<Emphasis Type="Italic">v</Emphasis>-Adic maximal extensions,spectral norms and absolute Galois groups

Let (K, v) be a perfect rank one valued field and let ([`(K<sub>v</sub>)],[`(v)]){(\overline{K_{v}},\overline{v})} be the canonical valued field obtained from (K, v) by the unique extension of the valuation [(v)\tilde]{\widetilde{v}} of K _v , the completion of K relative to v, to a fixed algebraic closure [`(K<sub>v</sub>)]{\overline{K_{v}}} of K <sub>v</sub> . Let [`(K)]{\overline{K}} be the algebraic closure of K in [`(K<sub>v</sub>)]{\overline {K_{v}}}. An algebraic extension L of K, L ì [`(K)]{L\subset\overline{K}}, is said to be a v-adic maximal extension, if [`(v)] | <sub>L</sub>{\overline{v}\mid_{L}} is the only extension of v to L and L is maximal with this property. In this paper we describe some basic properties of such extensions and we consider them in connection with the v-adic spectral norm on [`(K)]{\overline{K}} and with the absolute Galois groups Gal([`(K)]/K){(\overline{K}/K)} and Gal([`(K_v)] /K_v){(\overline{K_{v}} /K_{v})}. Some other auxiliary results are given, which may be useful for other purposes.     

N-Chlorosuccinimide is a convenient oxidant for the synthesis of 2,4-disubstituted 1,2,4-thiadiazolidine-3,5-diones

N-Chlorosuccinimide has been identified as a convenient and safe alternative oxidant for the oxidative condensation of isothiocyanates and isocyanates to afford 1,2,4-thiadiazolidine-3,5-diones.     

Synthesis of new substituted cylopentenone derivatives via a one-pot three-component reaction between arylglyoxals,acetylacetone, and amines in aqueous media

An efficient one-pot method for the synthesis of new substituted cylopentenone derivatives is described via reaction of arylglyoxals and acetylacetone with aliphatic amines. This reaction was carried out in aqueous media in the absence of any catalyst or promoter to produce substituted cylopentenone in high yield.     

A novel ternary GO@SiO2‐HPW nanocomposite as an efficient heterogeneous catalyst for the synthesis of benzazoles in aqueous media

A new solid acid catalyst, consisting of 12‐phosphotungstic heteropoly acid (HPW) supported on graphene oxide/silica nanocomposite (GO@SiO₂), has been developed via immobilizing HPW onto an amine‐functionalized GO/SiO₂ surface through coordination interaction (GO@SiO₂‐HPW). The GO@SiO₂‐HPW nanocomposite was characterized by Fourier transform infrared (FT‐IR) spectroscopy, thermogravimetric analysis (TGA), scanning electron microscopy (SEM), and powder X‐ray diffraction (XRD). The prepared nanocomposite could be dispersed homogeneously in water and further used as a heterogeneous, reusable, and efficient catalyst for the synthesis of benzimidazoles and benzothiazoles by the reaction of 1,2‐phenelynediamine or 2‐aminothiophenol with different aldehydes.     

State‐of‐the‐Art and Trends in Synthesis,Properties, and Application of Quantum Dots‐Based Nanomaterials

Quantum dots (QDs) with a nanoscale size range have attracted significant attention in various areas of nanotechnology due to their unique properties. Different strategies for the synthesis of QD nanoparticles are reported in which various factors, such as size, impurities, shape, and crystallinity, affect the QDs fundamental properties. Consequently, to obtain QDs with appropriate physical properties, it is required to select a synthesis method which allows enough control over the surface chemistry of QDs through fine‐tuning of the synthesis parameters. Moreover, QDs nanocrystals are recently used in multidisciplinary research integrated with biological interfaces. The state‐of‐the‐art methods for synthesizing QDs and bioconjugation strategies to provide insight into various applications of these nanomaterials are discussed herein.     

Radiative properties of matter based on quantum statistical method

We present the preliminary results of our code OPAQS(opacity calculation using quantum statistical model) that is based on the self consistent Hartree-Fock-Slater model for the average atom. The code is capable of performing robust calculations of average charge state, frequency-dependent and mean opacities. The accuracy of the atomic model is verified by comparing the calculations of average charge state with various published results. The monochromatic opacities for iron computed at different sets of temperatures and densities are compared with LEDCOP. The Rosseland and Planck opacities for iron and aluminum are validated with some state-of-the-art codes. The results are in good agreement with the published data.     

Measurement of the absolute branching fraction of Ds+ --> tau+ nutau decay

Using a sample of tagged D(s)(+) decays collected near the D(s)(*+/-)D(s)(-/+) peak production energy in e(+)e(-) collisions with the CLEO-c detector, we study the leptonic decay D(s)(+)-->tau(+)nu(tau) via the decay channel tau(+)-->e(+)nu(e)nu(tau). We measure B(D(s)(+)-->tau(+)nu(tau))=(6.17+/-0.71+/-0.34)%, where the first error is statistical and the second systematic. Combining this result with our measurements of D(s)(+)-->mu(+)nu(mu) and D(s)(+)-->tau(+)nu(tau) (via tau(+)-->pi(+)nu(tau)), we determine f(D(s))=(274+/-10+/-5) MeV.     

Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests

Due to the definition of second-order stochastic dominance (SSD) in terms of utility theory, portfolio optimization with SSD constraints is of major practical interest. We contribute to the field in two ways: first, we present a self-contained theory with some new results and new proofs of known results; second, we perform a set of tests for computational efficiency. We provide new and simple arguments for the formulation of SSD constraints in a mathematical programming framework. For many individuals, an SSD constraint may seem too severe wherefore various relaxations (ASSD), have been proposed. We introduce yet another relaxation, directional SSD, where a candidate portfolio is admissible if a step from the benchmark in the direction of the candidate yields a dominating portfolio. Optimal step size depends on individual preferences reflected by the objective function. We compare computational efficiency of seven approaches for SD constrained portfolio problems, including SSD and ASSD constrained cases.     

Dynamic Characteristics of a Microhollow Cathode Sustained Discharge with Split Third Electrodes for Potential Flow Application to Flow Velocimetry

The dynamic behavior of a microhollow cathode sustained discharge with split third electrodes is experimentally investigated. The sustained discharge swells isotropically in the presence of a small amount of argon gas flow that is not clearly detectable with a conventional single third electrode. At high flow rates, the sustained discharge transitions to a fast-moving constricted discharge with an are shape. The modified discharge structure causes a shift in current distribution over the third electrodes, and the current peak location varies linearly with the flow rate over a certain flow range. Such linear behavior may be applied to in situ flow velocity measurement.