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The enumeration of rooted cubic c-nets$^{\dag}$
Junliang Cai,Rongxia Hao,Yanpei Liu 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].
THE ENUMERATION OF ROOTED CUBIC C-NETS
CAI, JUNLIANG,HAO, RONGXIA,LID, YANPEI 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].
COUNING g-ESSENTIAL MAPS ON SURFACES WITH SMALL GENERA
Rongxia Hao,Junliang Cai,Yanpei Liu 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.9 No.2
This paper provides some functional equations and parametric expressions of {\t$g$}-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further. This paper provides some functional equations and parametric expressions of {\t$g$}-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.
COUNING g-ESSENTIAL MAPS ON SURFACES WITH SMALL GENERA
Hao, Rongxia,Cai, Junliang,Liu, Yanpel 한국전산응용수학회 2002 The Korean journal of computational & applied math Vol.9 No.2
This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.
Lin, Jia,Chen, Hong,Gao, Yang,Cai, Yao,Jin, Jianbo,Etman, Ahmed S.,Kang, Joohoon,Lei, Teng,Lin, Zhenni,Folgueras, Maria C.,Quan, Li Na,Kong, Qiao,Sherburne, Matthew,Asta, Mark,Sun, Junliang,Toney, Mic National Academy of Sciences 2019 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.116 No.47
<P><B>Significance</B></P><P>Metal halide perovskites attract great interest for a wide range of applications due to their remarkable optoelectronic properties. The development of environmentally friendly halide perovskite materials with various crystal structures and compositions offers unprecedented opportunities to achieve desired properties and applications. In this work, we demonstrated an In-based, charge-ordered all-inorganic halide double perovskite with the composition of Cs<SUB>2</SUB>In(I)In(III)Cl<SUB>6</SUB> synthesized by solid-state reaction. High-pressure optical properties were studied, and a pressure-driven, fully reversible semiconductor–metal phase transition was discovered. This In-based charge-ordered structure may inspire new understanding of halide perovskite as well as provide a platform for future discovery of exotic electronic phenomena such as high-<I>T</I><SUB>C</SUB> superconductivity in halide perovskite compounds.</P><P>Phase transitions in halide perovskites triggered by external stimuli generate significantly different material properties, providing a great opportunity for broad applications. Here, we demonstrate an In-based, charge-ordered (In<SUP>+</SUP>/In<SUP>3+</SUP>) inorganic halide perovskite with the composition of Cs<SUB>2</SUB>In(I)In(III)Cl<SUB>6</SUB> in which a pressure-driven semiconductor-to-metal phase transition exists. The single crystals, synthesized via a solid-state reaction method, crystallize in a distorted perovskite structure with space group <I>I</I>4/<I>m</I> with <I>a</I> = 17.2604(12) Å, <I>c</I> = 11.0113(16) Å if both the strong reflections and superstructures are considered. The supercell was further confirmed by rotation electron diffraction measurement. The pressure-induced semiconductor-to-metal phase transition was demonstrated by high-pressure Raman and absorbance spectroscopies and was consistent with theoretical modeling. This type of charge-ordered inorganic halide perovskite with a pressure-induced semiconductor-to-metal phase transition may inspire a range of potential applications.</P>