The Hamiltonian index of a graph and its branch-bonds

Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound. \u

No Cage, No Tube: Relative Stabilities of Nanostructures

Relative stabilities of nanostructures are important in the design and selection of components for nanodevices. Here, we use first-principles simulations to evaluate the relative stabilities of representative nanostructures of semimetal Bi, semiconductive C, and metallic Au. The Bi n cages are metastable and highly active and can readily transform to more stable three-dimensional amorphous structures upon activation. Both finite bismuth nanotubes and infinite nanotubes are even less stable than the cage structures. This is contrary to the cases for carbon, boron, and gold. The differences lie in their bonding characteristics and their responses to curvature. Our findings show tendencies of evolution of different types of nanostructures and also indicate that if a nanocage is (not) stable, then its nanotube is even more (less) stable. Hence, the stability of a cage structure predetermines the existence of a nanotube for a given element: i.e., no cage, no tube

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+-3 km (R/15km) except Cir X-1 at r = 30\+-5 km (R/15km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz.The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.Comment: Science China, Physics, Mechanics & Astronomy, 2010, 53, NO.

Projected wave functions for fractionalized phases of quantum spin systems

Gutzwiller projection allows a construction of an assortment of variational wave functions for strongly correlated systems. For quantum spin S=1/2 models, Gutzwiller-projected wave functions have resonating-valence-bond structure and may represent states with fractional quantum numbers for the excitations. Using insights obtained from field-theoretical descriptions of fractionalization in two dimensions, we construct candidate wave functions of fractionalized states by projecting specific superconducting states. We explicitly demonstrate the presence of topological order in these states.Comment: 10 pages, 3 figure

Microscopic models for fractionalized phases in strongly correlated systems

We construct explicit examples of microscopic models that stabilize a variety of fractionalized phases of strongly correlated systems in spatial dimension bigger than one, and in zero external magnetic field. These include models of charge fractionalization in boson-only systems, and various kinds of spin-charge separation in electronic systems. We determine the excitation spectrum and show the consistency with that expected from field theoretic descriptions of fractionalization. Our results are further substantiated by direct numerical calculation of the phase diagram of one of the models.Comment: 10 pages, 4 figure

Experimentally Engineering the Edge Termination of Graphene Nanoribbons

The edges of graphene nanoribbons (GNRs) have attracted much interest due to their potentially strong influence on GNR electronic and magnetic properties. Here we report the ability to engineer the microscopic edge termination of high quality GNRs via hydrogen plasma etching. Using a combination of high-resolution scanning tunneling microscopy and first-principles calculations, we have determined the exact atomic structure of plasma-etched GNR edges and established the chemical nature of terminating functional groups for zigzag, armchair and chiral edge orientations. We find that the edges of hydrogen-plasma-etched GNRs are generally flat, free of structural reconstructions and are terminated by hydrogen atoms with no rehybridization of the outermost carbon edge atoms. Both zigzag and chiral edges show the presence of edge states.Comment: 16+9 pages, 3+4 figure

A novel 3D imaging system for strawberry phenotyping

Accurate and quantitative phenotypic data in plant breeding programmes is vital in breeding to assess the performance of genotypes and to make selections. Traditional strawberry phenotyping relies on the human eye to assess most external fruit quality attributes, which is time-consuming and subjective. 3D imaging is a promising high-throughput technique that allows multiple external fruit quality attributes to be measured simultaneously. A low cost multi-view stereo (MVS) imaging system was developed, which captured data from 360° around a target strawberry fruit. A 3D point cloud of the sample was derived and analysed with custom-developed software to estimate berry height, length, width, volume, calyx size, colour and achene number. Analysis of these traits in 100 fruits showed good concordance with manual assessment methods. This study demonstrates the feasibility of an MVS based 3D imaging system for the rapid and quantitative phenotyping of seven agronomically important external strawberry traits. With further improvement, this method could be applied in strawberry breeding programmes as a cost effective phenotyping technique

Attenuation of Vaccinia Tian Tan Strain by Removal of Viral TC7L-TK2L and TA35R Genes

Vaccinia Tian Tan (VTT) was attenuated by deletion of the TC7L-TK2L and TA35R genes to generate MVTT3. The mutant was generated by replacing the open reading frames by a gene encoding enhanced green fluorescent protein (EGFP) flanked by loxP sites. Viruses expressing EGFP were then screened for and purified by serial plaque formation. In a second step the marker EGFP gene was removed by transfecting cells with a plasmid encoding cre recombinase and selecting for viruses that had lost the EGFP phenotype. The MVTT3 mutant was shown to be avirulent and immunogenic. These results support the conclusion that TC7L-TK2L and TA35R deletion mutants can be used as safe viral vectors or as platform for vaccines