Searching for the Center on the Mathematics-Science Continuum

The history of mathematics and science integration in American schools can be illustrated through the use of a continuum which runs from math for math's sake at one end to science for science's sake at the other. True integration occurs at the center point. While published examples of integration focusing on process skills are common, those featuring integration of content are less often found. Two such lessons, developed around radioactive decay and efficiency in nature, are presented as examples of science and mathematics concepts taught in concert. Changes in preservice and in-service teacher training must occur if the potential for this type of integration is to be realized.     

Spatially resolved micro-X-ray fluorescence and micro-X-ray absorption fine structure study of a fractured granite bore core following a radiotracer experiment

Spatially resolved X-ray absorption and fluorescence investigation with a micrometer-scale resolution on actinide-containing samples provide information necessary for safety assessment of nuclear waste disposal. In this paper one example of such an experiment is presented. This example entails neptunium speciation in a fractured granite bore core from the Swedish Äspö Hard Rock Laboratory following a radiotracer experiment using µ-XAFS and µ-XRF. In order to probe micro-volumes below the surface in the granite samples and thereby avoid potential changes in the Np speciation during cutting of the bore core, a confocal irradiation–detection geometry is employed. µ-XAFS results for a selected granite bore core cross section with ~ 3 nmol Np/g reveal that Np, originally introduced as Np(V) in the tracer cocktail, is present in the granite in its reduced Np(IV) form. The Np(IV) is often present as particles, tens of µm in size. Elemental distribution maps show the tracer Np to be located in fissures and permeable channels not larger than 100 µm. The Np distribution appears often correlated with Zn also present in some fissures. We observe small granite fissures containing Fe (presumably Fe(II)), where we do not detect any Np. It is feasible that inflowing Np(V) has a shorter residence time in large fractures, while in the smaller fissures migration is slower, leading to longer residence times, i.e., reaction times, where it is reduced to less soluble Np(IV) and becomes thereby immobilized.     

Practical asymmetric synthesis of alpha-branched 2-piperazinylbenzylamines by 1,2-additions of organometallic reagents to N-tert-butanesulfinyl imines

[reaction: see text] 2-[4-(tert-Butoxycarbonyl)piperazinyl]benzylidene-tert-butanesulfinamides underwent nucleophilic 1,2-addition with different organometallic reagents to give highly diastereomerically enriched adducts. X-ray crystallography of the resulting alpha-branched N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides confirms different mechanisms depending on the organometallic reagent used. Differential deprotection of the N-Boc and the tert-butanesulfinamides was investigated, and the dehydration byproducts have been identified and characterized. To avoid the formation of byproducts in the acidic deprotection step, the N-tert-butanesulfinamide group was converted to the corresponding N-tert-butanesulfonamide (Bus), which allowed for clean orthogonal deprotection. The efficient synthesis and deprotection of the N-Boc-2-piperazinylbenzyl-tert-butanesulfinamides herein described constitutes an attractive method for extensive structure-activity studies in the search for novel ligands of the human melanocortin 4 receptor.     

Branching ratio for radiative pion capture in 6Li and 12C

The radiative pion capture rate in ¹²C and ⁶Li leading to bound final states is calculated using the impulse approximation. The T-matrix is obtained from the time-reversed pion photo-production amplitude and initial-state distortion of the bound pion is taken into account. Using recently published capture schedules for pionic atoms the branching ratio R is calculated and compared to experimental values. The agreement is excellent if those experimental values are used that have been obtained by direct observation of the emitted γ-ray and if an optical-model value for the total 2P absorption width in ¹²C is used.     

Ultrasonic pretreatment of corn slurry for saccharification: A comparison of batch and continuous systems

The effects of ultrasound on corn slurry saccharification yield and particle size distribution was studied in both batch and continuous-flow ultrasonic systems operating at a frequency of 20 kHz. Ground corn slurry (28% w/v) was prepared and sonicated in batches at various amplitudes (192–320 μm_{peak-to-peak (p–p)}) for 20 or 40 s using a catenoidal horn. Continuous flow experiments were conducted by pumping corn slurry at various flow rates (10–28 l/min) through an ultrasonic reactor at constant amplitude of 12 μm_p–p. The reactor was equipped with a donut shaped horn. After ultrasonic treatment, commercial alpha- and gluco-amylases (STARGEN^TM 001) were added to the samples, and liquefaction and saccharification proceeded for 3 h. The sonicated samples were found to yield 2–3 times more reducing sugars than unsonicated controls. Although the continuous flow treatments released less reducing sugar compared to the batch systems, the continuous flow process was more energy efficient. The reduction of particle size due to sonication was approximately proportional to the dissipated ultrasonic energy regardless of the type of system used. Scanning electron microscopy (SEM) images were also used to observe the disruption of corn particles after sonication. Overall, the study suggests that both batch and continuous ultrasonication enhanced saccharification yields and reduced the particle size of corn slurry. However, due to the large volume involve in full scale processes, an ultrasonic continuous system is recommended.     

Gas-phase interaction of thiophene with the Ti(8)C(12)(+) and Ti(8)C(12) met-car clusters

The reactivity of the Ti(8)C(12)(+) met-car cation toward thiophene was investigated using density functional theory (DFT) and mass selective ion chemistry. It is shown that the experimentally observed mass spectrum can be well described by the DFT calculations. In contrast to the weak bonding interactions seen for thiophene on a TiC(001) surface, the Ti(8)C(12)(+) met-car cation is able to interact strongly with up to four thiophene molecules with the cluster staying intact. In the most stable conformation, the thiophene molecules bond to the four low-coordinated Ti(0) sites of Ti(8)C(12)(+) via a eta(5)-C,S coordination. The stability and the activity of the Ti(8)C(12)(+) met-car is observed to increase with an increasing number of attached thiophene molecules at the Ti(0) sites, which is associated with a significant transfer of electron density from thiophene to the cluster. The additional electron density on the Ti(8)C(12)(+) cation cluster, however, is not sufficient to cleave the C-S bonds of thiophene and the dissociation reaction of thiophene is predicted to be a highly activated process. By contrast, DFT calculations for the neutral Ti(8)C(12) met-car predict that the dissociation reaction leading to adsorbed S and C(4)H(4) fragments is energetically favorable for the first thiophene molecule. The binding behavior for subsequent addition of thiophene molecules to the neutral met-car is also presented and compared to that of the cation.     

Organogels derived from tetranitrated crown ethers

[reaction: see text] The 3,3',4'4'-tetranitrodibenzocrown ethers TNDB24C8 and TNDB30C10 form organogels with chloroalkanes at 3% w/v. Atomic force microscopy and scanning electron microscopy have been used to characterize the superstructure of the gels. Gels prepared using TNDB30C10 and CHCl(3) are more fibrous and are ordered into elongated domains attributable to exposed parts of intermingled fibers. Differential scanning calorimetry shows that the gel aids in the formation of supercooled CHCl(3) (DeltaT = 21 K, DeltaH(av) = 19.0 +/- 1.5 kJ mol(-)(1)) and that the gel liquefies at 307 K.     

The Hamilton-Waterloo Problem with 4-Cycles and a Single Factor of n-Cycles

A 2-factor in a graph G is a 2-regular spanning subgraph of G, and a 2-factorization of G is a decomposition of all the edges of G into edge-disjoint 2-factors. A ${\{C_{m}^{r}, C_{n}^{s}\}}$ -factorization of K _υ asks for a 2-factorization of K _υ , where r of the 2-factors consists of m-cycles, and s of the 2-factors consists of n-cycles. This is a case of the Hamilton-Waterloo problem with uniform cycle sizes m and n. If υ is even, then it is a decomposition of K _υ ? F where a 1-factor F is removed from K _υ . We present necessary and sufficient conditions for the existence of a ${\{C_{4}^{r}, C_{n}^{1}\}}$ -factorization of K _υ ? F.     

Stereoselective C-X and regioselective C-H activation to,and selective C(sp2)-C(sp3) reductive elimination from,platinum compounds with thiophene-derived ligands

Several thiophene-based N^C ligands were synthesized. Strategically, a bromide was incorporated on the 2-position of the thiophene ring. When allowed to react with the platinum tetramethyl dimer, [Pt₂Me₄(µ-SMe₂)₂], platinum(IV) platinacycles were formed by oxidative addition of the C(sp²)-X bond. These platinum(IV) compounds were characterized by NMR and HRMS. The platinum (IV) compounds were subsequently subjected to thermolysis. A series of reactions occurred, including selective C-C reduction elimination and selective C-H oxidative addition, giving mixtures of platinum(II) products with varying degrees of regioselectivity.