Topologies of some new sequence spaces, their duals, and the graphical representations of neighborhoods

Many interesting topologies arise in the theory of FK spaces. Here we present some new results on the topologies of certain FK spaces and the determinations of their dual spaces. We also apply our software package for visualization and animations in mathematics and its extensions to the representation of neighborhoods in various topologies.     

Regular Degenerate Separable Differential Operators and Applications

The boundary value problems for differential-operator equations with variable coefficients, degenerated on all boundary are studied. Several conditions for the separability, fredholmness and resolvent estimates in L _p -spaces are given. In applications degenerate Cauchy problem for parabolic equation, boundary value problems for degenerate partial differential equations and systems of degenerate elliptic equations on cylindrical domain are studied.     

Singular degenerate boundary value problems and applications

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove the well-posedeness of the linear problem and optimal regularity result for the nonlinear problem which occur in fluid mechanics, environmental engineering and in the atmospheric dispersion of pollutants.     

Formation of positive cluster ions LinBr (n = 2–7) and ionization energies studied by thermal ionization mass spectrometry

Clusters of the type Li_nX (X = halides) can be considered as potential building blocks of cluster‐assembly materials. In this work, Li_nBr (n = 2–7) clusters were obtained by a thermal ionization source of modified design and selected by a magnetic sector mass spectrometer. Positive ions of the Li_nBr (n = 4–7) cluster were detected for the first time. The order of ion intensities was Li₂Br⁺ > Li₄Br⁺ > Li₅Br⁺ > Li₆Br⁺ > Li₃Br⁺. The ionization energies (IEs) were measured and found to be 3.95 ± 0.20 eV for Li₂Br, 3.92 ± 0.20 eV for Li₃Br, 3.93 ± 0.20 eV for Li₄Br, 4.08 ± 0.20 eV for Li₅Br, 4.14 ± 0.20 eV for Li₆Br and 4.19 ± 0.20 eV for Li₇Br. All of these clusters have a much lower ionization potential than that of the lithium atom, so they belong to the superalkali class. The IEs of Li_nBr (n = 2–4) are slightly lower than those in the corresponding small Li_n or Li_nH clusters, whereas the IEs of Li_nBr are very similar to those of Li_n or Li_nH for n = 5 and 6. The thermal ionization source of modified design is an important means for simultaneously obtaining and measuring the IEs of Li_nBr (n = 2–7) clusters (because their ions are thermodynamically stable with respect to the loss of lithium atoms in the gas phase) and increasingly contributes toward the development of clusters for practical applications. Copyright © 2012 John Wiley & Sons, Ltd.     

Formation of positive cluster ions Li(n) Br (n = 2-7) and ionization energies studied by thermal ionization mass spectrometry

Clusters of the type Li(n)X (X = halides) can be considered as potential building blocks of cluster-assembly materials. In this work, Li(n)Br (n = 2-7) clusters were obtained by a thermal ionization source of modified design and selected by a magnetic sector mass spectrometer. Positive ions of the Li(n)Br (n = 4-7) cluster were detected for the first time. The order of ion intensities was Li(2)Br(+) > Li(4)Br(+) > Li(5)Br(+) > Li(6)Br(+) > Li(3)Br(+). The ionization energies (IEs) were measured and found to be 3.95 ± 0.20 eV for Li(2)Br, 3.92 ± 0.20 eV for Li(3)Br, 3.93 ± 0.20 eV for Li(4)Br, 4.08 ± 0.20 eV for Li(5)Br, 4.14 ± 0.20 eV for Li(6)Br and 4.19 ± 0.20 eV for Li(7)Br. All of these clusters have a much lower ionization potential than that of the lithium atom, so they belong to the superalkali class. The IEs of Li(n)Br (n = 2-4) are slightly lower than those in the corresponding small Li(n) or Li(n)H clusters, whereas the IEs of Li(n)Br are very similar to those of Li(n) or Li(n)H for n = 5 and 6. The thermal ionization source of modified design is an important means for simultaneously obtaining and measuring the IEs of Li(n)Br (n = 2-7) clusters (because their ions are hermodynamically stable with respect to the loss of lithium atoms in the gas phase) and increasingly contributes toward the development of clusters for practical applications.     

Synthesis, spectroscopic and redox properties of the copper(II) complexes of N-(di-methylphenyl)-3,5-Bu2t-salicylaldimines

A series of copper(II) complexes (CuL2x) with new N-di-methylphenyl-3,5-Bu2t-salicylaldimines (L(x)H) were prepared and characterized by IR, UV/vis, 1H NMR, ESR, cyclic voltammetry techniques and chemical oxidation. L(x)H ligands have been found selectively bind to a Cu(II), rather than to Ni(II), Co(II), Mn(II), VO(IV), Zn(II) and Cd(II). ESR examinations of the CuL2x complexes demonstrate that they exist in magnetically diluted mononuclear or coupled triplet-state structures in the solid. The temperature dependent (113-283 K) intensity of the powder ESR spectra for some CuL2x is characteristic of ferromagnetic coupling (J > 0). The reduction potentials of CuL2x in DMSO are sensitive to aniline moieties. Chemical oxidation of CuL2x with (NH4)2[Ce(NO3)6] in CHCl3 and MeCN solutions at 300 K affords gradually disappearance of their ESR signals and dramatic changes in the electronic spectra as well as the appearance of new maximum bands at 530-672 (CHCl3) and 670-700 nm (MeCN), suggesting generation of Cu(II)-phenoxyl radical species.