Baer sums for a natural class of monoid extensions

Semigroup Forum - It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this...     

Homological Algebra for Persistence Modules

Foundations of Computational Mathematics - We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either...     

Periodicity of Two-Dimensional Bonding of Main Group Elements

In the periodic table the position of each atom follows the ‘aufbau’ principle of the individual electron shells. The resulting intrinsic periodicity of atomic properties determines the overall behavior of atoms in two-dimensional (2D) bonding and structure formation. Insight into the type and strength of bonding is the key in the discovery of innovative 2D materials. The primary features of 2D bonding and the ensuing monolayer structures of the main-group II–VI elements result from the number of valence electrons and the change of atom size, which determine the type of hybridization. The results reveal the tight connection between strength of bonding and bond length in 2D networks. The predictive power of the periodic table reveals general rules of bonding, the bonding-structure relationship, and allows an assessment of published data of 2D materials.     

The Nonsmooth Dynamics of Combined Slip and Spin Motion Under Dry Friction

Journal of Nonlinear Science - The isothermal quasistatic (i.e. acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition...     

Supramolecular Tuning Enables Selective Oxygen Reduction Catalyzed by Cobalt Porphyrins for Direct Electrosynthesis of Hydrogen Peroxide

We report a supramolecular strategy for promoting the selective reduction of O₂ for direct electrosynthesis of H₂O₂. We utilized cobalt tetraphenylporphyrin (Co-TPP), an oxygen reduction reaction (ORR) catalyst with highly variable product selectivity, as a building block to assemble the permanently porous supramolecular cage Co-PB-1(6) bearing six Co-TPP subunits connected through twenty-four imine bonds. Reduction of these imine linkers to amines yields the more flexible cage Co-rPB-1(6). Both Co-PB-1(6) and Co-rPB-1(6) cages produce 90–100 % H₂O₂ from electrochemical ORR catalysis in neutral pH water, whereas the Co-TPP monomer gives a 50 % mixture of H₂O₂ and H₂O. Bimolecular pathways have been implicated in facilitating H₂O formation, therefore, we attribute this high H₂O₂ selectivity to site isolation of the discrete molecular units in each supramolecule. The ability to control reaction selectivity in supramolecular structures beyond traditional host–guest interactions offers new opportunities for designing such architectures for a broader range of catalytic applications.     

An Approach to Paracyclophane-Based Tetrathiafulvalenes: Synthesis and Characterization of a Pseudo-Geminal [2.2]Paracyclophane 1,3-Dithia-2-Thione

The synthesis of paracyclophane-based tetrathiafulvalene precursors is described in the context of the importance of these compounds in the field of material chemistry. Pseudo-geminal bis(1,3-dithia-2-thione) was synthesized via the corresponding 1,3-dithiol-2-ylium salt. The latter was obtained by a synthetic procedure that involves 4,15-bis(acetyl)[2.2]paracyclophane, a new compound of interest for many researchers.     

Solidifying framework nucleic acids

正Living organisms have developed their unique strategies during the natural evolution for building hard tissues with minerals, including silica, calcium carbonate, calcium phosphate, and ferric oxide [1]. Such biomineralized materials generally have complex hierarchical structures with excellent mechanical properties. Although bioinspired approaches have led to the creation of well-defined synthetic structural materials ranging from micro to macro scales, the rational design of discrete biomimetic structures at the nanoscale remains a grand challenge.     

Effects of multiple delays on dynamics of a five-neuron network model

A five-neuron network model with multiple delays is proposed. This paper presents the combined effect of different delays on the dynamics of the proposed network. Pitchfork bifurcation is discussed in detail with the variation of the value of coupled weight or attenuation rate of internal neurons. By analyzing the corresponding characteristic equation, some stable criteria on delay-dependence and delay-independence are derived including multiple delays and coupled weights and the periodic oscillation arises bifurcated from the trivial equilibrium after the network loses its stability. Stable regions on delay-dependence are displayed in the two delayed parameter plane. It is shown that multiple delays can produce stability switching between resting state and periodic activity. Finally, theoretical results are justified by providing two illustrative examples.     

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.