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20 June 2015
Volume 50 Issue 06
A discrete time working vacations queuing system with different arrival rates and negative customers
LIU Zai-ming, YU Sen-lin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 1-6. doi:
10.6040/j.issn.1671-9352.0.2014.328
Abstract
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1537
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A multiple working vacations Geo/Geo/1 queuing system with negative customers was proposed and studied in this paper. For this model, the positive customers have different arrival rates in the normal busy period and working vacation period. The quantities including the transition probability matrix of the queuing system, the equilibrium distribution of the queue length, the mean number of customers, the stochastic decomposition and the busy period analysis were obtained by using the matrix-analytical method of quasi birth-death chains. The cost function and two numerical examples were given to provide a basis for optimal design and illustrate the impact of parameters on the queue length.
Dividend problems in a Sparre-Andersen model with PH(
n
) interclaim times
LIU Xiao
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 7-12. doi:
10.6040/j.issn.1671-9352.0.2014.484
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1230
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Assuming that the surplus process is described by a Sparre-Andersen model, the interclaim times are PH(
n
) distributed, dividends can only be paid at some randomized observation times and the dividends are paid according to a barrier strategy, the integro-differential equations for the expected discounted dividends and the Laplace transform of ruin time were derived. The solutions of the equations were given with exponentially distributed claims and
n
=2.
Complete moment convergence of moving average process for END random variables
QIAN Shuo-ge, YANG Wen-zhi
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 13-18. doi:
10.6040/j.issn.1671-9352.0.2014.359
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1535
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The moving average process based on END random variables was constructed. By using the moment inequality of END random variables, the complete moment convergence for this moving average process was established. As a corollary, its complete convergence was also presented.
Power variation of weighted-fractional Brownian motion and application
DENG Long-juan, ZHU Dong-jin, SHEN Guang-jun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 19-26. doi:
10.6040/j.issn.1671-9352.0.2014.234
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1305
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The power variation of weighted-fractional Brownian motion was considened by using its stochastic calculus representation. As an application, the estimate of parameter
b
was obtainted.
Complete moment convergence of weighted sums of arrays of rowwise ND random variables
TAN Chuang, GUO Ming-le, ZHU Dong-jin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 27-32. doi:
10.6040/j.issn.1671-9352.0.2014.300
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1280
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By making good use of Hoffmann-type inequality and a series of moments inequalities, and some necessary scalings, the sufficient condition of complete moment convergence of weighted sums of arrays of rowwise ND random variables was obtained.
Minimax estimator for multivariate linear model of regression coefficient matrix
GAO Ting-ting, FAN Guo-liang
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 33-38. doi:
10.6040/j.issn.1671-9352.0.2014.201
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1680
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For the multivariate linear model
Y
=
XΘ
+
ε
, E(
ε
)=0, COV(
ε
)=
σ
2
▽
⊗
Σ
, where
▽
>0 and
Σ
≥0 are known matrix, the minimax estimator of regression coefficients matrix in the multivariate linear model was considered. Under the matrix loss function, the property of linear estimators was investigated. The unique minimax estimator of linearly estimable functions SΘ of coefficients matrix was obtained under the suitable hypotheses.
A stability theorem for solutions of a class of backward stochastic differential equations
FANG Rui, MA Jiao-jiao, FAN Sheng-jun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 39-44. doi:
10.6040/j.issn.1671-9352.0.2014.200
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1351
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By establishing an inequality between conditional mathematic expectations of random variables under two different but equivalent probability measures, we prove a stability theorem for solutions of backward stochastic differential equations whose generator
g
is monotonic in
y
and uniformly continuous in
z
,which generalizes some known results.
Dimensions of semilinear spaces over commutative semirings
ZHANG Hou-jun, CHU Mao-quan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 45-52. doi:
10.6040/j.issn.1671-9352.0.2014.229
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1303
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The dimensions of semilinear spaces over commutative semirings
L
are investigated. Some necessary and sufficient conditions that dim(
V
n
)=
n
are given, and the relationship between
V
n
and
V
1
are obtained, where
V
n
and
V
1
are finite dimensional semilinear spaces over
L
. Moreover, the concepts of semilinear transformation A, and the range A(
V
n
) and nuclear A
-1
(0) of A are introduced and the equation dim(A(
V
n
))+
dim
(A
-1
(0))=
dim
(
V
n
) is proved.
Gorenstein projective
N
-complexes
ZHU Rong-min
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 53-58. doi:
10.6040/j.issn.1671-9352.0.2014.331
Abstract
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1383
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The properties of Gorenstein projective of
N
-complexes are investigated, and the Gorenstein projective dimensions of
N
-complex are characterized. It is shown that for an arbitrary associative ring
R
, any
N
-complex
C
of
R
-module is Gorenstein projective if and only if each
C
n
is Gorenstein projective.
Near-MDR codes over finite principal ideal rings
ZHANG Xiao-yan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 59-63. doi:
10.6040/j.issn.1671-9352.0.2014.232
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1598
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The definition of Near-MDS codes over finite fields was generalized to near-MDR codes over finite principal ideal rings. Using the fact that a linear codes over a finite principal ideal ring is the Chinese product of the linear codes over finite chain rings, the criterion of near-MDR codes over finite principal ideal rings are changed into that of near-MDR codes over finite chain rings. Furthermore, the criterion of near-MDR codes over finite chain rings is changed into that of near-MDS codes over residue fields, so we describe near-MDR codes over finite principal ideal rings.
Weakly pullback flatness of
S
-posets and the homological classification
ZHAO Mei-mei
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 64-68. doi:
10.6040/j.issn.1671-9352.0.2014.244
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1179
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Let
S
be a pomonoid.
S
-poset satisfying condition (E') is defined and weakly pullback flatness is given over pomonoid. Furthermore, the homological classifications of pomonoids by their Rees factor
S
-posets are investigated.
Existence of positive periodic solutions of impulsive functional differential equations with two parameters
XU Man
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 69-74. doi:
10.6040/j.issn.1671-9352.0.2014.585
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1101
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We study the existence of positive periodic solutions of impulsive functional differential equations with two parameters
u
'(
t
)=
h
(
t
,
u
(
t
))-λ
f
(
t
,
u
(
t
-τ(
t
))),
t
∈R, t≠t
k
,
u
(
t
+
k
)-
u
(
t
k
)=μI
k
(
t
k
,
u
(
t
k
-τ(
t
k
))), where
λ
>0,
μ
≥0 are parameters and show the existence results of positive periodic solutions in more general conditions. The proof of the main results is based on the fixed point index theory.
Characterization and perturbations of
ε
-approximate square isosceles-orthogonality preserving mappings
KONG Liang, CAO Huai-xin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 75-82. doi:
10.6040/j.issn.1671-9352.0.2014.571
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1549
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Firstly, In real normed linear spaces, the definition of
ε-
approximate square isosceles-orthogonality preserving mapping is given. Some sufficient conditions for a linear mapping to be an
ε
-approximate square isosceles-orthogonality preserving mapping are given. Secondly, when the mapping is bounded, the characterization of
ε
-approximate square isosceles-orthogonality preserving linear mapping is obtained. Finally, the perturbations of
ε
-approximate square isosceles-orthogonality preserving linear mapping are given.
Generalized Jordan centralizers on CDC-algebras
MA Fei, ZHANG Jian-hua, HE Wen
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 83-88. doi:
10.6040/j.issn.1671-9352.0.2015.083
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1494
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Let
Alg
(
L
) be a CDC-algebra on a Hilbert space
H
, and
φ
:
Alg
L
→
Alg
L
be an additive mapping. We prove that if for some positive integer numbers
m
,
n
,
r
≥1, (
m
+
n
)
φ
(
A
r
+1
)=
m
φ
(
A
)
A
r
+
nA
r
φ
(
A
) hold for all
A
∈
A
, then there exists some
λ
∈
Z
(
Alg
L
), such that
φ
(A)
=
λA
, for all A∈
Alg
L
.
Quadratic Gröbner basis and the isomorphism of Orlik-Solomon algebras
GAO Rui-mei, SUN Yan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 89-94. doi:
10.6040/j.issn.1671-9352.0.2015.080
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1676
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The Orlik-Solomon algebra is the quotient of the exterior algebra
E
based on A by a homogeneous ideal
I
. The relations between a quadratic arrangement and a quadratic Gröbner basis are studied. And the proof of the conclusion that a central arrangement is a quadratic arrangement if and only if
I
has a quadratic Gröbner basis is given. We do some research on the Orlik-Solomon algebras for central and affine arrangements, and give the isomorphism theorems for the top dimensional parts of Orlik-Solomon algebras.
