-modified clay modified the mechanisms of degradation.     

Determination of polycyclic aromatic hydrocarbons from ambient air particulate matter using a cold fiber solid phase microextraction gas chromatography-mass spectrometry method

Polycyclic aromatic hydrocarbons (PAH) from ambient air particulate matter (PM) were analyzed by a new method that utilized direct immersion (DI) and cold fiber (CF) SPME-GC/MS. Experimental design was used to optimize the conditions of extraction by DI-CF-SPME with a 100μm polydimethylsiloxane (PDMS) fiber. The optimal conditions included a 5min equilibration at 70°C time in an ultrasonic bath with an extraction time of 60min. The optimized method was validated by the analysis of a NIST standard reference material (SRM), 1649b urban dust. The results obtained were in good agreement with certified values. PAH recoveries for reference materials were between 88 and 98%, with a relative standard deviation ranging from 5 to 17%. Detection limits (LOD) varied from 0.02 to 1.16ng and the quantification limits (LOQ) varied from 0.05 to 3.86ng. The optimized and validated method was applied to the determination of PAH from real particulate matter (PM10) and total suspended particulate (TPS) samples collected on quartz fiber filters with high volume samplers.