Changes in the measured image separation of the gravitational lens system, PKS 1830-211

We present eight epochs of 43 GHz, dual-polarisation VLBA observations of the gravitational lens system PKS 1830-211, made over fourteen weeks. A bright, compact ``core'' and a faint extended ``jet'' are clearly seen in maps of both lensed images at all eight epochs. The relative separation of the radio centroid of the cores (as measured on the sky) changes by up to 87 micro arcsec between subsequent epochs. A comparison with the previous 43 GHz VLBA observations (Garrett et al. 1997) made 8 months earlier show even larger deviations in the separation of up to 201 micro arcsec. The measured changes are most likely produced by changes in the brightness distribution of the background source, enhanced by the magnification of the lens. A relative magnification matrix that is applicable on the milliarcsecond scale has been determined by relating two vectors (the ``core-jet'' separations and the offsets of the polarised and total intensity emission) in the two lensed images. The determinant of this matrix, -1.13 +/-0.61, is in good agreement with the measured flux density ratio of the two images. The matrix predicts that the 10 mas long jet, that is clearly seen in previous 15 and 8.4 GHz VLBA observations (Garrett et al. 1997, Guirado et al. 1999), should correspond to a 4 mas long jet trailing to the south-east of the SW image. The clear non-detection of this trailing jet is a strong evidence for sub-structure in the lens and may require more realistic lens models to be invoked, e.g. Nair & Garrett (2000).Comment: 8 pages, 5 figure

Carrier mobility and scattering lifetime in electric double-layer gated few-layer graphene

We fabricate electric double-layer field-effect transistor (EDL-FET) devices on mechanically exfoliated few-layer graphene. We exploit the large capacitance of a polymeric electrolyte to study the transport properties of three, four and five-layer samples under a large induced surface charge density both above and below the glass transition temperature of the polymer. We find that the carrier mobility shows a strong asymmetry between the hole and electron doping regime. We then employ ab-initio density functional theory (DFT) calculations to determine the average scattering lifetime from the experimental data. We explain its peculiar dependence on the carrier density in terms of the specific properties of the electrolyte we used in our experiments.Comment: 6 pages, 3 figure

Strong Domination Index in Fuzzy Graphs

Topological indices play a vital role in the area of graph theory and fuzzy graph (FG) theory. It has wide applications in the areas such as chemical graph theory, mathematical chemistry, etc. Topological indices produce a numerical parameter associated with a graph. Numerous topological indices are studied due to its applications in various fields. In this article a novel idea of domination index in a FG is defined using weight of strong edges. The strong domination degree (SDD) of a vertex u is defined using the weight of minimal strong dominating set (MSDS) containing u. Idea of upper strong domination number, strong irredundance number, strong upper irredundance number, strong independent domination number, and strong independence number are explained and illustrated subsequently. Strong domination index (SDI) of a FG is defined using the SDD of each vertex. The concept is applied on various FGs like complete FG, complete bipartite and r-partite FG, fuzzy tree, fuzzy cycle and fuzzy stars. Inequalities involving the SDD and SDI are obtained. The union and join of FG is also considered in the study. Applications for SDD of a vertex is provided in later sections. An algorithm to obtain a MSDS containing a particular vertex is also discussed in the article

Domination Index in Graphs

The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index is introduced, which utilizes the domination degree of a vertex. The domination degree of a vertex a is defined as the minimum cardinality of a minimal dominating set that includes a. The idea of domination degree and domination index is conducted of graphs like complete graphs, complete bipartite, r partite graphs, cycles, wheels, paths, book graphs, windmill graphs, Kragujevac trees. The study is extended to operation in graphs. Inequalities involving domination degree and already established graph parameters are discussed. An application of domination degree is discussed in facility allocation in a city. Algorithm to find a MDS containing a particular vertex is also discussed in the study

Hyperfine interaction and electronic spin fluctuation study on Sr2−x_{2-x}Lax_xFeCoO6_6 (x = 0, 1, 2) by high-resolution back-scattering neutron spectroscopy

The study of hyperfine interaction by high-resolution inelastic neutron scattering is not very well known compared to the other competing techniques viz. NMR, M\"ossbauer, PACS etc. Also the study is limited mostly to magnetically ordered systems. Here we report such study on Sr$_{2-x}$La$_x$FeCoO$_6$ (x = 0, 1, 2) of which first (Sr$_2$FeCoO$_6$ with x = 0) has a canonical spin spin glass, the second (SrLaFeCoO$_6$ with x = 1) has a so-called magnetic glass and the third (La$_2$FeCoO$_6$ with x = 2) has a magnetically ordered ground state. Our present study revealed clear inelastic signal for SrLaFeCoO$_6$, possibly also inelastic signal for Sr$_2$FeCoO$_6$ below the spin freezing temperatures $T_{sf}$ but no inelastic signal at all for for the magnetically ordered La$_2$FeCoO$_6$ in the neutron scattering spectra. The broadened inelastic signals observed suggest hyperfine field distribution in the two disordered magnetic glassy systems and no signal for the third compound suggests no or very small hyperfine field at the Co nucleus due to Co electronic moment. For the two magnetic glassy system apart from the hyperfine signal due only to Co, we also observed electronic spin fluctuations probably from both Fe and Co electronic moments. \end{abstract