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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

Interaction of antitumoral drug erlotinib with biodegradable triblock copolymers: a molecular modeling study

Combination of molecular dynamics simulations and miscibility calculations was used to investigate erlotinib drug delivery systems based on poly-ε-caprolactone–polyethylene glycol–poly-ε-caprolactone (PCL–PEG–PCL) and poly-ε-caprolactone–polyglycolic acid–poly-ε-caprolactone (PCL–PGA–PCL) biodegradable copolymers. The molecular modeling strategy involving visual observation of models, concentration profile analysis, Flory–Huggins χ parameter, cohesive energy density, and mean square displacement calculations reproduced experimental evidence of erlotinib release from PCL–PEG–PCL matrix successfully. Increasing portion of PCL in PCL–PEG–PCL copolymer led to dissolution of erlotinib aggregates recorded in visual and concentration profile analyses. Higher portion of PCL led to higher cohesive energy density and lower mean square displacement values. Success of this strategy in reproduction of experimental data made an opportunity to utilize the same modeling design in prediction of erlotinib release from similar but not yet experimentally tested PCL–PGA–PCL matrix. In this case, agglomeration of erlotinib molecules and stronger cohesive energy density values were observed.     

Access to the Bis‐benzene Cobalt(I) Sandwich Cation and its Derivatives: Synthons for a “Naked” Cobalt(I) Source?

The synthesis and structural characterization of the hitherto unknown parent Co(bz)₂⁺ (bz=benzene) complex and several of its derivatives are described. Their synthesis starts either from a CoCO₅⁺ salt, or directly from Co₂(CO)₈ and a Ag⁺ salt. Stability and solubility of these complexes was achieved by using the weakly coordinating anions (WCAs) [Al(OR^F)₄]^? and [F{Al(OR^F)₃}₂]^? {R^F=C(CF₃)₃} and the solvent ortho‐difluorobenzene (o‐DFB). The magnetic properties of Co(bz)₂⁺ were measured and compared in the condensed and gas phases. The weakly bound Co(o‐dfb)₂⁺ salts are of particular interest for the preparation of further Co^I salts, for example, the structurally characterized low‐coordinate 12 valence electron Co(P^tBu₃)₂⁺ and Co(NHC)₂⁺ salts.     

Influence of constant magnetic field on electrodeposition of metals,alloys, conductive polymers,and organic reactions

The paper presents and summarizes some research on constant magnetic field effects in chemistry. Metals and alloys electrodeposited under constant magnetic field have greater thickness and smoother surface with finest grains. Metallic materials deposited under the influence of uniform magnetic field may have stronger corrosion resistance, than those obtained without the presence of magnetic field. Constant magnetic field also causes an increase of the electropolymerization rate and yield of some organic reactions. Our research also shows that the presence of constant magnetic field affects the electrodeposition process of alloys and their morphology to a great extent. The effects of magnetic field on metals, alloys, composites, polymers and other materials are due to the Lorentz force and the magnetohydrodynamic effect. It is possible that the further development of magnetoelectrodeposition will allow for using the constant magnetic field to improve the properties of metal coatings, alloys, polymers, and other materials in the industry.     

Nanobodies: Chemical Functionalization Strategies and Intracellular Applications

Nanobodies can be seen as next‐generation tools for the recognition and modulation of antigens that are inaccessible to conventional antibodies. Due to their compact structure and high stability, nanobodies see frequent usage in basic research, and their chemical functionalization opens the way towards promising diagnostic and therapeutic applications. In this Review, central aspects of nanobody functionalization are presented, together with selected applications. While early conjugation strategies relied on the random modification of natural amino acids, more recent studies have focused on the site‐specific attachment of functional moieties. Such techniques include chemoenzymatic approaches, expressed protein ligation, and amber suppression in combination with bioorthogonal modification strategies. Recent applications range from sophisticated imaging and mass spectrometry to the delivery of nanobodies into living cells for the visualization and manipulation of intracellular antigens.     

Solvation‐Induced Changes in the Mechanism of Alcohol Oxidation at Gold/Titania Nanocatalysts in the Aqueous Phase versus Gas Phase

Gold/titania catalysts are widely used for key reactions, notably including the selective oxidation of alcohols in the liquid phase. Our large‐scale ab initio simulations disclose that the liquid‐phase reaction mechanism is distinctly different from that in the gas phase because of active participation of water molecules. While concerted charge transfers related to O₂ splitting and abstraction of both protonic and hydridic hydrogens are enforced under dry conditions, stepwise charge transfer is preferred in the condensed phase. Dissociation of reactive water molecules and subsequent Grotthuss migration of protonic defects, H⁺(aq), allows for such a decoupling of the oxidation process, both in time and space. It is expected that these observations are paradigmatic for heterogeneous catalysis in aqueous phases.     

Hydrogen‐bonding motifs in 3‐carboxyanilinium bromide and iodide

In the title compounds, C₇H₈NO₂⁺·Br⁻, (I), and C₇H₈NO₂⁺·I⁻, (II), the asymmetric unit contains a discrete 3‐carboxyanilinium cation, with a protonated amine group, and a halide anion. The compounds are not isostructural, and the crystal structures of (I) and (II) are characterized by different two‐dimensional hydrogen‐bonded networks. The ions in (I) are connected into ladder‐like ribbons via N—H...Br hydrogen bonds, while classic cyclic O—H...O hydrogen bonds between adjacent carboxylic acid functions link adjacent ribbons to give three characteristic graph‐set motifs, viz. C₂¹(4), R₄²(8) and R₂²(8). The ions in (II) are connected via N—H...I, N—H...O and O—H...I hydrogen bonds, also with three characteristic graph‐set motifs, viz. C(7), C₂¹(4) and R₄²(18), but an O—H...O interaction is not present.     

The unique minimality of an averaging projection

In this paper we will prove that an averaging projection P _a : K (H) → Y, given by the formula , is the only norm-one projection. Here, K (H) is a space of compact operators on a separable real Hilbert space H, and Y is the subspace of K(H) consisting of all symmetric operators. Author’s address: Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland