eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
1
18
367
On the k-nullity foliations in Finsler geometry
B. Bidabad
1
M. Rafie-Rad
2
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.
http://bims.iranjournals.ir/article_367_fb2ca9742a5a21adfec049f51eb72767.pdf
Foliation
k-nullity
Finsler manifolds
curvature operator
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
19
33
368
Ranks of modules relative to a torsion theory
Sh. Asgari
sh_asgari@math.iut.ac.ir
1
A. Haghany
aghagh@cc.iut.ac.ir
2
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.
http://bims.iranjournals.ir/article_368_1af8f9a81692bba1f4aa0fc6001c47b7.pdf
Hereditary torsion theory
pseudo $tau$-essential
pseudo
$tau$-uniform
$tau$-rank
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
35
49
369
p-Lambda-bounded variation
M. Hormozi
hormozi@chalmers.se
1
A. Ledari
ahmadi@hamoon.usb.ac.ir
2
F. Prus-Wisniowski
wisniows@univ.szczecin.pl
3
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.
http://bims.iranjournals.ir/article_369_2f78b06d6a5160a8245779456a3ea786.pdf
generalized bounded variation
Helly's theorem
modulus of variation
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
51
71
370
Classical quasi-primary submodules
M. Behboodi
mbehbood@cc.iut.ac.ir
1
R. Jahani-Nezhad
jahanian@kashanu.ac.ir
2
M. Naderi
mh-naderi@qom.ac.ir
3
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 ${rm dim}(R)leq 1$.
http://bims.iranjournals.ir/article_370_b3fcf4d4cb2b75243cdd0e2e211d16d4.pdf
Primary
classical primary
Classical quasi-primary
decomposition
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
73
80
371
Proving the efficiency of pro-2-groups of fixed co-classes
A. Arjomandfar
ab.arj44@gmail.com
1
H. Doostie
doostih@saba.tmu.ac.ir
2
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.
http://bims.iranjournals.ir/article_371_17151d7069002f8270473ca5a99f0c9e.pdf
Pro-2-groups
modified Todd-Coxeter algorithm
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
81
94
372
Generalized sigma-derivation on Banach algebras
A. Hosseini
A.hosseini@mshdiau.ac.ir
1
M. Hassani
hassani@mshdiau.ac.ir
2
A. Niknam
niknam@math.um.ac.ir
3
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 $mathcal{A}$.
http://bims.iranjournals.ir/article_372_2bd8144ced2231b0e79316f9f7e66931.pdf
derivation
$sigma$-derivation
$(sigma
d)$-derivation
$sigma$-algebraic map
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
95
108
373
Upper bounds on the solutions to n = p+m^2
A. Nayebi
aran.nayebi@gmail.com
1
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
http://bims.iranjournals.ir/article_373_7f13a2f116adbcbc04a1fe39e84b7444.pdf
Additive
Conjecture H
circle method
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
109
126
374
Connections between C(X) and C(Y), where Y is a subspace of X
A. Aliabad
aliabady r@scu.ac.ir
1
M. Badie
badie@jsu.ac.ir
2
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 $Y$.
http://bims.iranjournals.ir/article_374_7ec399b754105013093d1f6f8694836b.pdf
$z$-filter
prime
$z$-ideal
prime $z^circ$-ideal
$P$-space
quasi $P$-space
$F$-space
$CC$-space
$G_delta$-point
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
127
139
375
Banach module valued separating maps and automatic continuity
L. Mousavi
l.mousavi@srbiau.ac.ir
1
F. Sady
sady@modares.ac.ir
2
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.
http://bims.iranjournals.ir/article_375_1bbfb6fc763d4e986298a5e63f05fd4c.pdf
Banach algebras
Banach modules
separating maps
cozero set
point multiplier
Automatic continuity
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
141
155
376
G-frames and Hilbert-Schmidt operators
M. Abdollahpour
mrabdollahpour@yahoo.com
1
A. Najati
a.nejati@yahoo.com
2
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.
http://bims.iranjournals.ir/article_376_dec38006d54dac2838992a1a939b821a.pdf
frame
g-frame
Besselian g-frame
alpha-dual
Hilbert-Schmidt operator
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
157
169
377
Module cohomology group of inverse semigroup algebras
E. Nasrabadi
enasrabadi@birjand.ac.ir
1
A. Pourabbas
arpabbas@aut.ac.ir
2
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 $ninmathbb{N}$.
http://bims.iranjournals.ir/article_377_75393a2b7b697c3d7471a03562fb7769.pdf
Module amenability
inverse semigroup algebra
module cohomology group
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
171
183
378
On module extension Banach algebras
A. Medghalchi
a_medghalchi@saba.tmu.ac.ir
1
H. Pourmahmood-Aghababa
h_p_aghababa@tabrizu.ac.ir
2
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 ${mathcal{S}}=Aoplus A$.
http://bims.iranjournals.ir/article_378_751f25bfc812837d15a214e91d2fd439.pdf
Module extension Banach algebras
Biflatness
biprojectivity
Weak amenability
Automatic continuity
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
185
197
379
On the Ishikawa iteration process in CAT(0) spaces
B. Panyanak
banchap@chiangmai.ac.th
1
T. Laokul
thanom kul@hotmail.com
2
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
http://bims.iranjournals.ir/article_379_7ba18a09e4d06147562df53a05b890b2.pdf
nonexpansive mappings
Fixed points
$Delta-$convergence
strong convergence
CAT(0) spaces
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
199
228
380
One-point extensions of locally compact paracompact spaces
M. Koushesh
koushesh@cc.iut.ac.ir
1
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.
http://bims.iranjournals.ir/article_380_10262d575074c5a2c6fc9d9e59a5e26c.pdf
Stone-v{C}ech compactification,
one-point extension, one-point compactification, locally compact, paracompact, v{C}ech complete
first-countable
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
229
234
381
Best proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
A. Amini-Harandi
aminih_a@yahoo.com
1
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 $$d(G(x_0),F(x_0))=d(A,B).$$
http://bims.iranjournals.ir/article_381_ecee2580be42e5630823af4e23482eb7.pdf
Best proximity pair
coincidence point
nonexpansive map
Hilbert space
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
235
242
382
On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$-group
B. Mashayekhy
bmashayekhyf@yahoo.com
1
A. Hokmabadi
hokmabadi-ah@yahoo.com
2
F. Mohammadzadeh
fa36407@yahoo.com
3
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.
http://bims.iranjournals.ir/article_382_68df8010020d3823167bee048a468638.pdf
Schur multiplier
nilpotent multiplier
exponent
finite $p$-groups
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
243
249
383
The unit sum number of discrete modules
N Ashrafi
nashrafi@semnan.ac.ir
1
N. Pouyan
neda.pouyan@gmail.com
2
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.
http://bims.iranjournals.ir/article_383_5a67a1df30a32a6ecb2227cca4f96ee1.pdf
unit sum number
discrete Module
hollow module
lifting property
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
251
267
384
On n-coherent rings, n-hereditary rings and n-regular rings
Z. Zhu
zhuzhanminzjxu@hotmail.com
1
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.
http://bims.iranjournals.ir/article_384_125e070a2fa775c36ec3c76ac7b10025.pdf
(n
0)-injective modules
0)-flat modules
n-coherent rings
n-hereditary rings n-regular rings
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2011-12-15
37
No. 4
269
279
385
Using Kullback-Leibler distance for performance evaluation of search designs
H. Talebi
h-talebi@sci.ui.ac.ir
1
N. Esmailzadeh
n.esmailzadeh@uok.ac.ir
2
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.
http://bims.iranjournals.ir/article_385_1934e053c892f8a8bb9b87f436d33a82.pdf
Search designs
search linear model
Kullback-Leibler distance
model discrimination