In-Degree and PageRank of Web pages: Why do they follow similar power laws?

The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a `power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this phenomenon. The relation between the PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of the PageRank, and is analogous to the well-known distributional identity for the busy period in the M/G/1 queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail behavior of the PageRank and the In-Degree differ only by a multiplicative factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.Comment: 20 pages, 3 figures; typos added; reference adde

Electrochemical and spectroscopic properties of technetium in fused alkali metal chlorides

The behavior of metallic technetium in chloride melts was studied for the first time. The experiments were conducted in NaCl-2CsCl eutectic melt at 550 °C using high temperature electronic absorption spectroscopy, cyclic voltammetry and chronopotentiometry. The anodic dissolution of Tc results in the formation of a mixture of Tc(IV) and a lower oxidation state species. Cyclic voltammograms of technetium-containing melts show two cathodic and two associated anodic peaks. One pair is around -0.35 V vs. Ag/AgCl reference electrode and is associated with the deposition of Tc metal. ©The Electrochemical Society.Physical and Analytical Electrochemistry;Electrodeposition;Energy Technolog

The effect of fission product elements on the behavior of uranyl species in alkali chloride melts: A contribution towards reprocessing spent oxide fuels

The reactions of uranyl(VI) containing chloride melts with molybdenum, niobium, zirconium and palladium were studied using high temperature electronic absorption spectroscopy. Depending on the nature of the added element uranium is reduced to uranyl(V) and uranium(IV) chloro-species and UO2. Palladium, niobium and zirconium can all be removed from a uranyl(VI)-containing melt using molybdenum metal and the melt can then be purified from Mo(III) ions by bubbling Cl2 gas. Such approach can be employed for removal a number of fission product elements from molten chloride baths during reprocessing spent oxide fuels. ©The Electrochemical Society.Physical and Analytical Electrochemistry;Electrodeposition;Energy Technolog

Tungsten chemistry in alkali chloride melts

Speciation of tungsten in alkali chloride melts (based on NaCl-2CsCl, NaCl-KCl and 3LiCl-2KCl mixtures) was studied between 550 and 750æC using electronic absorption spectroscopy. Only W(IV) and W(V) chloro and oxychloro species can be stabilized under the conditions studied. Tungsten(IV) chloride ions are very sensitive to oxide/hydroxide impurities present in the melt. Anodic dissolution of W metal at anodic current densities in the range of 0.005 - 0.1 A/cm2 produces only [WCl6]2- ions that can be electrochemically (on a glassy carbon anode) oxidized to [WCl 6]-. Small amounts of oxide ions present in the melt result in a gradual conversion of W(IV) chloro species into W(IV) oxychloro species. In the presence of O2 in the atmosphere [WCl 6]2- is oxidized into the tungsten(V) species [WOCl 5]2-. Dissolution of tungsten hexachloride, WCl 6, in an NaCl-2CsCl melt initially yields [WCl6] 2- (due to disproportionation). Reaction of metallic tungsten with Pd(II)-containing melts results in the formation of [WCl6] 2- species. The main spectroscopic parameters of [WCl 6]2- and [WCl6]- complex ions were calculated. © 2007 Verlag der Zeitschrift für Naturforschung

Processing of vanadium and niobium electrodeposited from alkali chloride melts

The methods of hydrometallurgical treatment of cathodic deposits obtained by electrorefining vanadium and niobium metals in chloride melts were studied. The effectiveness of employing nitric acid was demonstrated. The optimal conditions of leaching trapped salt were determined: HNO3 concentration of 2.5 wt. % for vanadium and 5 wt. % for niobium; solid-to-liquid ratio 1:10 for both metals. The effect of increasing duration of a washing cycle on number of process stages was investigated. The methods of final washing and drying metallic powders were considered. ©The Electrochemical Society.Physical and Analytical Electrochemistry;Electrodeposition;Energy Technolog

Electrode and redox potentials of molybdenum and stability of molybdenum chloro-species in alkali chloride melts

Molybdenum electrode and Mo(III)/(IV) redox potentials were measured in fused alkali chlorides. Experiments were performed in individual salts (LiCl, NaCl, KCl, RbCl and CsCl) and in several binary and ternary eutectic or low-melting mixtures between 633 and 1173 K (depending on the melting point of the solvent salt). Formal standard electrode potentials E∗ Mo/Mo(III) and redox potentials E∗ Mo(III)/Mo(IV) in respect to Cl-/Cl2 couple and Gibbs free energy change of formation of molybdenum(III) chloride in alkali chloride melts were calculated. Electronic absorption spectra of Mo(III) ions were recorded, and spectroscopic parameters of MoCl6 3- complex ions determined. High temperature spectroscopy measurements were used to study the stability of Mo(III) chloro-species in fused chlorides and the reaction rates of Mo(III) ions disproportionation were also determined. Diffusion coefficients of molybdenum ions in LiCl-KCl-CsCl and NaCl-CsCl eutectic based melts were determined from the results of electrochemical measurements. © The Author(s) 2017

Speciation of rhenium in chloride melts: Spectroscopic and electrochemical study

Speciation of rhenium in high-temperature alkali chloride-based melts was studied using electronic absorption and IR spectroscopy of molten salts and diffuse reflectance spectroscopy of quenched melts. Rhenium was added to the melts by anodic dissolution of the metal (at anodic current densities of 0.005-0.05 A/cm2), by reacting Re and ReO2 with Cl 2 and HCl, and by dissolving K2[ReCl6]. The melts included 3LiCl-2KCl and NaCl-2CsCl eutectics, an NaCl-KCl equimolar mixture, and pure NaCl, KCl and CsCl between 450 and 850 °C. Rhenium was present in the melts as Re(IV) hexachloro-ions, [ReCl6]2-; no evidence of species containing rhenium in oxidation states below four was obtained. The kinetics of [ReCl6]2- disproportionation in molten alkali chlorides were investigated, and the IR spectra of [ReO 4]- ions in molten CsCl-CsI and CsI were measured for the first time. © 2008 Verlag der Zeitschrift für Naturforschung, Tübingen

Study of causes of film formation on the electrolyte surface during niobium electrorefining

Formation of a conducting film on the surface of fused electrolyte during electrorefining of niobium in chloride melts was investigated. It was found that this film has metallic nature and is formed as a result of disproportionation of niobium(III) ions at a liquid-gas interface. Decreasing temperature gradient along the heated part of the electrolyser can be used to limit the influence of the disproportionation onto film formation. The metal film formation on solid ceramics can be used for creation of conducting layers on various oxide materials. copyright The Electrochemical Society.Electrochemical Society, Phys. Anal. Electrochem. Div.;Electrochemical Society, Electrodeposition Division;Electrochemical Society, High Temperature Materials Division;Electrochemical Society, Battery Division;Electrochemical Society, Energy Technology Divisio