A Rare Cyclic Dimolybdenum Triad with Three Weakly Interacting Unpaired Electrons

Oxidation of α-[Mo₂(cis-DAniF)₂]₃(μ-F)₆ with an excess of FeCp₂BF₄ produces the triply oxidized species {β-[Mo₂(cis-DAniF)₂]₃(μ-F)₆}(BF₄)₃. During the oxidation process, the conformation in the α triangular species changes from an arrangement in which two dimetal units are parallel and the third one essentially orthogonal to a structure in which all three dimetal units are parallel. Furthermore, upon removal of three electrons, the Mo–Mo distances increase by about 0.05–0.06 Å and the Mo–F bond distances decrease by 0.04 Å. The structural data, as well as EPR, are consistent with an electronically localized system and a decrease in bond order from 4 to 3.5 for each dimetal unit.     

Self-similarity of electrostatic fluctuations in a linear magnetised plasma system

In this Letter the long-range time correlations present in the fluctuation data in presence of electrostatic instability in a magnetised dc discharge plasma is presented. The electrostatic instability is generated due to the effect of crossed electric and magnetic field (E×B flow) and has intermediate frequency ranging from 50 to 100 MHz. Hurst exponent, the self-similarity parameter is calculated with the help of different statistical methods suggested by many researchers to determine the long-range time correlation present in fluctuation dynamics in the plasma column. The fluctuation in the ion saturation current is measured by a Langmuir probe for the study and the measurement is done both radially and axially in the plasma system. Estimated results clearly expose the self-similar character of the fluctuations with self-similarity parameters having values from 0.65 to 0.90 through the presence of long-range time correlation.     

On Sharpening of a Theorem of Ankeny and Rivlin

Let $p(z)=\sum^n_{v=0}a_vz^v$be a polynomial of degree $n$, $M(p,R)=:\underset{|z|=R\geq 0}{\max}|p(z)|$ and $M(p,1)=:||p||$.Then according to a well-known result of Ankeny and Rivlin [1], we have for $R\geq 1$, $$M(p,R)\leq (\frac{R^n+1}{2})||p||.$$This inequality has been sharpened by Govil [4], who proved that for $R\geq 1$, $$M(p,R)\leq (\frac{R^n+1}{2})||p||-\frac{n}{2}(\frac{||p||^2-4|a_n|^2}{||p||})\left\{\frac{(R-1||p||)}{||p||+2|a_n|}-ln(1+\frac{(R-1)||p||}{||p||+2|a_n|})\right\}.$$In this paper, we sharpen the above inequality of Govil [4], which in turn sharpens the inequality of Ankeny and Rivlin [1].     

On the Carey–Helton–Howe–Pincus trace formula

In this article, we give a new proof of the Carey–Helton–Howe–Pincus trace formula using Kato's theory of “relatively-smooth” operators and Krein's trace formula.     

Convergence of linear functions of Pfeifer records

The probabilistic behaviour of partial sums of upper and lower records has been studied in the literature. In this article, we take a broader view and study partial sums of record like sequences. We show that such sequences converge in distribution to normal and lognormal distribution. In particular our results apply to Pfeifer records. We also show the strong convergence of partial sums of lower Pfeifer records under suitable assumptions.     

Detection of Metal Ions by Quenching of Dye Laser Emission

A novel laser intracavity method for detecting metal ions is described in which a metal analyte is added directly to a dye ligand and the dye laser emission is monitored as a measure of the analyte's concentration. The technique is both sensitive and selective and may have applications as an indirect probe of chemical analysis and of energy transfer.