On the spectrum of linear combinations of two projections in C*-algebras

In this note, we study the spectrum and give estimations for the spectral radius of linear combinations of two projections in C*-algebras. We also study the commutator of two projections.     

Bases of spaces of matrices satisfying rank conditions

Motivated by the problem concerning the existence of non-singular bilinear maps, vector spaces of matrices consisting of matrices with rank bounded below are investigated. It is shown that bases for such spaces of maximum dimension can be chosen in such a way to consist of matrices of the minimal rank. An estimate of the ranks of matrices in particular types of bases for maximal such spaces is also given. This extends previously known results which were valid only in the case of spaces consisting of matrices of rank not equal to one.     

Sonochemically assisted synthesis of zinc-doped maghemite

Nanoparticles of zinc-doped maghemite were prepared using ultrasonic radiation. As a precursor, a suspension of maghemite in an alkaline aqueous solution of zinc nitrate at pH 9 was sonicated. The zinc-doped maghemite nanoparticles were investigated by X-ray diffraction, Mössbauer spectroscopy, high-resolution electron microscopy (HREM) and SQUID magnetometry. The Mössbauer measurements, which cover the temperature range 4.2 K to room temperature, were acquired in zero field and an applied field of 5 T. The results show that by using ultrasound radiation, zinc Zn²⁺ can substitute for Fe³⁺ up to a composition close to zinc ferrite (ZnFe₂O₄), which has a random distribution of Fe³⁺ ions over both A and B sublattices in the spinel structure with an inversity parameter of δ = 0.322. This leads to a maximum saturation magnetization (M_s) of 64.1 emu/g at 300 K and 73.5 emu/g at 2 K.     

Ultrasonic de-agglomeration of barium titanate powder

BaTiO3 (BT) powder, with average particle size of 1.4 microm, was synthesized by solid-state reaction. A high-intensity ultrasound irradiation (ultrasonication) was used to de-agglomerate micro-sized powder to nano-sized one. The crystal structure, crystallite size, morphology, particle size, particle size distribution, and specific surface area of the BT powder de-agglomerated for different ultrasonication times (0, 10, 60, and 180 min) were determined. It was found that the particles size of the BT powder was influenced by ultrasonic treatment, while its tetragonal structure was maintained. Therefore, ultrasonic irradiation can be proposed as an environmental-friendly, economical, and effective tool for the de-agglomeration of barium titanate powders.     

Analyzing the transition rates of the ionization of atoms by strong fields of a CO<Subscript>2</Subscript> laser including nonzero initial momenta

Here, the method of including nonzero initial momenta for ejected electrons in strong infrared laser fields is further developed [8]. It has been shown that, apart from being natural, including the nonzero initial momenta enables one to go into a deeper analysis of the process of tunnel ionization of atoms in strong laser fields (intensity up to 10¹⁶ W/cm²). This is due to looking closely at Fig. 2, which indicates that all electrons that could be ejected, under the circumstances, are ejected at a field intensity ～10¹³ W/cm², and that the effect of ionization after that is strongly diminished, which can be seen from the slope of the plates on Figs. 2 and 4. This also explains the saturation effect for fields up to 10¹⁶ W/cm² [1, 4, 5, 7], and probably this saturation goes on until the fields raising relativistic effects ～10¹⁸ W/cm² [7]. Opposite to what was believed earlier [7], the atomic field intensities could be increased to values over 10¹⁷ W/cm² only when more than 10 electrons are ejected from the atom, it is shown that the properly calculated ionization of 9 electrons increases the atomic field intensity to ～10¹⁸ W/cm².     

Theoretical scrutinization of nine benzoic acid dimers: Stability and energy decomposition analysis

Aromatic carboxylic acids are able to form diverse dimers and multimers due to their hydrogen bond donor and acceptor cites, as well as the aromatic rings. In this work, we examine nine benzoic acid dimers stabilized by hydrogen bonding and stacking interactions. Interacting quantum atoms methodology revealed that dominant attractive interactions in all of them, including hydrogen bonded systems, are due to exchange-correlation. Coulomb interactions are significant only in the most stable dimer with a double hydrogen bond, although the corresponding energy term is almost two times lower compared to the nonclassical one. Since interacting quantum atoms approach treats monomers binding by considering electronic energy only, in order to examine dissociation kinetics we performed density functional theory-based molecular dynamics simulations of selected stacked dimers: in 40% of the studied systems at 300 K thermal energy was sufficient to overpower barrier for dissociation within 1 ps, which resulted in the separation of the monomers, whereas 20% of them remained in the stacked position even after 5 ps. These results highlight the importance of noncovalent interactions, particularly weak stacking interactions, on the structure and dynamics of carboxylic acids and their derivatives.     

Synthesis,characterization and cytotoxic activity of organoruthenium(II)-halido complexes with 5-chloro-1H-benzimidazole-2-carboxylic acid

Three new ruthenium(II)-arene halido complexes, [(η⁶-p-cymene) RuX(L)] (1–3), were synthesized in a reaction of [(η⁶-p-cymene)RuX₂]₂ with 5-chloro-1H-benzimidazole-2-carboxylic acid (HL) in ethanol (X^– = Cl^– (1), Br^– (2), I^– (3)). The complexes were characterized by elemental analysis, mass spectrometry, IR, ¹H and ¹³C NMR spectroscopy. The cytotoxic activity of the ligand precursor and its ruthenium complexes was tested by MTT assay in human cancer cell lines: lung adenocarcinoma (A549), myelogenous leukemia (K562) as well as in one normal human fetal lung fibroblast cell line (MRC-5). The results show that ruthenium(II)-arene complexes possess enhanced cytotoxicity when compared to HL in the range of concentrations up to 300 µM. In terms of halido ligand substitution, cytotoxic activity toward A549 and K562 cell lines in 1–3 serie significantly increased (e.g., IC₅₀ values for K562: 1: 205.76 µM; 2: 174.77 µM; 3: 83.97 µM). All studied compounds were found to be ineffective toward MRC-5. Hydrolysis of 1–3 was followed by UV-vis spectroscopy at 25?°C, revealing ligand-substitution reactions at the Ru(II) center. Compounds 2 and 3 underwent rapid hydrolysis ranging from a few minutes for the aquation to ca. 20?min, confirming typical Ru-arene behavior in aqueous solutions.     

Comparative analysis of the full set of methylated β‐cyclodextrins as chiral selectors in capillary electrophoresis

The chiral separation ability of the full library of methylated‐β‐cyclodextrins towards pharmacologically significant racemic drugs including basic compounds was studied by chiral CE. The syntheses of all the methylated, single isomer β‐cyclodextrins were revised and optimized and the aqueous solubility of the derivatives was unambiguously established. The three most relevant commercially available methylated isomeric mixtures were also included in the screening, so a total of ten various methylated CDs were investigated. The effects of the selector concentration on the enantiorecognition properties at acidic pH were investigated. Among the dimethylated β‐cyclodextrins, the heptakis (2,6‐di‐O‐methyl)‐β‐cyclodextrin isomer (2,6‐DIMEB) resulted to be the most versatile chiral selector. Terbutaline was selected as a model compound for the in‐depth investigation of host‐guest enantiodiscrimination ability. The association constants between the two terbutaline enantiomers and 2,6‐DIMEB were determined in order to support that the enantioseparation is driven by differences is host‐guest binding. The migration order of the enantiomers was confirmed by performing spiking experiments with the pure enantiomers. 1D and 2D NMR spectroscopy was applied to the 2,3‐, and 2,6‐DIMEB/terbutaline systems to rationalize at molecular level the different enantioseparation ability of the dimethylated β‐cyclodextrin selectors.