Solution and solid-state structure of the anion [Ag(2)[closo-CB(11)H(12)](4)](2-)

Addition of the carbene 1,3-dimesitylimidazol-2-ylidene (IMes) to a toluene solution of Ag[closo-CB(11)H(12)] results in the formation of the complex [(IMes)(2)Ag](2)[Ag(2)[closo-CB(11)H(12)](4)], the anionic component of which contains two silver(I) centers bridged by two carboranes in addition to one terminally bound carborane on each metal, in the solid-state. Comparison of the observed (11)B[(1)H] NMR chemical shifts of [(IMes)(2)Ag](2)[Ag(2)[closo-CB(11)H(12)](4)] or Ag[closo-CB(11)H(12)] with [NBu(4)][closo-CB(11)H(12)] in CD(2)Cl(2) demonstrates that the silver ion interacts significantly with the cage in solution. Theoretical investigations using the ab initio/GIAO/NMR method of [closo-CB(11)H(12)](-) and Na[closo-CB(11)H(12)] as model geometries for the silver salts support experimental evidence for these Ag...[BH] interactions in solution.     

The two-photon excitation cross section of 6MAP, a fluorescent adenine analogue

6MAP is a fluorescent analogue of adenine that undergoes Watson-Crick base pairing and base stacking in double-stranded DNA. The one-photon absorption spectrum of 6MAP is characterized by a maximum around 330 nm with moderate quantum yield fluorescence centered at about 420 nm. To take advantage of this probe for confocal and single-molecule microscopy, it would be advantageous to be able to excite the analogue via two photons. We report the first determination of the two-photon excitation cross section and spectrum for 6MAP from 614 to 700 nm. The power dependence of the fluorescence indicates that emission results from the absorption of two photons. The one-photon and two-photon emission line shapes are identical within experimental error. A study of the concentration dependence of the fluorescence yield for one-photon excitation shows no measurable quenching up to about 5 microM. The maximum in the two-photon excitation spectrum gives a two-photon cross section, delta(TPE), of 3.4 +/- 0.1 Goeppert-Mayer (G.M.) at 659 nm, which correlates well with the one-photon absorption maximum. This compares quite favorably with cross sections of various naturally fluorescent biological molecules such as flavins and nicotiamide. In addition, we have also obtained the two-photon-induced fluorescence emission spectrum of quinine sulfate. It is approximately the same as that for one-photon excitation, suggesting that two-photon excitation of quinine sulfate may be used for calibration purposes.     

On the lower Markov spectrum

C. Hightower found two infinite sequences of gaps in the Markov spectrum, ( _n , _n ) and ( _n , _n ) with _n and _n both Markov elements, converging to . This paper exhibits Markov elements _n ^* and _n ^* such that, for alln 1, ( _n ^* , _n ) and ( _{n n} ^* ) are gaps in the Markov spectrum. Other results include showing that, for alln 1, _n is completely isolated, while the other endpoints of the gaps are limit points in the Markov spectrum.     

An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Modification of polystyrene maleic anhydride for efficient energy storage applications

Journal of Solid State Electrochemistry - The development of new energy storage devices has been gaining momentum in the wake of the energy crisis faced worldwide. New materials have been tried and...