Generalized fibonacci cubes are mostly hamiltonian

The Hamiltonian problem is to determine whether a graph contains a spanning (Hamiltonian) path or cycle. Here we study the Hamiltonian problem for the generalized Fibonacci cubes, which are a new family of graphs that have applications in interconnection topologies [J. Liuand W.-J. Hsu, ?Distributed Algorithms for Shortest-Path, Deadlock-Free Routing and Broadcasting in a Class of Interconnection Topologies,”? International Parallel Processing Symposium (1992)]. We show that each member of this family contains a Hamiltonian path. Furthermore, we also characterize the members of this family that contain a Hamiltonian cycle.     

Molecular mobility of free‐radical‐functionalized carbon‐nanotube/siloxane/poly(urea urethane) nanocomposites

Multiwalled carbon nanotubes (MWNTs) were functionalized by a free‐radical reaction of vinyltriethoxysilane and were blended with poly(urea urethane) (PUU) containing poly(dimethylsiloxane) as a soft segment. PUU was end‐capped with aminopropyltriethoxysilane (A‐silane) or phenyltriethoxysilane (P‐silane).A‐silane‐end‐capped PUU was covalently bonded to functionalized MWNTs, whereas P‐silane‐end‐capped PUU was noncovalently bonded to pristine MWNTs by a π–π interaction. Fourier transform infrared, Raman spectra, and thermogravimetric analysis confirmed the functionalization of MWNTs. The results showed that the optimal reaction time of the functionalization of MWNT was 8 h, and the organic content of the modified carbon nanotubes reached 35.22%. Solid‐state nuclear magnetic resonance and dynamic mechanical analysis were used to investigate the molecular structure and molecular mobility of the carbon‐nanotube/PUU nanocomposites. A‐silane PUU covalently bonded to MWNTs showed a considerable reduction in the molecular motion of the soft segment, which led to the glass‐transition temperature decreasing from ?117 to ?127 °C as MWNTs were incorporated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6084–6094, 2005     

Preparation and electromagnetic interference shielding characteristics of novel carbon‐nanotube/siloxane/poly‐(urea urethane) nanocomposites

Poly(urea urethane) (PUU) with a poly(dimethylsiloxane) soft segment was synthesized. Different types of conductive fillers—carbon nanotube (CNT), silver‐coated carbon nanotube (CNT–Ag), and nickel‐coated carbon nanotube (CNT–Ni)—were blended with PUU to form partially conductive polymer composites. The results showed that highly conductive metals could improve the conductivity of CNTs significantly. When the filler contents were 3, 4, and 5 parts per hundred parts of resin (phr), the PUU/CNT composites possessed electromagnetic interference shielding effectiveness (SE) at 8.5, 28.4, and 26.0 dB as the electromagnetic wave frequencies were 12.3, 16.2, and 15.9 GHz, respectively. SE of the composites that contained CNT–Ni and CNT–Ag increased with the filler loading. At the same modified‐CNT loading, the CNT–Ni‐filled composites had a higher SE than those filled with CNT–Ag. Tensile stresses ranged from 5.7 to 15.6 MPa (a 177.3% increase) when the CNT concentration reached 8 phr. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 345–358, 2005     

Flocculation by very high molecular weight polymers

Polymer-induced flocculation in which the size of polymer molecules is much greater than that of colloidal particles is investigated. A dynamic analysis is conducted which takes the transient behaviors of the adsorption of particles to a polymer molecule and the particle-particle interactions into account. We show that the number of particles adsorbed to a polymer molecule follows approximately a binomial distribution. An approximate expression for the degree of flocculation of the system under consideration is presented.     

Ion transport and clustering in nafion perfluorinated membranes

A theory of ion-clustering is presented for Nation resins. An expression for the cluster diameter is derived; it correctly describes the experimental variations in cluster diameter with cation form, equivalent weight, and water content of the polymers. The theory further suggests that short channels connecting adjacent clusters are thermodynamically stable in support of the cluster-network model proposed by one of us earlier. The percolative aspects of ion transport and an ionic insulator-to-conductor transition in Nation resins are discussed.     

Studies on the thermotropic liquid crystalline polymer. VI. Synthesis and properties of homo- and co-poly(amide-azomethine-ether)

Two series of poly(amide-azomethine-ether)s and poly(ester-azomethine-ether)s were prepared by the condensation of dialdehydes with N,N'-bis(aminobenzamide)s and 4,4′-bis(p-aminophenyl)terephthalester, respectively. The thermotropic liquid crystalline properties were examined by DSC microscopic observations. Almost half of the synthesized polymers exhibit thermotropic liquid crystalline properties which are in the nematic phase since threaded and/or Schlieren textures are observed under polarizing microscope. The effects of the number of amide group and the nature of the nonlinear bibenzamide moiety, which link in the rigid segment, on the thermotropic liquid crystalline properties of the homo- and co-poly(amide-azomethine-ether)s were also investigated.     

Magnetic-bubble conservative logic

Among integrated-circuit devices, magnetic bubbles are a particularly interesting candidate to implement the Fredkin gate and conservative logic. The magnetostatic repulsion of magnetic bubbles simulates the bouncing-ball model of conservative logic.