The Road to Reform: A Grounded Theory Study of Parents' and Teachers' Influence on Elementary School Science and Mathematics

Though elementary teacher educators introduce new, reform‐based strategies in science and mathematics methods courses, researchers wondered how novices negotiate reform strategies once they enter the elementary school culture. Given that the extent of parents' and veteran teachers' influence on novice teachers is largely unknown, this grounded theory study explored parents' and teachers' expectations of children's optimal science and mathematics learning in the current era of reform. Data consisted of semi‐structured, open‐ended interviews with novice teachers (n = 20), veteran teachers (n = 9), and parents (n = 28). Researchers followed three stages of coding procedures to develop a logic model connecting participants' discrete designations of the landscape, regulating phenomena, contextual orientation, and desired outcomes. This logic model helped researchers develop propositions for future research on the interactive nature of parents' and teachers' influential role in elementary science and mathematics education. Implications encourage science and mathematics teacher educators—as well as school administrators—to explicitly develop and support novice teachers' ability to initiate and sustain parent/family engagement in order to create a school climate where teachers and parents are synergistically motivated to change.     

Edge-transitive products

This paper concerns finite, edge-transitive direct and strong products, as well as infinite weak Cartesian products. We prove that the direct product of two connected, non-bipartite graphs is edge-transitive if and only if both factors are edge-transitive and at least one is arc-transitive, or one factor is edge-transitive and the other is a complete graph with loops at each vertex. Also, a strong product is edge-transitive if and only if all factors are complete graphs. In addition, a connected, infinite non-trivial Cartesian product graph G is edge-transitive if and only if it is vertex-transitive and if G is a finite weak Cartesian power of a connected, edge- and vertex-transitive graph H, or if G is the weak Cartesian power of a connected, bipartite, edge-transitive graph H that is not vertex-transitive.     

Distance-Balanced Graphs

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property The number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. The new concept is connected with symmetry conditions in graphs and local operations on graphs are studied with respect to it. Distance-balanced Cartesian and lexicographic products of graphs are also characterized. Several open problems are posed along the way. Received August 31, 2005     

Plasmon‐enhanced polarized Raman spectroscopy for sensitive surface characterization

Local‐mode and localized surface plasmons generated on the silver thin film can selectively enhance the Raman signal from the surface. Further improvement of surface signal can be obtained by using the polarized Raman technique that results in a dramatic enhancement of the surface sensitivity by up to 25.4 times as compared to that without a silver coating. This technique will be very useful for Raman study on samples that suffer overlapping background signal. In this article, we show that it can be used to significantly improve the signal of thin strained‐Si layer on top of SiGe buffer layer. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal packings of up to six equal circles on a triangular flat torus

For each n between 1 and 6, we prove that a certain arrangement of n equal circles is the unique optimally dense packing on a standard triangular flat torus (the quotient of the plane by the lattice generated by two unit vectors with a 60^? angle). The packings of 1, 2, 3, 4 and 6 circles are based on either a toroidal triangular close packing or a toroidal triangular close packing with one circle removed. The packing of 5 circles is irregular. This proves two cases of a conjecture stronger than L. Fejes Toth??s conjecture about the strong solidity of the triangular close packing on the plane.     

Influence of Dye Content on the Conduction Band Edge of Titania in the Steam‐treated Dye‐dispersing Titania Electrodes

The titania and dye‐dispersing titania electrodes were prepared by a nitric acid‐catalyzed sol‐gel process. The dye‐dispersing titania contains the dye molecules dispersed on the surface of the individual nanosized titania particles. The photo‐cyclic voltammetry (Photo‐CV) and photoelectric measurements of the dye‐dispersing titania electrodes were conducted to clarify the factors changing the conduction band edge of the titania and the open‐circuit voltage (V_oc) of the electrodes. The remaining nitrate ions caused a negative shift of conduction band edge of the titania of the dye‐dispersing titania. The conduction band edge of the titania was shifted in a negative direction in the electrode containing a greater amount of the dye. These results are due to the adsorption of nitrate ions and the dye‐titania complex formation on the titania particle surface. The effect of the dye‐titania complex formation on the shift in the titania conduction band edge was greater than that of the adsorption of nitrate ions due to strong interaction between the dye and titania through the carboxylate and quinone‐like groups of the dye. The shift in the titania conduction band edge corresponded to the change in the V_oc value.     

The domination game played on diameter 2 graphs

Aequationes mathematicae - Let $$\gamma _g(G)$$ be the game domination number of a graph G. It is proved that if $$\mathrm{diam}(G) = 2$$ , then $$\gamma _g(G) \le \left\lceil \frac{n(G)}{2}...     

Improved Upper Bounds on the Domination Number of Graphs With Minimum Degree at Least Five

An algorithmic upper bound on the domination number \(\gamma \) of graphs in terms of the order n and the minimum degree \(\delta \) is proved. It is demonstrated that the bound improves best previous bounds for any \(5\le \delta \le 50\). In particular, for \(\delta =5\), Xing et al. (Graphs Comb. 22:127–143, 2006) proved that \(\gamma \le 5n/14 < 0.3572 n\). This bound is improved to 0.3440 n. For \(\delta =6\), Clark et al. (Congr. Numer. 132:99–123, 1998) established \(\gamma <0.3377 n\), while Biró et al. (Bull. Inst. Comb. Appl. 64:73–83, 2012) recently improved it to \(\gamma <0.3340 n\). Here the bound is further improved to \(\gamma < 0.3159n\). For \(\delta =7\), the best earlier bound 0.3088n is improved to \(\gamma < 0.2927n\).     

Critical velocity for superfluid flow across the BEC-BCS crossover

Critical velocities have been observed in an ultracold superfluid Fermi gas throughout the BEC-BCS crossover. A pronounced peak of the critical velocity at unitarity demonstrates that superfluidity is most robust for resonant atomic interactions. Critical velocities were determined from the abrupt onset of dissipation when the velocity of a moving one-dimensional optical lattice was varied. The dependence of the critical velocity on lattice depth and on the inhomogeneous density profile was studied.