On weighted q-Daehee polynomials with their applications

In this paper, we first consider a generalization of Kim’s $p$-adic $q$-integral on ${\mathbb{Z}}_p$ including parameters $\alpha$ and $\beta$. By using this integral, we introduce the $q$-Daehee polynomials and numbers with weight $\left(\alpha ,\beta \right)$. Then, we obtain some interesting relationships and identities for these numbers and polynomials. We also derive some correlations among $q$-Daehee polynomials with weight $\left(\alpha ,\beta \right)$, $q$-Bernoulli polynomials with weight $\left(\alpha ,\beta \right)$ and Stirling numbers of second kind.     

Synthesis of Tetraalkenylmethane: Building Blocks for Three-Dimensional Hydrocarbon Networks

In this paper, we show a common strategy to synthesize tetraalkenylmethanes, a cross-linker series for building three-dimensional hydrocarbon networks. To demonstrate the feasibility of this method, we have synthesized tetrapentenylmethane. Attempts to synthesize this cross-linker from pentaerythrityl tetrabromide using substitution reactions resulted in the formation of a spiro compound due to intramolecular cyclization. We also show that the difficulty in reactions at the neopentyl carbon site is due to the neopentyl carbanion stability, not the sterics.     

Comparison of high-performance liquid chromatography of cyclotriphosphazene derivatives with one or two equivalent stereogenic centres

High-performance liquid chromatographic (HPLC) methods have been developed for investigating the stereogenic properties of two analogous series of dibenzylamino derivatives of cyclotriphosphazene containing either one or two equivalent stereogenic centres. Separation of the enantiomers of all the racemic compounds has been investigated by chiral HPLC using Whelk-01 and Chiralcel OD columns. In all cases, conditions for separation of enantiomers have been found using a Whelk-01 column with different ratios of tetrahydrofuran in n-hexane as the mobile phase. It is found that both the separation factor (alpha) and resolution factor (R(S)) of molecules with two equivalent stereogenic centres are greater than those for analogues with only one centre.     

Stochastic Ordering Among Success Runs Statistics in a Sequence of Exchangeable Binary Trials

A new scheme-distribution-based representation is presented for the cumulative distribution function of the number of success runs of length k in a sequence of exchangeable binary trials. By utilizing this new representation, some stochastic ordering results are obtained to compare success runs. The results are illustrated for beta-binomial distributions of order k.     

An on-line preconcentration/separation system for the determination of bismuth in environmental samples by FAAS

An on-line preconcentration procedure for the determination of bismuth by flame atomic absorption spectrometry (FAAS) has been described. Lewatit TP-207 chelating resin, including iminodiacetate group, packed in a minicolumn was used as adsorbent material. Bi(III) was sorbed on the chelating resin, from which it could be eluted with 3 mol L⁻¹ HNO₃ and then introduced directly to the nebulizer-burner system of FAAS. Best preconcentration conditions were established by testing different resin quantities, acidity of sample, types of eluent, sample and eluent solution volumes, adsorption and elution flow rates, and effect of interfering ions. The detection limit of the method was 2.75 μg L⁻¹ while the relative standard deviation was 3.0% for 0.4 μg mL⁻¹ Bi(III) concentration. The developed method has been applied successfully to the determination of bismuth in pharmaceutical cream, standard reference materials and various natural water samples with satisfactory results.     

N1‐(2,6‐Di­methyl­phenyl)‐N2‐hydroxy‐α‐oxo‐α‐phenyl­acet­amidine

The structure of the title compound, C₁₆H₁₆N₂O₂, consists of a dimeric arrangement around an inversion centre of acet­amidine mol­ecules linked via O—H⋯N hydrogen bonds. There are also H⋯π‐ring interactions. All these interactions result in the formation of infinite chains parallel to the (101) axis. The oxime group has an E conformation.