Molecular quantum-dot cellular automata

Molecular electronics is commonly conceived as reproducing diode or transistor action at the molecular level. The quantum-dot cellular automata (QCA) approach offers an attractive alternative in which binary information is encoded in the configuration of charge among redox-active molecular sites. The Coulomb interaction between neighboring molecules provides device-device coupling. No current flow between molecules is required. We present an ab initio analysis of a simple molecular system which acts as a molecular QCA cell. The intrinsic bistability of the charge configuration results in dipole or quadrupole fields which couple strongly to the state of neighboring molecules. We show how logic gates can be implemented. We examine the role of the relaxation of nuclear coordinates in the molecular charge reconfiguration.     

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and influencing their actual teaching practice. This study reports how 25 elementary teachers from schools with minority and economically disadvantaged populations responded to a math circle experience. A pretest and posttest showed a significant increase in problem‐solving ability. Through analysis of journals, all but 4 of the 25 teachers indicated that participation in the math circle increased their understanding of problem solving and advanced their use of problem solving in the classroom.     

Linking Semiconductor Nanocrystals into Gel Networks through All‐Inorganic Bridges

For colloidal semiconductor nanocrystals (NCs), replacement of insulating organic capping ligands with chemically diverse inorganic clusters enables the development of functional solids in which adjacent NCs are strongly coupled. Yet controlled assembly methods are lacking to direct the arrangement of charged, inorganic cluster‐capped NCs into open networks. Herein, we introduce coordination bonds between the clusters capping the NCs thus linking the NCs into highly open gel networks. As linking cations (Pt²⁺) are added to dilute (under 1 vol %) chalcogenidometallate‐capped CdSe NC dispersions, the NCs first form clusters, then gels with viscoelastic properties. The phase behavior of the gels for variable [Pt²⁺] suggests they may represent nanoscale analogues of bridged particle gels, which have been observed to form in certain polymer colloidal suspensions.     

Fault Tolerance of Cayley Graphs

It is a difficult problem in general to decide whether a Cayley graph Cay(G; S) is connected where G is an arbitrary finite group and S a subset of G. For example, testing primitivity of an element in a finite field is a special case of this problem but notoriously hard. In this paper, it is shown that if a Cayley graph Cay(G; S) is known to be connected then its fault tolerance can be determined in polynomial time in |S|log(|G|). This is accomplished by establishing a new structural result for Cayley graphs. This result also yields a simple proof of optimal fault tolerance for an infinite class of Cayley graphs, namely exchange graphs. We also use the proof technique for our structural result to give a new proof of a known result on quasiminimal graphs. Received March 10, 2006     

Conformational control of HCl co-transporter: imidazole functionalised isophthalamide vs. 2,6-dicarboxamidopyridine

Replacement of the central isophthalamide core in a synthetic HCl receptor, with a 2,6-dicarboxamidopyridine, leads to a more preorganised molecular structure that exhibits higher chloride affinity and membrane transport flux.     

Absence of discrete spectrum in highly negative ions

We extend the results of [1] to fermions, i.e., we show that ifH _N is the Hamiltonian forN electrons in the field of a fixed point chargeZ, then there is a constantc such thatH _N has no discrete spectrum forN≧N ₀=cZ ^6/5.     

Minimum-weight two-connected spanning networks

We consider the problem of constructing a minimum-weight, two-connected network spanning all the points in a setV. We assume a symmetric, nonnegative distance functiond(·) defined onV × V which satisfies the triangle inequality. We obtain a structural characterization of optimal solutions. Specifically, there exists an optimal two-connected solution whose vertices all have degree 2 or 3, and such that the removal of any edge or pair of edges leaves a bridge in the resulting connected components. These are the strongest possible conditions on the structure of an optimal solution since we also show thatany two-connected graph satisfying these conditions is theunique optimal solution for a particular choice of canonical distances satisfying the triangle inequality. We use these properties to show that the weight of an optimal traveling salesman cycle is at most 4/3 times the weight of an optimal two-connected solution; examples are provided which approach this bound arbitrarily closely. In addition, we obtain similar results for the variation of this problem where the network need only span a prespecified subset of the points.     

Limits on stability of positive molecular ions

It is shown that a positive diatomic molecule consisting of N electrons and two nuclei with charges Z ₁ and Z ₂ is unstable with respect to breakup into two atomic subsystems if the nuclear charges are sufficiently large. Bounds on the critical charge are obtained in the limit as N .Research supported in part by NSF grants DMS-8709805 and DMS-8808112.     

A novel oxidative degradation pathway of indomethacin under the stressing by hydrogen peroxide

The structures of two oxidative degradation products of indomethacin were determined and their formation through a novel oxidative degradation mechanism is proposed. The synthesis of one of the degradation products is described.