Vertex and Edge Orbits of Fibonacci and Lucas Cubes

The Fibonacci cube \({\Gamma_{n}}\) is obtained from the n-cube Q _n by removing all the vertices that contain two consecutive 1s. If, in addition, the vertices that start and end with 1 are removed, the Lucas cube \({\Lambda_{n}}\) is obtained. The number of vertex and edge orbits, the sets of the sizes of the orbits, and the number of orbits of each size, are determined for the Fibonacci cubes and the Lucas cubes under the action of the automorphism group. In particular, the set of vertex orbit sizes of \({\Lambda_{n}}\) is \({\{k \geq 1; k |n\} \cup \{k \geq 18; k |2n\}}\), the number of vertex orbits of \({\Lambda_{n}}\) of size k, where k is odd and divides n, is equal to \({\sum_{d | k} \mu (\frac{k}{d})F_{\lfloor{\frac{d}{2}}\rfloor+2}}\), and the number of edge orbits of \({\Lambda_{n}}\) is equal to the number of vertex orbits of \({\Gamma_{n-3}}\). Dihedral transformations of strings and primitive strings are essential tools to prove these results.     

Microwave-promoted total synthesis of N-(α-hydroxybenzyl)formamides using DMSO/H2O under neutral conditions

A total synthesis route toward N-(α-hydroxybenzyl)formamides by microwave-assisted reaction of dichloroaziridines and aqueous dimethyl sulfoxide is described. The corresponding products were obtained in excellent yields with reduced reaction times. The obtained formamides were characterized by various techniques such as Infra red (IR), Nuclear Magnetic Resonance (NMR) and mass spectroscopy data.     

Absolute stereostructures of cytotoxic metabolites, chaetomugilins A-C, produced by a Chaetomium species separated from a marine fish

Chaetomugilins A-C were isolated from a strain of Chaetomium globosum originally isolated from the marine fish Mugil cephalus, and their absolute stereostructures have been elucidated on the basis of spectroscopic analyses using 1D and 2D NMR techniques, some chemical transformations, and an X-ray analysis. This compound exhibited significant cytotoxicity against cultured P388 cells and HL-60 cells.     

Tetrahedral tellurate

A tetraethylammonium (TEA) salt of TeO 4 (2-) was synthesized by reacting Te(OH) 6 with tetraethylammonium hydroxide. X-ray structural analysis of (TEA) 2TeO 4.2H 2O confirmed that this new compound consists of discrete TeO 4 (2-) anions of distorted tetrahedral structure together with TEA cations and water molecules of crystallization [ a = 8.0820(9) A, b = 13.7730(12) A, c = 20.1590(18) A, V = 2244.0(4) A (3), Z = 4, and space group Pccb]. The (125)Te NMR spectrum indicated that water reacts with the TeO 4 (2-) anion to regenerate octahedral tellurate species in solution.     

Infrared multiple photon dissociation spectra of proton- and sodium ion-bound glycine dimers in the N-H and O-H stretching region

The proton- and the sodium ion-bound glycine homodimers are studied by a combination of infrared multiple photon dissociation (IRMPD) spectroscopy in the N-H and O-H stretching region and electronic structure calculations. For the proton-bound glycine dimer, in the region above 3100 cm (-1), the present spectrum agrees well with one recorded previously. The present work also reveals a weak, broad absorption spanning the region from 2650 to 3300 cm (-1). This feature is assigned to the strongly hydrogen-bonded and anharmonic N-H and O-H stretching modes. As well, the shared proton stretch is observed at 2440 cm (-1). The IRMPD spectra for the proton-bound glycine dimer confirms that the lowest energy structure is an ion-dipole complex between N-protonated glycine and the carboxyl group of the second glycine. This spectrum also helps to eliminate the existence of any of the higher-energy structures considered. The IRMPD spectrum for the sodium ion-bound dimer is a much simpler spectrum consisting of three bands assigned to the O-H stretch and the asymmetric and symmetric NH 2 stretching modes. The positions of these bands are very similar to those observed for the proton-bound glycine dimer. Numerous structures were considered and the experimental spectrum agrees with the B3LYP/6-31+G(d,p) predicted spectrum for the lowest energy structure, two bidentate glycine molecules bound to Na (+). Though some of the structures cannot be completely ruled out by comparing the experimental and theoretical spectra, they are energetically disfavored by at least 20 kJ mol (-1).     

N-spiro chiral quaternary ammonium bromide catalyzed diastereo- and enantioselective conjugate addition of nitroalkanes to cyclic alpha,beta-unsaturated ketones under phase-transfer conditions

[reaction, structure: see text] Conjugate addition of various prochiral nitroalkanes to cyclic alpha,beta-unsaturated ketones was found to be efficiently catalyzed by N-spiro C2-symmetric chiral quaternary ammonium bromide 1b possessing a 3,5-bis(3,4,5-trifluorophenyl)phenyl substituent under solid-liquid phase-transfer conditions to afford the corresponding gamma-nitro ketones in excellent chemical yields with unprecedented levels of diastereo- and enantiocontrol.     

Preparation of ion-imprinted polyvinyl sulfonate-grafted silica particles for trace enrichment of Th(IV) prior to determination by inductively coupled plasma-mass spectrometry

Grafting from polymerisation technique has been used to prepare Th(IV) ion-imprinted polyvinyl sulfonate (IIPVS)-bonded silica particles. The graft polymerisation of vinyl sulfonate (VS) on the surface of silica particles was achieved in aqueous medium through thermal decomposition of surface-bound azo initiators (60°C) in the presence of thorium ion. The prepared material was characterised by Fourier transform infrared spectroscopy, differential scanning calorimetry and thermogravimetric analysis. The entrapped template ion was then removed using 2 M HCl. The experimental batch rebinding data were successfully described by the Langmuir–Freundlich model. The prepared material was then packed to a PTFE micro-column (20 mm × 3.0 mm, id) to evaluate its efficiency in column operations prior to determination by inductively coupled plasma-mass spectrometry (ICP-MS). The limit of detection of the method and breakthrough capacity of the column was evaluated as 0.074 µg L^?1 and 0.83 mg g^?1, respectively. The selectivity of the prepared polymer towards Th(IV) ion was investigated in the presence of some foreign competitor ions, including U(VI). Finally, the proposed method has been used to determine Th(IV) ion in real samples.     

邻苯三酚红多壁碳纳米管糊电极为传感器分析制药和生物样品中异丙基肾上腺素

异丙基肾上腺素(ISPR)是一种重要的邻苯二酚胺类药物,广泛用于治疗心脏疾病.然而,过量服用该药对人体非常危险.本文采用邻苯三酚红修饰多壁碳纳米管糊电极(PGRMMWCNTPE)制备了一种新型传感器,用于高灵敏度检测水溶液中的ISPR.采用计时电流法、循环伏安法和方波伏安法考察了PGRMMWCNTPE电极电催化氧化ISPR性能.通过伏安数据计算了ISPR氧化的催化反应速率常数、电子传递系数和扩散系数.在ISPR浓度0.8–570μmol/L范围内建立了线性标准曲线,检测限为0.47μmol/L ISPR.将该传感器用于尿液和药物样品中ISPR检测得到满意结果.