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学者姓名：赖降周
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Abstract ：
Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K-2 X C-4 X P-n)) approximate to (-1.171. n(-1.1223) + 3.146)n, and log(M(K-2 X P-4 X P-n)) approximate to (-1.164. n(-1.196) + 2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy. (C) 2015 Elsevier B.V. All rights reserved.
Keyword ：
Dimer Dimer Entropy Entropy Three dimensional lattice Three dimensional lattice
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| GB/T 7714 | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs [J]. | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 : 347-354 . |
| MLA | Lin, Fenggen 等. "Dimer problem for some three dimensional lattice graphs" . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 443 (2016) : 347-354 . |
| APA | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 , 347-354 . |
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Abstract ：
It is well known that the flops for complex operations are usually 4 times of real cases. In the paper, using real operations instead of complex, a real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices is given. We make use of the real symmetric and skew-Hamiltonian structure transformed by Wilkinson's way, focus on symplectic orthogonal similarity transformations and their structure-preserving property, and then reduce it into a two-by-two block tridiagonal symmetric matrix. Finally a real algorithm can be quickly obtained for eigenvalue problems of the original Hermitian matrix. Numerical experiments show that the fast algorithm can solve real complex Hermitian matrix efficiently, stably, and with high precision.
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| GB/T 7714 | Lai, Jiangzhou , Lu, Linzhang . Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices [J]. | MATHEMATICAL PROBLEMS IN ENGINEERING , 2013 , 2013 . |
| MLA | Lai, Jiangzhou 等. "Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices" . | MATHEMATICAL PROBLEMS IN ENGINEERING 2013 (2013) . |
| APA | Lai, Jiangzhou , Lu, Linzhang . Real Fast Structure-Preserving Algorithm for Eigenproblem of Complex Hermitian Matrices . | MATHEMATICAL PROBLEMS IN ENGINEERING , 2013 , 2013 . |
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Abstract ：
研究了复Hermite矩阵经Wilkinson实数转化后矩阵的性质,利用其对称性和反Hamiltonian结构,给出了特征值问题的隐式重启Isotropic Lanczos保结构算法.数值试验表明,这种方法求解出的特征对残量很小,具有较高的精度.
Keyword ：
Hamihonian结构 Hamihonian结构 Hermite矩阵 Hermite矩阵 Isotropic Lanczos算法 Isotropic Lanczos算法 特征值问题 特征值问题
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| GB/T 7714 | 赖降周 , 卢琳璋 . 复Hermite矩阵特征值问题的实Isotropic Lanczos算法 [J]. | 福州大学学报（自然科学版） , 2013 , 41 (3) : 261-265 . |
| MLA | 赖降周 等. "复Hermite矩阵特征值问题的实Isotropic Lanczos算法" . | 福州大学学报（自然科学版） 41 . 3 (2013) : 261-265 . |
| APA | 赖降周 , 卢琳璋 . 复Hermite矩阵特征值问题的实Isotropic Lanczos算法 . | 福州大学学报（自然科学版） , 2013 , 41 (3) , 261-265 . |
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Abstract ：
研究了一类秩1扰动矩阵谱条件数问题,根据原正定矩阵的特征值分解,利用秩1扰动矩阵的性质,给出了谱条件数的最大最小值.
Keyword ：
奇异值分解 奇异值分解 特征值分解 特征值分解 秩1扰动矩阵 秩1扰动矩阵 谱条件数 谱条件数
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| GB/T 7714 | 赖降周 , 卢琳璋 . 秩1扰动矩阵谱条件数的界 [J]. | 贵州师范大学学报（自然科学版） , 2013 , 31 (4) : 35-36 . |
| MLA | 赖降周 等. "秩1扰动矩阵谱条件数的界" . | 贵州师范大学学报（自然科学版） 31 . 4 (2013) : 35-36 . |
| APA | 赖降周 , 卢琳璋 . 秩1扰动矩阵谱条件数的界 . | 贵州师范大学学报（自然科学版） , 2013 , 31 (4) , 35-36 . |
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Abstract ：
给出了HR分解的分量型和范数型的一阶扰动界.对于范数型,新的精化扰动界至少优于已有结果,特别的,新的关于R因子的扰动界远远优于已有的扰动界.
Keyword ：
HR分解 HR分解 扰动分析 扰动分析 条件估值 条件估值
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| GB/T 7714 | 赖降周 , 卢琳璋 . HR分解的精化扰动界(英文) [J]. | 数学研究 , 2012 , 45 (03) : 263-270 . |
| MLA | 赖降周 等. "HR分解的精化扰动界(英文)" . | 数学研究 45 . 03 (2012) : 263-270 . |
| APA | 赖降周 , 卢琳璋 . HR分解的精化扰动界(英文) . | 数学研究 , 2012 , 45 (03) , 263-270 . |
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Abstract ：
给出了HR分解的分量型和范数型的一阶扰动界.对于范数型,新的精化扰动界至少优于已有结果,特别的,新的关于R因子的扰动界远远优于已有的扰动界.
Keyword ：
HR分解 HR分解 扰动分析 扰动分析 条件估值 条件估值
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| GB/T 7714 | 赖降周 , 卢琳璋 . HR分解的精化扰动界 [J]. | 数学研究 , 2012 , 45 (3) : 263-270 . |
| MLA | 赖降周 等. "HR分解的精化扰动界" . | 数学研究 45 . 3 (2012) : 263-270 . |
| APA | 赖降周 , 卢琳璋 . HR分解的精化扰动界 . | 数学研究 , 2012 , 45 (3) , 263-270 . |
| Export to | NoteExpress RIS BibTex |
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