Every connected,locally connected nontrivial graph with no induced claw is hamiltonian

A graph is locally connected if every neighborthood induces a connected subgraph. We show here that every connected, locally connected graph on p ≥ 3 vertices and having no induced K_1,3 is Hamiltonian. Several sufficient conditions for a line graph to be Hamiltonian are obtained as corollaries.     

Addition sets in a finite group

Addition sets with parameters (υ,k,λ,α) are defined in a finite group G of order υ, where α: G → G is a homomorphism or anti-homomorphism. It is shown that addition sets in a finite group have similar properties to that of (υ,k,λ,g) cyclic addition sets. The case α = I, where I: G → G is the identity automorphism, is studied and it is shown that no (υ,k,λ,I) group addition sets exist in an Abelian group of order υ, where ether υ is odd, υ≡2 (mod 4), or in certain cases when υ≡0 (mod 4). Many examples of group addition sets in both Abelian and non-Abelian groups are provided.     

Point determination in graphs

A point determining graph is defined to be a graph in which distinct nonadjacent points have distinct neighborhoods. Those graphs which are critical with respect to this property are studied. We show that a graph is complete if and only if it is connected, point determining, but fails to remain point determining upon the removal of any edge. We also show that every connected, point determining graph contains at least two points, the removal of either of which will result again in a point determining graph. Graphs which are point determining and contain exactly two such points are shown to have the property that every point is adjacent to exactly one of these two points.     

Graphs indecomposable with respect to the X-join

In his paper [3], Sabidussi defined the X-join of a family of graphs. This concept has also appeared in the work of Foulis and Randall on empirical logic [1,2]. In this paper, we investigate those graphs which do not have a nontrivial representation as the X-join of some family of graphs.     

Alexa Fluor 488 as an iron sensing molecule and its application in PEBBLE nanosensors

Molecular Probes' Alexa Fluor dyes are generally used for biological labeling because of their ideal fluorescent properties, but here we detail Alexa Fluor 488's nanomolar sensitivity to free iron. Furthermore, the dye has been encapsulated into a polymer nanosphere by a microemulsion method, producing <100 nm particles. These nanosensors, PEBBLEs (Probe Encapsulated By Biologically Localized Embedding) have micromolar sensitivity and are non-responsive to other metal ions of biological interest.     

A fluorescent PEBBLE nanosensor for intracellular free zinc

The development and characterisation of a fluorescent optical PEBBLE (Probe Encapsulated By Biologically Localised Embedding) nanosensor for the detection of zinc is detailed. A ratiometric sensor has been fabricated that incorporates two fluorescent dyes; one is sensitive to zinc and the other acts as a reference. The sensing components are entrapped within a polymer matrix by a microemulsion polymerisation process that produces spherical sensors that are in the size region of 20 to 200 nm. Cellular measurements are made possible by the small sensor size and the biocompatibility of the matrix. The effects of reversibility, photobleaching and leaching have been examined, as well as the selectivity towards zinc over other cellular ions such as Na+, Ca2+, K+, and Mg2+. The dynamic range of these sensors was found to be 4 to 50 microM Zn2+ with a linear range from 15 to 40 microM. The response time for the PEBBLE is less than 4 s and the sensor is reversible. In addition, the nanosensors are photostable and leaching from the matrix, determined using a novel method, is minimal. These sensors are capable of real-time inter- and intra-cellular imaging and are insensitive to interference from proteins.     

Heat convection and transport barriers in low-magnetic-shear rijnhuizen tokamak project plasmas

Layers of reduced electron heat transport ("transport barriers") have been observed in the Rijnhuizen Tokamak Project when the plasma is dominantly heated by electron cyclotron heating (ECH). Experiments into the properties of the transport barriers are reported. Modulation of the ECH power was used to probe electron heat transport in the barriers by means of propagating electron temperature perturbations. The observed propagation shows that transport inside the barriers is dominated by heat convection. This convection is inward, i.e., up the temperature gradient.