Chinese Quarterly Journal of Mathematics

On Some Recent Progress in Complex Geometry|the Area Related to Homogeneous Manifolds

GUAN Daniel

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

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In this article, we give a survey of some progress of the complex geometry, mostly related to the Lie group actions on compact complex manifolds and complex homogeneous spaces in the last thirty years. In particular, we explore some works in the special area in Dierential Geometry, Lie Group and Complex Homogeneous Space. Together with the special area in nonlinear analysis on complex manifolds, they are the two major aspects of my research interests.

Singularities of the Moduli Space of n Unordered Points on the Riemann Sphere

WU Yue, XU Bin

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

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We classify the nite groups associated to the orbifold singularities of the moduli space of n5 unordered points on the Riemann sphere.

On Relationship between Lower-order of Coefficients and Growth of Solutions of Complex Differential Equations near a Singular Point

LIU Yuan-zhu, LONG Jian-ren, ZENG San-gui

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.

Some Notes on Relative Projective and Injective Dimensions

HE Dong-lin, LI Yu-yan

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.

Left Annihilator of Power Values with Derivations on Lie Ideals in Prime Rings

HUANG Shu-liang

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

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Let R be a prime ring with characteristic di®erent from two, d a derivation of R, L a noncentral Lie ideal of R, and a \in R. In the present paper it is showed that if

a(d(u^m)\pm u^m)^n=0

for all u \in L, where m; n are fixed positive integers, then a = 0 unless R satisfies s4, the standard polynomial identity in four variables.

The Maximal Subgroups of n * n Nonnegative Integral Matrices

YANG Lin, REN Miao-miao

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

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In this paper we study the subgroup structure of the semigroup Mn(Z+) of all n * n nonnegative integral matrices under multiplication. We prove that every maximal subgroup of Mn(Z+) containing an idempotent element of rank r is isormorphic to Sr.

Simple Bounded Weight Modules for the Vector Field Lie Algebras of Infinite Rank

NIU Meng-nan

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

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In this paper, we classify the simple uniformly bounded weight modules for the vector eld Lie algebra W1 of innite rank. It turns out that any such modules are intermediate series modules. This result is very different from the vector eld Lie algebra Wd of nite rank.

Extinction and Non-simultaneous Blow-up of Solutions in Fast Diffusion Equations

LIU Bing-chen, WANG Yu-xi, WANG Lu

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.

A New F-C Function for Box Constrained Global Optimization

ZHAN Yue, SHANG You-lin, QU De-qiang

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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