Topological Configuration and Rotation Analysis of the Three⁃Order Rubik􀆳s Cube

The mechanism of three⁃order Rubik􀆳s Cube(RC)has the characteristics of recombination and variable degree of freedom,and it is difficult to accurately describe the degree of its freedom.This paper takes RC as the research object,and the adjacency matrix is constructed based on topology and graph theory in order to describe the variation rule of topological configuration in the single layer rotation of RC.In this paper,the degree of freedom of the RC in any shape can be described by defining the concept of entanglement degree of freedom,establishing a set of adjacency matrix,and determining the degree of freedom of the RC which is attributed to the number of non⁃zero elements in the set of adjacent matrix.The prime number is proposed to describe the rotation of the RC combined with the rotation recognition of RC,which is simple and convenient for computer processing.The research contents in this paper are beneficial to the study of RC from the perspective of mechanism science.Meanwhile,it is of great significance to the study of other complex mechanisms with variable degrees of freedom.

Behavioral Diversity and Complexity Indicated by Metazoan Traces at a Topological Level since Proterozoic

On the basis of topological criteria, metazoan traces can be classified as four ichnoorders (clusters) and twenty two ichnofamilies (kinds), which consist of nine basic and three combined topological configurations. At a topological level, the behavioral diversity and complexity indicated by metazoan traces have remained quite stable since the Early Cambrian. Dramatic changes of these traits took place in the Neoproterozoic, in which 75% (12/16) of the topoichnotaxa and all nine basic topological configurations of metazoan traces occurred, but the most complex and highest level topological configuration occurred in the Early Cambrian of the coelomate animal explosive evolution, showing that in the Neoproterozoic and Early Cambrian gestated not only the Ediacarian fauna and all the basic types of multi cellular animals known today, but also all the basic and the most complex metazoan traces through geological time.

Removal and fluorescence detection of antibiotics from wastewater by layered double oxides/metal-organic frameworks with different topological configurations

Owing to the serious potential side-effects on the environment and human health,the rapid detection and removal of antibiotics have become an important research focus.In this work,four zinc-based metal-organic frameworks(MOFs)with different functional groups,i.e.,Zn-MOF,Zn-MOF-CH_(3),Zn-MOF-NO_(2),Zn-MOF-COOH,were utilized for the construction of LDO/MOF composite materials with a nickel-iron-cobalt-based layered double oxide,NiFeCo-LDO.The results showed that the LDO/MOF composites not only had high sensitivity in detecting sulfonamide and quinolone antibiotics,but also had an appreciable ability to adsorb them from wastewater.The maximum adsorption capacities of all the four types of LDO@Zn-MOFs to all antibiotics can at least reach 150 mg/g,and the limits of detection in relation to all four antibiotics were at least as low as 100μg/L.Our work suggested the dual-function extraction performance can be attributed to the synergistic effects between the LDO and the MOFs.Moreover,the strong ferromagnetism derived from the LDO provided great convenience for the separation and regeneration of the LDO/MOF composites.

METAMORPHIC MECHANISMSAND THEIR CONFIGURATION MODELS

The concept of metamorphic mechanisms is presented, configuration models and configuration transformations relating to a set of new matrix operations are discussed and proposed. The configuration of a metamorphic mechanism reflects the connectivity change in the mechanism during motions which results in mobility change and presents the characteristics of the mechanism which is discussed in various applications particularly in decorative artifacts. The characteristics is further investigated with mobility analysis.

High-Q resonances governed by the quasi-bound states in the continuum in all-dielectric metasurfaces

The realization of high-Q resonances in a silicon metasurface with various broken-symmetry blocks is reported. Theoretical analysis reveals that the sharp resonances in the metasurfaces originate from symmetry-protected bound in the continuum(BIC) and the magnetic dipole dominates these peculiar states. A smaller size of the defect in the broken-symmetry block gives rise to the resonance with a larger Q factor. Importantly, this relationship can be tuned by changing the structural parameter, resulting from the modulation of the topological configuration of BICs. Consequently, a Q factor of more than 3,000 can be easily achieved by optimizing dimensions of the nanostructure. At this sharp resonance, the intensity of the third harmonic generation signal in the patterned structure can be 368 times larger than that of the flat silicon film. The proposed strategy and underlying theory can open up new avenues to realize ultrasharp resonances, which may promote the development of the potential meta-devices for nonlinearity, lasing action, and sensing.

Rational design of imine-linked three-dimensional mesoporous covalent organic frameworks with bor topology

Three-dimensional(3D)covalent organic frameworks(COFs)possess great potential applications in various fields.Constructing 3D COFs with large pore sizes is extremely challenging due to the interpenetration and collapse.Herein,we report a series of crystalline imine-linked 3D COFs(3D-bor-COF-1,3D-borCOF-2,3D-bor-COF-3)with mesoporous channels through rationally designing the topology configuration.These 3D-bor-COFs display permanent porosity and Brunauer–Emmett–Teller(BET)surfaces of 3205.5,1752.7,and 2077.3 m2 g−1(SLangmuir=4277.7,2480.3,and 2698.0 m2 g−1),respectively.The pore sizes of 3Dbor-COFs were confirmed by the lattice fringes from high-resolution transmission electron microscopy,as well as structural simulation and nitrogen adsorption isotherm analysis.3D-bor-COFs display large pore sizes(3.8 nm for 3D-borCOF-3),which is among the highest record of 3D COFs.Owing to the unstackedaromatic pore environment and high specific surface area,3D-bor-COFs display excellent adsorption capacity for benzene vapor(1203.9 mg g−1 for 3D-bor-COF-3)under 298 K,which is three times higher than that of the best-reported 2D COF.This work not only provides inspiration for designing 3D mesoporous imineCOFs,but also demonstrates a strategy for constructing aromatics adsorption materials.