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.     

Wetting of nanogrooved polymer surfaces

Molecular dynamics simulations were used to study the wetting of nanogrooved PE and PVC polymer surfaces. The contact angles, equilibrium states, and equilibrium shapes of two nanosized water droplets were analyzed on surfaces with 1D-arranged periodic roughness of various dimensions. The composite solid-liquid contact, which is preferred in practical applications and in which a droplet rests on top of the surface asperities, was observed on the roughest PE surfaces, whereas water filled the similar but slightly deeper grooves on PVC surfaces. The transition from the wetted to composite contact regime occurred when the contact angle with a flat surface reached the value at which the apparent Wenzel and Cassie contact angles are equal. Droplets on grooved PE surfaces with the composite contact exhibited contact angles in agreement with Cassie's equation, but the increase in hydrophobicity on smoother surfaces with the wetted contact was less than expected from Wenzel's equation. The difference between the simulated and theoretical values decreased as the dimensions of the surface grooves increased. Only a slight increase or even a slight decrease in the contact angles was observed on the grooved PVC surfaces, owing to the less hydrophobic nature of the flat PVC surface. On both polymers, the nanodroplet assumed a spherical shape in the composite contact. Only minor anisotropy was observed in the wetted contact on PE surfaces, whereas even a highly anisotropic shape was seen on the grooved PVC surfaces. The contact angle in the direction of the grooves was smaller than that in the perpendicular direction, and the difference between the two angles decreased with the increasing size of the water droplet.