Evolving groups

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.     

Rapid Learning-Based and Geologically Consistent History Matching

Various types of data become available at different stages of a reservoir’s life. The production data are integrated into the flow simulation models through a process referred to as history matching. The history-matching process is iterative, and it usually involves a large number of simulation runs. Hence, this process requires significant computational time. In most history-matching methods, the initial geological assumptions in the reservoir model are destroyed or significantly altered in the process. Furthermore, they do not account for the information obtained during the previous trials, and lack learning from the previous failures. In this paper, we introduce a new methodology that maintains the geological realism. The candidate realizations are selected through a learning-based history-matching (LHM) algorithm by which all the previously successful patterns are preserved and used to assist the construction of the next realizations. The various pieces of matching regions are assembled together to make a pool of the successful candidates. Such regions are then utilized for making an auxiliary dataset in a multiscale framework by which the next model is generated. To prevent from trapping in local minima, ideas from the genetic algorithm is adapted. The LHM algorithm can be applied to both categorical and continuous distributions. The LHM provides a conditional map by which the new production data are immediately incorporated into the existing reservoir models. We apply the LHM algorithm to various 2D and 3D examples with very complex binary and continuous properties. The algorithm is shown to produce history-matched models with significantly smaller CPU times.     

Infinitely many reducts of homogeneous structures

It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts.     

Synthesis of <Emphasis Type="Italic">N</Emphasis>-hydroxy-imidamide-functionalized graphene: an efficient metal-free electrocatalyst for oxygen reduction

Metal-free electrocatalysts for oxygen reduction reaction (ORR) are key to the development of efficient, durable, and low-cost alternatives to noble-metal-based electrocatalysts in fuel cell cathodes. In recent years, many efforts are directed to the metal-free catalyst based on heteroatom-doped graphene. In this work, we demonstrate that the graphene surface can be converted into the catalyst for the oxygen reduction by chemical functionalization. In this context, we first synthesized malononitrile-functionalized graphene oxide. Amidoximation of nitrile group and reduction in graphene oxide were then carried out by hydroxylamine in one step. The electrochemical behavior of functionalized graphene-modified electrode for the reduction in oxygen was studied. The results showed that the electrocatalyst fabricated by this method exhibited striking catalytic activities in alkaline solution. In alkaline solution, this catalyst showed a competitive activity to the commercial Pt catalyst via four-electron transfer pathway with better ORR selectivity and stability. In addition, this metal-free electrocatalyst exhibited tolerance to methanol crossover effect. Based on its outstanding performance, this functionalized graphene electrocatalyst showed the promising prospect of a metal-free catalyst for fuel cell with much lower cost than currently used Pt/C catalyst.     

Explicit formulas,symmetry and symmetry breaking for Willmore surfaces of revolution

In this paper, we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an explicit example that symmetric Dirichlet boundary conditions do in general not entail the symmetry of the surface. In addition, we prove a symmetry result for a subclass of Willmore surfaces satisfying symmetric Dirichlet boundary data.     

Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.     

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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