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20 October 2016
Volume 51 Issue 10
Boundedness of the parameterized Marcinkiewicz integral operators with variable kernels on weighted Campanato spaces
HUANG Lingling, ZHAO Kai
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 15. doi:
10.6040/j.issn.16719352.0.2016.037
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Based on the results of the boundedness of parameterized Marcinkiewicz integral operators on weighted
L
^{p}
spaces, by using the estimates of classical inequalities and the properties of the weighted Campanato spaces, the boundedness of the parameterized Marcinkiewicz integral operators
μ
^{ρ}
_{Ω}
with variable kernel on weighted Campanato and BMO spaces is obtained.
Lipschitz commutators of fractional integrals on Herztype spaces with variable exponents
WANG Jinping, ZHAO Kai
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 610. doi:
10.6040/j.issn.16719352.0.2016.128
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449
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By the boundedness of commutators for fractional integrals with Lipschitz functions and the Riesz potential on variable Lebesgue spaces, based on the atomic decomposition of Herztype Hardy spaces with variable exponents, using the properties of Lipschitz functions and the estimations of the classical inequalities, we proved that the Lipschitz commutators of fractional integrals are bounded from Herztype Hardy spaces with variable exponents to variable Herz spaces.
The average error of linear tensor product multivariate polynomial interpolation based on Chebyshev nodes on the Brownian sheet measure
XIONG Liyan, XU Guiqiao
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 1115. doi:
10.6040/j.issn.16719352.0.2015.541
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394
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Based on univariate Lagrange polynomial interpolation, a kind of linear tensor product polynomial interpolation is constructed to approximate multivariate functions. For the weighted
L
_{}
2
norm,their average errors is studied on the Brownian sheet measure and obtained the corresponding stronger asymptotic order. Compared with the past algorithms based on linear functional information, our algorithms are based on standard information and it is constructive. It can also be applied to solve practical problems. From the perspective of average error, it is showed that algorithms are order optimal to the univariate function case setting, and have a similar approximation order to the optimal algorithms based on linear functional information to the multivariate function case setting.
Generalized nil
α
skew Armendariz rings
LIU Dajun, WU Jun, YANG Suyun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 1621. doi:
10.6040/j.issn.16719352.0.2015.626
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540
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The notion of a generalized nil
α
skew Armendariz ring is introduced, and this article also obtain some basic properties of such rings.
On covers of S acts
LI Huanyun, QIAO Husheng
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 2227. doi:
10.6040／j.issn.1671.9352.0.2016.037
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421
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Let S be a monoid, FGWI, WPF and STF denote the class of finitely generated weakly injective right S acts, weakly pullback flat right S acts and strongly torsion free right Sacts respectively. It is proved that if S is a left reversible monoid with a left zero, then every rightS actAi∈FGWI if and only if the coproduct ∪[DD(*3]·[DD)]i∈IAi∈FGWI. IfS is a Noetherian monoid, then the directed colimit of fgweakly injective Sacts is fgweakly injective. At the same time, WPF covers and STF covers are investigated, the condition over which every right Sact has a FGWI cover is obtained. It is proved that every right Sact has a WPF cover over a finitely generated monoid with a finite geometric type and every right Sact has a STFcover over any monoid S.
Quasidimodule algebras over Hopf quasigroups and YetterDrinfeld quasimodule algebras
WU Zijuan, CHEN Yuanyuan, ZHANG Liangyun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 2833. doi:
10.6040/j.issn.16719352.0.2016.031
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A sufficient and necessary condition for a Long skew Hopf quasigroup to be a quasidimodule algebra is given, and the relation between the braided Hopf quasigroup and the YetterDrinfeld quasimodule algebra is studied. At the end, the quantization of Long skew Hopf quasigroups is constructed by Harrison 2cocycle, and the conclusion for a quantized Long skew Hopf quasigroup to be a quasidimodule algebras is proved.
Meromorphic solutions of a type of system of complex difference equations
LIU Manli, GAO Lingyun
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 3440. doi:
106040／j.issn.16719352.0.2015628
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303
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The method of Nevanlinna value distribution theory concerning meromorphic functions is used, a problem for the existence of meromorphic solutions on a type of system of complex difference equations and the form about a type of system of complex difference equations are investigated. Under the assumption restricted to certain proper conditions, two results about the type of system of complex difference equations are obtained, and some examples show that the results are precise.
Cauchy problem for nonlinear parabolic equation systems with initial data measures
SONG Mengmeng, SHANG Haifeng
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 4147. doi:
10.6040/j.issn.16719352.0.2015.613
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535
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The Cauchy problem for a class of degenerate parabolic system with strongly coupling source is studied, where initial data are measured. When the known parameters satisfy some conditions, the difficulties are avoided which come from the interactions between the degeneracy of the principal and the strongly coupling source, and the existence of solutions is obtained. Moreover, it is proved that these conditions are optimal for the existence of solutions.
Multiplicity of solutions for Kirchhoff type equation involving the
p(x)
biharnonic operator
ZHANG Shengui
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 4853. doi:
10.6040/j.issn.16719352.0.2015.309
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374
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A class of Kirchhoff type equation involving the
p(x)
biharnonic operator is ivestigated. By using fountain theorem in critical point theory, some sufficient conditions for the existence of multiplicity of solutions are obtained, which generalize and improve some existing resuls.
On the 2harmonic timelike submanifolds in locally symmetric pseudoriemannian manifolds
HE Chao, LI Ying, SONG Weidong
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 5458. doi:
10.6040/j.issn.16719352.0.2015.496
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399
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Based on the moving frames, the 2harmonic timelike submanifolds in locally symmetric pseudoRiemannian manifolds is studied. Also, an integral inequality of Simonss type and a pinching theorem about the squared norm of the second fundamental form in this submanifolds are obtained.
Two results on Chens inequalities for spacelike submanifolds of a pseudoRiemannian space form
SU Man, ZHANG Liang
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 5964. doi:
10.6040/j.issn.16719352.0.2015.505
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410
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The equality case of the inequality which concerns Chens
δ
invariant
δ
_{M}
for spacelike submanifolds of a pseudoRiemannian space form. Then the inequality involving the generalized
δ
invariant
δ(n
_{}
1
,…,n
_{k}
)
is generalized. Moreover, some examples are provided which satisfy the inequality.
A class of trigonometric Bézier curve and surface which satisfy
G
^{2}
continuity
LIU Huayong, XIE Xinping, LI Lu, ZHANG Daming, WANG Huanbao
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 6571. doi:
10.6040/j.issn.16719352.0.2015.429
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In order to meet the relatively high smooth jointing in relatively simple conditions, at the same time we can also modify the shape of curve and surface under without changing the control points, and then a group of low order trigonometric Bézier basis function with two shape parameters was constructed. Based on the group of basic functions, a class of curve and surface of arbitrary order trigonometric Bézier is defined by trigonometric function. The basic properties of the curves are discussed, and the conditions of the smooth blending of curves and surfaces are also discussed. According to the blending condition, the combination curves and surfaces of the piecewise smooth curves can be constructed. The blending curves and surfaces will not be changed the continuity of curve and surface by modifying the control points and parameters of the method and automatically meet with the
G
^{2}
continuity and simple calculation. The results of numerical examples show the effectiveness of this method.
The characteristic polynomials of the graphical arrangements corresponding to the simplyconnected polygons
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 7277. doi:
10.6040/j.issn.16719352.0.2015.569
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The graphical arrangements are the arrangements relative to graphs. The definitions of simplyconnected and pointconnected of the polygons were given, the characteristic polynomials of the graphical arrangements corresponding to the simplyconnected polygons were studied, and the specific forms of the characteristic polynomials were obtained. By using the concrete example, the effect on the intersection relationships of the hyperplanes in an arrangement by the different connection methods or the different sequential manners of the polygons was pointed out.
Disturbing fuzzy ideals of BLalgebras
PENG Jiayin
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(10): 7894. doi:
10.6040/j.issn.16719352.0.2016.123
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Utilizing the notion of disturbing fuzzy sets, the properties of disturbing fuzzy ideals of BLalgebras are investigated. The concept of disturbing fuzzy ideal is introduced and its several properties are studied. A quotient BLalgebra via a disturbing fuzzy ideal is constructed, and the disturbing fuzzy homomorphism fundamental theorem is given. Moreover, a procedure to generate a disturbing fuzzy ideal is given by a disturbing fuzzy set. Some classes of disturbing fuzzy ideals are defined and the relations of them are investigated. Some characterizations of disturbing fuzzy Boolean ideals, disturbing fuzzy prime ideals, disturbing fuzzy irreducible ideals, disturbing fuzzy ultra ideals, disturbing fuzzy Godel ideals are established.