A Districtwide Study of Automaticity When Included in Concept‐Based Elementary School Mathematics Instruction

While conceptual understanding of properties, operations, and the base‐ten number system is certainly associated with the ability to access math facts fluently, the role of math fact memorization to promote conceptual understanding remains contested. In order to gain insight into this question, this study looks at the results when one of three elementary schools in a school district implements mandatory automaticity drills for 10 minutes each day while the remaining two elementary schools, with the same curriculum and very similar demographics, do not. This study looks at (a) the impact that schoolwide implementation of automaticity drills has on schoolwide computational math skills as measured by the ITBS and (b) the relationship between automaticity and conceptual understanding as measured by statewide standardized testing. The results suggest that while there may be an association between automaticity and higher performance on standardized tests, caution should be taken before assuming there are benefits to promoting automaticity drills. These results are consistent with those that support a process‐driven approach to automaticity based on familiarity with properties and strategies associated with the base‐ten number system; they are not consistent with those that support an answer‐driven approach to automaticity based on memorization of answers.     

Mono‐, di‐ and trimethylated homologues of isoprenoid tetraether lipid cores in archaea and environmental samples: mass spectrometric identification and significance

Higher homologues of widely reported C₈₆ isoprenoid diglycerol tetraether lipid cores, containing 0–6 cyclopentyl rings, have been identified in (hyper)thermophilic archaea, representing up to 21% of total tetraether lipids in the cells. Liquid chromatography‐tandem mass spectrometry confirms that the additional carbon atoms in the C_87‐88 homologues are located in the etherified chains. Structures identified include dialkyl and monoalkyl (‘H‐shaped’) tetraethers containing C_40‐42 or C_81‐82 hydrocarbons, respectively, many representing novel compounds. Gas chromatography‐mass spectrometric analysis of hydrocarbons released from the lipid cores by ether cleavage suggests that the C₄₀ chains are biphytanes and the C₄₁ chains 13‐methylbiphytanes. Multiple isomers, having different chain combinations, were recognised among the dialkyl lipids. Methylated tetraethers are produced by Methanothermobacter thermautotrophicus in varying proportions depending on growth conditions, suggesting that methylation may be an adaptive mechanism to regulate cellular function. The detection of methylated lipids in Pyrobaculum sp. AQ1.S2 and Sulfolobus acidocaldarius represents the first reported occurrences in Crenarchaeota. Soils and aquatic sediments from geographically distinct mesotemperate environments that were screened for homologues contained monomethylated tetraethers, with di‐ and trimethylated structures being detected occasionally. The structural diversity and range of occurrences of the C_87‐89 tetraethers highlight their potential as complementary biomarkers for archaea in natural environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Nuclear charge and matter distributions

The experimental methods used to determine nuclear charge and matter distributions are described, together with their theoretical interpretation in terms of nuclear structure.     

Synthesis of the Anti‐HIV Agent (−)‐Hyperolactone C by Using Oxonium Ylide Formation–Rearrangement

Starting from readily available (S)‐styrene oxide an asymmetric synthesis is described of the naturally occurring anti‐HIV spirolactone (?)‐hyperolactone C, which possesses adjacent fully substituted stereocenters. The key step involves a stereocontrolled Rh^II‐catalysed oxonium ylide formation–[2,3] sigmatropic rearrangement of an α‐diazo‐β‐ketoester bearing allylic ether functionality. From the resulting furanone, an acid‐catalysed lactonisation and dehydrogenation gives the natural product.     

High-power solid-state lasers with unstable resonators

The thermal lensing properties of stable and unstable resonators are compared and rules are given for the design of optimized unstable resonators containing a focusing rod. Experimental verification with a high-power Nd: YAG system proved that for unstable resonators the restricting relationship between beam quality and output power no longer holds. Careful resonator design enables high output power to be extracted with unstable resonators without destroying the output couplers.     

S K-edge X-ray absorption studies of tetranuclear iron-sulfur clusters: mu-sulfide bonding and its contribution to electron delocalization.

X-ray absorption spectroscopy (XAS) at the sulfur ( approximately 2470 eV) and chlorine ( approximately 2822 eV) K-edges has been applied to a series of 4Fe-4S model complexes. These are compared to 2Fe-2S model complexes to obtain insight into the localized ground state in the mixed-valence dimer versus the delocalized ground state in the mixed-valence tetramer. The preedges of hypothetical delocalized mixed-valence dimers [Fe(2)S(2)](+) are estimated using trends from experimental data and density functional calculations, for comparison to the delocalized mixed-valence tetramer [Fe(4)S(4)](2+). The differences between these two mixed-valence sites are due to the change of the sulfide-bridging mode from micro(2) to micro(3). The terminal chloride and thiolate ligands are used as spectator ligands for the electron density of the iron center. From the intensity of the preedge, the covalency of the terminal ligands is found to increase in the tetramer as compared to the dimer. This is associated with a higher effective nuclear charge on the iron in the tetramer (derived from the energies of the preedge). The micro(3)-bridging sulfide in the tetramer has a reduced covalency per bond (39%) as compared to the micro(2)-bridging sulfide in the dimer (51%). A simple perturbation model is used to derive a quadratic dependence of the superexchange coupling constant J on the covalency of the metal ions with the bridging ligands. This relationship is used to estimate the superexchange contribution in the tetramer (J = -156 cm(-)(1)) as compared to the mixed-valence dimer (J = -360 cm(-)(1)). These results, combined with estimates for the double exchange and the vibronic coupling contributions of the dimer sub-site of the tetramer, lead to a delocalized S(t) = (9)/(2) spin ground state for the mixed-valence dimer in the tetramer. Thus, the decrease in the covalency, hence the superexchange pathway associated with changing the bridging mode of the sulfides from micro(2) to micro(3) on going from the dimer to the tetramer, significantly contributes to the delocalization of the excess electron over the dimer sub-site in the tetramer.     

Highly Bright White Organic Light-Emitting Diode

A highly bright white organic light-emitting diode (OLED) was realized by using a highly bright blue emitting layer, 1,7-diphenyl-4-biphenyl-3,5-dimethyl-l,7-dihydrodipyrazolo[3,4-b;4',3'-e]pyridine (PAP-Ph), together with a 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM)-doped Alq [tris(8-hydroxyquinolinato) aluminum (Ⅲ)] layer to provide the blue, red and green emission for color mixing. With appropriate thickness control, the white-light OLED has a performance that reaches 24700 cd/m2 at 15 V, 1.93 lm/W at 6.5 V, and ＞300 cd/m2 at 7.7 mA/em2. The Commission Internationale de l'Eclairage (CIE) coordinates of the emitted light vary in a very small range, from (0.35, 0.34) to (0.34, 0.35), when forward voltages change from 6 to 12 V.     

Coxeter groups A4, B4 and D4 for two-qubit systems

The Coxeter–Weyl groups W(A₄), W(B₄), and W(D₄) have proven very useful for two-qubit systems in quantum information theory. A simple technique is employed to construct the unitary matrix representations of the groups, based on quaternionic transformation of the usual reflection matrices. The von Neumann entropy of each reduced density matrix is calculated. It is shown that these unitary matrix representations are naturally related to various universal quantum gates and they lead to entangled states. Canonical decomposition of generators in terms of fundamental gate representations is given to construct the quantum circuits.     

Multi-Service Facility Location Models

The multi-service facility (MSF) concept proposes the co-location of a range of human services under a single roof. Thus, for example, services for preschoolers, teens, and seniors might be co-located within a joint facility. MSFs are a response to economies of scale; co-location reduces the monetary costs of providing a variety of services. Yet, the spatial distributions of different societal groups are different within a city – an MSF system will not provide optimum geographical accessibility to individual groups. We introduce two p-median based location–allocation models that trade off the fixed costs of providing services and opening facilities with the travel costs of three societal groups. We observe that some mixes of single- and multi-service facilities can provide efficient service systems without unduly compromising the accessibility needs of individual groups.