فهرست مطالب

Bulletin of Iranian Mathematical Society
Volume:40 Issue: 6, 2014

  • تاریخ انتشار: 1393/10/03
  • تعداد عناوین: 17
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  • H. Hiu_LÝ. Ý Jingwen Pages 1347-1372
    ‎For 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 $mathca {S}-$equivalence‎, ‎where $mathcal{S}=mathcal{R}_{mathcal{G}},~mathcal{R}_{mathca {A}}‎, ‎~mathcal{K}_{mathcal{G}},~mathcal{K}_{mathcal{A}}$.‎ ‎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.
    Keywords: Finite $mathcal{R}, {mathcal{G}}~(mathcal{R}, {mathcal{A}}), $determinacyý, ýfinite $mathcal{K}, {mathcal{G}}~(mathcal{K}, {mathcal{A}}), $ determinacyý, ýthe relative $mathcal{G}(mathcal{A}), $Milnor numberý, ýrelative $mathcal{G}(mathcal{A}), $ Tjurina numberý
  • D. W. Yoon, J. W. Lee Pages 1373-1385
    ‎In this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional Heisenberg group $rm Nil_3$‎. ‎In particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm Nil_3$‎ ‎whose position vector $x$ satisfies the equation $Delta x = Ax$‎, ‎where $Delta$ is the Laplacian operator of the surface and $A$‎ ‎is a $3 times 3$-real matrix‎.
    Keywords: Heisenberg groupý, ýfinite type surfaceý, ýinvariantý ýsurfaceý
  • S. Rashidi, N. Ýsoltankhah Pages 1387-1401
    ‎A $mu$-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 $T_i (1leq‎ ‎ileq mu)$‎. ‎In other words any pair of collections ${T_i,T_j}$‎, ‎$1leq i‎In 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 $m,mgeq2$‎. ‎(ii) 3-way $(v,k,2)$ trades of‎ ‎each volume $m,mgeq6$ 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 ‎$kgeq4$‎. ‎Also the spectrum of 3-way $(v,k,2)$ Steiner trades for‎ ‎$k=3$ and 4 are specified‎.
    Keywords: $mu$, way $(v, k, t)$ tradeý, ý3, way $(v, 2)$ tradeý, ýone, solelyý
  • TÝ. ÝnÝ. Ý Shanmugam_JÝ. Ýlourthu Mary Pages 1403-1411
    ‎Universally prestarlike functions of order $alphaleq 1$ in the‎ ‎slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been‎ ‎recently introduced by S‎. ‎Ruscheweyh.This notion generalizes the‎ ‎corresponding one for functions in the unit disk $Delta$ (and‎ ‎other circular domains in $mathbb{C}$)‎. ‎In this paper‎, ‎we obtain‎ ‎the Fekete-Szegö coefficient functional for transforms of such‎ ‎functions‎.
    Keywords: restarlike functionsý, ýuniversallyý ýprestarlike functionsý, ýFekete, Szeg{o}ý ýfinctionalý
  • B. Taeri, H. Ahmadi Pages 1413-1431
    ‎Let $G$ be a finite group which is not a cyclic $p$-group‎, ‎$p$ a prime number‎. ‎We define an undirected simple graph $Delta(G)$ whose‎ ‎vertices are the proper subgroups of $G$, which are not contained in the‎ ‎Frattini subgroup of $G$ and two vertices $H$ and $K$ are joined by an edge‎ ‎if and only if $G=langle H‎, ‎Krangle$‎. ‎In this paper we classify finite groups with planar graph‎. ‎%For this‎, ‎by Kuratowski's Theorem‎, ‎we have to study subdivisions‎ ‎%of the Kuratowski graphs $K_{3‎, ‎3}$ and $K_5$ in the graph $Delta(G)$‎. ‎Our result shows that only few groups have planar graphs‎.
    Keywords: Graph on groupý, ýplannar graphý, ýfinite groupý
  • L. Stanciu, D. Breaz Pages 1433-1439
    In 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 $mathcal{KD}(mu,beta).$‎
    Keywords: Analytic functionsý, ýintegral operatorý, ýstarlike functionsý, ýconvex functionsý
  • A. Khaksari, S. Mehri, R. Safakish Pages 1441-1451
    ‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show that an $R$-module $M$ admits a‎ ‎powerful submodule if and only if it admits a strongly primary‎ ‎submodule‎. ‎Finally we study finitely generated torsion free‎ ‎modules over domain each of whose prime submodules are strongly‎ ‎primary‎.
    Keywords: Prime submoduleý, ýstrongly prime submoduleý, primary submoduleý, ýpower submoduleý
  • T. Honary, A. Nikou, A. H. Sanatpour Pages 1453-1468
    We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we then identify the character space of the vector-valued polynomial Lipschitz algebra $Lip_P^{alpha}(X, E)$, generated by the polynomials on the compact space $Xsubseteq Bbb{C}^{n}$. It is also shown that $Lip_P^{alpha}(X, E)$ is the injective tensor product $Lip_P^{alpha}(X)widehat{otimes}_epsilon E$. Finally, we characterize the form of each character on $Lip_{P}^{alpha}(X, E)$.
    Keywords: Vector, valued Lipschitz algebras, character space, injective tensor product, polynomial approximation
  • Ouml, . Acar, G. Durmaz, G. Minak Pages 1469-1478
    In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadlers‎.
    Keywords: Fixed point, Multivalued map, generalized F, contraction
  • M. N. Iradmusa Pages 1479-1489
    For any $kin mathbb{N}$, 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.
    Keywords: Domination number_Subdivision of a graph_Power of a graph
  • A. Behtoei Pages 1491-1504
    ‎Let $f$ be a proper $k$-coloring of a connected graph $G$ and‎ ‎$Pi=(V_1,V_2,ldots,V_k)$ be an ordered partition of $V(G)$ into‎ ‎the resulting color classes‎. ‎For a vertex $v$ of $G$‎, ‎the color‎ ‎code of $v$ with respect to $Pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_Pi}(v)=(d(v,V_1),d(v,V_2),ldots,d(v,V_k))$‎, ‎where $d(v,V_i)=min{d(v,x):~xin V_i}‎, ‎1leq ileq k$‎. ‎If‎ ‎distinct vertices have distinct color codes‎, ‎then $f$ is called a‎ ‎locating coloring‎. ‎The minimum number of colors needed in a‎ ‎locating coloring of $G$ is the locating chromatic number of $G$‎, ‎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 ‎locating chromatic number of the join of paths‎, ‎cycles and complete multipartite graphs‎.
    Keywords: Locating coloringý, ýlocating chromatic numberý, ýfaný, ýwheelý, ýjoiný
  • H. Haghighi Pages 1505-1514
    ‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.
    Keywords: Well, covered graphý, ýunmixed graphý, ýperfect matchingý
  • J. ÝzhangÝ, Wei He, L. Xie Pages 1515-1526
    In 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. ‎Arhangelskii 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.
    Keywords: Rectifiable spaceý, ýsymmetrizable spaceý, ýcharacterý
  • F. Abtahi, B. Khodsiani, A. Rejali Pages 1527-1538
    ‎We 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.
    Keywords: Arens regularityý, ýcompletely simple semigroupý, ýinverseý ýsemigroupý, ýleft (right) groupý, ýweaklyý
  • T. Seoudy Pages 1539-1551
    In this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎Some of our results improve‎ ‎and generalize previously known results‎.
    Keywords: Analytic functionsý, ýharmonic functionsý, ýextreme pointsý, ýdistortion boundsý
  • B. P. ÝallahverdievÝ Pages 1553-1571
    In 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).
    Keywords: Discrete Hamiltonian system, dissipative operator, selfadjoint dilation, characteristic function, completeness
  • S. Fouladi Pages 1573-1585
    Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.
    Keywords: Metacyclic $p$, groupý, powerful 2, groupý, coveringý, pairwiseý ýnon, commuting elementsý