Fixed points and additive $${\rho}$$-functional equations

In this paper, we solve the additive \({\rho}\)-functional equations

$$\begin{aligned} f(x+y)-f(x)-f(y)= & {} \rho(2f(\frac{x+y}{2})-f(x)-f(y)), \\ 2f(\frac{x+y}{2})-f(x)-f(y)= & {} \rho(f(x+y)-f(x)-f(y)), \end{aligned}$$

where \({\rho}\) is a fixed non-Archimedean number or a fixed real or complex number with \({\rho \neq 1}\). Using the fixed point method, we prove the Hyers–Ulam stability of the above additive \({\rho}\)-functional equations in non-Archimedean Banach spaces and in Banach spaces.

     

Two Phases of the Non-Commutative Quantum Mechanics with the Generalized Uncertainty Relations

We consider the quantum mechanics on the noncommutative plane with the generalized uncertainty relations \({\Delta } x_{1} {\Delta } x_{2} \ge \frac {\theta }{2}, {\Delta } p_{1} {\Delta } p_{2} \ge \frac {\bar {\theta }}{2}, {\Delta } x_{i} {\Delta } p_{i} \ge \frac {\hbar }{2}, {\Delta } x_{1} {\Delta } p_{2} \ge \frac {\eta }{2}\). We show that the model has two essentially different phases which is determined by \(\kappa = 1 + \frac {1}{\hbar ^{2} } (\eta ^{2} - \theta \bar {\theta })\). We construct a operator \(\hat {\pi }_{i}\) commuting with \(\hat {x}_{j} \) and discuss the harmonic oscillator model in two dimensional non-commutative space for three case κ > 0, κ = 0, κ < 0. Finally, we discuss the thermodynamics of a particle whose hamiltonian is related to the harmonic oscillator model in two dimensional non-commutative space.     

类Be离子(Z=8-54)内壳层激发态1s2s~22p退激发过程的理论研究

采用基于全相对论框架的多组态Dirac-Fock方法,系统研究了类Be离子(Z=8-54)内壳层激发态1s2s22p的能量、辐射退激发和Auger退激发过程.详细讨论了电子关联效应对相关结构和退激发过程的影响.结果表明,来自于n=2和3壳层的电子关联效应最重要.另外,随着Z的增大,辐射退激发几率逐渐而平滑的增大,而Auger退激发几率的变化则不显著.本文计算结果与其它理论计算结果符合很好.     

噻吩基钌配合物与酵母RNA的相互作用研究

通过紫外-可见吸收光谱和荧光光谱滴定、稳态荧光猝灭以及盐效应实验研究了噻吩基钌配合物[Ru(bpy)2(Htip)]Cl2(1)、[Ru(Htip)2(dppz)]Cl2(2)、[Ru(Htip)3]Cl2(3)和[Ru2(bpy)4(H2bipt)]Cl4(4){bpy=2,2'-联吡啶;Htip=2-噻吩咪唑[4,5-f][1,10]邻菲咯啉;H2bipt=2,5-二(2-咪唑[4,5-f][1,10]邻菲咯啉)噻吩;dppz=二吡啶并[3,2-a:2',3'-c]吩嗪}与酵母RNA(yeast-RNA)的相互作用,并比较了该类配合物与yeast-RNA和小牛胸腺DNA(ct-DNA)的键合性质。结果表明,该类噻吩基钌配合物是较强的RNA嵌入试剂,其中配合物2和3的RNA键合强度大于其DNA键合强度;此系列配合物在低盐和高盐浓度时均能与RNA较强地结合,即使在100 mmol/L Na Cl条件下仍具有较大的RNA键合常数;配合物1与RNA键合时荧光强度下降,配合物2在水溶液中以及与RNA键合时几乎无荧光,而它们与DNA作用时荧光强度明显增大,显示出良好的区分RNA和DNA的荧光特性。     

Dimethyl carbonate synthesis via transesterification of ethylene carbonate and methanol using ionic liquid catalysts immobilized on mesoporous cellular foams

Dimethyl carbonate (DMC) was synthesized via transesterification of ethylene carbonate and methanol with ionic liquid catalysts. For this reaction, 1,4-diazobicyclo[2.2.2]octane (DABCO), [Choline]OH, and [BMIM]Cl were used as a homogeneous catalyst, and hydrotalcite, [DABCO]OH@MCF, [DABCO]Cl@MCF, and DABCO/MCF were used as a heterogeneous catalyst. To support the ionic liquids, mesoporous cellular foam (MCF) was prepared and characterized by SEM, TEM and BET surface area analyzer. The average cell and window sizes of the prepared MCF were 34.4 and 21.3 nm, respectively. The prepared MCF had a well structured three-dimensional structure. Among the homogeneous catalysts used, DABCO showed the highest DMC yield about 84 %, and among the heterogeneous catalysts, [DABCO]OH@MCF showed the highest DMC yield about 77 %. In the reusability test of the used catalysts, there was only 8 % point decrease in DMC yield with [DABCO]OH@MCF, whereas 58 percent point decrease in DMC yield with DABCO/MCF after four times recycling tests. The effects of an anion on the catalytic activity were investigated. The optimum reaction condition for DMC synthesis was also investigated with [DABCO]OH@MCF catalyst.     

Phosgene-free decomposition of dimethylhexane-1,6-dicarbamate over ZnO

In catalytic decomposition of dimethylhexane-1,6-dicarbamate (HDC) into hexamethylene-1,6-diisocyanate (HDI), Zn-containing homogeneous (i.e., zinc acetate) and heterogeneous (i.e., ZnO) catalysts were active among a number of catalysts tested, due to the great electron withdrawing ability of Zn ions. Particularly, when polyethylene glycol dimethyl ether was used as a solvent, ZnO was found to be relatively robust, because the catalytic performance was maintained up to the third use (HDC conversion of 93 % and HDI yield of 67 % at 180 °C for 1 h). Through investigation of a HDC/ZnO mixture at elevated temperatures by IR spectroscopy, a possible reaction scheme of ZnO-catalyzed decomposition of HDC was proposed. The H atom is removed from the N–H group of HDC by hydrogen bonding with an O site on the ZnO surface, followed by coordination of an O–C=O group in monodentate mode to a Zn site. The C–O group in the O–C=O linkage is then cleaved yielding the isocyanate and surface methoxide species. Finally, methanol is released from ZnO by a reaction between the surface methoxide and the hydroxyl species.     

Syngas conversion beyond chemical equilibrium by in situ bimolecular reaction

An in situ bimolecular reaction, in which syngas is fed with toluene as a secondary reactant (hereafter Tol in situ methylation), was studied over bifunctional catalysts comprised of methanol synthesis catalyst and H-ZSM-5 in a fixed-bed down-flow reactor at 460 psig. When physically mixed with H-ZSM-5 to form bifunctional catalysts, CrZ_HZ (Cr₂O₃/ZnO + HZSM-5) catalyst showed much higher activity than CZA_HZ (CuO/ZnO/Al₂O₃ + H-ZSM-5) in the Tol in situ methylation, while CrZ catalyst exhibited substantially lower activity than CZA in methanol synthesis. CO conversion to methanol in the Tol in situ methylation was estimated by Bz in situ methylation. The CO conversion to methanol was calculated to be in the range of 11–27 %, while that in methanol synthesis over CrZ was about 5 % at most due to chemical equilibrium limitation. By employing a silicalite-coated H-ZSM-5 (Sil/HZ) in bifunctional catalyst, xylene selectivity and para-xylene yield were much improved in the Tol in situ methylation.     

Immobilization of the Gas Signaling Molecule H2S by Radioisotopes: Detection,Quantification, and In Vivo Imaging

Hydrogen sulfide (H₂S) has multifunctional roles as a gas signaling molecule in living systems. However, the efficient detection and imaging of H₂S in live animals is very challenging. Herein, we report the first radioisotope‐based immobilization technique for the detection, quantification, and in vivo imaging of endogenous H₂S. Macrocyclic ⁶⁴Cu complexes that instantly reacted with gaseous H₂S to form insoluble ⁶⁴CuS in a highly sensitive and selective manner were prepared. The H₂S concentration in biological samples was measured by a thin‐layer radiochromatography method. When ⁶⁴Cu–cyclen was injected into mice, an elevated H₂S concentration in the inflamed paw was clearly visualized and quantified by Cerenkov luminescence and positron emission tomography (PET) imaging. PET imaging was also able to pinpoint increased H₂S levels in a millimeter‐sized infarcted lesion of the rat heart.     

Separation efficiency of free‐solution conjugated electrophoresis with drag‐tags incorporating a synthetic amino acid

DNA sequencing or separation by conventional capillary electrophoresis with a polymer matrix has some inherent drawbacks, such as the expense of polymer matrix and limitations in sequencing read length. As DNA fragments have a linear charge‐to‐friction ratio in free solution, DNA fragments cannot be separated by size. However, size‐based separation of DNA is possible in free‐solution conjugate electrophoresis (FSCE) if a “drag‐tag” is attached to DNA fragments because the tag breaks the linear charge‐to‐friction scaling. Although several previous studies have demonstrated the feasibility of DNA separation by free‐solution conjugated electrophoresis, generation of a monodisperse drag‐tag and identification of a strong, site‐specific conjugation method between a DNA fragment and a drag‐tag are challenges that still remain. In this study, we demonstrate an efficient FSCE method by conjugating a biologically synthesized elastin‐like polypeptide (ELP) and green fluorescent protein (GFP) to DNA fragments. In addition, to produce strong and site‐specific conjugation, a methionine residue in drag‐tags is replaced with homopropargylglycine (Hpg), which can be conjugated specifically to a DNA fragment with an azide site.     

Metal Oxide/Graphene Composites for Supercapacitive Electrode Materials

Graphene composites with metal or metal oxide nanoparticles have been extensively investigated owing to their potential applications in the fields of fuel cells, batteries, sensing, solar cells, and catalysis. Among them, much research has focused on supercapacitor applications and have come close to realization. Composites include monometal oxides of cobalt, nickel, manganese, and iron, as well as their binary and ternary oxides. In addition, their morphological control and hybrid systems of carbon nanotubes have also been investigated. This review presents the current trends in research on metal oxide/graphene composites for supercapacitors. Furthermore, methods are suggested to improve the properties of electrochemical capacitor electrodes.