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Table of Content
30 September 2015, Volume 30 Issue 3
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Gradient Estimates for a Simple Lichnerowicz Equation on Compact Manifolds
XING Jie
2015, 30(3): 317-322. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.001
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Let（M,g） be a smooth compact Riemannian manifold of dimension n.Denote△f=△-▽f.▽ the weighted Laplacian operator,where f is a smooth real valued function on M.When N is finite and the N-Bakry-Emery Ricci tensor is bounded from below by a constant,we establish local gradient estimates for positive solutions of the following simple Lichnerowicz equation△fu+cu
-α
=0 on a compact Riemannian manifold,where α is a positive constant and c is a smooth function.
The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation
CHENG Zhi-long, HAO Xiao-hong
2015, 30(3): 323-329. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.002
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Based on the travelling wave method, a（2 + 1）-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.
Scheduling and Outsourcing with Multiple Customers
FENG Yan-ling, ZHANG Yu-zhong, JIA Guo-zhu
2015, 30(3): 330-338. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.003
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In this paper, we study a new scheduling and outsourcing model with multiple customers in which jobs can be processed by either in-house machine or outsourcing machine.All processed jobs have to be delivered in batches to their respective customers and each shipment incurs a delivery cost as well as a fixed amount of time. We discuss three commonly used objective functions, analyze their complexity and solve them by dynamic programming algorithms.
Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydrodynamic Equations
LIU Kun-hong, YUAN Bao-quan
2015, 30(3): 339-348. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.004
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In this paper,we study the regularity criterion of weak solutions to the3 D incompressible Hall-magnetohydrodynamics,which is ifu and Bsatisfy the condition∫
0
T
‖
\alpha
x3
u（t）‖
q
LP
+‖▽B‖γLβdt<∞ with 3/p+2/q≤1,3/β+2/γ≤1,p>3,β>3,then the weak solution（u,B） is a smooth one on(0,T].
On Similarity Measures and Distance Measures of Fuzzy Soft Sets
LIU Ya-ya, QIN Ke-yun, WANG Ling
2015, 30(3): 349-357. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.005
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In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.
Symmetric Positive Solutions of Nonlinear Singular Second-order Three-point Boundary Value Problem
WU Hong-ping
2015, 30(3): 358-365. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.006
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In this paper, the second-order three-point boundary value problem
{u"（t）+λa（t）f（t,u（t））=0,0<t<1,u（t）=u（1-t）,u′（0）-u′（1）=u（1/2）is studied,where
λ
is a positive parameter,under various assumption on a and f,we establish intervals of the parameter
λ
,which yield the existence of positive solution,our proof based on Krasnosel’skii fixed-point theorem in cone.
An Identity and Its Applications Concerning Two Mass-points Systems
ZHOU Yong-guo
2015, 30(3): 366-372. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.007
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In this paper, we first give and prove a geometric identity for distance between any point and mass-points of two mass-points systems in n-dimensional Euclidean space Rn.As its application, we obtain an equality for two mass-points systems and its radius of the circumscribed sphere and an inequality for distance between mass-points of two mass-points systems and its k-dimensional volume.
Generalized
（∈,∈∨q）
-fuzzy Ideals in BCK-algebras
LIU Chun-hui
2015, 30(3): 373-380. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.008
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In this paper, as a generalization of the notion of（∈, ∈∨ q）-fuzzy ideals, we introduced the notion of（∈, ∈∨ q
δ
）-fuzzy ideals and investigated their properties in BCKalgebras. Several equivalent characterizations of（∈, ∈∨ q
δ
）-fuzzy ideals are obtained and relations between（∈, ∈∨ q
δ
）-fuzzy ideals and ideals are discussed in BCK-algebras.
On s
¤
-Completions of Maximal Subgroups of Finite Groups
GAO Hui, GAO Sheng-zhe, YIN Li
2015, 30(3): 381-388. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.009
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Given a maximal subgroup M of a group G, a θ*-completion C of M is called an s*-completion if either C = G or there exists a subgroup D of G which is not a θ*-completion of M such that D contains C as a maximal subgroup. In this paper, we obtain several results on s*-completions which imply G to be solvable or supersolvable.
Tight Relative 6-designs on Binary Hamming Association Schemes
LI Zeng-ti, GAO Suo-gang, FENG Guang-hui
2015, 30(3): 389-407. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.010
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The concept of relative t-designs for Q-polynomial association schemes is due to Delsarte（Philips Res Rep 32: 373C411, 1997）. In this paper, we discuss the Fisher type lower bounds of tight relative 6-designs very explicitly for binary Hamming association schemes H（n, 2）.
Global Convergence of a Hybrid Conjugate Gradient Method
WU Xue-sha
2015, 30(3): 408-415. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.011
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Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.
On the Coe±cients for
ε
- Starlike Mappings in \mathbb{C}^{n}
YAN Chun-yan, SUN Lin-po, AN Man
2015, 30(3): 416-419. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.012
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In this paper, we study ε-starlike mappings on the unit ball in
\mathbb{C}^{n}
, the upper bounds of coefficients of kth item of homogeneous expansion for ε-starlike mappings are obtained.
Calculation Method of Power Law Fluid Equivalent Permeability Considering Capillary Shape
YANG Er-long, LI Huan, GAO Hui-juan, GU Ting-ting
2015, 30(3): 420-428. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.013
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While studying the flow of oil and gas in the reservoir, it is not realistic that capillary with circular section is only used to express the pores. It is more representative to simulate porous media pore with kinds of capillary with triangle or rectangle section etc. In the condition of the same diameter, when polymer for oil displacement flows in the porous medium, there only exists shear flow which can be expressed with power law model. Based on fluid flow-pressure drop equation in single capillary, this paper gives a calculation method of equivalent permeability of power law fluid of single capillary and capillary bundles with different sections.
Product Image Classification Based on Fusion Features
YANG Xiao-hui, LIU Jing-jing, YANG Li-jun
2015, 30(3): 429-441. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.014
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Two key challenges raised by a product images classification system are classification precision and classification time. In some categories, classification precision of the latest techniques, in the product images classification system, is still low. In this paper, we propose a local texture descriptor termed fan refined local binary pattern, which captures more detailed information by integrating the spatial distribution into the local binary pattern feature. We compare our approach with different methods on a subset of product images on Amazon/e Bay and parts of PI100 and experimental results have demonstrated that our proposed approach is superior to the current existing methods. The highest classification precision is increased by 21% and the average classification time is reduced by 2/3.
On the Fekete-
Szeg
\"{o}
Problem for a Class of Analytic Functions
GUO Dong, LI Zong-tao, HUANG Jin-chao
2015, 30(3): 442-449. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.015
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The Fekete-Szego inequality for a subclass H（α,λ,A,B） of the class H of normalized analytic functions is studied.For each f（z）=z+∞∑n=2α
n
z
n
∈ H（α,λ,A,B）,the sharp upper bounds of |α
3
-α
2
2
|for any complex parameter u are obtained by using the fundamental inequalities of analytic functions and analytical techniques and the applications of the inequality of functions defined with Hadaniard product are proved.
A Non-autonomous SIR Epidemic Model of Prey-predator with Vaccination and Time Delay
KANG Rui-ni, ZHANG Tai-lei, LIU Jun-li
2015, 30(3): 450-461. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.016
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A non-autonomous SIR epidemic model of prey-predator with vaccination and time delay is investigated in this paper. And an infectious disease is only considered to spread among the prey population. By using comparison principle and Lyapunov functional methods, we obtain the sufficient criteria for the permanence, extinction of infectious disease and the global attractively of the model. Furthermore, some numerical simulations illustrate that the vaccination has a better effect for disease controlling of infective prey.
Monomials with t-value
≤6
in Canonical Basis of Quantized Enveloping Algebra of Type B
3
HU Yu-wang, GENG Ya-jun
2015, 30(3): 462-474. doi:
10.13371/j.cnki.chin.q.j.m.2015.03.017
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All monomials with t-value ≤ 6 in Canonical basis of quantized enveloping algebra of type B
3
are determined in this paper.
