Formulae for the generalized Drazin inverse of a block matrix in terms of Banachiewicz–Schur forms

We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.     

Synthesis Of 1,8‐dioxa‐dibenzo[e,h]azulenese

A novel synthetic route to 2‐methyl‐1,8‐dioxa‐dibenzo[e,h]azulenes [1] via cyclisation of the corresponding 1,4‐dicarbonyl compound is described. 1,4‐Dicarbonyl compounds were synthesized by the alkylation reaction of the 11H‐dibenzo[b,f]oxepine‐10‐one while analogous alkylation of 11H‐dibenzo[b,f]thiepine‐10‐one resulted in formation of O‐alkylated products. Selective oxidation of 2‐methyl group afforded 1,8‐dioxa‐dibenzo[e,h]azulenes with formyl and hydroxymethyl functionality at C(2) position.     

Equations arising from Jordan *-derivation pairs

Summary. We study certain functional equations derived from the definition of a Jordan *-derivation pair. More precisely, if A is a complex *-algebra and M is a bimodule over A, having the structure of a complex vector space compatible with the structure of A, such that implies m = 0 and implies m = 0 and if are unknown additive mappings satisfying then E and F can be represented by double centralizers. The obtained result implies that one of the equations in the definition of a Jordan *-derivation pair is redundant. Furthermore, a remark on the extension of this result to unknown additive mappings such that is given in a special case.     

ESI‐MS studies of the non‐covalent interactions between biologically important metal ions and N‐sulfonylcytosine derivatives

The aim of this report is to present the electrospray ionization mass spectrometry results of the non‐covalent interaction of two biologically active ligands, N‐1 ‐ (p‐toluenesulfonyl)cytosine, 1‐TsC, 1 and N‐1 ‐ methanesulfonylcytosine, 1‐MsC, 2 and their Cu(II) complexes Cu(1‐TsC‐N3)₂Cl₂, 3 and Cu(1‐MsC‐N3)₂Cl₂ and 4 with biologically important cations: Na⁺, K⁺, Ca²⁺, Mg²⁺ and Zn²⁺. The formation of various complex metal ions was observed. The alkali metals Na⁺ and K⁺ formed clusters because of electrostatic interactions. Ca²⁺ and Mg²⁺ salts produced the tris ligand and mixed ligand complexes. The interaction of Zn²⁺ with 1–4 produced monometal and dimetal Zn²⁺ complexes as a result of the affinity of Zn²⁺ ions toward both O and N atoms. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of H<Subscript>2</Subscript>SeO<Subscript>3</Subscript> on the early stages of nucleation and growth during Cu electrocrystallization in acidic medium on glassy carbon electrode

The early stages of Cu electrodeposition onto a GC electrode were investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] was 1.10⁴ to 2.10². The H₂SeO₃ solution in 0.5 M H₂SO₄ was also used. The electrochemical techniques such as cyclic voltammetry and chronoamperometry and structural investigation using ex situ AFM were applied to study the nucleation and growth of Cu onto a GC electrode. Chronoamperometric results were shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model by Scharifker and Hills. The values of number of Cu nuclei N and average nuclei radius r _av were calculated. It was shown that, in the presence of H₂SeO₃ in amounts of 0.001 to 0.005 mM, N increases and r _av decreases. At higher concentrations of the additive, the changes of these parameters with the deposition potential E _dep were shown to be somewhat more complex. The dependences of N and r _av on the concentration of H₂SeO₃ in different regions of Cu overpotentials were also revealed.     

Purification of plant viral and satellite double-stranded RNAs on DEAE monoliths

Replicative double-stranded RNA (dsRNA) is useful in preliminary identification of Cucumber mosaic virus and its satellite RNA (satRNA). This plant pathogen complex yields sufficient quantity of the replicative RNA form that can be isolated by chromatography on chemically unmodified graded cellulose powder (CF-11). In this work, much faster and more efficient procedure using DEAE monoliths was developed in which dsRNA was separated from other species in total nucleic acids extract originating from the infected plant tissue. The developed chromatographic method revealed the pathogens' presence in only 15 min, avoiding nucleic acid precipitation and electrophoretic analysis.     

Interaction of humic acids with human DNA: proposed mechanisms and kinetics

Human DNA quantification by quantitative real-time PCR (QRT-PCR) has gained great importance in forensic DNA and ancient DNA studies. However, in such samples, DNA quantification is impaired by the frequently present humic acid (HA). We have previously shown that the addition of synthetic HA inhibits QRT-PCR. In this study we investigated the possible mechanisms of HA interaction with human DNA, and kinetics of QRT-PCR inhibition. In QRT-PCR with pure human DNA and no HA added, VMAX was 40. With DNA sample containing 4 microg/mL of HA, VMAX was 30.30 while the addition of extra Taq polymerase to the same sample changed VMAX into 38.91, amplifying between 80 and 90% of input DNA. The KM/VMAX ratio in all the samples remained constant, indicating that the mechanism of HA inhibition of QRT-PCR is uncompetitive by nature. Moreover, HA shifts the human DNA melting temperature point (Tm) from 75 to 87 degrees C and inhibits DNase I-mediated DNA cleavage, most probably affecting the enzyme's activity.     

Spontaneous CO Release from RuII(CO)2–Protein Complexes in Aqueous Solution,Cells, and Mice

We demonstrate that Ru^II(CO)₂–protein complexes, formed by the reaction of the hydrolytic decomposition products of [fac‐RuCl(κ²‐H₂NCH₂CO₂)(CO)₃] (CORM‐3) with histidine residues exposed on the surface of proteins, spontaneously release CO in aqueous solution, cells, and mice. CO release was detected by mass spectrometry (MS) and confocal microscopy using a CO‐responsive turn‐on fluorescent probe. These findings support our hypothesis that plasma proteins act as CO carriers after in vivo administration of CORM‐3. CO released from a synthetic bovine serum albumin (BSA)–Ru^II(CO)₂ complex leads to downregulation of the cytokines interleukin (IL)‐6, IL‐10, and tumor necrosis factor (TNF)‐α in cancer cells. Finally, administration of BSA–Ru^II(CO)₂ in mice bearing a colon carcinoma tumor results in enhanced CO accumulation at the tumor. Our data suggest the use of Ru^II(CO)₂–protein complexes as viable alternatives for the safe and spatially controlled delivery of therapeutic CO in vivo.     

Limits of Multiplicities in Excellent Filtrations and Tensor Product Decompositions for Affine Kac-Moody Algebras

We express the multiplicities of the irreducible summands of certain tensor products of irreducible integrable modules for an affine Kac-Moody algebra over a simply laced Lie algebra as sums of multiplicities in appropriate excellent filtrations (Demazure flags). As an application, we obtain expressions for the outer multiplicities of tensor products of two fundamental modules for \(\widehat {\mathfrak {sl}}_{2}\) in terms of partitions with bounded parts, which subsequently lead to certain partition identities.