Two-ended regular median graphs

We show that regular median graphs of linear growth are the Cartesian product of finite hypercubes with the two-way infinite path. Such graphs are Cayley graphs and have only two ends.For cubic median graphs G the condition of linear growth can be weakened to the condition that G has two ends. For higher degree the relaxation to two-ended graphs is not possible, which we demonstrate by an example of a median graph of degree four that has two ends, but nonlinear growth.     

Asymptotic Properties of Fibonacci Cubes and Lucas Cubes

It is proved that the asymptotic average eccentricity and the asymptotic average degree of both Fibonacci cubes and Lucas cubes are \({(5+\sqrt{5})/10}\) and \({(5-\sqrt{5}) /5}\) , respectively. A new labeling of the leaves of Fibonacci trees is introduced and it is proved that the eccentricity of a vertex of a given Fibonacci cube is equal to the depth of the associated leaf in the corresponding Fibonacci tree. Hypercube density is also introduced and studied. The hypercube density of both Fibonacci cubes and Lucas cubes is shown to be \({(1-1/\sqrt{5})/ \rm log_ {2}\varphi}\) , where \({\varphi}\) is the golden ratio, and the Cartesian product of graphs is used to construct families of graphs with a fixed, non-zero hypercube density. It is also proved that the average ratio of the numbers of Fibonacci strings with a 0 (a 1, respectively) in a given position, where the average is taken over all positions, converges to \({\varphi^{2}}\) , and likewise for Lucas strings.     

Engineering process as a focus: STEM professional development with elementary STEM‐focused professional development schools

Young children are capable of engaging in STEM investigations when they are guided by skilled and knowledgeable teachers. However, many elementary teachers may lack sufficient STEM content knowledge and report feeling unprepared to teach STEM content. Two university faculty members in mathematics and science education, worked to cultivate and advance two designated Elementary STEM‐Focused professional development schools through a two year series of an after‐school STEM professional development (PD) Program. As the STEM PD Program progressed, it became evident that teachers were interested in and needed more experiences with the elements of the engineering process for young learners. With this in mind, several of the PD sessions were designed to highlight the engineering process and allow teachers to experience various activities that would engage young learners. To examine how this focus on the engineering process impacted the teachers in this STEM PD Program, a research study was organized during year two of the STEM PD Program. The results of this study provide evidence that this program had a positive influence on the teacher participants’ engineering teacher efficacy and implementation of engineering lessons and activities within their classrooms.     

Coloring graph bundles

Graph bundles generalize the notion of covering graphs and products of graphs. Several results about the chromatic numbers of graph bundles based on the Cartesian product, the strong product and the tensor product are presented. © 1995 John Wiley & Sons, Inc.     

Cortistatins A, B, C, and D, anti-angiogenic steroidal alkaloids, from the marine sponge Corticium simplex

Four novel steroidal alkaloids named cortistatins A (1), B (2), C (3), and D (4) consisting of a 9(10-19)-abeo-androstane and isoquinoline skeleton have been isolated from the marine sponge Corticium simplex. The absolute stereostructures of 1-4 were elucidated by detailed 2D NMR, CD, and X-ray crystallographic analyses. Cortistatins A-D inhibited proliferation of human umbilical vein endothelial cells (HUVECs) with high selectivity. Among the four substances, cortistatin A (1) showed the strongest anti-proliferative activity (IC50 = 0.0018 muM) against HUVECs, in which the selective index was more than 3000-fold in comparison with that of normal fibroblast or several tumor cell lines.     

Investigation of corannulene for molecular hydrogen storage via computational chemistry and experimentation

Molecular simulations for hydrogen physisorption with corannulene molecules arranged according to their crystal structure result in good agreement with the weight-percent hydrogen stored as determined experimentally employing a 3-g sample of highly crystalline corannulene at ambient temperatures and 72 bar of pressure. Calculated enthalpies of adsorption for corannulene/hydrogen molecular systems obtained from ab initio calculations which take into account electron correlation via second-order M?ller-Plesset perturbation theory are in good agreement with literature experimental enthalpies of adsorption for activated carbons interacting with molecular hydrogen. Ab initio results also show that corannulene molecules arranged in a sandwich structure are important for approximately doubling the binding energy of corannulene interacting with molecular hydrogen through a cooperative interaction. To test the effects of finite temperatures and pressures, stack arrays were used as input for molecular dynamics simulations and indicate that physisorption mechanisms including van der Waals forces and dipole-induced dipole interactions may yield enhanced adsorption capacity in relation to other carbon-based materials. These results will be instrumental in identifying interlayer separations of an array of corannulene or related molecules that may provide a high weight percent of physisorbed hydrogen.     

The Clar formulas of a benzenoid system and the resonance graph

It is shown that the number of Clar formulas of a Kekuléan benzenoid system B is equal to the number of subgraphs of the resonance graph of B isomorphic to the Cl(B)-dimensional hypercube, where Cl(B) is the Clar number of B.     

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.