Wandering Subspaces of the Bergman Space and the Dirichlet Space Over {{\mathbb{D}^{n}}}

Doubly commuting invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc \({\mathbb{D}^n}\) (with \({n \geq 2}\) ) are investigated. We show that for any non-empty subset \({\alpha=\{\alpha_1,\ldots,\alpha_k\}}\) of \({\{1,\ldots,n\}}\) and doubly commuting invariant subspace \({\mathcal{S}}\) of the Bergman space or the Dirichlet space over \({\mathbb{D}^n}\) , restriction of the multiplication operator tuple on \({\mathcal{S}, M_{\alpha}|_\mathcal{S}:=(M_{z_{\alpha_1}}|_\mathcal{S},\ldots, M_{z_{\alpha_k}}|_\mathcal{S})}\) , always possesses generating wandering subspace of the form $$\bigcap_{i=1}^k(\mathcal{S}\ominus z_{\alpha_i}\mathcal{S})$$ .     

Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.     

Full Dissolution of the Whole Lithium Sulfide Family (Li2S8 to Li2S) in a Safe Eutectic Solvent for Rechargeable Lithium–Sulfur Batteries

The lithium–sulfur battery is an attractive option for next‐generation energy storage owing to its much higher theoretical energy density than state‐of‐the‐art lithium‐ion batteries. However, the massive volume changes of the sulfur cathode and the uncontrollable deposition of Li₂S₂/Li₂S significantly deteriorate cycling life and increase voltage polarization. To address these challenges, we develop an ?‐caprolactam/acetamide based eutectic‐solvent electrolyte, which can dissolve all lithium polysulfides and lithium sulfide (Li₂S₈–Li₂S). With this new electrolyte, high specific capacity (1360 mAh g^?1) and reasonable cycling stability are achieved. Moreover, in contrast to conventional ether electrolyte with a low flash point (ca. 2 °C), such low‐cost eutectic‐solvent‐based electrolyte is difficult to ignite, and thus can dramatically enhance battery safety. This research provides a new approach to improving lithium–sulfur batteries in aspects of both safety and performance.     

Solid-supported palladium nano and microparticles: an efficient heterogeneous catalyst for ligand-free Suzuki-Miyaura cross coupling reaction

Solid-supported nano and microparticles of Pd(0) (SS-Pd) were prepared and used as heterogeneous catalysts for Suzuki-Miyaura cross coupling reactions of aryl halides (chloro, bromo and iodo) and phenyl boronic acid under mild and ligand-free conditions. Scanning electron microscope (SEM) and UV-vis based studies were performed to observe the distribution of nano and microparticles of palladium over solid surface and their oxidation states. In addition, the catalyst could be reused up to seven runs without significant loss of activity and stable enough under moist conditions.     

Dielectric relaxation of CdSe nanoparticles

Nanoparticles of cadmium selenide (CdSe) have been synthesized by soft chemical route using mercaptoethanol as a capping agent. X-ray diffraction and transmission electron microscope measurements show that the prepared sample belongs to sphalerite structure with the average particle size of 25 nm. The band gap of the material is found to be 2.1 eV. The photoluminescence (PL) emission spectra of the sample are measured at various excitation wavelengths. The PL spectra appear in the visible region, and the emission feature depends on the wavelength of the excitation. Impedance spectroscopy is applied to investigate the dielectric relaxation of the sample in a temperature range from 323 to 473 K and in a frequency range from 42 Hz to 1.1 MHz. The complex impedance plane plot has been analyzed by an equivalent circuit consisting of two serially connected R-CPE units, each containing a resistance (R) and a constant phase element (CPE). The dielectric relaxation of the sample is investigated in the electric modulus formalism. The temperature dependent relaxation times obey the Arrhenius law. The Havriliak–Negami model is used to investigate the dielectric relaxation mechanism in the sample. The frequency dependent conductivity spectra are found to obey the power law.     

Synthesis,Characterization, Electrochemical and Antimicrobial Studies of Iron(II) and Nickel(II) Macrocyclic Complexes

Russian Journal of Electrochemistry - Herein, we synthesized [12] membered pyridine based transition metal macrocyclic complexes [MIILCl2] (M = Fe(II) and Ni(II), L = 6,12,5,11-tetraphenyl...     

Polymerization of Methyl Methacrylate: Kinetics of the Reaction Initiated by the Mn(III)-1,2-Propanediol Redox System

Kinetics of polymerization of methyl methacrylate initiated by Mn³⁺/1,2-propanedlol has been investigated in aqueous sulfuric acid at the temperature range of 25–35°C. The rate of polymerization (R_p) and the rate of manganic ion disappearance (-R_Mn) have been computed. The effects of organic solvents, certain cationic and anionic detergents, added electrolytes on the initial rate of polymerization, and maximum conversion have been examined. Depending on the kinetic results, a reaction scheme has been suggested involving the formation of a complex between Mn³⁺ and the alcohol, which subsequently decomposed in an unimolecular step to generate the initiating free-radical which initiates polymerization and termination of the growing polymer chain by metal ion.     

Determination of photopeak energy in instrumental neutron activation analysis

The precision and accuracy of the peak energy allocation in γ-ray spectrometry govern the subsequent computer processing of the data. By applying the main procedures for peak energy determination to a well-defined case, it is possible to define the minimal statistical uncertainties to be expected. The systematic bias of the energies obtained is caused mainly by changes in the total count rate. A correction can be applied based on the pulser peak. From the precision and the accuracy of the peak energy determination, the scanning width for automatic peak indexing follows.