Crystallographic and Computational Studies of Non-Covalent Interactions of Molecular Clips with a Series of Small Solvent Molecules

Molecular clips hold the potential of self-association and the ability to form host–guest complexes. Here we describe the synthesis of a 1,2-dimethoxyphenyl terminated glycoluril molecular clip (2) that binds with smaller solvent molecules by π?H–C and C=O?H–O non-covalent interactions. We obtained single crystals of 2 and 2 + CH₂Cl₂, CH₃OH, CH₃CN, and DMF solvents complexed within the clip. These solvents always form two π?H–C interactions between the aromatic rings in the clip, and CH₃OH formed an additional C=O?H–O hydrogen bond with the glycoluril carbonyl group. Based on single crystal data we found that π?H–C interactions of 2 + CH₂Cl₂ are stronger than 2 + CH₃CN and 2?+?DMF, due to the presence of stronger electron withdrawing groups in CH₂Cl₂, which lead to a decrease in dihedral angle of two glycoluril aromatic planes. We also investigated the non-covalent interaction energies of these solvent molecules with 2 using computational methods.

Graphical Abstract

Several solvent adducts of a glycoluril derivative have been isolated and characterized by single crystal X-ray diffraction, revealing two common pi?H–C non-covalent bonds within the molecular clip.

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Vortex Shedding: A Review on Flat Plate

Flat plates, both single and in tandem or side by side arrangement, are widely used in many engineering applications. Despite vast investigations of the flow structures and wakes downstream of these bluff bodies, this unsteady phenomenon yet remains a fundamental issue in many industrial applications. This paper reviews the state of the art concerning the flow over flat plates in different arrangements focusing on plates normal to the flow. Turbulent wake regions are discussed for the flat plates in side by side or tandem arrangement. Numerical studies are reviewed with emphasis on the realized turbulent models. The effect of the chosen turbulence model on the prediction of the wake region is discussed.     

An improved neuronal energy model that better captures of dynamic property of neuronal activity

Among the theories of neural information coding, the neural energy coding is more accessible to global coding features than traditional neural encoding. According to the shortcomings existing in the neuronal energy model, that is, the non-smooth nature of the energy curve, we proposed an improved neuronal energy model in this paper. The modified energy model is a good choice for establishment of the global model of brain function. And it is also the basis of energy calculation for functional cognitive neural networks in the future.     

Games with guaranteed scores and waiting moves

Combinatorial scoring games, with the property ‘extra pass moves for a player will do him no harm’, are characterized. The characterization involves an order embedding of Conway’s normal play games, and we call our class the universe of Guaranteed scoring games. Also, we give a theorem for comparing guaranteed games with scores (numbers) which extends Ettinger’s work on Dicot scoring games.     

Optimization of Fishing Strategies in Space and Time as a Non-convex Optimal Control Problem

The behavior of a fishing fleet and its impact onto the biomass of fish can be described by a nonlinear parabolic diffusion–reaction equation. Looking for an optimal fishing strategy leads to a non-convex optimal control problem with a bilinear control action. In this work, we present such an optimal control formulation, prove its well-posedness and derive first- and second-order optimality conditions. These results provide a basis for tailored finite element discretization as well as for Newton type optimization algorithms. First numerical test problems show typical features as so-called No-Take-Zones and maximal fishing quota (total allowable catches) as parts of an optimal fishing strategy.     

Higher dimensional Apollonian packings,revisited

The Apollonian circle and sphere packings are well known objects that have attracted the attention of mathematicians throughout the ages. The historically natural generalization of the procedure for generating the packing breaks down in higher dimensions, as it leads to overlapping hyperspheres. There is, however, an alternative interpretation that allows one to extend the concept to higher dimensions and in a unique way. For relatively small dimensions (2 through at least 8), those packings can be thought of as ample cones for classes of K3 surfaces. We describe the packings in some detail for dimensions 4 (with plenty of pictures), 5, and 6.     

On the Strong Convergence of Subgradients of Convex Functions

In this paper, results on the strong convergence of subgradients of convex functions along a given direction are presented; that is, the relative compactness (with respect to the norm) of the union of subdifferentials of a convex function along a given direction is investigated.     

Study on the mechanism of catalytic synthesis of dimethyldichlorosilane by AlCl3/MIL‐53(Al)@γ‐Al2O3

Dimethyldichlorosilane, one of the most consumed organosilicon monomers in the industry, can be prepared in a highly efficient and environmentally friendly synthesis method of disproportionating methylchlorosilanes. However, the internal mechanism of the reaction remains unclear. In this paper, the mechanism catalyzed by AlCl₃/MIL‐53(Al) and AlCl₃/MIL‐53(Al)@γ‐Al₂O₃ catalysts was calculated at B3LYP/6‐311++G(3df, 2pd) level by using the density functional theory (DFT). The results showed that although the two catalysts had similar active structures, the catalytic effects were significantly different. The Lewis acid center on the surface of γ‐Al₂O₃ in the core‐shell catalyst is complementary to the classic Lewis acid AlCl₃ through the spatial superposition effect, which greatly improves the Lewis acid catalytic activity of AlCl₃/MIL‐53(Al)@γ‐Al₂O₃.