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20 December 2017
Volume 52 Issue 12
GPcoherent monoids
QIAO Husheng, LIAO Minying
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 14. doi:
10.6040/j.issn.16719352.0.2017.254
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284
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GPflat
S
act is a genetalization of principally weakly flat
S
act. Monoids over which GPflatness property of
S
acts is preserved under direct product are characterized, and some known results of the case
n
=1 according to principally weakly coherent monoids to any other natural numbers is extended.
Simple dual Rickart modules
WANG Yongduo, MA Yajun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 59. doi:
10.6040/j.issn.16719352.0.2017.219
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380
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The concept of simple dual Rickart modules is introduced. Its basic properties are studies and it is proved that a ring
R
is
V
ring if and only if every right
R
module is simple dual Rickart module.
When is
^{}
B
_{H}
Q a prebraided category over quasiHopf algebras
GUO Shuangjian, LI Yizheng
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 1015. doi:
10.6040/j.issn.16719352.0.2017.177
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240
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Let
H
be a quasiHopf algebra with invertible antipode,
B
a left quasi YetterDrinfeld module algebra and
^{H}
_{B}
Q the category of quasi Hopf YetterDrinfeld
(H,B)
modules. It is discussed when the category
^{H}
_{B}
Q is a prebraided monoidal category. The following is proved: assume that
B
is
H
commutative, then the braiding on the category of quasi YetterDrinfeld modules
^{}
H
Q induces a prebraiding on
^{H}
_{B}
Q if and only if every object of
^{}
H
_{B}
Q is dyslectic.
Nil *clean rings
WANG Huixing, CUI Jian, CHEN Yining
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 1624. doi:
10.6040/j.issn.16719352.0.2017.153
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420
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The concepts of nil *clean rings and uniquely nil *clean rings are introduced. Basic properties and extension properties of such rings are investigated. Moreover, the relations of several classes of *rings are discussed.
Strongly Gorenstein
C
flat modules
LI Jinlan, LIANG Chunli
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 2531. doi:
10.6040/j.issn.16719352.0.2017.136
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371
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As a generalization of strongly Gorenstein flat modules, the strongly Gorenstein flat modules with respect to a semidualizing modules
C
, that is, strongly Gorenstein
C
flat module are introduced, and some properties and equivalent characterizations are given, for example, the class of Strongly Gorenstein
C
flat modules is P
_{C}
resolving and closed under direct sums as well as direct summands. Morever, the stability of strongly Gorenstein
C
flat modules are investigated.
LR smash product for bialgebroids
LU Daowei, WANG Zhen
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 3235. doi:
10.6040/j.issn.16719352.0.2017.202
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493
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The LR smash product for the bialgebroid is constructed, and examples are given. As an application, it is proved that twosided smash product is actually an LR smash product.
Linear 2arboricity of planar graphs with 4cycles have no common vertex
CHEN Hongyu, ZHANG Li
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 3641. doi:
10.6040/j.issn.16719352.0.2016.597
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309
)
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The linear 2arboricity la
_{2}
(G)
of
G
is the least integer
k
to divide
G
into
k
edgedisjoint forests, and each branch of the forests is a path with the length at most 2. We prove that if
G
is a planar graph with 4cycles without common vertex, then la
_{2}
(
G)≤「Δ/
2
+
5
.
Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements
WU Li, ZHANG Jianhua
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 4247. doi:
10.6040/j.issn.16719352.0.2017.255
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342
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Let U=Tri(A, M, B )be a 2torsion free triangular algebra, and Q={u∈U:u
^{2}
=0}. We prove that if a map
φ
:U→U satisfies
φ(ab)=φ(a)b+aφ(b)
for any
a,b
∈U with
［a,b］
∈Q, then
φ
is an additive derivation, where
［a,b］=abba
is the Lie product and
ab=ab+ba
is the Jordan product.
Multiple positive solutions of a system of high order nonlinear fractional differential equations
FENG Haixing, ZHAI Chengbo
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 4857. doi:
10.6040/j.issn.16719352.0.2017.380
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The existence of multiple positive solutions for a system of highorder nonlinear fractional differential equations is studied. Two or three positive solutions are obtained for the system by using LeggettWilliams fixed point theorem and Krasnoselskiion cone.
Pseudo Drazin inverse of 2×2 antitriangular matrix in Banach algebras
SUN Xiaoqing, WANG Xin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 5866. doi:
10.6040/j.issn.16719352.0.2017.094
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436
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We give formulae for the pseudo Drazin inverse M
^{‡}
of an 2×2 antitriangular matrix M=(a db 0)under some conditions. Moreover, some particular cases of these results are also considered.
Finite dimensional approximation of linear stochastic Schrödinger equation in terms of localization of quantum Bernoulli noises
HUANG Ailing, LIN Shuai
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 6771. doi:
10.6040/j.issn.16719352.0.2017.174
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317
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Local quantum Bernoulli noise is the family of local annihilation and creation operators, which is localization of quantum Bernoulli noise and satisfies a local canonical anticommunication relation in equal time. A linear stochastic Schrödinger equation in terms of local quantum Bernoulli noise is considered. The existence and uniqueness of a solution to the equation, its priori estimates as well as its finite dimensional approximation are discussed.
Existence of solutions for
p(t)
Laplacian fractional infinitepoint boundary value problems at resonance
ZHANG Di, LIU Wenbin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 7280. doi:
10.6040/j.issn.16719352.0.2017.312
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358
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By using Mawhins continuation theorem, through the reasonable control of the nonlinear term, an existence result for the solutions of fractional infinitepoint boundary value problems at resounce with
p(t)
Laplacian operator is presented.
Existence and controllability of nonlocal stochastcic integrodifferential equations driven by fractional Brownian motion
CUI Jing, LIANG Qiuju
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 8188. doi:
10.6040/j.issn.16719352.0.2017.089
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438
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We study the existence and controllability of nonlocal stochastcic integrodifferential equations driven by fractional Brownian motion in a real separable Hilbert space. Sufficient conditions are derived by using the Banach fixed point theorem and stochastic analysis thoery. An example is provided to illustrate the theory.
Data separation and its attribute state characteristics
GUO Hualong, ZHANG Ling
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 8994. doi:
10.6040/j.issn.16719352.0.2017.436
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This article gives the basic theory of data separation as well as the generation theory of attribute state characteristics for data separation. By employing the structures and dynamic characteristics of inverse Psets, the concepts of data outer separation, data internal separation and data outerinternal separation are proposed. Moreover, the data separation characteristics and the attribute state characteristics are generated by data separation are analyzed. Then the data supplement theorem, the data deleting theorem and the data supplementdeleting theorem are given. The attribute cardinal theorems of data outer separation, data internal separation and data outerinternal separation are provided. The theoretical results presented in this article show the generation characteristics of data separation.
Attribute reduction in formal decision contexts based on AEconcept lattices
CHEN Xue, WEI Ling, QIAN Ting
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 95103. doi:
10.6040/j.issn.16719352.0.2017.190
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522
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This paper proposes the attribute reduction in the attribute threeway consistent formal decision context, which preserves irredundant rules information without loss for AEconcept lattices. For this purpose, the related properties in subcontext of a formal context are discussed. Then based on them, the set of irredundant rules consistent in the attribute threeway consistent formal decision context is defined, and the corresponding judgment theorems of the set of irredundant rules consistent is obtained. Finally, the methods to find these reductions by discernibility matrix and discernibility function are presented.
Design and implementation of P2Pbased network measurement cloud platform
ZHAO Guangyuan, QIN Fenglin, GUO Xiaodong
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(12): 104110. doi:
10.6040/j.issn.16719352.0.2017.358
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This paper proposes the concept, architecture and principles of Network Measurement as a Service(NMaaS)based on the analysis of the weak points of existing measurement systems. The architecture design and key technology of a P2Pbased network measurement cloud platform are studied. And its implementation supports the dynamic awareness of network quality of service and user quality of experience. A typical application scenario is finally presented to demonstrate the effectiveness of the system.