Bulletin of the Iranian Mathematical Society
text
article
2014
eng
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
http://bims.iranjournals.ir/article_579_b3c2028ba54d98a990d8b6e0c24c378e.pdf
The finite $S$-determinacy of singularities in positive characteristic $S=R_G,R_A, K_G,K_A$
L.
Hengxing
School of Mathematics and Statistics,Wuhan University, Wuhan,
assistance professor
author
L.
Jingwen
School of Mathematics and Statistics, Wuhan University, P.O. Box 430072, Wuhan, People's Republic of China
author
text
article
2014
eng
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 $\mathcal{S}-$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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1347
1372
http://bims.iranjournals.ir/article_569_70f1e9f320d0a1472bd40687d8e6305f.pdf
Translation invariant surfaces in the 3-dimensional Heisenberg group
D. W.
Yoon
Gyeongsang National University
author
J. W.
Lee
University of Missouri-Columbia
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1373
1385
http://bims.iranjournals.ir/article_570_2d5e9aaa628503656c1fca0f40716d28.pdf
On the possible volume of $\mu$-$(v,k,t)$ trades
S.
Rashidi
Alzahra Uni
author
N.
Soltankhah
Alzahra Uni.
author
text
article
2014
eng
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 $T_i (1\leq i \leq \mu)$. 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1387
1401
http://bims.iranjournals.ir/article_571_a228d214fe2139e3f118bdf489628d23.pdf
Fekete-Szegö coefficient functional for transforms of universally prestarlike functions
T. N.
Shanmugam
Anna University,
Chennai.
author
J. Lourthu
Mary
Anna University
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1403
1411
http://bims.iranjournals.ir/article_572_ff424dbe0b30d42017cb0a6e1a47f648.pdf
On the planarity of a graph related to the join of subgroups of a finite group
B.
Taeri
Isfahan University of Technology
author
H.
Ahmadi
Isfahan University of Technology
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1413
1431
http://bims.iranjournals.ir/article_573_026d933a1762fba8b0e0f563507e5038.pdf
Some properties of a general integral operator
L
Stanciu
University of Pitesti
author
D.
Breaz
"1 Decembrie 1918" University of Alba Iulia
author
text
article
2014
eng
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 $\mathcal{KD}(\mu,\beta).$
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1433
1439
http://bims.iranjournals.ir/article_574_8800a771df387746d78b58972f7a2a33.pdf
On special submodule of modules
A
Khaksari
iranian
author
S.
Mehri
Buali sina University
author
R.
Safakish
iranian
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1441
1451
http://bims.iranjournals.ir/article_575_4ce533cb54b8165a410f211ae94a09e4.pdf
On the character space of vector-valued Lipschitz algebras
T.
Honary
Kharazmi University
author
A.
Nikou
Kharazmi University
author
A. H.
Sanatpour
Kharazmi University
author
text
article
2014
eng
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 $Lip_{P}^{alpha}(X, E)$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1453
1468
http://bims.iranjournals.ir/article_576_f9f5524bf4345a77d76c6c1453d51115.pdf
Generalized multivalued $F$-contractions on complete metric spaces
Ö.
Acar
Kirikkale University
author
G.
Durmaz
Kirikkale University
author
G
Minak
Kirikkale University
author
text
article
2014
eng
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 Nadler's.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1469
1478
http://bims.iranjournals.ir/article_577_eb149301c126a1c617e997eaa742c7a6.pdf
Domination number of graph fractional powers
M. N.
Iradmusa
Shahid Beheshti University
author
text
article
2014
eng
For 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1479
1489
http://bims.iranjournals.ir/article_578_75c4cbe02b1125c194ec33ac260ea658.pdf
The locating chromatic number of the join of graphs
A.
Behtoei
Isfahan university of techmology
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1491
1504
http://bims.iranjournals.ir/article_580_08d06f76db2f31d9d9da80fbbb8f887f.pdf
A generalization of Villarreal's result for unmixed tripartite graphs
H.
Haghighi
K. N. Toosi University of Technology
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1505
1514
http://bims.iranjournals.ir/article_581_aeadceab31733934bd4246afae35af37.pdf
A note on the remainders of rectifiable spaces
J.
Zhang
Nanjing Normal University
author
Wei
He
Nanjing Normal University
author
L.
Xie
Wuyi University
author
text
article
2014
eng
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. 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1515
1526
http://bims.iranjournals.ir/article_582_fc25324569a17b2dc2d7c459dfd6fd49.pdf
Arens regularity of inverse semigroup algebras
F.
Abtahi
University of Isfahan
author
B.
Khodsiani
University of Isfahan
author
A.
Rejali
University of Isfahan
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1527
1538
http://bims.iranjournals.ir/article_583_ce605ef8523902e55f9e1f2d1945c558.pdf
On a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator
T.
Seoudy
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt.
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1539
1551
http://bims.iranjournals.ir/article_584_80f49ae4626a72fd21eb056231c7bca7.pdf
Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
B. P.
Allahverdiev
Department of Mathematics, Suleyman Demirel University, 32260 Isparta, Turkey
author
text
article
2014
eng
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).
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1553
1571
http://bims.iranjournals.ir/article_585_77af4265ca75fc6b62d5faa12246c9ae.pdf
Pairwise non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups
S.
Fouladi
Academic Staff
author
text
article
2014
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
6
no.
2014
1573
1585
http://bims.iranjournals.ir/article_586_eb37771cbcb78fcf88705e63931f44eb.pdf