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 <br />curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain <br />subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. <br /> 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 <br />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 <br />a dimension for a module $M$, called {em $tau$-rank of} $M$, <br />which coincides with the reduced rank of $M$ whenever $tau$ is <br />the Goldie torsion theory. It is shown that the $tau$-rank of $M$ <br />is measured by the length of certain decompositions of the <br />$tau$-injective hull of $M$. Moreover, some relations between the <br />$tau$-rank of $M$ and complements to $tau$-torsionfree <br />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 <br /> the Helly's selection principle for <br /> $Lambda BV^{(p)}$ functions is established. <br />A characterization of the inclusion of Waterman-Shiba classes into <br />classes of functions with given integral modulus of continuity is given. <br />A useful estimate on modulus of variation of functions of class $Lambda <br />BV^{(p)}$ 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. <br /> Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of <br /> classical quasi-primary decompositions in finitely generated modules over Noetherian <br /> rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same <br /> 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 <br />of finite and fixed co-classes and trivial Schur Multiplicator <br />which studied by Abdolzadeh and Eick in 2009, there are two <br />classes <br />$$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, <br />(b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid <br />a^2=b^2,[b,a]^2=1, t^a=t^{-1}[b,a], b^t=abarangle$$that have been <br />conjectured to have deficiency zero presentations. In this paper <br />we prove these conjectures. This completes the efficiency of all <br />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 <br />Banach $mathcal{A}$-bimodule. We say that a linear mapping <br />$delta:mathcal{A} rightarrow mathcal{M}$ is a generalized <br />$sigma$-derivation whenever there exists a $sigma$-derivation <br />$d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = <br />delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. <br />Giving some facts concerning generalized $sigma$-derivations, we <br />prove that if $mathcal{A}$ is unital and if $delta:mathcal{A} <br />rightarrow mathcal{A}$ is a generalized $sigma$-derivation and <br />there exists an element $a in mathcal{A}$ such that emph{d(a)} is <br />invertible, then $delta$ is continuous if and only if emph{d} is <br />continuous. We also show that if $mathcal{M}$ is unital, has no <br />zero divisor and $delta:mathcal{A} rightarrow mathcal{M}$ is a <br />generalized $sigma$-derivation such that $d(textbf{1}) neq 0$, <br />then $ker(delta)$ is a bi-ideal of $mathcal{A}$ and $ker(delta) = <br />ker(sigma) = ker(d)$, where textbf{1} denotes the unit element of <br />$mathcal{A}$.
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 <br />begin{equation*} <br />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), <br />end{equation*} <br />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 <br />can find a close connection between the set of prime $z$-ideals <br />of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. <br />For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there <br />exists a one-to-one correspondence between the set of prime <br />$z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ <br />not containing $f$. Moreover, considering these relations, we <br />obtain some new characterizations of classical concepts in the <br />context of $C(X)$. For example, $X$ is an $F$-space if and only if <br />the extension $Phi : beta Yrightarrowbeta X$ of the identity <br />map $imath: Yrightarrow X$ is one-to-one, for each $z$-embedded <br />subspace $Y$ of $X$. Supposing $p$ is a non-isolated <br />$G_delta$-point in $X$ and $Y=Xsetminus{p}$, we prove that <br />$M^p(X)$ contains no non-trivial maximal $z$-ideal if and only if <br />$pinbe X$ is a quasi $P$-point if and only if each point of <br />$beta Y setminus Y$ 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 $T:A longrightarrow <br />B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for <br />all $x,yin A$. The general form and the automatic continuity of <br />separating maps between various Banach algebras have been studied <br />extensively. In this paper, we first extend the notion of separating <br />map for module case and then we give a description of a linear <br />separating map $T:B longrightarrow X$, where $B$ is a unital <br />commutative semisimple regular Banach algebra satisfying the <br />Ditkin's condition and $X$ is a left Banach module over a unital <br />commutative Banach algebra. We also show that if $X$ is hyper <br />semisimple and $T$ is bijective, then $T$ is automatically <br />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 <br />that the kernel of associated synthesis operator for a Besselian <br />$g$-frame is finite dimensional. We also introduce $alpha$-dual of <br />a $g$-frame and we get some results when we use the Hilbert-Schmidt <br />norm for the members of a $g$-frame in a finite dimensional Hilbert <br />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 <br />subsemigroup of idempotents. In this paper we define the $n$-th <br />module cohomology group of Banach algebras and <br /> show that the first module <br />cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is <br />zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ <br />we show that <br />$HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ 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 <br />${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ <br />becomes a module extension Banach algebra when equipped with the <br />algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we <br />investigate biflatness and biprojectivity for these Banach algebras. <br />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 <br />iterations for nonexpansive mappings in the framework of CAT(0) <br />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 $Y$ <br />contains $X$ as a dense subspace. <br />Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. <br />For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ <br />which fixes $X$ point-wise. An extension $Y$ of $X$ is called a {em one-point extension}, if $Yackslash X$ is a singleton. <br />An extension $Y$ of $X$ is called {em first-countable}, if $Y$ is first-countable at points of $Yackslash X$. <br />Let ${mathcal P}$ be a topological <br />property. An extension $Y$ of $X$ is called a {em <br />${mathcal P}$-extension}, if it has ${mathcal P}$. <br /> <br /> <br />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 ${mathcal P}$ <br />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 <br />Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space <br />$H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, <br />where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin <br />B}$, best proximity pair theorems provide sufficient conditions <br />that ensure the existence of an $x_0in A$ such that <br />$$d(G(x_0),F(x_0))=d(A,B).$$
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 <br />$k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides <br />$exp(G)p^{m(k-1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that <br />$exp( M(G))$ divides $exp(G)$, for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result <br />is an improvement of some previous bounds for the exponent of <br />$M^{(c)}(G)$ 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 <br />sum of two units if and only if its endomorphism ring has no <br />factor ring isomorphic to $Z_{2}$. We also characterize unit sum <br />number equal to two for the endomorphism ring of quasi-discrete <br />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 <br />search linear models, discrimination ability of search designs <br />has been studied by several researchers. Some criteria have been <br />developed to measure this capability, however, they are restricted <br />in a sense of being able to work for searching only one <br />possible nonzero effect. In this paper, two criteria are <br />proposed, based on Kullback-Leibler distance. These criteria are <br />able to evaluate the search ability of designs, without any <br />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