Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Topological centers of the n-th dual of module actions
1
16
EN
K.
Haghnejad Azar
University of Mohghegh Ardabili
A.
Riazi
Amirkabir University of Technology
We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let $mathcal{B}$ be a Banach $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}^{(n)}}(mathcal{A}^{(n)})=mathcal{A}^{(n)}$. We get some conclusions on group algebras.
Arens regularity,bilinear mapping,topological
center
http://bims.iranjournals.ir/article_387.html
http://bims.iranjournals.ir/article_387_cd1a28bd46a6adf2fd6bf0a3fd1322c3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Lie triple derivation algebra of Virasoro-like algebra
17
26
EN
H.
T.
Wang
Hunan University, China
N.
Jing
South China University of Technology, China
Q. G.
Li
Hunan University, China
Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.
Lie derivation,Lie triple derivation,Virasoro-like algebra
http://bims.iranjournals.ir/article_388.html
http://bims.iranjournals.ir/article_388_4ddeb63a9ac76b95a5711ce7787b4f74.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Function spaces of Rees matrix semigroups
27
38
EN
H.
Rahimi
Islamic Azad University, Iran
rahimi@iauctb.ac.ir
We characterize function spaces of Rees matrixsemigroups. Then we study these spaces by using the topologicaltensor product technique.
Semigroup compactification,completely 0-simple
semigroup,topological tensor product
http://bims.iranjournals.ir/article_389.html
http://bims.iranjournals.ir/article_389_a776904facf379b7bc84321bd942fa54.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Construction of a class of trivariate nonseparable compactly
supported wavelets with special dilation matrix
39
54
EN
L.
Lan
Xi'an University of Arts and Science
C.
Zhengxing
Xi'an Jiaotong University
H.
Yongdong
The Northwest Secondly National
College
We present a method for the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 & 0 & 1\end{array}right )$-wavelets under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an example is provided.
http://bims.iranjournals.ir/article_390.html
http://bims.iranjournals.ir/article_390_5971fe402882bf91ce2224f6141594a0.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On skew Armendariz and skew quasi-Armendariz
modules
55
84
EN
A.
Alhevaz
Tarbiat Modares University
a.alhevaz@yahoo.com
A.
Moussavi
Tarbiat Modares University
moussavi.a@modares.ac.ir
Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$. In this paper we study the relationship between an$R$-module $M_R$ and the general polynomial module $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend theclasses of non-reduced skew-Armendariz modules. An equivalentcharacterization of an $alpha$-skew Armendariz module is given.Some properties of this generalization are established, andconnections of properties of a skew-Armendariz module $M_R$ withthose of $M[x]_{R[x;alpha,delta]}$ are investigated. As aconsequence we extend and unify several known results related toArmendariz modules.
http://bims.iranjournals.ir/article_391.html
http://bims.iranjournals.ir/article_391_faa8203cae36d2ab955dfe7cff11023e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Compact composition operators on certain analytic Lipschitz spaces
85
99
EN
H.
Mahyar
Kharazmi University
A.
H.
Sanatpour
Kharazmi University
We investigate compact composition operators on ceratin Lipschitzspaces of analytic functions on the closed unit disc of the plane.Our approach also leads to some results about compositionoperators on Zygmund type spaces.
Compact operators,Bloch type spaces,Zygmund type
spaces,analytic Lipschitz spaces,differentiable Lipschitz
spaces
http://bims.iranjournals.ir/article_392.html
http://bims.iranjournals.ir/article_392_68613fe870e50c12191861e98cadfcf1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On a decomposition of Hardy--Hilbert's type inequality
101
112
EN
R.
Lashkaripour
University of Sistan and Baluchestan
A.
Moazzen
University of Sistan and Baluchestan
In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.
Hilbert's inequality,Hilbert-type inequality,integral inequality
http://bims.iranjournals.ir/article_393.html
http://bims.iranjournals.ir/article_393_590b376cd7b26b3fc6a94b9b95691cb4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On co-Noetherian dimension of rings
113
122
EN
A.
Haghany
Isfahan University of Technology
aghagh@cc.iut.ac.ir
M.
R.
Vedadi
Isfahan University of Technology
mrvedadi@cc.iut.ac.ir
We define and studyco-Noetherian dimension of rings for which the injective envelopeof simple modules have finite Krull-dimension. This is a Moritainvariant dimension that measures how far the ring is from beingco-Noetherian. The co-Noetherian dimension of certain rings,including commutative rings, are determined. It is shown that the class ${mathcal W}_n$ of rings with co-Noetherian dimension $leqn$ is closed under homomorphic images and finite normalizingextensions, and that for each $n$ there exist rings withco-Noetherian dimension $n$. The possible relations between Krull and co-Noetherian dimensions are investigated, and examples are provided to show that these dimensions are independent of eachother.
Co-Noetherian,finitely cogenerated,Krull dimension,normalizing extension
http://bims.iranjournals.ir/article_394.html
http://bims.iranjournals.ir/article_394_22246e6a6d66013fdfd1ed4b2e6cbbf3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On topological transitive maps on operator algebras
123
130
EN
H.
Rezaei
University of Yasouj
rezaei@mail.yu.ac.ir
We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.
Hypercyclic operator,transitive map,strong operator topology
http://bims.iranjournals.ir/article_395.html
http://bims.iranjournals.ir/article_395_7f397c884503a656306bf029f5887d11.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Ranks of the common solution to some quaternion matrix equations
with applications
131
157
EN
Q.
Wang
Shanghai University
wqw858@yahoo.com.cn
S.
Yu
East China University of Science and Technology
yushawn@163.com
We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. We give the expressions of such solutions to this systemwhen the solvability conditions are met. Moreover, we presentnecessary and sufficient conditions for the existence of real andcomplex solutions to the system of quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3},A_{4}%XB_{4}=C_{4}$. The findings of this paper extend some known resultsin the literature.
Quaternion matrix equation,maximal and minimal rank,generalized inverse,real solution,complex solution
http://bims.iranjournals.ir/article_396.html
http://bims.iranjournals.ir/article_396_b3c2a4e18ed3cb578254fb893db94ade.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On Heyting algebras and dual BCK-algebras
159
168
EN
Y.
Yon
Mokwon University
yhyon@mokwon.ac.kr
K.
H.
Kim
Chungju National University
ghkim@cjnu.ac.kr
A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equivalent to an $i$-invariant and $m$-invariant dual $BCK$-semilattices, and show that a commutative Heyting algebra is equivalent to a bounded implicative dual $BCK$-algebra.
Heyting semilattice,Heyting algebra,dual $BCK$-algebra
http://bims.iranjournals.ir/article_397.html
http://bims.iranjournals.ir/article_397_0b7c6a289b3214ec9be3fec521a61f1a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Application of fundamental relations on n-ary polygroups
169
184
EN
S.
Mirvakili
Payame Noor University
saeed mirvakili@yahoo.com
B.
Davvaz
Yazd University
davvaz@yazduni.ac.ir
The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-relation and the $gamma^*$-relation on a given$n$-ary polygroup and obtain some new results and somefundamental theorems in this respect. In particular, we prove that the relation $gamma$ is transitive on an $n$-arypolygroup.
Hypergroup,polygroup,$n$-ary
hypergroup,$n$-ary polygroup,derived $n$-ary subgroup,fundamental relation
http://bims.iranjournals.ir/article_398.html
http://bims.iranjournals.ir/article_398_343a6bc9bb99db6c78480f38fbc278d8.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Bivariate mean value interpolation on circles of the same radius
185
192
EN
Kh.
Rahsepar Fard
University of Qom
rahseparfard@gmail.com
We consider bivariate mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem is described over circles of the same radius and with centers are on astraight line and it is shown that in this case the interpolation is not correct.
Bivariate,correct,mean-value interpolation
http://bims.iranjournals.ir/article_399.html
http://bims.iranjournals.ir/article_399_b95dcaa7d9bc7d748d78d1b8e2d96805.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
k-forested choosability of graphs with bounded maximum average degree
193
201
EN
X.
Zhang
Xidian University
xzhang@xidian.edu.cn
G.
Liu
Shandong University
gzliu@sdu.edu.cn
J.
L.
Wu
Shandong University
jlwu@sdu.edu.cn
A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prove that the $k$-forested choosability of a graph with maximum degree $Deltageq kgeq 4$ is at most $leftlceilfrac{Delta}{k-1}rightrceil+1$, $leftlceilfrac{Delta}{k-1}rightrceil+2$ or $leftlceilfrac{Delta}{k-1}rightrceil+3$ if its maximum average degree is less than $frac{12}{5}$, $frac{8}{3}$ or $3$, respectively.
k-forested coloring,linear coloring,maximum average degree
http://bims.iranjournals.ir/article_400.html
http://bims.iranjournals.ir/article_400_33c983c4321f08451943d77a341f126b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
c-Frames and c-Bessel mappings
203
222
EN
M.
Faroughi
Islamic Azad University
mhfaroughi@yahoo.com
E.
Osgooei
University of Tabriz
Oskouei@yahoo.com
The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which weakly belongs to the null space of the pre-frame operatorof $f$. Also, we prove that composition of pre-frame operator withanalysis operator of two square norm integrable c-Bessel mappingsare trace class operators.
Lebesque integral,Hilbert space,C*-algebra,trace class operator,frame theory
http://bims.iranjournals.ir/article_401.html
http://bims.iranjournals.ir/article_401_8c30c121871d0918061a85cbc216a1ae.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
A variational approach to the problem of oscillations of an
elastic half cylinder
223
240
EN
M.
Hasansoy
Dogus University
mhasansoy@dogus.edu.tr
This paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder. We use variational methods to investigateseveral aspects of propagating waves, including localization (seeFigure 1), existence criteria and the formulas to find them. Weapproach the problem using two complementary methods: Thevariational methods for non-overdamped operator pencils todescribe eigenvalues in definite spectral zones, andLjusternik-Schnirelman critical point theory to investigateeigenvalues in the mixed spectral zone where the classicalvariational theory of operator pencils is not applicable.
Propagating waves,Eigenvalue,variational principle,critical point
http://bims.iranjournals.ir/article_402.html
http://bims.iranjournals.ir/article_402_a5aba3e401d0e7ee3449edaa65081a67.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
01
01
On the existence and uniqueness of solution of initial value problem for fractional order differential equations on time scales
241
252
EN
A.
Ahmadkhanlu
Azarbayjan University of Tarbiat Moallem
s.a.ahmadkhanlu@azaruniv.edu
M.
Jahanshahi
Azarbayjan University of Tarbiat Moallem
jahanshahi@azaruniv.edu
n this paper, at first the concept of Caputo fractionalderivative is generalized on time scales. Then the fractional orderdifferential equations are introduced on time scales. Finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.
Time scales,differential equations,initial value problem,fractional order derivative
http://bims.iranjournals.ir/article_403.html
http://bims.iranjournals.ir/article_403_01350f088186d1293a225495267a033a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
On the stability of generalized derivations on Banach algebras
253
263
EN
E.
Ansari-Piri
University of Guilan
e−ansari@guilan.ac.ir
E.
Anjidani
University of Guilan
ehsan−anjidani@guilan.ac.ir
We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.
Hyers-Ulam-Rassias stability,generalized
derivation,bounded central approximate identity,faithful Banach
algebra
http://bims.iranjournals.ir/article_404.html
http://bims.iranjournals.ir/article_404_995234a601e9852e2877afdf4d4a996d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Non-regularity of multiplications for general measure algebras
265
274
EN
J.
Laali
Kharazmi University
Laali@tmu.ac.ir
M.
Ettefagh
Islamic Azad University
etefagh@iaut.ac.ir
Let $fM(X)$ be the space of all finite regular Borel measures on $X$. A general measure algebra is a subspace of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We find conditionsunder which the Arens regularity of $fL$ implies the compactness of $X$.Weshow that these conditions are necessary.We also present some examples in showing that the new conditions aredifferent from Theorem 3.1 of cite{7}.
http://bims.iranjournals.ir/article_405.html
http://bims.iranjournals.ir/article_405_227f292f58bd40a514de4597f4abbad2.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
38
1
2012
04
01
Extensions of strongly alpha-reversible rings
275
292
EN
L.
Zhao
Nanjing University
lzhao78@gmail.com
X.
Zhu
Nanjing University
zhuxs@nju.edu.cn
We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown that a ring$R$ is strongly right $alpha$-reversible if and only if itspolynomial ring $R[x]$ is strongly right $alpha$-reversible if andonly if its Laurent polynomial ring $R[x, x^{-1}]$ is strongly right$alpha$-reversible. Moreover, we introduce the concept ofNil-$alpha$-reversible rings to investigate the nilpotent elementsin $alpha$-reversible rings. Examples are given to show that rightNil-$alpha$-reversible rings need not be right $alpha$-reversible.
reversible rings,strongly $\alpha$-reversible rings,Nil-$\alpha$-reversible rings,weakly reversible rings
http://bims.iranjournals.ir/article_406.html
http://bims.iranjournals.ir/article_406_9c2daebbe954621c0aa88d44f49c476e.pdf