Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
01
Generalized numerical ranges of matrix polynomials
789
803
EN
G.
Aghamollaei
Shahid Bahonar University of Kerman, Kerman, Iran
aghamollaei@uk.ac.ir
N.
Avizeh
Shahid Bahonar University of Kerman, Kerman, Iran
avizeh_narjes@yahoo.com
Y.
Jahanshahi
Shahid Bahonar University of Kerman, Kerman, Iran
yaser_j1986@yahoo.com
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
matrix polynomial,C-numerical range,Joint C-numerical range,C-spectrum
http://bims.iranjournals.ir/article_443.html
http://bims.iranjournals.ir/article_443_674a1b7f8ad80f809ad9ae7135dde7f9.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
A new proof for the Banach-Zarecki theorem: A light
on integrability and continuity
805
819
EN
A.
Mahdipour Shirayeh
Postdoctoral Researcher, Brock University, Canada
ali.mahdipour@gmail.com
H.
Eshraghi
Assistant Professor, Iran University of Science and Technology
eshraghi@iust.ac.ir
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuous and of bounded variation when itsatisfies Lusin's condition. In the present proof indeed a moregeneral result is obtained for the Jordan decomposition of $F$.
Banach-Zarecki theorem,Radon-Nikodym theorem,Lusin's condition
http://bims.iranjournals.ir/article_444.html
http://bims.iranjournals.ir/article_444_c68c238e1dfeb0e5bc9a083db174fee9.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
On a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations
821
840
EN
S.
Heidarkhani
Razi university of Kermanshah
s.heidarkhani@razi.ac.ir
Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.
Sturm-Liouville type System,Multiplicity results,Critical point theory
http://bims.iranjournals.ir/article_445.html
http://bims.iranjournals.ir/article_445_696e71ccb7bc3450096d4b5d2c3603ef.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Some combinatorial aspects of finite Hamiltonian groups
841
854
EN
M.
Tarnauceanu
Faculty of Mathematics, "Al. I. Cuza" University
tarnauc@uaic.ro
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite Hamiltonian group.
Hamiltonian groups,Abelian groups,automorphisms,subgroups,subgroup coverings
http://bims.iranjournals.ir/article_446.html
http://bims.iranjournals.ir/article_446_709d30bd2ac8176682140ee62d6a4254.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
01
Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations
855
864
EN
M.
Jahanshahi
Azarbaijan university of Tarbiat Moallem
jahanshahi@azaruniv.edu
M.
Sajjadmanesh
Azarbaijan university of Tarbiat Moallem
s.sajjadmanesh@azaruniv.edu
In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and boundary conditions of main problem, analytic solution of unknown function of main inverse problem is calculated.
Local boundary conditions,Inverse problem,Fundamental solution,Dirac's delta function
http://bims.iranjournals.ir/article_447.html
http://bims.iranjournals.ir/article_447_4872092001e98d09eefc38bf2ce9a651.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Linear preservers of g-row and g-column majorization on
M_{n,m}
865
880
EN
A.
Armandnejad
Vali-e-Asr University of Rafsanjan
armandnejad@gmail.com
Z.
Mohammadi
Vali-e-Asr University of Rafsanjan
z.mohammadi@stu.vru.ac.ir
F.
Akbarzadeh
Vali-e-Asr University of Rafsanjan
f.akbarzadeh@stu.vru.ac.ir
Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, if every row (respectively column) of B, is g-majorized by the corresponding row (respectively column) of A. In this paper all kinds of g-majorization are studied on Mn,m, and the possible structure of their linear preservers will be found. Also all linear operators T : Mn,m ---> Mn,m preserving (or strongly preserving) g-row or g-column majorization will be characterized.
Linear preserver,g-row stochastic matrices,rgw-majorization,lgw-majorization
http://bims.iranjournals.ir/article_448.html
http://bims.iranjournals.ir/article_448_1a08baec65b24a4816d12f8601a75dd7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Tutte polynomials of wheels via generating functions
881
891
EN
C.
Brennan
University of the Witwatersrand
charlotte.brennan@wits.ac.za
T.
Mansour
University of Haifa
toufik@math.haifa.ac.il
E.
Mphako-Banda
University of Witwatersrand
eunice.mphako-banda@wits.ac.za
We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
Tutte polynomial,wheel,fan,generating function
http://bims.iranjournals.ir/article_449.html
http://bims.iranjournals.ir/article_449_8f1dce2d9821f65d9680e61e1825f866.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
A degree bound for the Graver basis of non-saturated lattices
893
901
EN
H.
Sabzrou
Assistant Professor of University of Tehran
hossein@ipm.ir
Let $L$ be a lattice in $ZZ^n$ of dimension $m$. We prove that there exist integer constants $D$ and $M$ which are basis-independent such that the total degree of any Graver element of $L$ is not greater than $m(n-m+1)MD$. The case $M=1$ occurs precisely when $L$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show that the Castelnuovo-Mumford regularity of the corresponding lattice ideal $I_L$ is not greater than $rac{1}{2}m(n-1)(n-m+1)MD$.
Non-saturated lattices,Graver bases,lattice ideals
http://bims.iranjournals.ir/article_450.html
http://bims.iranjournals.ir/article_450_c921d0b4177605ebd0c5e86cc49f45eb.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Applications of Epi-Retractable and Co-Epi-Retractable Modules
903
917
EN
H.
Mostafanasab
Isfahan university of Technology
h.mostafanasab@gmail.com
A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.
MSC(2010): Primary: 16D10, 16S50,Secondary: 16D40, 16E60
http://bims.iranjournals.ir/article_451.html
http://bims.iranjournals.ir/article_451_a85b04c9d7350c032000bab9ef5951af.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
On Generalization of prime submodules
919
939
EN
M.
Ebrahimpour
Shahid Bahonar University Of Kerman
mahdieh_ebrahimpour@yahoo.com
R.
Nekooei
Shahid Bahonar University of Kerman
rnekooei@mail.uk.ac.ir
Let R be a commutative ring with identity and M be a unitary R-module. Let : S(M) −! S(M) [ {;} be a function, where S(M) is the set of submodules ofM. Suppose n 2 is a positive integer. A proper submodule P of M is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 R and x 2 M and a1 . . . an−1x 2P(P), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x 2 Por a1 . . . an−1 2 (P : M). In this paper we study (n − 1, n) − -prime submodules(n 2). A number of results concerning (n−1, n)−-prime submodules are given.Modules with the property that for some , every proper submodule is (n−1, n)−-prime, are characterized and we show that under some assumptions (n−1, n)-primesubmodules and (n − 1, n) − m-prime submodules coincide (n,m 2).
(n − 1, n) − prime submodule,Local ring,multiplication module
http://bims.iranjournals.ir/article_452.html
http://bims.iranjournals.ir/article_452_42eb5d8e97c6430058365474fa12dd8f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
01
POS-groups with some cyclic Sylow
subgroups
941
957
EN
R.
Shen
Department of Mathematics, Hubei University for Nationalities,
Enshi, Hubei Province, 445000, P. R. China
shenrulin@hotmail.com
W. J.
Shi
wjshi@suda.edu.cn
J.
Shi
LMAM & School of Mathematical Sciences, Peking University,
Beijing, 100871, P. R. China
shi@suda.edu.cn
A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.
perfect order subset,POS-group,Frobenius group
http://bims.iranjournals.ir/article_453.html
http://bims.iranjournals.ir/article_453_d4b01d3e0d15bc7e4701de7239c02219.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
01
Biflatness of certain semigroup algebras
959
969
EN
M.
Essmaili
Kharazmi university (Tarbiat Moallem )
m.essmaili@tmu.ac.ir
A.
Medghalchi
Kharazmi University (Tarbiat Moallem)
medghal2000@yahoo.com
In the present paper, we consider biflatness of certain classes of semigroupalgebras. Indeed, we give a necessary condition for a band semigroup algebra to bebiflat and show that this condition is not sufficient. Also, for a certain class of inversesemigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is equivalent to the biprojectivity of ell^{1}(S).
Biflatness,biprojectivity,semigroup algebras,inverse semigroup
http://bims.iranjournals.ir/article_454.html
http://bims.iranjournals.ir/article_454_f4fa201bf0a879cd7aca81e3b061050e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules
971
992
EN
G.
J.
Song
University of Weifang, P. R. China
sgjshu@yahoo.com.cn
Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the literature.
Hilbert C^{∗}-module,generalized inverse,Operator equation
http://bims.iranjournals.ir/article_455.html
http://bims.iranjournals.ir/article_455_cdee254edff96f8755573457f8b11ff8.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Geodesic metric spaces and generalized nonexpansive multivalued mappings
993
1008
EN
A.
Abkar
Imam Khomeini International University
aliabkar99@gmail.com
M.
Eslamian
Imam Khomeini International University
mhmdeslamian@gmail.com
In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex subset is nonempty and singleton. The results obtained in this paper extend and improve some recent results.
fixed point,generalized nonexpansive mapping,CAT(0) space,geodesic metric space,asymptotic center
http://bims.iranjournals.ir/article_456.html
http://bims.iranjournals.ir/article_456_9a60fdb5fa9a311ab14cfc56137c9f3b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds
1009
1029
EN
R.
Nagaich
Department of Mathematics, Punjabi University,
Patiala 147 002. India
nagaichrakesh@yahoo.co.in
R.
Kumar
University College of Engineering
Punjabi University, Patiala, India
dr_rk37c@yahoo.co.in
S.
Kumar
Department of Applied Sciences, Chitkara University, India
sp7maths@gmail.com
We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.
indefinite Kaehler Manifolds,GCR-lightlike submanifold,totally umbilical
lightlike submanifold
http://bims.iranjournals.ir/article_457.html
http://bims.iranjournals.ir/article_457_30835d587e52fae1944d0dcc1ecbd3ab.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
01
Limit distribution of the degrees in scaled attachment random recursive trees
1031
1036
EN
M.
Javanian
Department of Statistics, Zanjan University, Zanjan, Iran
javanian_m@yahoo.com
We study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor iX_i floor$ where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random variables, with support in [0, 1) and distribution function $F$. By imposing a condition on $F$, we show that the degree of a given node is asymptotically normal.
trees,Recursive trees,Lyapunov's Theorem
http://bims.iranjournals.ir/article_458.html
http://bims.iranjournals.ir/article_458_63e25d39e913e72ed5c4039ad4b7b99d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
39
5
2013
10
15
On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly
1037
1052
EN
J.
Moori
University of North-West, Mafikeng, South Africa
jamshid.moori@nwu.ac.za
T.
Seretlo
University of North-West, Mafikeng, South Africa
thekiso.seretlo@nwu.ac.za
The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated partial character tables of the inertia factor groups, are used to compute a full character table of $overline{G}$. A partial projective character table corresponding to $5^2{:}2A_5$ is required, hence we have to compute the Schur multiplier and projective character table of $5^2{:}2A_5$.
Group extensions,Lyons group,character table,Clifford theory Fischer-Clifford matrices
http://bims.iranjournals.ir/article_459.html
http://bims.iranjournals.ir/article_459_58273f9efd05d9a6da2fc3790b5110c6.pdf