L E Grigorescu is a Physicist from 1955 in IFIN-HH and Nuclear Researcher & Head of Radionuclides Metrology Laboratory within IFIN-HH. He is the former Vice-president of ICRM (International Committee for Radionuclide Metrology) and has published more than 50 papers.
Statistics is involved in every physical measurement.The weighted mean appears when a physical quantity is measured by different methods in different laboratories, producing different results. The formula is: The formula is:\r\n (1)\r\nwith - absolute weights and - relative weights.\r\n\r\nA relation exists:\r\n (2)\r\nwith - the individual standard deviations.\r\n\r\nTo , two different dispersions are associated, D1 (internal) and D2 (external).\r\nThe ratio D2/D1 is:\r\n (3)\r\n\r\nIn practice (D2/D1)>1. So D2 is the confident one.\r\nIn principle should produce as great deviations , as the associated are great.\r\nFor equal treatment of these deviations, relative deviations may be considered:\r\n (4)\r\nwhich express the deviations in units .\r\nThe n values from (4) must have same near (equivalent) values.Their arithmetical mean tends to zero.Thus, as in the case of a unique , we may reach the minimum of the expression:\r\n (5)\r\nThe annulation of the derivative for , gives:\r\n (6)\r\n\r\nand finally formulas (1) and (2) are obtained.\r\nThis calculus accepts great even with systematic uncertainties.In practice the theoretical unknown values , are replaced in formulae (1), (2) by the experimental value , which fluctuate. \r\n\r\nA dispersion D3 is obtained, by error propagation, and added to D1, D2.\r\nFirst are calculates:\r\n (7)\r\nThen:\r\n (8)\r\nwith - the relative standard deviation for and is the values of measurements which provided .For (8) it was used the equality:\r\n (9)\r\n\r\n express the fluctuation of the only statistical part of (systematic components do not fluctuate) and so formulae (9) may be applied. Adding D2 with D3, a correct D2c results. To neglect D3, ni must have same values (rarely the cases).\r\n
Gayan Prasad Hettiarachchi has completed his PhD in Physics from Osaka University in 2015. He is currently working as a specially appointed Assistant Professor for the Insititute of NanoScience Design at Osaka University. He is interested in experimentally investigating strongly correlated electron systems in order to elucidate vital correlation effects and the underlying causes that ultimately lead to interesting physical properties and quantum phase transitions.
Guest Na and Rb atoms are introduced into a quasi-2D cage-type host with the chemical formula per unit cell M7.8Al7.8Si.8.2O32.0 (M = Na or Rb). The cages contain a deformable lattice made up of cations (M), whose locations can change due to the interactions with the guest elements. The quasi-2D host framework has open zigzag channels along a- and b-axes, and a rather closed structure along the c-axis. At dilute densities of guest Na-atoms, optical absorptions are observed that indicate a rigid confinement of the guest electron’s wave function within a single cage. At higher densities, changes in the absorption spectra indicate a possible extension of the excited state of the wave function to neighboring cages. At dilute densities of guest Rb-atoms, a low energy absorption is observed that may be explained by excitations to the p-like first excited-state with a wave length similar to the lattice constant. At higher densities, a new peak appears that may be explained in terms of surface plasmon excitations of many electrons within the zigzag channels. It is expected that, in addtion to the framework structure, the deformable lattice (in terms of the deformation potential energy provided by the lattice distortions of the deformable lattice coupled with the size of the constituent cations) has a crucial role to play in the evolution of optical properties in such materials. Polaron effects on optical properties require further considerations towards applications and theory.