JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

On central automorphisms and class-preserving
automorphisms of finite groups

HAI Jin-ke, LI Zheng-xing

J4. 2011, 46(6): 1-3.

Abstract ( 1592 )

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Connections between class-preserving automorphisms and central automorphisms of finite groups are established. Some sufficient conditions for classpreserving automorphisms of finite p-groups to be inner automorphisms are obtained by means of certain properties of central automorphisms.

On the rank of order-preserving and compressing singular
transformation semigroups

GAO Rong-hai1,2, XU Bo1

J4. 2011, 46(6): 4-7.

Abstract ( 1370 )

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RC-semigroups of N(2,2,0) algebra

DENG Fang-an

J4. 2011, 46(6): 8-11.

Abstract ( 1306 )

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A condition for constructing a right closure—semigroup (RC-semigroup) by an operator on N(2,2,0) algebra is investigated. Some properties of RCsemigroup of N(2,2,0) algebra are obtained, and the property that every RC-semigroup of N(2,2,0) algebra satisfies the congruence condition and is also a twisted RC-semigroup.

Strong reduced Groebner bases of quantum algebra A_n(q₁,…,q_n,K)

SU Cang

J4. 2011, 46(6): 12-17.

Abstract ( 1322 )

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Strong reduced Groebner bases for left ideals of quantum algebra An(q1,…,qn,K) are introduced, the existence and uniqueness of such a basis is proved, and an algorithm for constructing a strong reduced Groebner basis is given.

A new characterization of the distribution areas of matrix eigen-values

WANG Da-fei, WU Jun-liang

J4. 2011, 46(6): 18-21.

Abstract ( 1336 )

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The new distribution areas of matrix eigenvalues are discussed. All the eigenvalues of an arbitrarily given matrix are located in the same disc, which accurately estimates eigenvalues of any matrix and their distribution. An example shows the effectiveness of the results.

L^p boundedness for a class of Marcinkiewicz integral
operators with rough kernel

QU Meng, SHU Li-sheng

J4. 2011, 46(6): 22-28.

Abstract ( 1180 )

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The L^p boundedness for a class of Marcinkiewicz integral operators with rough kernel is considered, which improves some known results.

Generalized graded Betti numbers of characteristic module over dual extension algebras of A_n type

TANG Guo-ming1, ZENG Ni1, ZHANG Yue-hui2

J4. 2011, 46(6): 29-33.

Abstract ( 1356 )

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The notion of generalized graded Betti numbers for any algebra is introduced, and the generalized graded Betti numbers of characteristic module over dual extension algebras of A_n type are explicitly given.

Boundary blow-up problems for fully nonlinear uniformly elliptic equations

DAI Li-mei

J4. 2011, 46(6): 34-36.

Abstract ( 1204 )

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A spectral stochastic multi-scale finite element method for
the exterior problem of the Helmholtz equation

PAN Qingfei1, SHAN Wei2*, WU Jianliang3

J4. 2011, 46(6): 37-40.

Abstract ( 1408 )

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The interaction of acoustic waves with a scattering object in a stochastic and multi-scale media is studied. A spectral stochastic multi-scale finite-element method is developed to solve numerically the acoustic scattering problem based on the variation principle and the DtN mapping method. The results show that the proposed method is valid and its numerical implementation is very fast.

Boundedness of a class of weighted Hardy-Steklov averaging operators

ZHENG Qing-yu, ZHANG Lei

J4. 2011, 46(6): 41-44.

Abstract ( 1541 )

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The sufficient and necessary conditions of boundedness are given about the weights of a class of weighted HardySteklov operators on both Lp and BMO spaces. Also, the corresponding operator norms are obtained, which provide a considerable important technical analysis in the study of predicting the future of a stock price.

Eigen-value problem of a bi-harmonic equation in R⁴

WU Yun1, YAO Yangxin2

J4. 2011, 46(6): 45-48.

Abstract ( 1169 )

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The eigen-value problem of bi-harmonic equations with Hardy potential is considered. The results of references by introducing a new Hilbert space are improved.

On the island sequences of L(2,1)-labeling of graphs

LUO Jin-mei, ZUO Lian-cui*

J4. 2011, 46(6): 49-52.

Abstract ( 1265 )

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A class of connected graphs with the hole index ρ(G)≥1 possessing different ordered sequences of island cardinalities is provided.

A bound of the vertex-distinguishing total chromatic number of graphs

QIANG Hui-ying

J4. 2011, 46(6): 53-56.

Abstract ( 1496 )

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A proper total coloring of the graph G is called vertex-distinguishing total coloring, if any two vertices have different color sets, where the color set of a vertex is the set composed of all colors of the vertex and the edges incident to it. On the base of the bound of vertex-distinguishing total chromatic number（ χ_vt( G)≤|V(G)|+2）. The new upper bound of vertex-distinguishing total chromatic number is obtained by way of probability.

Oscillation criteria for high order nonlinear neutral
type differential equations with distribute delay

LIU Fengyan1, ZHANG Shufang2

J4. 2011, 46(6): 57-59.

Abstract ( 1199 )

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The oscillation of high order nonlinear neutral type differential equations are considered with distribute delay. The oscillation criteria are established for this kind of boundary value problem by using the Philos integral average method.

Constructing cospectral graphs

WU Tingzeng

J4. 2011, 46(6): 60-63.

Abstract ( 1704 )

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A method for constructing cospectral forests is given,and a factor of cospectral graphs is defined. Four factors of cospectral graphs are given, and some cospectral graphs are also obtained.

Existence of multiple solutions for boundary value problem
of a singular differential system on the half-line

WANG Minggao1,2, TANG Qiuyun3

J4. 2011, 46(6): 64-66.

Abstract ( 1141 )

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Using the fixed point theorem of cone expansion and compression, the existence of multiple positive solutions for a boundary value problem of a nonlinear singular differential system on the half-line are investigated.

Nonlinear strong *- commutativity preserving maps on prime *-rings

ZHANG Fangjuan

J4. 2011, 46(6): 67-69.

Abstract ( 1251 )

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Eigen-value functions of some functions of orthogonal projections

XU Junlian

J4. 2011, 46(6): 70-74.

Abstract ( 1350 )

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A class of geometric inequalities about generalized metric addition

YANG Shiguo1, QI Jibing1, WANG Wen2*

J4. 2011, 46(6): 75-78.

Abstract ( 1303 )

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The problem about generalized metric addition of n-simplex in Euclidean space En is investigated, one class of geometric inequalities on generalized metric addition about simplex volume is obtained, which generalizes the known results about simplex generalized metric and metric addition.

Reflected BSDEs with a stochastic Lipschitz coefficient

LV Wen1,2

J4. 2011, 46(6): 79-83.

Abstract ( 1469 )

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A class of reflected backward stochastic differential equations with a stochastic Lipschitz coefficient is considered. First, the existence and uniqueness of the solutions for those equations in a special form are proved via Snell envelope. Then the same result for those equations in general form is obtained by using the fixed point theorem.

Redundancy of empirical likelihood for missing data problems

ZHU Liping1,2

J4. 2011, 46(6): 84-89.

Abstract ( 1390 )

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The redundancy of empirical likelihood is considered, and some redundancy results of empirical likelihood are obtained. Then the redundancy results of GMM are extended, and the counterintuitive result is also explained. Simulations results prove the influence of the redundancy of empirical likelihood on the efficiency of estimators.

On designing H_∞ fault estimator for switched Lur′e
systems with time-varying delay

YUAN Shuai1, LIU Xinzhi1, 2*

J4. 2011, 46(6): 90-98.

Abstract ( 1284 )

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The problem of fault estimation for a class of switched nonlinear systems with timevarying delay is studied. The nonlinearity satisfies certain sector condition. By employing a switched observer-based fault estimator, the problem is formulated as an H∞ filtering problem. Some delaydependent sufficient conditions are derived to ensure both the absolute stability and a prescribed L₂-gain bound of an augmented system from the original system and a fault estimation error system. Also, the parameter matrices of the fault estimator are obtained based on the cone complementarity algorithm. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

A new algorithm for solving minimum cost flow with the duality principle

XIONG Deguo1, HU Yongwen1, SHI Jianming2

J4. 2011, 46(6): 99-102.

Abstract ( 1550 )

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A new algorithm is proposed to solve the problem of minimum cost flow by a dual approach, which held complementarity conditions to the dual problem and found a desired flow by modifying the potential and labeling for each node of the network. Unlike existing algorithms, the new algorithm did not construct a residual network nor find the shortest path. The validity of the new algorithm is proved, and an example is given to illustrate the behavior of the proposed algorithm.

The Geom／Geom／1 queue system with generalized
random working vacation policy

WEI Caimin, ZOU Zongbao

J4. 2011, 46(6): 103-109.

Abstract ( 1307 )

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A discretetime Geom／Geom／1 queue with generalized random working vacation policy is studied. By using the quasi birth and death chain and matrixgeometric solution approaches, the generating functions and the expectations of the steady state queue length and sojourn time are derived. In addition, the generating functions and the means of the regular busy period, busy cycle and vacation period are obtained. Finally, two special cases of the model are given.

F-rough law separation and the operation-recognition of FCU

DU Yingling1, SUN Zongbao2

J4. 2011, 46(6): 110-114.

Abstract ( 1291 )

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F-rough law separation and F-rough law separation cluster are proposed, and the relation theorem of F-rough law separation is given. Using Frough law separation and F-rough law separation cluster in the operation and recognition of FCU (fan coil units), a new method to realize the intelligent characteristic and stable characteristic of system operation and recognition of FCU is presented.

Attribute dependence of function P-sets and its application

ZHAO Wenju1, FAN Chengxian2*

J4. 2011, 46(6): 115-120.

Abstract ( 1342 )

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Using the structure of function P-sets, the attribute dependence, dependence measure and attribute dependence theorems of function P-sets are given. The application of attribute dependence of function P-sets is obtained.

Identification and recovery of inward-recursion information

LI Yuying1,2, RUAN Qunsheng1, ZHANG Shiliang1, YANG Huiling1, MAO Yanming1

J4. 2011, 46(6): 121-126.

Abstract ( 1327 )

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Information which has a recursive characteristic in the process of transmission is generated because its information elements are continuously lost. By using P-sets which is a new mathematic tool and has dynamic characteristics, the concept of inwardrecursion information is proposed, and the structure of inward-recursion is given. Theorems are obtained such as the sequence theorem of inwardrecursion information, the merging theorem of loss information, identification and recovery theorems of inwardrecursion information. By defining the modulus and the identification measure on inwardrecursion information, the numerical value methods of identification and recovery are obtained. Also, the identification criterion of inwardrecursion information is given. Finally, the application of identification and recovery is presented.

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