Highly luminescent octanuclear Au(I)-Cu(I) clusters adopting two structural motifs: the effect of aliphatic alkynyl ligands

Reactions of the homoleptic (AuC(2)R)(n) precursors with stoichiometric amount of diphosphine ligand PPh(2)C(6)H(4)PPh(2) (P^P) and Cu(+) ions lead to an assembly of a new family of bimetallic clusters [Au(6)Cu(2)(C(2)R)(6)(P^P)(2)](2+) (type I; R=9-fluorenolyl (1), diphenylmethanolyl (2), 2,6-dimethyl-4-heptanolyl (3), 1-cyclohexanolyl (4), Cy (5), tBu (6)). In the case of R=1-cyclohexanolyl, a structurally different complex [Au(6)Cu(2)(C(2)C(6)H(11)O)(6)(P^P)(3)](2+) (7, type II) could be obtained by treatment of 4 with one equivalent of the diphosphine, while for R=isopropanolyl only the latter type of cluster [Au(6)Cu(2)(C(2)C(3)H(7)O)(6)(P^P)(3)](2+) (8) was detected. Steric bulkiness of the alkynyl ligands and O···H-O hydrogen bonding are suggested to play an important role in stabilizing the type I and type II cluster structural motif, respectively. All the complexes exhibit intense photoluminescence in solution with emission parameters that depending on the geometrical arrangement of the octanuclear metal core. The clusters 1-4 and 6 show single emission band in a blue region (469-488 nm) with maximum quantum yield of 94% (4), while structurally different 7 and 8 emit yellow-orange (590 nm) with unity quantum efficiency. The theoretical DFT calculations of the electronic structures have been carried out to demonstrate that the metal-centered triplet emission within the heterometallic core plays a key role for the observed phosphorescence.     

Heterogeneous modification of various celluloses with fatty acids

Heterogeneous modification of various types of cellulose (microcrystalline cellulose, cellulose whiskers and regenerated cellulose) was performed with long-chain fatty acids by an esterification reaction. The differences in reactivity between the celluloses were studied as well as the influences of the chain length and double bond content of the fatty acids. The success of the modification reaction and the structure of modified samples were studied with diverse characterization methods. Surface modification changed the thermal stability of cellulose by decreasing the degradation temperature but also made the pyrolysis curve two-stepped due to the double bonds in the fatty acid chain. It was observed that the nature of the fatty acid affected the degree of substitution (DS). The longer the fatty acid chain was, the lower was the DS. Fatty acids with increased double bond content gave decreased DS. Regenerated cellulose seemed to have the highest surface reactivity due to the distinct morphological structure, which also led to a much lower quantity of fatty acids attached to the structure than for other modified cellulose particles. The mixture of tall oil fatty acids behaved in the same manner as the commercial fatty acids, proving to be an excellent “green” choice for this kind of application.     

New Findings on the Bank–Sauer Approach in Oscillation Theory

In 1988, S. Bank showed that if {z _n } is a sparse sequence in the complex plane, with convergence exponent zero, then there exists a transcendental entire A(z) of order zero such that f″+A(z)f=0 possesses a solution having {z _n } as its zeros. Further, Bank constructed an example of a zero sequence {z _n } violating the sparseness condition, in which case the corresponding coefficient A(z) is of infinite order. In 1997, A. Sauer introduced a condition for the density of the points in the zero sequence {z _n } of finite convergence exponent such that the corresponding coefficient A(z) is of finite order.     

Modeling uncertain passenger arrivals in the elevator dispatching problem with destination control

An Elevator Group Control System (EGCS) assigns an elevator of a group to each passenger transportation request by solving a snapshot optimization problem, the Elevator Dispatching Problem (EDP). In the destination control, passengers register their destination floors in the elevator lobbies, after which the EGCS completes the assignment at once and is not allowed to change it later. Therefore, the EDP is formulated as a stochastic optimal control problem, where uncertain future passenger arrivals are modeled by a Poisson and a geometric Poisson process. The EDP is considered as a certainty equivalent controller in which the uncertain quantities are replaced by their expected values, and as a robust controller in which they take multiple values according to risk scenarios. Numerical experiments show that the expectations do not accurately predict EDP variables. The modeling with the geometric Poisson process results in better forecasting accuracy than with the Poisson process and many scenarios that closely match the realizations of the variables. Hence, the scenarios can be used as a basis for a robust EDP which simultaneously minimizes a passenger service quality criterion and its variation due to uncertain demand.     

Dual exponential polynomials and linear differential equations

We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.     

Screening of Hydrogels for Human Pluripotent Stem Cell–Derived Neural Cells: Hyaluronan‐Polyvinyl Alcohol‐Collagen‐Based Interpenetrating Polymer Network Provides an Improved Hydrogel Scaffold

There is a clear need for novel in vitro models, especially for neuronal applications. Development of in vitro models is a multiparameter task consisting of cell‐, biomaterial‐, and environment‐related parameters. Here, three different human origin neuronal cell sources are studied and cultured in various hydrogel 3D scaffolds. For the efficient evaluation of complex results, an indexing method for data is developed and used in principal component analysis (PCA). It is found that no single hydrogel is superior to other hydrogels, and collagen I (Col1) and hyaluronan–poly(vinyl alcohol) (HA1‐PVA) gels are combined into an interpenetrating network (IPN) hydrogel. The IPN gel combines cell supportiveness of the collagen gel and stability of the HA1‐PVA gel. Moreover, cell adhesion is studied in particular and it is found that adhesion of neurons differs from that observed for fibroblasts. In conclusion, the HA1‐PVA‐col1 hydrogel is a suitable scaffold for neuronal cells and supports adhesion formation in 3D.     

Probing lattice defects in Sr2MgSi2O7:Eu2+,Dy3+

The Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ materials were prepared with a solid state reaction and their microscopic structure (at 295 K only) and luminescence were studied at selected temperatures between 150 and 295 K. Undisturbed Sr crystal planes were common in the TEM images of the undoped Sr₂MgSi₂O₇ material, whereas with Eu²⁺ doping more disturbed planes were observed even in the nanometer scale. With Dy³⁺ co-doping, a large number of small lattice domains created by the discontinuities in the crystal structure was observed. The domains with different orientations seem to be centered around point defects. The decay curves of Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ showed fast (ms scale) persistent luminescence. The intensity of persistent luminescence increased considerably between 200 and 250 K while remaining constant in the ranges of 150–200 and 250–295 K. The changes were used to study the depth of the traps. In general, Dy³⁺ co-doping was found to deepen the traps.