We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if ...We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.展开更多
In this paper,the method of Information Synthesis of Seismogenic System(ISSS)has been used to describe and evaluate the evolution process of self-organization of seismcgenic system in the Capital circle.Through the sy...In this paper,the method of Information Synthesis of Seismogenic System(ISSS)has been used to describe and evaluate the evolution process of self-organization of seismcgenic system in the Capital circle.Through the synthesis of precursory information,the criterion and possible index which characterize the transition of the seismogenic system from steady-state to unsteady-state and then towards the attractor cif a new steady-state have been investigated.The result shows that the synthesis of comprehensive precursor)deformation anomalies of the seismogenic large system(fault-network in the Capital circle),the information synthesis of precursory anomalies of sub-system(a few main fault zones in the Capital circle),and the unweighted or weighted synthesis of anomalous frequencies recognized by the dynamic grey-box method can all raise remarkably the reliability and distinctness of precursory information associated with the Datong Ms 6.1 earthquake.It has provided a criterion and index for evaluation and展开更多
In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corre...In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation展开更多
In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
基金supported by National Natural Science Foundation of China (Grant Nos. 11871094 and 12122119)supported by National Natural Science Foundation of China (Grant No. 12171480)+1 种基金Hunan Provincial Natural Science Foundation of China (Grant Nos. 2020JJ4658 and 2022JJ10059)Scientific Research Program Funds of National University of Defense Technology (Grant No. 22-ZZCX-016)。
文摘We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool.
文摘In this paper,the method of Information Synthesis of Seismogenic System(ISSS)has been used to describe and evaluate the evolution process of self-organization of seismcgenic system in the Capital circle.Through the synthesis of precursory information,the criterion and possible index which characterize the transition of the seismogenic system from steady-state to unsteady-state and then towards the attractor cif a new steady-state have been investigated.The result shows that the synthesis of comprehensive precursor)deformation anomalies of the seismogenic large system(fault-network in the Capital circle),the information synthesis of precursory anomalies of sub-system(a few main fault zones in the Capital circle),and the unweighted or weighted synthesis of anomalous frequencies recognized by the dynamic grey-box method can all raise remarkably the reliability and distinctness of precursory information associated with the Datong Ms 6.1 earthquake.It has provided a criterion and index for evaluation and
文摘In 1923, Hardy and Littlewood[1] conjectured that each integer n can be written asp+m12+ m22 = n,and Linnik[2,3] proved that this conjecture is true. But if these mi with i = 1,2 are restricted to primes Pi, the corresponding result is out of reach at present. We consider the following Diophantine equation
基金Project supported by National Natural Science Foundation(No. 90304009)Foundation of Qufu Normal University for Ph.D.
文摘In this paper we prove that, with at most O（N^5/12＋ε） exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1（mod 3） can be written as a sum of a prime and two squares of primes.
