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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 Zaiming, YU Senlin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 16. doi:
10.6040/j.issn.16719352.0.2014.328
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(
591
)
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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 matrixanalytical method of quasi birthdeath 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 SparreAndersen model with PH(
n
) interclaim times
LIU Xiao
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 712. doi:
10.6040/j.issn.16719352.0.2014.484
Abstract
(
472
)
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Assuming that the surplus process is described by a SparreAndersen 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 integrodifferential 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 Shuoge, YANG Wenzhi
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 1318. doi:
10.6040/j.issn.16719352.0.2014.359
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525
)
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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 weightedfractional Brownian motion and application
DENG Longjuan, ZHU Dongjin, SHEN Guangjun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 1926. doi:
10.6040/j.issn.16719352.0.2014.234
Abstract
(
491
)
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The power variation of weightedfractional 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 Mingle, ZHU Dongjin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 2732. doi:
10.6040/j.issn.16719352.0.2014.300
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(
456
)
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By making good use of Hoffmanntype 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 Tingting, FAN Guoliang
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 3338. doi:
10.6040/j.issn.16719352.0.2014.201
Abstract
(
658
)
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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 Jiaojiao, FAN Shengjun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 3944. doi:
10.6040/j.issn.16719352.0.2014.200
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486
)
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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 Houjun, CHU Maoquan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 4552. doi:
10.6040/j.issn.16719352.0.2014.229
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(
428
)
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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 Rongmin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 5358. doi:
10.6040/j.issn.16719352.0.2014.331
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496
)
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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.
NearMDR codes over finite principal ideal rings
ZHANG Xiaoyan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 5963. doi:
10.6040/j.issn.16719352.0.2014.232
Abstract
(
638
)
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The definition of NearMDS codes over finite fields was generalized to nearMDR 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 nearMDR codes over finite principal ideal rings are changed into that of nearMDR codes over finite chain rings. Furthermore, the criterion of nearMDR codes over finite chain rings is changed into that of nearMDS codes over residue fields, so we describe nearMDR codes over finite principal ideal rings.
Weakly pullback flatness of
S
posets and the homological classification
ZHAO Meimei
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 6468. doi:
10.6040/j.issn.16719352.0.2014.244
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(
480
)
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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): 6974. doi:
10.6040/j.issn.16719352.0.2014.585
Abstract
(
390
)
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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 isoscelesorthogonality preserving mappings
KONG Liang, CAO Huaixin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 7582. doi:
10.6040/j.issn.16719352.0.2014.571
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606
)
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Firstly, In real normed linear spaces, the definition of
ε
approximate square isoscelesorthogonality preserving mapping is given. Some sufficient conditions for a linear mapping to be an
ε
approximate square isoscelesorthogonality preserving mapping are given. Secondly, when the mapping is bounded, the characterization of
ε
approximate square isoscelesorthogonality preserving linear mapping is obtained. Finally, the perturbations of
ε
approximate square isoscelesorthogonality preserving linear mapping are given.
Generalized Jordan centralizers on CDCalgebras
MA Fei, ZHANG Jianhua, HE Wen
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 8388. doi:
10.6040/j.issn.16719352.0.2015.083
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615
)
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Let
Alg
(
L
) be a CDCalgebra 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 OrlikSolomon algebras
GAO Ruimei, SUN Yan
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(06): 8994. doi:
10.6040/j.issn.16719352.0.2015.080
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653
)
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The OrlikSolomon 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 OrlikSolomon algebras for central and affine arrangements, and give the isomorphism theorems for the top dimensional parts of OrlikSolomon algebras.