On-line covering a cube by a sequence of cubes

A procedure for packing or covering a given convex bodyK with a sequence of convex bodies {C _i} is anon-line method if the setC _i are given in sequence. andC _i+1 is presented only afterC _i has been put in place, without the option of changing the placement afterward. The “one-line” idea was introduced by Lassak and Zhang [6] who found an asymptotic volume bound for the problem of on-line packing a cube with a sequence of convex bodies. In this note a problem of Lassak is solved, concerning on-line covering a cube with a sequence of cubes, by proving that every sequence of cubes in the Euclidean spaceE ^d whose total volume is greater than 4 ^d admits an on-line covering of the unit cube. Without the “on-line” restriction, the best possible volume bound is known to be 2 ^d −1, obtained by Groemer [2] and, independently, by Bezdek and Bezdek [1]. The on-line covering method described in this note is based on a suitable cube-filling Peano curve.     

New approach for natural products screening by real-time monitoring of hemoglobin hydrolysis using quartz crystal microbalance

The hemoglobin (Hb) released from erythrocytes is a primary nutritive component for many blood-feeding parasites. The aspartic protease cathepsin D is a hemoglobinase that is involved in the Hb degradation process and is considered an interesting target for chemotherapy intervention. However, traditional enzymatic assays for studying Hb degradation utilize spectrophotometric techniques, which do not allow real-time monitoring and can present serious interference problems. Herein, we describe a biosensor using simple approach for the real-time monitoring of Hb hydrolysis as well as an efficient screening method for natural products as enzymatic inhibitors using a quartz crystal microbalance (QCM) technique. Hemoglobin was anchored on the quartz crystal surface using mixed self-assembled monolayers. The addition of the enzyme caused a mass change (frequency shift) due to Hb hydrolysis, which was monitored in real time. From the frequency change patterns of the Hb-functionalized QCM, we evaluated the enzymatic reaction by determining the kinetic parameters of product formation (k_cat). The QCM enzymatic assay using immobilized human Hb was shown to be an excellent approach for screening possible inhibitors in complex mixtures, opening up a new avenue for the discovery of novel inhibitors.     

The effects of counter anions on the dynamic mechanical response in polymer networks crosslinked by metal–ligand coordination

Metal–ligand coordination has been proven to be an attractive strategy to tune a polymer network's dynamic mechanical properties, such as self-healing ability. Nonetheless, the role of counter anions is often overlooked. To address this, a series of polydimethylsiloxane (PDMS) films crosslinked through lanthanide metal cations (Eu³⁺, Tb³⁺)–bipyridine interactions have been prepared and studied. Neutral 2,2'-bipyridine ligands were embedded into the linear polydimethylsiloxane (PDMS) chain through polycondensation. With nitrate ( ) as the coordinating anions, metal salts Eu(NO₃)₃ and Tb(NO₃)₃ were found to be ineffective crosslinkers. With noncoordinating anions, such as triflate (OTf^-: CF₃ ), metal salts Eu(OTf)₃ and Tb(OTf)₃ showed improved interaction strength with bipyridine ligands. Surprisingly, the addition of Eu(OTf)₃ and Tb(OTf)₃ salts also increased the d-spacing distances of the phase-segregated domains between metal–ligand complexes and the PDMS polymer backbone. For the Eu(OTf)₃-, Tb(OTf)₃-PDMS films, the much-improved self-healing abilities are attributed to the crosslinker dynamics and the enhanced chain mobility. This work underlines the importance of counter anions on the mechanical properties, and provides further guidance on the future design of self-healing metal−ligand crosslinked polymers.) © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3110–3116     

A highly selective bifunctional luminescence probe for potassium and fluoride ions

A novel bifunctional molecule 1 by a combination of 1,3-alternate calix[4]-crown-5 and triarylborane moieties through alkynyl linkers has been designed and synthesized. Compound 1 shows intense fluorescence with a photoluminescence quantum yield of 0.70 in CH(2)Cl(2) solution and can serve as a bifunctional luminescent probe for potassium and fluoride ions with high sensitivity and selectivity.     

Alternating-Sign Matrices and Domino Tilings (Part II)

We continue the study of the family of planar regions dubbed Aztec diamonds in our earlier article and study the ways in which these regions can be tiled by dominoes. Two more proofs of the main formula are given. The first uses the representation theory of GL(n). The second is more combinatorial and produces a generating function that gives not only the number of domino tilings of the Aztec diamond of order n but also information about the orientation of the dominoes (vertical versus horizontal) and the accessibility of one tiling from another by means of local modifications. Lastly, we explore a connection between the combinatorial objects studied in this paper and the square-ice model studied by Lieb.     

Synthesis, characterization, spectroscopic, and electrochemiluminescence properties of a solvatochromic azacrown-containing cyanoruthenate(II): potential applications in separation and indirect photometric detection of cations and amino acids in HPLC

A new anionic ruthenium(II) complex, (Et4N)[Ru(tpyA18C6)(CN)3] (tpyA18C6=N-[4'-(2,2':6',2'-terpyridyl)]-1,4,7,10,13-pentaoxa-16-azacyclohexadodecane), has been synthesized and characterized. The complex was found to show pronounced solvatochromic behavior and, when dissolved in solution, changed its color from purple to yellow when the solvent system was varied from pure acetonitrile to pure water. Its absorption and emission energies in various solvents showed a linear dependence of the Gutman's acceptor number. The characteristic photoluminescence and electrochemiluminescence (ECL) of the complex were also found to be progressively quenched as the proportion of water in a water/acetonitrile mixture increased. Large changes in the chemical shifts of the 1H NMR and 13C NMR signals of [Ru(tpyA18C6)(CN)3]- in different solvents were observed. The complex has also been demonstrated to serve as a mobile-phase additive in high-performance liquid chromatography for separation of metal cations and amino acids. Comparison studies with the crown-free analogue, (Et4N)[Ru(tpy)(CN)3] (tpy = 2,2':6',2'-terpyridine), showed that other than the ion-pair effect, the allosteric host-guest interaction provided by the presence of the pendant crown was essential to the separation performance of the complex. Indirect detection of nonabsorbing analytes has been achieved by monitoring the absorbance changes of the eluent at the metal-to-ligand charge-transfer (MLCT) absorption band maximum of the complex at 445 nm. The effects of pH, ionic strength, and polarity of the mobile phase as well as the complex concentration on the selectivity and resolution have also been studied.     

Sensitive single-layered oxygen-sensing systems: polypyridyl ruthenium(II) complexes covalently attached or deposited as langmuir-blodgett monolayer on glass surfaces

Oxygen-sensing elements containing single-layered structures of luminescent indicators of ruthenium(II) bipyridyl complexes on glass surfaces prepared by covalent attachment and LB deposition are described. They are capable of detecting gaseous oxygen concentration by luminescence quenching of the indicator with reproducible and large quenching efficiencies that are comparable to the best quenching efficiencies obtained by other ruthenium(II) polypyridine based complexes immobilized in matrixes. The large quenching efficiencies for both films imply that the probe complexes are effectively quenched by oxygen, which is probably due to the thin single-layered structures with large surface-to-area ratio and short distance between the probe complexes and oxygen.