数学季刊

关于复几何中的一些新进展—与齐性流形相关的领域

关庄丹

2020, 35(2): 111-144. doi:10.13371/j.cnki.chin.q.j.m.2020.02.001

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黎曼球上n点组的模空间奇点

吴悦, 许斌

2020, 35(2): 145-162. doi:10.13371/j.cnki.chin.q.j.m.2020.02.002

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We classify the finite groups associated to the orbifold singularities of the moduli space of n ≥ 5 unordered points on the Riemann sphere.

奇异点附近的复微分方程解的增长性与系数下级的关系

刘元竹, 龙见仁, 曾三桂

2020, 35(2): 163-170. doi:10.13371/j.cnki.chin.q.j.m.2020.02.003

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We investigate the growth of solutions of the following complex linear differential equation f’’+ A（z）f’+ B（z）f = 0,where A（z） and B（z） are analytic functions in C-{z₀}, z₀∈ C. Some estimations of lower bounded of growth of solutions of the differential equation are obtained by using the concept of lower order.

相对投射与内射维数的若干注记

何东林, 李煜彦

2020, 35(2): 171-178. doi:10.13371/j.cnki.chin.q.j.m.2020.02.004

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Let R be an associative（not necessary commutative） ring. In this paper,we give some properties of Hom-faithful and Hom-cofaithful R-modules. We investigate Σ-self-orthogonal R-modules and P_C-projective dimensions, and give a characterization when the inequality P_C-pd V max{P_C-pd U, P_C-pd W } is strict for an exact sequence 0 → U → V → W → 0. Dually, we study Π-self-orthogonal modules and I_C-injective dimensions, and give a similar characterization when the inequality I_C-id V max{I_C-idU, I_C-idW } is strict.

素环李理想上带有导子幂值的左零化子

黄述亮

2020, 35(2): 179-185. doi:10.13371/j.cnki.chin.q.j.m.2020.02.005

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n*n非负整数矩阵的极大子群

杨琳, 任苗苗

2020, 35(2): 186-193. doi:10.13371/j.cnki.chin.q.j.m.2020.02.006

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无限秩向量场李代数的有界单权模

牛梦楠

2020, 35(2): 194-198. doi:10.13371/j.cnki.chin.q.j.m.2020.02.007

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快速扩散方程组解的熄灭和非同时爆破

刘丙辰, 王煜羲, 王璐

2020, 35(2): 199-213. doi:10.13371/j.cnki.chin.q.j.m.2020.02.008

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In this paper, we deal with some fast diffusion equations u_t= ?u^m+ au^αv^p and v_t= ?vⁿ+ bu^qv^β subject to null Dirichlet boundary conditions. We prove that every solution vanishes in finite time for pq >（m-α）（n-β）, m > α and n > β, where the exact relation of initial data is determined with the aid of some Sobolev Embedding inequalities.If pq <（m-α）（n-β）, m > α and n > β, we show the barriers of the initial data which lead to the non-extinction of solutions. For the case pq =（m-α）（n-β）, the solutions vanish for small initial data. The results fill in a gap for the case pq < mn in Nonlinear Anal. Real World Appl. 4（2013） 1931-1937. The coefficients a and b play a vital role in the existence of non-extinction weak solution provided that a and b are large enough. At last, we use the scaling methods to determine some exponent regions where one of the components would blow up alone for some suitable initial data.

求解箱式约束全局优化问题的新的F-C函数

詹悦, 尚有林, 屈德强

2020, 35(2): 214-220. doi:10.13371/j.cnki.chin.q.j.m.2020.02.009

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To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a filled function and a cross function. The properties of the F-C function are discussed and the corresponding algorithm is given in this paper. F-C function has the same local minimizers with the objective function.Therefore, the F-C function method only needs to minimize the objective function once in the first iteration. Numerical experiments are performed and the results show that the proposed method is very effective.

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