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In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a nonadditive generalization of Shannon entropy. We obtain several results of Tsallis entropy including bounds, monotonic properties, stochastic orders, and sharp bounds under some assumptions. We also compare the uncertainty and information content of MRSSU with its counterpart in the simple random sampling (SRS) data. Finally, we develop some characterization results in terms of cumulative Tsallis entropy and residual Tsallis entropy of MRSSU and SRS data.

In this paper, we obtain a measure of inaccuracy between rth concomitant of generalized order statistic and the parent random variable in Morgenstern family. Applications of this result are given for concomitants of order statistics and record values. We also study some results of cumulative past inaccuracy (CPI) between the distribution function of rth concomitant of order statistic (record value) and the distribution function of parent random variable. Finally, we discuss on a problem of estimating the CPI by means of the empirical CPI in concomitants of generalized order statistics.

Atomic nanolines are one dimensional systems realized by assembling many atoms on a substrate into long arrays. The electronic properties of the nanolines depend on those of the substrate. Here, we demonstrate that to fully understand the electronic properties of Bi nanolines on clean Si(001) several different contributions must be accounted for. Scanning tunneling microscopy reveals a variety of different patterns along the nanolines as the imaging bias is varied. We observe an electronic phase shift of the Bi dimers, associated with imaging atomic p-orbitals, and an electronic coupling between the Bi nanoline and neighbouring Si dimers, which influences the appearance of both. Understanding the interplay between the Bi nanolines and Si substrate could open a novel route to modifying the electronic properties of the nanolines., Comment: 6 pages (main), 2 pages (SI), accepted by Phys. Rev. B

Scanning tunneling microscopy (STM) reveals unusual sharp features in otherwise defect free bismuth nanolines self-assembled on Si(001). They appear as subatomic thin lines perpendicular to the bismuth nanoline at positive biases and as atomic size beads at negative biases. Density functional theory (DFT) simulations show that these features can be attributed to buckled Si dimers substituting for Bi dimers in the nanoline, where the sharp feature is the counterintuitive signature of these dimers flipping during scanning. The perfect correspondence between the STM data and the DFT simulation demonstrated in this study highlights the detailed understanding we have of the complex Bi-Si(001) Haiku system., Comment: Five pages, six figures, submitted to PRL

Mn has been found to self-assemble into atomic chains running perpendicular to the surface dimer reconstruction on Si(001). They differ from other atomic chains by a striking asymmetric appearance in filled state scanning tunneling microscopy (STM) images. This has prompted complicated structural models involving up to three Mn atoms per chain unit. Combining STM, atomic force microscopy and density functional theory we find that a simple necklace-like chain of single Mn atoms reproduces all their prominent features, including their asymmetry not captured by current models. The upshot is a remarkably simpler structure for modelling the electronic and magnetic properties of Mn atom chains on Si(001)., Comment: 5 pages, 4 figures