supported by the Strategic Priority Research Program of CAS(No.XDB0520201);the National Natural Science Foundation of China((Nos.22132007,22372175,22202208,22372030);CAS Project for Young Scientists in Basic Research(No.YSBR-053).
Achieving seamless tiling through the self-assembly of organic species has long fascinated scientists for its potential applications across various fields.However,constructing periodic nanostructures with high-order t...
supported by the Key Projects of Zhejiang Natural Science Foundation(No.LZ22A010003);ZJNU Shuang-Long Distinguished Professorship Fund(No.YS304319159)。
Edge-to-edge tilings of the sphere by congruent a^(2)bc-quadrilaterals are classified as 3 classes:(1)A 1-parameter family of quadrilateral subdivisions of the octahedron with24 tiles,and a flip modification for one s...
supported by the Key R&D Programs of Zhejiang Province(Nos.2023C01224 and 2022C01220);the National Natural Science Foundation of China(No.61702458);Yun Zhang was partially supported by Zhejiang Province Public Welfare Technology Application Research(No.LGG22F020009);Key Lab of Film and TV Media Technology of Zhejiang Province(No.2020E10015).
Computer-generated aesthetic patterns arewidely used as design materials in various fields. Themost common methods use fractals or dynamicalsystems as basic tools to create various patterns. Toenhance aesthetics and c...
financially supported by the National Natural Science Foundation of China (Nos. 21925102, 21991132, 92056118 and 22101010);the financial support from the National Key R&D Program of China (No. 2018YFB0703702);Beijing National Laboratory for Molecular Sciences (No. BNLMS-CXXM-202006)
This review summarizes the self-assembly of block molecules forming unconventional two-dimensional(2D)periodic nanopatterns.Especially,we emphasize the structural evolution from simple columnar phases to complex 2D ti...
In this paper, we deduce Wiener number of some connected subgraphs in tilings (4, 4, 4, 4) and (4, 6, 12), which are in Archimedean tilings. And compute their average distance.
Supported by the National Natural Science Foundation of China under Grant No.11471273 and No.11271307;Youth Research Fund Project of Chengyi College of Jimei University under Grant No.CK17007
Some physicists depicted the molecular structure SnCl_2 · 2(H_2O) by a piece of an Archimedean tiling(4.8.8) that is a partial cube. Inspired by this fact, we determine Archimedean tilings whose connected subgrap...
We consider tilings of deficient rectangles by the set T4 of ribbon L-tetro-minoes. A tiling exists if and only if the rectangle is a square of odd side. The missing cell has to be on the main NW-SE diagonal, in an od...
We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is tha...
Let Tn be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T+n be Tn with an extra 2 x 2 square. We investigate signed tilings of rectangles by Tn...
Supported by FEDER funds through COMPETE Operational Programme Factors of Competitiveness(Programa Operacional Factores de Competitividade);Supported by FSE;Supported by Portuguese funds through the Center for Researchand Development in Mathematics and Applications(University of Aveiro);the Portuguese Foundation for Science and Technology(FCT Fundao para a Ciência e a Tecnologia);project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690;supported partially by an NSERC Canada Discovery Grant
In this work,we give a complete classification of spherical dihedral f-tilings when the prototiles are two noncongruent isosceles triangles with certain adjacency pattern.As it will be shown,this class is composed by ...