Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$13471372569ENL.HengxingSchool of Mathematics and Statistics,Wuhan University, Wuhan,
assistance professorL. JingwenSchool of Mathematics and Statistics, Wuhan University, P.O. Box 430072, Wuhan, People's Republic of ChinaJournal Article20120316For singularities $fin K[[x_{1},ldots,x_{n}]]$ over an algebraically closed field $K$ of arbitrary characteristic, we introduce the finite $\mathcal{S}-$determinacy under $\mathcal{S}-$equivalence, where $\mathcal{S}=\mathcal{R}_{\mathcal{G}},~\mathcal{R}_{\mathcal{A}}, ~\mathcal{K}_{\mathcal{G}},~\mathcal{K}_{\mathcal{A}}$. It is proved that the finite $\mathcal{R}_{\mathcal{G}}(\mathcal{K}_{\mathcal{G}})-$determinacy is equivalent to the finiteness of the relative $\mathcal{G}-$Milnor ($\mathcal{G}-$Tjurina) number and the finite $\mathcal{R}_{\mathcal{A}}(\mathcal{K}_{\mathcal{A}})-$determinacy is equivalent to the finiteness of the relative $\mathcal{A}-$Milnor ($\mathcal{A}-$Tjurina) number. Moreover, some estimates are provided on the degree of the $\mathcal{S}-$determinacy in positive characteristic.http://bims.iranjournals.ir/article_569_8b16ebc056e613024c057be590b542eb.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Translation invariant surfaces in the 3-dimensional Heisenberg group13731385570END. W.YoonGyeongsang National UniversityJ. W.LeeUniversity of Missouri-ColumbiaJournal Article20130402In this paper, we study translation invariant surfaces in the <br />3-dimensional Heisenberg group $rm Nil_3$. In particular, we <br />completely classify translation invariant surfaces in $rm Nil_3$ <br />whose position vector $x$ satisfies the equation $Delta x = Ax$, <br />where $Delta$ is the Laplacian operator of the surface and $A$ <br />is a $3 times 3$-real matrix.http://bims.iranjournals.ir/article_570_a86c450b76fb8c371afead6410d55534.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201On the possible volume of $\mu$-$(v,k,t)$ trades13871401571ENS.RashidiAlzahra UniN.SoltankhahAlzahra Uni.Journal Article20121215A $\mu$-way $(v,k,t)$ $trade$ of volume $m$ consists of $\mu$ disjoint collections $T_1$, $T_2, \dots T_{\mu}$, each of $m$ blocks, such that for every $t$-subset of $v$-set $V$ the number of blocks containing this t-subset is the same in each $T_i (1\leq i \leq \mu)$. In other words any pair of collections $\{T_i,T_j\}$, $1\leq i< j \leq \mu$ is a $(v,k,t)$ trade of volume $m$. In this paper we investigate the existence of $\mu$-way $(v,k,t)$ trades and prove the existence of: (i)~3-way $(v,k,1)$ trades (Steiner trades) of each volume $m,m\geq2$. (ii) 3-way $(v,k,2)$ trades of each volume $m,m\geq6$ except possibly $m=7$. We establish the non-existence of 3-way $(v,3,2)$ trade of volume 7. It is shown that the volume of a 3-way $(v,k,2)$ Steiner trade is at least $2k$ for $k\geq4$. Also the spectrum of 3-way $(v,k,2)$ Steiner trades for $k=3$ and 4 are specified.http://bims.iranjournals.ir/article_571_c9892a989183de32e976c6f04e700201.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Fekete-Szegö coefficient functional for transforms of universally prestarlike functions14031411572ENT. N. ShanmugamAnna University,
Chennai.J. LourthuMaryAnna UniversityJournal Article20120528Universally prestarlike functions of order $alphaleq 1$ in the <br />slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been <br />recently introduced by S. Ruscheweyh.This notion generalizes the <br />corresponding one for functions in the unit disk $Delta$ (and <br />other circular domains in $mathbb{C}$). In this paper, we obtain <br />the Fekete-Szegö coefficient functional for transforms of such <br />functions.http://bims.iranjournals.ir/article_572_e6b4b2a746ed40e1af829d1fa82daa10.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201On the planarity of a graph related to the join of subgroups of a finite group14131431573ENB.TaeriIsfahan University of TechnologyH.AhmadiIsfahan University of TechnologyJournal Article20130422Let $G$ be a finite group which is not a cyclic $p$-group, $p$ a prime number. <br />We define an undirected simple graph $Delta(G)$ whose <br />vertices are the proper subgroups of $G$, which are not contained in the <br />Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge <br />if and only if $G=langle H , Krangle$. In this paper we classify finite groups with planar graph. <br />%For this, by Kuratowski's Theorem, we have to study subdivisions <br />%of the Kuratowski graphs $K_{3 , 3}$ and $K_5$ in the graph $Delta(G)$. <br />Our result shows that only few groups have planar graphs.http://bims.iranjournals.ir/article_573_e5f6ad6ce374177eef023bf5d0c018b6.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Some properties of a general integral operator14331439574ENLStanciuUniversity of PitestiD.Breaz"1 Decembrie 1918" University of Alba IuliaJournal Article20111010In this paper, we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $\mathcal{S}^{*}(\alpha),$ $\mathcal{K}(\alpha),$ $\mathcal{M}(\beta),$ $\mathcal{N}(\beta)$ and $\mathcal{KD}(\mu,\beta).$http://bims.iranjournals.ir/article_574_f0e52b27a7a5d6a1a87373dffa53dbe5.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201On special submodule of modules14411451575ENAKhaksariiranianS.MehriBuali sina UniversityR.SafakishiranianJournal Article20121226Let $R$ be a domain with quotiont field $K$, and <br />let $N$ be a submodule of an $R$-module $M$. We say that $N$ is <br />powerful (strongly primary) if $x,yin K$ and <br />$xyMsubseteq N$, then $xin R$ or $yin R$ ($xMsubseteq N$ <br />or $y^nMsubseteq N$ for some $ngeq1$). We show that a submodule <br />with either of these properties is comparable to every prime <br />submodule of $M$, also we show that an $R$-module $M$ admits a <br />powerful submodule if and only if it admits a strongly primary <br />submodule. Finally we study finitely generated torsion free <br />modules over domain each of whose prime submodules are strongly <br />primary.http://bims.iranjournals.ir/article_575_ffeabd223de0d4eacb9a3e6e53e5448d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201On the character space of vector-valued Lipschitz algebras14531468576ENT.HonaryKharazmi UniversityA.NikouKharazmi UniversityA. H.SanatpourKharazmi UniversityJournal Article20130304We show that the character space of the <br />vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order <br />$alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in <br />the product topology, where $X$ is a compact metric space and $E$ <br />is a unital commutative Banach algebra. We also characterize the <br />form of each character on $Lip^{alpha}(X, E)$. <br /> <br />By appealing to the injective tensor product, we then identify the <br />character space of the vector-valued polynomial Lipschitz algebra <br />$Lip_P^{alpha}(X, E)$, generated by the polynomials on the <br />compact space $Xsubseteq Bbb{C}^{n}$. It is also shown that <br />$Lip_P^{alpha}(X, E)$ is the injective tensor product <br />$Lip_P^{alpha}(X)widehat{otimes}_epsilon E$. <br /> Finally, we characterize the form of each character on $Lip_{P}^{alpha}(X, E)$.http://bims.iranjournals.ir/article_576_a7aeed74714116f3b292a982238f83d2.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Generalized multivalued $F$-contractions on complete metric spaces14691478577ENÖ.AcarKirikkale UniversityG.DurmazKirikkale UniversityGMinakKirikkale UniversityJournal Article20130709In the present paper, we introduce the concept of generalized multivalued $F$ <br />-contraction mappings and give a fixed point result, which is a proper <br />generalization of some multivalued fixed point theorems including Nadler's.http://bims.iranjournals.ir/article_577_fde9264cf376fffe2ee4ddf4a988880d.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Domination number of graph fractional powers14791489578ENM. N.IradmusaShahid Beheshti UniversityJournal Article20130101For any $k \in \mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{\frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by $G^{\frac{m}{n}}$. In this regard, we investigate domination number and independent domination number of fractional powers of graphs.http://bims.iranjournals.ir/article_578_a8849b052492b5106526b2331e526138.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201The locating chromatic number of the join of graphs14911504580ENA.BehtoeiIsfahan university of techmologyJournal Article20120504Let $f$ be a proper $k$-coloring of a connected graph $G$ and <br />$Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into <br />the resulting color classes. For a vertex $v$ of $G$, the color <br />code of $v$ with respect to $Pi$ is defined to be the ordered <br />$k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$, <br />where $d(v,V_i)=min{d(v,x):~xin V_i}, 1leq ileq k$. If <br />distinct vertices have distinct color codes, then $f$ is called a <br />locating coloring. The minimum number of colors needed in a <br />locating coloring of $G$ is the locating chromatic number of $G$, <br />denoted by $Cchi_{{}_L}(G)$. In this paper, we study the locating chromatic number of the join of graphs. We show that when $G_1$ and $G_2$ are two connected graphs with diameter at most two, then $Cchi_{{}_L}(G_1vee G_2)=Cchi_{{}_L}(G_1)+Cchi_{{}_L}(G_2)$, where $G_1vee G_2$ is the join of $G_1$ and $G_2$. Also, we determine the <br />locating chromatic number of the join of paths, cycles and complete multipartite graphs.http://bims.iranjournals.ir/article_580_069d3bb002acd8d7dd095917f9efe4cb.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201A generalization of Villarreal's result for unmixed tripartite graphs15051514581ENH.HaghighiK. N. Toosi University of TechnologyJournal Article20130508In this paper we give a characterization of unmixed tripartite <br />graphs under certain conditions which is a generalization of a <br />result of Villarreal on bipartite graphs. For bipartite graphs two <br />different characterizations were given by Ravindra and Villarreal. <br />We show that these two characterizations imply each other.http://bims.iranjournals.ir/article_581_c6e19e830859f2cb9f7c8f8cacb8d2a6.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201A note on the remainders of rectifiable spaces15151526582ENJ.ZhangNanjing Normal UniversityWeiHeNanjing Normal UniversityL.XieWuyi UniversityJournal Article20130409In this paper, we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces, and how the character of the remainders affects the character
and the size of a rectifiable space. Some results in [A. V. Arhangel'skii and J. Van Mill, On topological groups with a first-countable remainder, Topology Proc. 42 (2013) 157--163.] and [F. C. Lin, C. Liu, S. Lin, A note on rectifiable spaces, Topology Appl. 159 (2012), no. 8, 2090--2101.] are improved, respectively.http://bims.iranjournals.ir/article_582_46922a0880a8f11f8f69cbb52b1396be.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Arens regularity of inverse semigroup algebras15271538583ENF.AbtahiUniversity of IsfahanB.KhodsianiUniversity of IsfahanA.RejaliUniversity of IsfahanJournal Article20130411We present a characterization of Arens regular semigroup algebras
$\ell^1(S)$, for a large class of semigroups. Mainly, we show that
if the set of idempotents of an inverse semigroup $S$ is finite,
then $\ell^1(S)$ is Arens regular if and only if $S$ is finite.http://bims.iranjournals.ir/article_583_9ad6aaed513b73148b7d49f70afcfb32.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator15391551584ENT.SeoudyDepartment of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt.Journal Article20121024In this paper we obtain coefficient characterization, extreme points and <br />distortion bounds for the classes of harmonic $p-$valent functions <br />defined by certain modified operator. Some of our results improve <br />and generalize previously known results.http://bims.iranjournals.ir/article_584_f5deaeeae1538fb6c45901d524ee2f98.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems15531571585ENB. P.AllahverdievDepartment of Mathematics, Suleyman Demirel University, 32260 Isparta, TurkeyJournal Article20130628In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a selfadjoint dilation of the dissipative operator and construct the incoming and outgoing spectral representations that makes it possible to determine the scattering function (matrix) of the dilation. Further a functional model of the dissipative operator and its characteristic function in terms of the Weyl function of a selfadjoint operator are constructed. Finally we show that the system of root vectors of the dissipative operators are complete in the Hilbert space ℓ_{Ω}²(Z;C²).http://bims.iranjournals.ir/article_585_a9a1d5317a33ae8cef33961c34144f84.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40620141201Pairwise non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups15731585586ENS.FouladiAcademic StaffJournal Article20130801Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements <br />if any two distinct elements of $X$ do not commute. In this paper <br />we determine the maximum size of these subsets in any finite <br />non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.http://bims.iranjournals.ir/article_586_605ff764c617d3cd28dbbdd72be8f9a2.pdf