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Table of Content
30 September 2019, Volume 34 Issue 3
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Normality Criteria of Zero-free Meromorphic Functions
XIE JIE, DENG Bing-mao
2019, 34(3): 221-231. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.001
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Let k be a positive integer,let h（z）■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P（f）（z）-h（z） has at most k+l-1 distinct zeros（ignoring multiplicity） in D,where P（f）（z）=f
（k）
（z）+a
1
（z）f
(
（k-1）（z）+…+ak（z）f（z） is a differential polynomial of f and aj（z）（j=1,2,···,k） are holomorphic functions in D,then F is normal in D.
On Uniqueness Problem of Meromorphic Functins Sharing Values with Their q-shifts
ZHANG Shui-ying, LIU Hui-fang
2019, 34(3): 232-241. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.002
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In this paper, the uniqueness problems on meromorphic function f(z) of zero order sharing values with their q-shift f(qz + c) are studied. It is shown that if f(z) and f(qz + c) share one values CM and IM respectively, or share four values partially, then they are identical under an appropriate deficiency assumption.
Algorithm on the Optimal Vertex-Distinguishing Total Coloring of mC9
HE Yu-ping, CHEN Xiang'en
2019, 34(3): 242-258. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.003
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Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to be the color set of vertex u under f. If Cf(u) = Cf(v)for any two distinct vertices u and v of G, then f is called vertex-distinguishing total coloring of G(in brief VDTC), a vertex distinguishing total coloring using k colors is called k-vertexdistinguishing total coloring of G(in brief k-VDTC). The minimum number k for which there exists a k-vertex-distinguishing total coloring of G is called the vertex-distinguishing total chromatic number of G, denoted by χvt(G). By the method of prior distributing the color sets, we obtain vertex-distinguishing total chromatic number of m C9 in this paper.
Finite Difference Methods for the Time Fractional Advection-diffusion Equation
MA Yan, MUSBAH F.S.
2019, 34(3): 259-273. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.004
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In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.
Globally Bounded Solutions in A Chemotaxis Model of Quasilinear Parabolic Type
LIU Bing-chen, DONG Meng-zhen
2019, 34(3): 274-282. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.005
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In this paper,we consider a quasilinear parabolic-parabolic chemotaxis model with nonlinear diffusivity,aggregation and logistic damping source: where k
1
e
pu
≤D（u） or k
1
u
p
≤D（u）;k
2
e
qu
≤S（u）≤k
3
e
qu
;g（u）≤a-be
ku
.It is proved that,if q <k-1 or q=k-1 and b> b
0
for some constant b
0
> 0,then there exists a unique classical solution which is globally bounded.The results show the effect of the aggregation and the logistic damping source on the existence of globally bounded solutions.
Triple Positive Solutions for a Third-order Three-point Boundary Value Problem
WU Hong-ping
2019, 34(3): 283-289. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.006
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In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.
Fixed-time Consensus for Leader-follower Second-order Multi-agent Systems
CHEN Mao-li, WANG Xiao
2019, 34(3): 290-300. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.007
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We analyse the fixed-time consensus problem for multi-agent systems with leaderfollower mode. Based on a follower’s observation structure for the leader’s information, it is proved that the estimation errors can be converged to zero at a fixed time. From this stability and a sliding mode structure, we derive a control input of followers, which provides a critical support for fixed-time consensus. The simulation results demonstrate that this control approach does conduce to the implementation of the fixed-time synchronization.
On the Solution of Fermat-type Differential-di®erence Equations
LIU Dan, DENG Bing-mao, YANG De-gui
2019, 34(3): 301-313. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.008
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In this paper,we mainly discuss entire solutions of finite order of the following Fermat type differential-difference equation[f
（k）
（z）]
2
+[△
c
f（z）]
2
=1,and the systems of differential-difference equations of the from. Our results can be proved to be the sufficient and necessary solutions to both equation and systems of equations.
Multimodal Learning Using Haar Scattering Transform
WANG Juan, ZHAO Jie
2019, 34(3): 314-322. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.009
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In this paper, we propose a novel application of Haar scattering transform to learn features over multiple modalities data. A series of tasks for multimodal learning are presented, and the way of multimodal feature learning is shown. Furthermore, we validate our methods on several datasets with an classification task, demonstrating that the approach is effective.
A Regularity Criterion Via the Pressure on the Three-dimensional Boussinesq Fluid Equations
LI Xiao, LI-Ying-chao
2019, 34(3): 323-330. doi:
10.13371/j.cnki.chin.q.j.m.2019.03.010
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In this paper,we investigate the regularity criterion via the pressure of weak solutions to the Boussinesq fluid equations in three dimensions.We obtain that for ,then the weak solution(u,θ) is regular on(0,T].
