Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self‐identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.     

Ultrasound-Assisted Microencapsulation of Soybean Oil and Vitamin D Using Bare Glycogen Nanoparticles

Ultrasonically synthesized core-shell microcapsules can be made of synthetic polymers or natural biopolymers, such as proteins and polysaccharides, and have found applications in food, drug delivery and cosmetics. This study reports on the ultrasonic synthesis of microcapsules using unmodified (natural) and biodegradable glycogen nanoparticles derived from various sources, such as rabbit and bovine liver, oyster and sweet corn, for the encapsulation of soybean oil and vitamin D. Depending on their source, glycogen nanoparticles exhibited differences in size and ‘bound’ proteins. We optimized various synthetic parameters, such as ultrasonic power, time and concentration of glycogens and the oil phase to obtain stable core-shell microcapsules. Particularly, under ultrasound-induced emulsification conditions (sonication time 45 s and sonication power 160 W), native glycogens formed microcapsules with diameter between 0.3 μm and 8 μm. It was found that the size of glycogen as well as the protein component play an important role in stabilizing the Pickering emulsion and the microcapsules shell. This study highlights that native glycogen nanoparticles without any further tedious chemical modification steps can be successfully used for the encapsulation of nutrients.     

Kinetics and mechanism of the anation of (αβ)-hydroxo(tetraethylenepentamine)cobalt(III) by thiosulfate, the base hydrolysis of the (sulfur-bonded) thiosulfato(tetraethylenepentamine)-cobalt(III) and photochemistry of oxygen and sulfur-bonded thiosulfato complexes

Summary The reaction of ()-(tetren)CoOH²⁺ with S₂O ₃ ^2- in the 7.25–8.28 pH range at 20–40 °C yielded S- (yellow) and O- (purple) bonded thiosulfato(tetren)cobalt(III) complexes, the former in larger quantities. The rate determining step is preceded by diffusion-controlled ion-pair [(tetren)CoOH²⁺,S₂O ₃ ^2- ] formation. Replacement of coordinated OH^- by S₂O ₃ ^2- is interpreted in terms of an internal conjugate base mechanism: (tetren)CoOH²⁺ (tetren-H)CoOH ₂ ²⁺ , the reactive amido conjugate base being generated by intramolecular proton transfer from the coordinated NH site.In acid medium the S-bonded (tetren)Co(S₂O₃)⁺ is highly stable to redox decomposition, in contrast to its pentaammine analogue. The complex however, undergoes base hydrolysis yielding the corresponding hydroxo complex. The rate and activation parameters for the base hydrolysis have been reported. Photolysis of O- and S-bonded isomers of [(tetren)CoS₂O₃]⁺ in acidic medium at 254 and 313 nm, respectively, yielded aquation products accompanied by some decomposition of S₂O ₃ ^2- .     

A Formal Total Synthesis of (+)-Methyl Trachyloban-18-oate and (+)-Methyl 16-Oxo-17-norkauran-18-oate: Regio- and Diastereoselective Preparation of Methyl (13S)-13-Hydroxyisoatisiren-18-oate from (−)-Abietic Acid

A novel preparation of methyl (13S)-13-hydroxyisoatisiren-18-oate ( 4 ), a key-intermediate in a synthesis of (+)-methyl trachyloban-18-oate ((+)- 1 ), from (?)-abietic acid, is described. Since (?)- 1 has been previously converted into (?)-methyl 16-oxo-17-norkauran-18-oate ((?)- 16 ), our preparation of 4 constitutes also a formal total synthesis, from (?)-abietic acid, of (+)- 16 . Key steps in this approach were the allene photoaddition to podocarp-8(14)-en-13-one ( 5 ) and the conversion of the endo-toluene-4-sulfonate 11 into the exo-benzoate 12b .     

Carboxylate anions binding and sensing by a novel tetraazamacrocycle containing ferrocene as receptor

A tetraazamacrocycle containing ferrocene moieties has been synthesized and characterized. The tetraprotonated form of this compound was evaluated as a receptor (R) for anion recognition of several substrates (S), Cl(-), PF(6)(-), HSO(4)(-), H(2)PO(4)(-) and carboxylates, such as p-nitrobenzoate (p-nbz(-)), phthalate (ph(2-)), isophthalate (iph(2-)) and dipicolinate (dipic(2-)). (1)H NMR titrations in CD(3)OD indicated that this receptor is not suitable for recognizing HSO(4)(-) and H(2)PO(4)(-), but weakly binds p-nbz(-), and strongly interacts with ph(2-), dipic(2-), and iph(2-) anions forming 1 : 2 assembled species. The largest beta(2) binding constant was determined for ph(2-), followed by dipic(2-) and finally iph(2-). The effect of the anionic substrates on the electron-transfer process of the ferrocene units of R was evaluated using cyclic voltammetry (CV) and square wave voltammetry (SWV) in methanol solution and 0.1 mol dm(-3)(CH(3))(4)NCl as the supporting electrolyte. Titrations of the receptor were undertaken by addition of anion solutions in their tetrabutylammonium or tetramethylammonium forms. The protonated ligand exhibits a reversible voltammogram, which shifts cathodically in the presence of the substrates. The data revealed kinetic constraints in the formation of the receptor/substrate entity for dipic(2-), ph(2-) and iph(2-) anions, but not for p-nbz(-). In spite of the slow kinetics of assembled species formation with the ph(2-) substrate, this anion provides the largest redox-response when the supramolecular entity is formed, followed by dipic(2-), iph(2-) and finally p-nbz(-) anions. This trend is in agreement with the (1)H NMR results and the values of the binding constants. Single crystal X-ray structures of the receptor with PF(6)(-), ph(2-), iph(2-) and p-nbz(-) were carried out and showed that supermolecules with a RS(2) stoichiometry are formed with the first three anions, but RS(4) with p-nbz(-). In all cases the binding occurs outside the macrocyclic cavity via N-H...O=C hydrogen bonds for carboxylate anions and N-H...F hydrogen bonds for the PF(6)(-) anion, which is in agreement with the solution results. The macrocyclic framework adopts different conformations in order to interact with each substrate having Fe...Fe intramolecular distances ranging from 10.125(14) to 12.783(15)A.     

Preparation and characterisation of thermoresponsive poly[(N-isopropylacrylamide-co-acrylamide-co-(hydroxyethyl acrylate)] microspheres as a matrix for the pulsed release of drugs

Despite the large number of publications and patents concerning pH/thermoresponsive polymers, few data are available concerning the preparation of thermoresponsive cross-linked microspheres from preformed polymers. Therefore, N-isopropylacrylamide-co-acrylamide-co-(2-hydroxyethyl acrylate) copolymers were obtained as a new thermoresponsive material with a lower critical solution temperature (LCST) around 36 degrees C, in phosphate buffer at pH 7.4, and with a cross-linkable OH group in their structure. The LCST value was determined both by UV spectroscopy and microcalorimetric analysis. These copolymers were solubilised in acidified aqueous solution below their LCST, dispersed in mineral oil, and transformed into stable microspheres by cross-linking with glutaraldehyde. The thermoresponsive microspheres were characterised by optical and scanning electron microscopy, degree of swelling, and water retention. The pore dimensions of the microspheres and the retention volumes of some drugs and typical compounds were evaluated at different temperatures by liquid chromatography. Indomethacin, as a model drug, was included in the microspheres by the solvent evaporation method. Finally, the influence of temperature and of temperature cycling on drug release was investigated.     

Electrophoretic properties of complexes between DNA and the cationic surfactant cetyltrimethylammonium bromide

We use agarose gel electrophoresis to characterize how the monovalent catioinic surfactant cetyltrimethylammonium bromide (CTAB) compacts double-stranded DNA, which is detected as a reduction in electrophoretic DNA velocity. The velocity reaches a plateau at a ratio R = 1.8 of CTAB to DNA-phosphate charges, i.e., above the neutralization point, and the complexes retain a net negative charge at least up to R = 200. Condensation experiments on a mixture of two DNA sizes show that the complexes formed contain only one condensed DNA molecule each. These CTAB-DNA globules were further characterized by time-resolved measurements of their velocity inside the gel, which showed that CTAB does not dissociate during the migration but possibly upon entry into the gel. Using the Ogston-model for electrophoresis of spherical particles, the measured in-gel velocity of the globule is quantitatively consistent with CTAB having two opposite effects, reduction of both the electrophoretic charge and DNA coil size. In the case of CTAB the two effects nearly cancel, which can explain why opposite velocity shifts (globule faster than uncomplexed DNA) have been observed with some catioinic condensation agents. Dissociation of the complexes by addition of anionic surfactants was also studied. The DNA release from the globule was complete at a mixing ratio between anionic and cationic surfactants equal to 1, in agreement with equilibrium studies. Circular DNA retained its supercoiling, and this demonstrates a lack of DNA nicking in the compaction-release cycle which is important in DNA transfection and purification applications.     

Chromium‐Mediated Dearomatization: Application to the Synthesis of Racemic 15‐Acetoxytubipofuran and Asymmetric Synthesis of Both Enantiomers

An efficient dearomatization process of [Cr(arene)(CO)₃] complexes initiated by a nucleophilic acetaldehyde equivalent is detailed. It generates in a one‐pot reaction three C? C bonds and two stereogenic centers. This process allowed a rapid assembly of a cis‐decalin ring system incorporating a homoannular diene unit in just two steps starting from aromatic precursors (Scheme 2). The method was applied to the total synthesis of the eudesmane‐type marine furanosesquiterpene (±)‐15‐acetoxytubipofuran ( 2 ). Two routes were successfully used to synthesize the γ‐lactone precursor of the furan ring. The key step in the first approach was a Pd‐catalyzed allylic substitution (Scheme 3), while in the second approach, an Eschenmoser–Claisen rearrangement was highly successful (Scheme 4). The Pd‐catalyzed allylic substitution could be directed to give either the (normal) product with overall retention as major diastereoisomer or the unusual product with inversion of configuration (see Table). For the synthesis of the (?)‐enantiomer (R,R)‐ 2 of 15‐acetoxytubipofuran, an enantioselective dearomatization in the presence of a chiral diether ligand was implemented (Scheme 7), while the (+)‐enantiomer (S,S)‐ 2 was obtained via a diastereoselective dearomatization of an arene‐bound chiral imine auxiliary (Scheme 8). Chiroptical data suggest that a revision of the previously assigned absolute configuration of the natural product is required.     

High Sensitive Microsensor Based on Organic‐Inorganic Composite for Two‐Dimensional Mapping of H2O2 by SECM

The present work describes the development of a selective, sensitive and stable sensing microsensor for scanning electrochemical microscopy (SECM) to measure H₂O₂ during electrochemical reduction of oxygen. The microsensor is based on graphene and Poly(3,4‐ethylenedioxythiophene) composite as support to iron (III) hexacyanoferrate (II) (PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor). The electrochemical properties of the PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor were investigated by cyclic voltammetry (CV) and scanning electrochemical microscopy (SECM). The PEDOT/graphene/Fe^III₄[Fe^II(CN)₆]₃ microsensor showed an excellent electrocatalytic activity toward hydrogen peroxide (H₂O₂) reduction with a diminution of the overpotential of about 500 mV in comparison to the process at a bare gold microelectrode. The microsensor presented excellent performance for two dimensional mapping of H₂O₂ by SECM in 0.1 mol L^?1 phosphate buffer solution (pH 7.0). Under optimized conditions, a linear response range from 1 up to 1000 µmol L^?1 was obtained with a sensitivity of 0.08 nA L µmol^?1 and limit of detection of 0.5 µmol L^?1.