Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
On the k-nullity foliations in Finsler geometry
1
18
EN
B.
Bidabad
M.
Rafie-Rad
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Characterization of the $k$-nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of $(M,F)$. The introduced $k$-nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and enlarged to Finsler setting by Akbar-Zadeh and contains it as a special case.
Foliation,k-nullity,Finsler manifolds,curvature operator
http://bims.iranjournals.ir/article_367.html
http://bims.iranjournals.ir/article_367_fb2ca9742a5a21adfec049f51eb72767.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Ranks of modules relative to a torsion theory
19
33
EN
Sh.
Asgari
sh_asgari@math.iut.ac.ir
A.
Haghany
aghagh@cc.iut.ac.ir
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$-rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$-rank of $M$ is measured by the length of certain decompositions of the $tau$-injective hull of $M$. Moreover, some relations between the $tau$-rank of $M$ and complements to $tau$-torsionfree submodules of $M$ are obtained.
Hereditary torsion theory,pseudo $tau$-essential,pseudo
$tau$-uniform,$tau$-rank
http://bims.iranjournals.ir/article_368.html
http://bims.iranjournals.ir/article_368_1af8f9a81692bba1f4aa0fc6001c47b7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
p-Lambda-bounded variation
35
49
EN
M.
Hormozi
hormozi@chalmers.se
A.
A.
Ledari
ahmadi@hamoon.usb.ac.ir
F.
Prus-Wisniowski
wisniows@univ.szczecin.pl
A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.
generalized bounded variation,Helly's theorem,modulus of variation
http://bims.iranjournals.ir/article_369.html
http://bims.iranjournals.ir/article_369_2f78b06d6a5160a8245779456a3ea786.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Classical quasi-primary submodules
51
71
EN
M.
Behboodi
mbehbood@cc.iut.ac.ir
R.
Jahani-Nezhad
jahanian@kashanu.ac.ir
M.
H.
Naderi
mh-naderi@qom.ac.ir
In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same when $R$ is a domain with ${rm dim}(R)leq 1$.
Primary,classical primary,Classical quasi-primary,decomposition
http://bims.iranjournals.ir/article_370.html
http://bims.iranjournals.ir/article_370_b3fcf4d4cb2b75243cdd0e2e211d16d4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Proving the efficiency of pro-2-groups of fixed co-classes
73
80
EN
A.
Arjomandfar
ab.arj44@gmail.com
H.
Doostie
doostih@saba.tmu.ac.ir
Among the six classes of pro-2-groups of finite and fixed co-classes and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classes $$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. In this paper we prove these conjectures. This completes the efficiency of all six classes of pro-$2$-groups of fixed co-classes.
Pro-2-groups,modified Todd-Coxeter algorithm
http://bims.iranjournals.ir/article_371.html
http://bims.iranjournals.ir/article_371_17151d7069002f8270473ca5a99f0c9e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Generalized sigma-derivation on Banach algebras
81
94
EN
A.
Hosseini
A.hosseini@mshdiau.ac.ir
M.
Hassani
hassani@mshdiau.ac.ir
A.
Niknam
niknam@math.um.ac.ir
Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning generalized $sigma$-derivations, we prove that if $mathcal{A}$ is unital and if $delta:mathcal{A} rightarrow mathcal{A}$ is a generalized $sigma$-derivation and there exists an element $a in mathcal{A}$ such that emph{d(a)} is invertible, then $delta$ is continuous if and only if emph{d} is continuous. We also show that if $mathcal{M}$ is unital, has no zero divisor and $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation such that $d(textbf{1}) neq 0$, then $ker(delta)$ is a bi-ideal of $mathcal{A}$ and $ker(delta) = ker(sigma) = ker(d)$, where textbf{1} denotes the unit element of $mathcal{A}$.
derivation,$sigma$-derivation,$(sigma,d)$-derivation,$sigma$-algebraic map
http://bims.iranjournals.ir/article_372.html
http://bims.iranjournals.ir/article_372_2bd8144ced2231b0e79316f9f7e66931.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Upper bounds on the solutions to n = p+m^2
95
108
EN
A.
Nayebi
aran.nayebi@gmail.com
ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is an integer, and $left(frac{n}{p}right)$ denotes the Legendre symbol. Unfortunately, as we will later point out, this conjecture is difficult to prove and not emph{all} integers that are nonsquares can be represented as the sum of a prime and a square. Instead in this paper we prove two upper bounds for $mathcal{R}(n)$ for $n le N$. The first upper bound applies to emph{all} $n le N$. The second upper bound depends on the possible existence of the Siegel zero, and assumes its existence, and applies to all $N/2 < n le N$ but at most $ll N^{1-delta_1}$ of these integers, where $N$ is a sufficiently large positive integer and $0
Additive,Conjecture H,circle method
http://bims.iranjournals.ir/article_373.html
http://bims.iranjournals.ir/article_373_7f13a2f116adbcbc04a1fe39e84b7444.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Connections between C(X) and C(Y), where Y is a subspace of X
109
126
EN
A.
Aliabad
aliabady r@scu.ac.ir
M.
Badie
badie@jsu.ac.ir
In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, considering these relations, we obtain some new characterizations of classical concepts in the context of $C(X)$. For example, $X$ is an $F$-space if and only if the extension $Phi : beta Yrightarrowbeta X$ of the identity map $imath: Yrightarrow X$ is one-to-one, for each $z$-embedded subspace $Y$ of $X$. Supposing $p$ is a non-isolated $G_delta$-point in $X$ and $Y=Xsetminus{p}$, we prove that $M^p(X)$ contains no non-trivial maximal $z$-ideal if and only if $pinbe X$ is a quasi $P$-point if and only if each point of $beta Y setminus Y$ is a $P$-point with respect to $Y$.
$z$-filter,prime
$z$-ideal,prime $z^circ$-ideal,$P$-space,quasi $P$-space,$F$-space,$CC$-space,$G_delta$-point
http://bims.iranjournals.ir/article_374.html
http://bims.iranjournals.ir/article_374_7ec399b754105013093d1f6f8694836b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Banach module valued separating maps and automatic continuity
127
139
EN
L.
Mousavi
l.mousavi@srbiau.ac.ir
F.
Sady
sady@modares.ac.ir
For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear separating map $T:B longrightarrow X$, where $B$ is a unital commutative semisimple regular Banach algebra satisfying the Ditkin's condition and $X$ is a left Banach module over a unital commutative Banach algebra. We also show that if $X$ is hyper semisimple and $T$ is bijective, then $T$ is automatically continuous and $T^{-1}$ is separating as well.
Banach algebras,Banach modules,separating maps,cozero set,point multiplier,Automatic continuity
http://bims.iranjournals.ir/article_375.html
http://bims.iranjournals.ir/article_375_1bbfb6fc763d4e986298a5e63f05fd4c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
G-frames and Hilbert-Schmidt operators
141
155
EN
M.
R.
Abdollahpour
mrabdollahpour@yahoo.com
A.
Najati
a.nejati@yahoo.com
In this paper we introduce and study Besselian $g$-frames. We show that the kernel of associated synthesis operator for a Besselian $g$-frame is finite dimensional. We also introduce $alpha$-dual of a $g$-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a $g$-frame in a finite dimensional Hilbert space.
frame,g-frame,Besselian g-frame,alpha-dual,Hilbert-Schmidt operator
http://bims.iranjournals.ir/article_376.html
http://bims.iranjournals.ir/article_376_dec38006d54dac2838992a1a939b821a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Module cohomology group of inverse semigroup algebras
157
169
EN
E.
Nasrabadi
enasrabadi@birjand.ac.ir
A.
Pourabbas
arpabbas@aut.ac.ir
Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach space, for every odd $ninmathbb{N}$.
Module amenability,inverse semigroup algebra,module cohomology group
http://bims.iranjournals.ir/article_377.html
http://bims.iranjournals.ir/article_377_75393a2b7b697c3d7471a03562fb7769.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
On module extension Banach algebras
171
183
EN
A.
Medghalchi
a_medghalchi@saba.tmu.ac.ir
H.
Pourmahmood-Aghababa
h_p_aghababa@tabrizu.ac.ir
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S}}=Aoplus A$.
Module extension Banach algebras,Biflatness,biprojectivity,Weak amenability,Automatic continuity
http://bims.iranjournals.ir/article_378.html
http://bims.iranjournals.ir/article_378_751f25bfc812837d15a214e91d2fd439.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
On the Ishikawa iteration process in CAT(0) spaces
185
197
EN
B.
Panyanak
banchap@chiangmai.ac.th
T.
Laokul
thanom kul@hotmail.com
In this paper, several $Delta$ and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results
nonexpansive mappings,Fixed points,$Delta-$convergence,strong convergence,CAT(0) spaces
http://bims.iranjournals.ir/article_379.html
http://bims.iranjournals.ir/article_379_7ba18a09e4d06147562df53a05b890b2.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
One-point extensions of locally compact paracompact spaces
199
228
EN
M.
R.
Koushesh
koushesh@cc.iut.ac.ir
A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ of $X$ is called a {em one-point extension}, if $Yackslash X$ is a singleton. An extension $Y$ of $X$ is called {em first-countable}, if $Y$ is first-countable at points of $Yackslash X$. Let ${mathcal P}$ be a topological property. An extension $Y$ of $X$ is called a {em ${mathcal P}$-extension}, if it has ${mathcal P}$. In this article, for a given locally compact paracompact space $X$, we consider the two classes of one-point v{C}ech-complete; ${mathcal P}$-extensions of $X$ and one-point first-countable locally-${mathcal P}$ extensions of $X$, and we study their order-structures, by relating them to the topology of a certain subspace of the outgrowth $eta Xackslash X$. Here ${mathcal P}$ is subject to some requirements and include $sigma$-compactness and the Lindel"{o}f property as special cases.
Stone-v{C}ech compactification,
one-point extension, one-point compactification, locally compact, paracompact, v{C}ech complete,first-countable
http://bims.iranjournals.ir/article_380.html
http://bims.iranjournals.ir/article_380_10262d575074c5a2c6fc9d9e59a5e26c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
229
234
EN
A.
Amini-Harandi
aminih_a@yahoo.com
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
Best proximity pair,coincidence point,nonexpansive map,Hilbert space
http://bims.iranjournals.ir/article_381.html
http://bims.iranjournals.ir/article_381_ecee2580be42e5630823af4e23482eb7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group
235
242
EN
B.
Mashayekhy
bmashayekhyf@yahoo.com
A.
Hokmabadi
hokmabadi-ah@yahoo.com
F.
Mohammadzadeh
fa36407@yahoo.com
Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement of some previous bounds for the exponent of $M^{(c)}(G)$ given by M. R. Jones, G. Ellis and P. Moravec in some cases.
Schur multiplier,nilpotent multiplier,exponent,finite $p$-groups
http://bims.iranjournals.ir/article_382.html
http://bims.iranjournals.ir/article_382_68df8010020d3823167bee048a468638.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
The unit sum number of discrete modules
243
249
EN
N
Ashrafi
nashrafi@semnan.ac.ir
N.
Pouyan
neda.pouyan@gmail.com
In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.
unit sum number,discrete Module,hollow module,lifting property
http://bims.iranjournals.ir/article_383.html
http://bims.iranjournals.ir/article_383_5a67a1df30a32a6ecb2227cca4f96ee1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
On n-coherent rings, n-hereditary rings and n-regular rings
251
267
EN
Z.
Zhu
zhuzhanminzjxu@hotmail.com
We observe some new characterizations of $n$-presented modules. Using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.
(n,0)-injective modules,0)-flat modules,n-coherent rings,n-hereditary rings n-regular rings
http://bims.iranjournals.ir/article_384.html
http://bims.iranjournals.ir/article_384_125e070a2fa775c36ec3c76ac7b10025.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 4
2011
12
15
Using Kullback-Leibler distance for performance evaluation of search designs
269
279
EN
H.
Talebi
h-talebi@sci.ui.ac.ir
N.
Esmailzadeh
n.esmailzadeh@uok.ac.ir
This paper considers the search problem, introduced by Srivastava cite{Sr}. This is a model discrimination problem. In the context of search linear models, discrimination ability of search designs has been studied by several researchers. Some criteria have been developed to measure this capability, however, they are restricted in a sense of being able to work for searching only one possible nonzero effect. In this paper, two criteria are proposed, based on Kullback-Leibler distance. These criteria are able to evaluate the search ability of designs, without any restriction on the number of nonzero effects.
Search designs,search linear model,Kullback-Leibler distance,model discrimination
http://bims.iranjournals.ir/article_385.html
http://bims.iranjournals.ir/article_385_1934e053c892f8a8bb9b87f436d33a82.pdf