2019-03-24T08:14:58Z
http://bims.iranjournals.ir/?_action=export&rf=summon&issue=83
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Bulletin of the Iranian Mathematical Society
2016
06
01
http://bims.iranjournals.ir/article_796_dc33b7469948b4c04368c4273c896ac2.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Total perfect codes, OO-irredundant and total subdivision in graphs
H.
Hosseinzadeh
N.
Soltankhah
Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, we determine the value of $ooir(G)$ for some classes of graphs.
Total domination number
OO- irredundance number
total subdivision number
2016
06
01
499
506
http://bims.iranjournals.ir/article_778_fa2994302d0b573b33b69934d84dde37.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
The theory of matrix-valued multiresolution analysis frames
P.
Zhao
C.
Zhao
A generalization of matrix-valued multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame multiresolution analysis is defined in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.
Matrix-valued wavelet
frame
wavelets
matrix-valued dual Riesz basis
2016
06
01
507
519
http://bims.iranjournals.ir/article_779_bb10aaa73cdd7d1d0904b351010f3dbf.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Polynomially bounded solutions of the Loewner differential equation in several complex variables
A.
Ebadian
S.
Rahrovi
S.
Shams
J.
Sokol
We determine the form of polynomially bounded solutions to the Loewner differential equation that is satisfied by univalent subordination chains of the form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$, where $A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally Lebesgue integrable mapping and satisfying the condition $$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t [A(tau)-2m(A(tau))I_n]rm {d}tauright}right|{rm d}t<infty,$$ and $m(A(t))>0$ for $tgeq0$, where $m(A)=min{mathfrak{Re}leftlangle A(z),zrightrangle:|z|=1}$. We also give sufficient conditions for $g(z,t)=M(f(z,t))$ to be polynomially bounded, where $f(z,t)$ is an $A(t)$-normalized polynomially bounded Loewner chain solution to the Loewner differential equation and $M$ is an entire function. On the other hand, we show that all $A(t)$-normalized polynomially bounded solutions to the Loewner differential equation are Loewner chains.
Biholomorphic mapping
Loewner differential equation
polynomially bounded
subordination chain
parametric representation.
2016
06
01
521
537
http://bims.iranjournals.ir/article_777_1bac89a6fb0e82c7a49584552cbe52f2.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
$k$-power centralizing and $k$-power skew-centralizing maps on triangular rings
X. F.
Qi
Let $mathcal A$ and $mathcal B$ be unital rings, and $mathcal M$ be an $(mathcal A, mathcal B)$-bimodule, which is faithful as a left $mathcal A$-module and also as a right $mathcal B$-module. Let ${mathcal U}=Tri(mathcal A, mathcal M, mathcal B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its center. Assume that $f:{mathcal U}rightarrow{mathcal U}$ is a map satisfying $f(x+y)-f(x)-f(y)in{mathcal Z}({mathcal U})$ for all $x, yin{mathcal U}$ and $k$ is a positive integer. It is shown that, under some mild conditions, the following statements are equivalent: (1) $[f(x),x^k]in{mathcal Z}({mathcal U})$ for all $xin{mathcal U}$; (2) $[f(x),x^k]=0$ for all $xin{mathcal U}$; (3) $[f(x),x]=0$ for all $xin{mathcal U}$; (4) there exist a central element $zin{mathcal Z}({mathcal U})$ and an additive modulo ${mathcal Z}({mathcal U})$ map $h:{mathcal <br />U}rightarrow{mathcal Z}({mathcal U})$ such that $f(x)=zx+h(x)$ for all $xin{mathcal U}$. It is also shown that there is no nonzero additive $k$-skew-centralizing maps on triangular rings. <br />
Triangular rings
centralizing maps
$k$-skew-centralizing maps
nest algebras
2016
06
01
539
554
http://bims.iranjournals.ir/article_776_5f93e5da86761d28483d66373943f57e.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
On radical formula and Prufer domains
R.
Nekooei
F.
Mirzaei
In this paper we characterize the radical of an arbitrary submodule $N$ of a finitely generated free module $F$ over a commutatitve ring $R$ with identity. Also we study submodules of $F$ which satisfy the radical formula. Finally we derive necessary and sufficient conditions for $R$ to be a Pr$ddot{mbox{u}}$fer domain, in terms of the radical of a cyclic submodule in $Rbigoplus R$. <br />
Prime submodules
Radical of a submodule
Radical formula
Pr$ddot{mbox{u}}$fer domains
Dedekind domains
2016
06
01
555
563
http://bims.iranjournals.ir/article_797_18ddba9d7a3f373b64964a1c3fa7e85c.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature
M.
Zarei
S.M.B.
Kashani
H.
Abedi
In this paper, we give a classification of non simply connected seven dimensional Reimannian manifolds of constant positive curvature which admit irreducible cohomogeneity-one actions. We characterize the acting groups and describe the orbits. The first and second homo-<br />topy groups of the orbits have been presented as well.
Positively curved manifold
irreducible representation
cohomogeneity one action
2016
06
01
565
584
http://bims.iranjournals.ir/article_798_57c6204c6001577ab8221c3c84ec415c.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Complete characterization of the Mordell-Weil group of some families of elliptic curves
H.
Daghigh
S.
Didari
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p$ the rank of elliptic curve $y^2=x^3-3px$ is at most two. In this paper we go further, and using height function, we will determine the Mordell-Weil group of a family of elliptic curves of the form $y^2=x^3-3nx$, and give a set of its generators under certain conditions. We will introduce an infinite family of elliptic curves with rank at least two. The full Mordell-Weil group and the generators of a family (which is expected to be infinite under the assumption of a standard conjecture) of elliptic curves with exact rank two will be described.
Elliptic Curve
Mordell-Weil Group
Generators
Height Function
2016
06
01
585
594
http://bims.iranjournals.ir/article_799_3ad7f75a4be58868ac2adcc0d33b1d9f.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix
X.
Liu
J.
Benitez
M.
Zhang
In this article, we characterize the involutiveness of the linear combination of the form<br />a1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,<br />and A2 is arbitrary, under certain properties imposed on A1 and A2.
Quadratic matrix
involutive matrix
linear combination
2016
06
01
595
610
http://bims.iranjournals.ir/article_800_4cbebc1a2c9731758eba450931c50d7d.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions
Y.
Jalilian
In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.
Infinitely many solutions
Nehari manifold
sign-changing weight function
Bi-nonlocal equation
2016
06
01
611
626
http://bims.iranjournals.ir/article_801_4e0cfaca570cffce5b5d67eec547dff4.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
T-dual Rickart modules
S.
Ebrahimi Atani
M.
Khoramdel
S.
Dolati Pish Hesari
We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is shown that, while a direct summand of a (strongly) T-dual Rickart module inherits the property, direct sums of T-dual Rickart modules do not. Moreover, when a direct sum of T-dual Rickart modules is T-dual Rickart, is included. Examples<br />illustrating the results are presented.
Dual Rickart modules
t-lifting modules
t-dual Baer modules
T-dual Rickart modules
strongly T-dual Rickart modules
2016
06
01
611
642
http://bims.iranjournals.ir/article_802_ff60a17a6bbe853afe2fa8050110df8e.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
H.
Tang
C.
Liu
Z.
Zhao
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in $H^k(0<=k<5)$ space of this equation, and it attracts any bounded subset of $H^k(omega)$ in the $H^k$-norm.
Cahn-Hilliard/Allen-Cahn equation
existence
global attractor
2016
06
01
643
658
http://bims.iranjournals.ir/article_803_0b5005164973791b8218766a77550508.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Nonlinear $*$-Lie higher derivations on factor von Neumann algebras
F.
Zhang
X.
Qi
J.
Zhang
Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.
von Neumann algebra
nonlinear $*$-Lie higher derivation
additive $*$-higher derivation
2016
06
01
659
678
http://bims.iranjournals.ir/article_804_014d235291f660ccf7545720818e036c.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Bounding cochordal cover number of graphs via vertex stretching
M. R.
Fander
It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipartite or weakly chordal graph.
Castelnuovo-Mumford regularity
Induced matching number
Cochordal cover number
2016
06
01
679
685
http://bims.iranjournals.ir/article_805_81bd74ccf92af8a92a50edd4ec90271f.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
P-stability, TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation
A.
Shokri
H.
Saadat
Many simulation algorithms (chemical reaction systems, differential systems arising from the modeling of transient behavior in the process industries and etc.) contain the numerical solution of systems of differential equations. For the efficient solution of the above mentioned problems, linear multistep methods or Runge-Kutta technique are used. For the simulation of chemical procedures the radial Schrodinger equation is used frequently. In the present paper we will study a symmetric two-step Obrechkoff method, in which we will use of technique of VSDPL (vanished some of derivatives of<br />phase-lag), for the numerical integration of the one-dimensional Schrodinger equation. We will show superiority of new method in stability, accuracy and efficiency. So we present a stability analysis and an error analysis based on the radial Schrodinger equation. Also we will apply the new proposed method to the resonance problem of the radial Schrodinger equation.
P-stable
Phase-lag
Schr"{o}dinger equation
trigonometrically fitted
2016
06
01
687
706
http://bims.iranjournals.ir/article_806_30e8c4d6d6c54025669e5872bc7174c3.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
On subdifferential in Hadamard spaces
M.
Soleimani-damaneh
M.
Movahedi
D.
Behmardi
In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and suficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdifferential set is established.
Subdifferential
Hadamard Space
Flat space
Hilbert space
Convexity
2016
06
01
707
717
http://bims.iranjournals.ir/article_807_c964b05ed4b54e1642cbd753e007a371.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
W.
Zhu
S.
Ling
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Let ${S_n}$ and ${T_n}$ be sequences of nonexpansive self-mappings of $C$, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)S_n(alpha_nu+(1-alpha_n)T_nx_n)$ for finding the common fixed point of ${S_n}$ and ${T_n}$, where $uin C$ is an arbitrarily (but fixed) element in $C$, $x_0in C$ arbitrarily, ${alpha_n}$ and ${beta_n}$ are sequences in $[0,1]$. But in the case where $unotin C$, the iterative scheme above becomes invalid because $x_n$ may not belong to $C$. To overcome this weakness, a new iterative scheme based on the thought of boundary point method is proposed and the strong convergence theorem is proved. As a special case, we can find the minimum-norm common fixed point of ${S_n}$ and ${T_n}$ whether $0in C$ or $0notin C$.
minimum-norm common fixed point
strongly nonexpansive mappings
strong convergence
boundary point method
variational inequality
2016
06
01
719
730
http://bims.iranjournals.ir/article_808_2c7750cdcd7019d6e876e332881bea9f.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
On strongly dense submodules
E.
Ghashghaei
M.
Namdari
The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bigcap N=0$. We also introduce a class of modules in which the two concepts of strong essentiality and strong density coincide. It is also shown that for any module $M$, dense submodules in $M$ are strongly dense if and only if $Mleq_{sd} tilde{E}(M)$, where $tilde{E}(M)$ is the rational hull of $M$. It is proved that $R$ has no strongly dense left ideal if and only if no nonzero-element of every cyclic $R$-module $M$ has a strongly dense annihilator in $R$. Finally, some appropriate properties and new concepts related to strong density are defined and studied.
Strongly essential submodule
strongly dense submodule
singular submodule
special submodule
column submodule
2016
06
01
731
747
http://bims.iranjournals.ir/article_809_9508d8b8a48f740c5b8f741a57040ea9.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
The power digraphs of safe primes
U.
Ahmad
S. M.
Husnine
A power digraph, denoted by $G(n,k)$, is a directed graph with $Z_{n}={0,1,..., n-1}$ as the set of vertices and<br /> $L={(x,y):x^{k}equiv y~(mod , n)}$ as the edge set, where $n$ and $k$ are any positive integers. In this paper, the structure of $G(2q+1,k)$, where $q$ is a Sophie Germain prime is investigated. The primality tests for the integers of the form $n=2q+1$ are established in terms of the structure of components of $G(n,k)$. The digraphs in which all components look like directed star graphs are completely classified. This work generalizes the results of M. Krizekek, L. Somer, Sophie Germain Little Suns, Math. Slovaca 54(5) (2004), 433-442.
Iteration digraph
Carmichael lambda function
fixed point
Sophie Germain primes
Safe primes
2016
06
01
749
759
http://bims.iranjournals.ir/article_810_0df6b481f1fb0fa44a9e1d04a5d4fa1a.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Applications of subordination theory to starlike functions
K.
Sharma
V.
Ravichandran
Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ when the functions $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)$ , $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ or $p(z)+beta zp'(z)/p^{2}(z)$ is subordinate to $varphi_{C}(z)$. Related results for $p$ to be in the parabolic region bounded by the $RE w=|w-1|$ are investigated.
convex and starlike functions
differential subordination
univalent functions
2016
06
01
761
777
http://bims.iranjournals.ir/article_811_b56bdeb24d06f65b35a6ba3a70fd9fd6.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2016
42
3
Weak $F$-contractions and some fixed point results
N. A.
Secelean
In this paper we define weak $F$-contractions on a metric space into itself by extending $F$-contractions introduced by D. Wardowski (2012) and provide some fixed point results in complete metric spaces and in partially ordered complete generalized metric spaces. Some relationships between weak $F$-contractions and $varphi$-contractions are highlighted. We also give some applications on fractal theory improving the classical Hutchinson-Barnsley's theory of iterated function systems. Some illustrative examples are provided.
F-contraction
partially ordered metric space
generalized metric
iterated function system
fixed point theorem
2016
06
01
779
798
http://bims.iranjournals.ir/article_812_f9360006c4cf94034e472005a0ef6475.pdf