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.     

An Unprecedented Two‐Fold Nested Super‐Polyrotaxane: Sulfate‐Directed Hierarchical Polythreading Assembly of Uranyl Polyrotaxane Moieties

The hierarchical assembly of well‐organized submoieties could lead to more complicated superstructures with intriguing properties. We describe herein an unprecedented polyrotaxane polythreading framework containing a two‐fold nested super‐polyrotaxane substructure, which was synthesized through a uranyl‐directed hierarchical polythreading assembly of one‐dimensional polyrotaxane chains and two‐dimensional polyrotaxane networks. This special assembly mode actually affords a new way of supramolecular chemistry instead of covalently linked bulky stoppers to construct stable interlocked rotaxane moieties. An investigation of the synthesis condition shows that sulfate can assume a vital role in mediating the formation of different uranyl species, especially the unique trinuclear uranyl moiety [(UO₂)₃O(OH)₂]²⁺, involving a notable bent [O=U=O] bond with a bond angle of 172.0(9)°. Detailed analysis of the coordination features, the thermal stability as well as a fluorescence, and electrochemical characterization demonstrate that the uniqueness of this super‐polyrotaxane structure is mainly closely related to the trinuclear uranyl moiety, which is confirmed by quantum chemical calculations.     

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Synthesis of Spirocyclic Indolenines

This Review provides an in‐depth account of the synthesis of spirocyclic indolenines. Over the last 77 years, a wide array of diverse synthetic methods has been developed in order to generate these synthetically useful and biologically important spirocyclic scaffolds. The main synthetic strategies discussed are grouped into three main categories, namely interrupted Fischer indolisations, dearomatisation reactions of indoles and condensation reactions. The historical background, common synthetic challenges, current state‐of‐the‐art and future perspectives of this field are examined.