Property of Kelley for the Cartesian products and hyperspaces

A continuum having the property of Kelley is constructed such that neither , nor the hyperspace , nor small Whitney levels in have the property of Kelley. This answers several questions asked in the literature.

     

Synthesis,structure and magnetic properties of unsymmetrical dodecanuclear Mn–Ln clusters

Reaction of manganese acetate and lanthanide nitrates in the presence of excess of PhCOOH affords highly asymmetric dodecanuclear mixed-metal [Mn₁₀Ln₂(OH)(O)₈(PhCOOH)(PhCOO)₁₉] (Ln = Pr^III (1), Nd^III (2)) clusters. The similar reaction, but with only 2 equiv. of PhCOOH resulted in the compounds with higher nuclearity [Mn₁₁Eu₄(O)₈(OH)₈(PhCOO)₁₈(NO₃)₂(H₂O)₆]NO₃ · 4CH₃CN (3). Variable-temperature solid-state magnetic susceptibility of 1 and 2 in the temperature range 1.8–300 K were carried out, and for both complexes antiferromagnetic exchange interactions between the metal centers were observed, giving an estimated S = 17/2 ground state. AC magnetic susceptibility data have revealed out-of-phase signals, which suggest that these complexes exhibit a slow relaxation of magnetization as observed in single-molecule magnets.     

Lanthanide complexes of the heterochiral nonaaza macrocycle: switching the orientation of the helix axis

The La(III), Ce(III), Pr(III), Nd(III), Sm(III), and Eu(III) complexes of the racemic heterochiral nonaaza macrocyclic amine L have been synthesized and characterized by spectroscopic methods. The X-ray crystal structures of the [PrL][Pr(NO(3))(6)].CH(3)OH and the isomorphic [NdL][Nd(NO(3))(6)].CH(3)OH complexes show that all nine nitrogen atoms of the macrocycle coordinate to the Ln(3+) ion, completing its coordination sphere. The macrocycle wraps tightly around the metal ion in double-helical fashion. The structures reveal the RRRRSS/SSSSRR configuration at the stereogenic carbon atoms of the three cyclohexane rings, confirming the heterochiral nature of the parent 3 + 3 macrocycle obtained in the condensation of racemic trans-1,2-diaminocyclohexane and 2,6-diformylpyridine. The NMR spectra of the isolated complexes indicate the presence of low C(1) symmetry [LnL](3+) complexes. The same symmetry is indicated by the X-ray crystal structures of Pr(III) and Nd(III) complexes, which show that for the RRRRSS enantiomer of the macrocycle L, the helix axis passes through the cyclohexane ring of RR chirality and the opposite pyridine ring. The NMR studies of complex formation in solution by the paramagnetic Pr(3+) and Eu(3+) ions indicate that the initially formed [LnL](3+) complexes are of C(2) symmetry. For the RRRRSS enantiomer of the macrocycle L in the C(2)-symmetric species, the helix axis passes through the cyclohexane ring of SS chirality and the opposite pyridine ring. The C(1)-symmetric and C(2)-symmetric forms of the [LnL](3+) complexes constitute a new kind of isomers and the conversion of the kinetic complexation product of C(2) symmetry into the thermodynamic product of C(1) symmetry corresponds to an unprecedented switching of the orientation of the helix axis within the macrocycle framework.     

Applying Mechanochemistry for Bottom‐Up Synthesis and Host–Guest Surface Modification of Semiconducting Nanocrystals: A Case of Water‐Soluble β‐Cyclodextrin‐Coated Zinc Oxide

Mechanochemistry has recently emerged as an environmentally friendly solventless synthesis method enabling a variety of transformations including those impracticable in solution. However, its application in the synthesis of well‐defined nanomaterials remains very limited. Here, we report a new bottom‐up mechanochemical strategy to rapid mild‐conditions synthesis of organic ligand‐coated ZnO nanocrystals (NCs) and their further host–guest modification with β‐cyclodextrin (β‐CD) leading to water‐soluble amide‐β‐CD‐coated ZnO NCs. The transformations can be achieved by either one‐pot sequential or one‐step three‐component process. The developed bottom‐up methodology is based on employing oxo‐zinc benzamidate, [Zn₄(μ₄‐O)(NHOCPh)₆], as a predesigned molecular precursor undergoing mild solid‐state transformation to ZnO NCs in the presence of water in a rapid, clean and sustainable process.     

Packing rectangles into a large square

If \( c>5 \) and if \(x\) is sufficiently large, then any collection of rectangles of sides of length not greater than \(1\) with total area smaller than \(\ x^2-cx^{5/6}\ \) can be packed into a square of side length \(x\).     

Coevolution of information processing and topology in hierarchical adaptive random Boolean networks

Random Boolean Networks (RBNs) are frequently used for modeling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive random Boolean Network (HARBN) as a system consisting of distinct adaptive RBNs (ARBNs) – subnetworks – connected by a set of permanent interlinks. We investigate mean node information, mean edge information as well as mean node degree. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. The main natural feature of ARBNs, i.e. their adaptability, is preserved in HARBNs and they evolve towards critical configurations which is documented by power law distributions of network attractor lengths. The mean information processed by a single node or a single link increases with the number of interlinks added to the system. The mean length of network attractors and the mean steady-state connectivity possess minima for certain specific values of the quotient between the density of interlinks and the density of all links in networks. It means that the modular network displays extremal values of its observables when subnetworks are connected with a density a few times lower than a mean density of all links.     

Directed formation of micro- and nanoscale patterns of functional light-harvesting LH2 complexes

The precision placement of the desired protein components on a suitable substrate is an essential prelude to any hybrid "biochip" device, but a second and equally important condition must also be met: the retention of full biological activity. Here we demonstrate the selective binding of an optically active membrane protein, the light-harvesting LH2 complex from Rhodobacter sphaeroides, to patterned self-assembled monolayers at the micron scale and the fabrication of nanometer-scale patterns of these molecules using near-field photolithographic methods. In contrast to plasma proteins, which are reversibly adsorbed on many surfaces, the LH2 complex is readily patterned simply by spatial control of surface polarity. Near-field photolithography has yielded rows of light-harvesting complexes only 98 nm wide. Retention of the native optical properties of patterned LH2 molecules was demonstrated using in situ fluorescence emission spectroscopy.     

Hydration of aprotic donor solvents studied by means of FTIR spectroscopy

The paper attempts to explain the mutual influence of nonpolar and electron-donor groups on solute hydration, the problem of big importance for biological aqueous systems. Aprotic organic solvents have been used as model solutes, differing in electron-donating power. Hydration of acetonitrile, acetone, 2-butanone, and triethylamine has been studied by HDO and (partially) H2O spectra. The quantitative version of difference spectra method has been applied to determine solute-affected water spectra. Analysis of the data suggests that solvent-water interaction via the donor center of the solute is averaged between water-water interactions around the solute. Such behavior can be simply explained by the model of solute rotating in a cavity of water structure, which is formed by clathratelike hydrogen-bonded water network. On the basis of the band shape of solute-affected HDO spectra and the corresponding distribution of intermolecular distances, the criterion for hydrophobic type hydration has been proposed. From that point of view, all the studied solutes could be treated as hydrophobic ones. The limiting band position and the corresponding intermolecular distance of affected water, gained with increasing electron-donating power of solutes, has been inferred from the data obtained. These observations are important for interpretation of vibrational spectra of water as well as for volumetric measurements of solutions. The simple model of hydration, proposed to better justify the results, connects the values obtained from the methods providing microscopic and macroscopic characteristics of the system studied.     

Templated crystal nucleation: mixed crystals of very different copper(II) N,N',N'-trimethyltriazacyclononane complexes

Templation of a daughter phase by a parent crystal results from an equilibrating mixture of two very different copper(ii) N,N',N'-trimethyltriazacyclononane complexes.