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中文
Table of Content
30 December 2015, Volume 30 Issue 4
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Polynomial Complexity Bounds of Mehrotra-type Predictor-corrector Algorithms for Linear Programming over Symmetric Cones
LIU Chang-he, SHANG You-lin, LI Zhen-guo
2015, 30(4): 475-494. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.001
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We establish polynomial complexity bounds of the Mehrotra-type predictorcorrector algorithms for linear programming over symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al[18]. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε-1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
Overlapping Domain Decomposition Finite Difference Algorithm for Compact Difference Scheme of the Heat Conduction Equation
ZHANG Hong-mei
2015, 30(4): 495-502. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.002
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In this paper, a modified additive Schwarz finite difference algorithm is applied in the heat conduction equation of the compact difference scheme. The algorithm is on the basis of domain decomposition and the subspace correction. The basic train of thought is the introduction of the units function decomposition and reasonable distribution of the overlap of correction. The residual correction is conducted on each subspace while the computation is completely parallel. The theoretical analysis shows that this method is completely characterized by parallel.
A New Finite-dimensional Integrable System Associated to (1+1)-dimensional Soliton Equations
WEI Han-yu, GUO Han-dong, XIA Tie-cheng
2015, 30(4): 503-514. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.003
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In this paper, a new spectral problem is proposed and the corresponding soliton equations hierarchy are also obtained. Under a constraint between the potentials and the eigenfunctions, the eigenvalue problem is nonlinearized so as to be a new finitedimensional Hamiltonian system. By resotring to the generating function approach, we obtain conserved integrals and the involutivity of the conserved integrals. The finite-dimensional Hamiltonian system is further proved to be completely integrable in the Liouville sense. Finally, we show the decomposition of the soliton equations.
Order of Dirichlet Series in the Whole Plane and Remainder Estimation
HUANG Hui-jun, NING Ju-hong
2015, 30(4): 515-523. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.004
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In this paper, firstly, the ρ order and ρ
β
order of Dirichlet series which converges in the whole plane are studied. Secondly, the equivalence relation between remainder logarithm ln E
n-1
（f, α）, ln R
n
（f, α） and coefficients logarithm ln |a
n
| is discussed respectively. Finally,the theory of applying remainder to estimate ρ order and ρ
β
order can be obtained by using the equivalence relation.
Bicriteria Scheduling on Single Machine with Outsourcing
CHEN Rong-jun, QIN Li-zhen, TANG Guo-chun
2015, 30(4): 524-531. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.005
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Scheduling with outsourcing is studied in this paper. It is assumed that both manufacturer and subcontractor have a single machine to process n jobs. The manufacturer needs to determine simultaneously a set of outsourced jobs and the schedule of the jobs in-house such that two criterias, i.e., outsourcing cost and production cost, are minimized.The production cost is measured by the number of tardy jobs or the total tardiness of jobs in-house, and the outsourcing cost is proportional to the total processing time of jobs outsourced. Two kinds of problems with different criterias are considered. We analyze the computational complexity and provide pseudo-polynomial time optimization algorithms for the NP-hard version of the problems.
Some New Subclasses of Meromorphically Multivalent Uniformly Reciprocal Starlike Functions Defined by the Generalized Dziok-Srivastava Operator and Its Integral Operator
MA Li-na, LI Shu-hai
2015, 30(4): 532-544. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.006
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In this paper, we introduce some new subclasses of meromorphically uniformly reciprocal starlike functions associated with the generalized Dziok-Srivastava operator and its corresponding integral operator defined by subordination. We obtain the inclusion relation,sufficient conditions and majorization property of the class. Moreover, we point out some new and interesting corollaries of our main result. These results generalize some known results.
Diophantine Inequalities with Mixed Powers
MU Quan-wu, LÄU Xiao-dong
2015, 30(4): 545-554. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.007
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It is proved that if λ
1
, λ
2
, ···, λ
7
are nonzero real numbers, not all of the same sign and not all in rational ratios, then for any given real numbers η and σ, 0 < σ <1/16, the inequality |λ
1
x
1
2
+ λ
2
x
2
2
+∑7 i=3λ
i
x
i
4
+ η| <（ max1≤i≤7|x
i
|）
-σ
has infinitely many solutions in positive integers
λ
1
, λ
2
, ···, λ
7
Similar result is proved for |
λ
1
x
1
2
+ λ
2
x
2
2
+ λ
3
x
3
2
+ λ
4
x
4
4
+ λ
5
x
5
4
+ λ
6
x
6
4
+ η| <（ max1≤i≤6|x
i
|）
-σ
.These results constitute an improvement upon those of Shi and Li.
A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems
SUN Jia, WANG Shi-heng, WANG Ke
2015, 30(4): 555-561. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.008
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Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting（PHSS） method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose（1,1） block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones.
Optimal Control for Insurers with a Jump-diffusion Risk Process
WU Kun, XIAO Jian-wu, LUO Rong-hua
2015, 30(4): 562-569. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.009
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In this paper, the optimal XL-reinsurance of an insurer with jump-diffusion risk process is studied. With the assumptions that the risk process is a compound Possion process perturbed by a standard Brownian motion and the reinsurance premium is calculated according to the variance principle, the implicit expression of the priority and corresponding value function when the utility function is exponential are obtained. At last, the value function is argued, the properties of the priority about parameters are discussed and numerical results of the priority for various claim-size distributions are shown.
Boundedness of Some Multilinear Hardy Type Operators on Herz-Morrey Spaces with Variable Exponent
CHENG Xing-xing, QU Meng, SHU Li-sheng
2015, 30(4): 570-578. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.010
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In this paper, we will obtain that the boundedness of multilinear n-dimensional fractional Hardy operators of variable order β（x） on variable exponent Herz-Morrey spaces.
The Group of Automorphisms of Transitive 2 - (v; 23; 1) Designs
LI Shang-zhao
2015, 30(4): 579-586. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.011
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This paper is a contribution to the study of the automorphism groups of 2-（v, k, 1） designs. Let D be a 2-（v, 23, 1） design and G a block-transitive and point-primitive group of automorphism of D. Then the socle of G is not Sz（q） and
2
G
2
（q）.Key words: block-transitive; point-primitive; design; socle
Some Approximation Properties of Certain q-Sz
\acute{a}
sz-Mirakyan-Baskakov Operators
MO Qing-feng, HU Xiao-min, WU Peng
2015, 30(4): 587-595. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.012
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In this paper we propose the q analogues of modified Baskakov-Sz′asz operators.we estimate the moments and establish the direct results in term of modulus of continuity.An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained.
On the Analog of Shephard Problem for L
p
-polar Projection Bodies
MA Tong-yi
2015, 30(4): 596-609. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.013
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For p > 0, Lutwak, Yang and Zhang introduced the concept of L
p
-polar projection body Γ
-p
K of a convex body K in R
n
. Let p ≥ 1 and K, L
\subset
R
n
be two origin-symmetric convex bodies, we consider the question of whether Γ
-p
K
\subset
Γ
-p
L implies
\Omega
p
（L） ≤
\Omega
p
（K）,where
\Omega
p
（K） denotes the L
p
-affine surface area of K and K = Voln（K）
-1/p
K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L
p
-polar projection bodies.
Continuous Dependence of Bounded
Φ
-variation Solutions on Parameter for a Class of Discontinuous Systems
MA Xue-min, LI Bao-lin, LIN Chang-wei
2015, 30(4): 610-619. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.014
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The functions of bounded Φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded Φ-variation solutions on parameter for a class of discontinuous systems on the base of Φ-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
On the Transitivity of the Strong Product of Graphs
DONG Li-xin, LI Feng, ZHAO Hai-xing
2015, 30(4): 620-623. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.015
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Since many large graphs are composed from some existing smaller graphs by using graph operations, say, the Cartesian product, the Lexicographic product and the Strong product. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this short note, we give some properties of the Strong product of vertex-transitive graphs. In particular, we show that the Strong product of Cayley graphs is still a Cayley graph.
The Interior of Numerical Ranges of Operators
DOU Yan-ni, LI Chen-xin, LI Rong, DU Hong-ke
2015, 30(4): 624-632. doi:
10.13371/j.cnki.chin.q.j.m.2015.04.016
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In this note, some properties of the interior of numerical ranges of operators are established, and an alternative proof of Embry’s theorem associated with the interior of a numerical ranges of an operator is given(see [3]).
