Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131001Generalized numerical ranges of matrix polynomials789803443ENG. AghamollaeiShahid Bahonar University of Kerman, Kerman, IranN. AvizehShahid Bahonar University of Kerman, Kerman, IranY. JahanshahiShahid Bahonar University of Kerman, Kerman, IranJournal Article20111001In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix <br />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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015A new proof for the Banach-Zarecki theorem: A light
on integrability and continuity805819444ENA. Mahdipour ShirayehPostdoctoral Researcher, Brock University, CanadaH. EshraghiAssistant Professor, Iran University of Science and TechnologyJournal Article20110920To demonstrate more visibly the close relation between the<br />continuity and integrability, a new proof for the Banach-Zarecki<br />theorem is presented on the basis of the Radon-Nikodym theorem<br />which emphasizes on measure-type properties of the Lebesgue<br />integral. The Banach-Zarecki theorem says that a real-valued<br />function $F$ is absolutely continuous on a finite closed interval<br />if and only if it is continuous and of bounded variation when it<br />satisfies Lusin's condition. In the present proof indeed a more<br />general result is obtained for the Jordan decomposition of $F$.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015On a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations821840445ENS. HeidarkhaniRazi university of KermanshahJournal Article20120427Employing a three critical points theorem, we prove the existence of<br />multiple solutions for a class of Neumann two-point boundary value<br />Sturm-Liouville type equations. Using a local minimum theorem for<br />differentiable functionals the existence of at least one non-trivial<br />solution is also ensured.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Some combinatorial aspects of finite Hamiltonian groups841854446ENM. TarnauceanuFaculty of Mathematics, "Al. I. Cuza" UniversityJournal Article20110903In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131001Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations855864447ENM. JahanshahiAzarbaijan university of Tarbiat MoallemM. SajjadmaneshAzarbaijan university of Tarbiat MoallemJournal Article20111225In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Linear preservers of g-row and g-column majorization on
M_{n,m}865880448ENA. ArmandnejadVali-e-Asr University of RafsanjanZ. MohammadiVali-e-Asr University of RafsanjanF. AkbarzadehVali-e-Asr University of RafsanjanJournal Article20111225Let A and B be n × m matrices. The matrix B is <br />said to be g-row majorized (respectively g-column majorized) by <br />A, if every row <br />(respectively column) of B, is g-majorized by the corresponding row <br />(respectively column) of A. In this paper all kinds of g-majorization <br />are studied on Mn,m, and the possible structure of their linear preservers <br />will be found. Also all linear operators T : Mn,m ---> Mn,m <br />preserving (or strongly preserving) g-row or g-column majorization <br />will be characterized.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Tutte polynomials of wheels via generating functions881891449ENC. BrennanUniversity of the WitwatersrandT. MansourUniversity of HaifaE. Mphako-BandaUniversity of WitwatersrandJournal Article20110626We 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015A degree bound for the Graver basis of non-saturated lattices893901450ENH. SabzrouAssistant Professor of University of TehranJournal Article20111013Let $L$ 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 $rac{1}{2}m(n-1)(n-m+1)MD$.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Applications of Epi-Retractable and Co-Epi-Retractable Modules903917451ENH. MostafanasabIsfahan university of TechnologyJournal Article20120604A module M is called epi-retractable if every submodule of M is a homomorphic image of M. <br />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 <br />ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015On Generalization of prime submodules919939452ENM. EbrahimpourShahid Bahonar University Of KermanR. NekooeiShahid Bahonar University of KermanJournal Article20110629Let R be a commutative ring with identity and M be a unitary R-module. Let<br /> : S(M) −! S(M) [ {;} be a function, where S(M) is the set of submodules of<br />M. Suppose n 2 is a positive integer. A proper submodule P of M is called<br />(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 R and x 2 M and a1 . . . an−1x 2<br />P(P), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x 2 P<br />or a1 . . . an−1 2 (P : M). In this paper we study (n − 1, n) − -prime submodules<br />(n 2). A number of results concerning (n−1, n)−-prime submodules are given.<br />Modules with the property that for some , every proper submodule is (n−1, n)−-<br />prime, are characterized and we show that under some assumptions (n−1, n)-prime<br />submodules and (n − 1, n) − m-prime submodules coincide (n,m 2).Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131001POS-groups with some cyclic Sylow
subgroups941957453ENR. ShenDepartment of Mathematics, Hubei University for Nationalities,
Enshi, Hubei Province, 445000, P. R. ChinaW. J. ShiJ. ShiLMAM & School of Mathematical Sciences, Peking University,
Beijing, 100871, P. R. ChinaJournal Article20120413A finite group G is said to be a POS-group if for each x in G the cardinality of <br />the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study <br />the structure of POS-groups with some cyclic Sylow subgroups.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131001Biflatness of certain semigroup algebras959969454ENM. EssmailiKharazmi university (Tarbiat Moallem )A. MedghalchiKharazmi University (Tarbiat Moallem)Journal Article20101218In the present paper, we consider biflatness of certain classes of semigroup<br /><br />algebras. Indeed, we give a necessary condition for a band semigroup algebra to be<br /><br />biflat and show that this condition is not sufficient. Also, for a certain class of inverse<br /><br />semigroups S, we show that the biflatness of ell^{1}(S)^{primeprime} is <br /><br />equivalent to the biprojectivity of ell^{1}(S).Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules971992455ENG. J.SongUniversity of Weifang, P. R. ChinaJournal Article20110702Some necessary and sufficient <br />conditions are given for the existence of a G-positive <br />(G-repositive) solution to adjointable operator equations <br />$AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert <br />$C^{ast}$-modules, respectively. Moreover, the expressions of these <br />general G-positive (G-repositive) solutions are also derived. Some <br />of the findings of this paper extend some known results in the <br />literature.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Geodesic metric spaces and generalized nonexpansive multivalued mappings9931008456ENA. AbkarImam Khomeini International UniversityM. EslamianImam Khomeini International UniversityJournal Article20120102In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds10091029457ENR. NagaichDepartment of Mathematics, Punjabi University,
Patiala 147 002. IndiaR. KumarUniversity College of Engineering
Punjabi University, Patiala, IndiaS. KumarDepartment of Applied Sciences, Chitkara University, IndiaJournal Article20111207We obtain the expression of Ricci tensor for a $GCR$-lightlike<br />submanifold of indefinite complex space form and discuss its<br />properties on a totally geodesic $GCR$-lightlike submanifold of an<br />indefinite complex space form. Moreover, we have proved that every<br />proper totally umbilical $GCR$-lightlike submanifold of an<br />indefinite Kaehler manifold is a totally geodesic $GCR$-lightlike<br />submanifold.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131001Limit distribution of the degrees in scaled attachment random recursive trees10311036458ENM. JavanianDepartment of Statistics, Zanjan University, Zanjan, IranJournal Article20120519We study the limiting distribution of the degree of a <br />given node in a scaled attachment random recursive tree, a <br />generalized random recursive tree, which is introduced by Devroye <br />et. al (2011). In a scaled attachment random recursive tree, every <br />node $i$ is attached to the node labeled $lfloor iX_i <br />floor$ <br />where $X_0$, $ldots$ , $X_n$ is a sequence of i.i.d. random <br />variables, with support in [0, 1) and distribution function $F$. <br />By imposing a condition on $F$, we show that the degree of a given <br />node is asymptotically normal.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39520131015On the Fischer-Clifford matrices of a maximal subgroup of the Lyons group Ly10371052459ENJ. MooriUniversity of North-West, Mafikeng, South AfricaT. SeretloUniversity of North-West, Mafikeng, South AfricaJournal Article20120618The 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 $5^2{:}2A_5$.