Bulletin of the Iranian Mathematical Society
text
article
2016
eng
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
http://bims.iranjournals.ir/article_796_dc33b7469948b4c04368c4273c896ac2.pdf
Total perfect codes, OO-irredundant and total subdivision in graphs
H.
Hosseinzadeh
Department of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.
author
N.
Soltankhah
Department of Mathematics, Alzahra University,
P.O. Box 19834, Tehran, Iran.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
499
506
http://bims.iranjournals.ir/article_778_fa2994302d0b573b33b69934d84dde37.pdf
The theory of matrix-valued multiresolution analysis frames
P.
Zhao
School of Science, Beijing Jiaotong University,
Beijing, 100044, China.
author
C.
Zhao
Faculty of Mathematics Science , Tianjin normal
University, Tianjin, 300074, China
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
507
519
http://bims.iranjournals.ir/article_779_bb10aaa73cdd7d1d0904b351010f3dbf.pdf
Polynomially bounded solutions of the Loewner differential equation in several complex variables
A.
Ebadian
Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.
author
S.
Rahrovi
Department of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.
author
S.
Shams
Department of Mathematics, Urmia University, Urmia,
Iran.
author
J.
Sokol
Department of Mathematics, Rzesz'ow University of Technology, Poland.
author
text
article
2016
eng
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 $$\sup_{s\geq0}\int_0^\infty\left\|\exp\left\{\int_s^t [A(\tau)-2m(A(\tau))I_n]\rm {d}\tau\right\}\right\|{\rm d}t<\infty,$$ and $m(A(t))>0$ for $t\geq0$, where $m(A)=\min\{\mathfrak{Re}\left\langle A(z),z\right\rangle:\|z\|=1\}$. 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
521
537
http://bims.iranjournals.ir/article_777_1bac89a6fb0e82c7a49584552cbe52f2.pdf
$k$-power centralizing and $k$-power skew-centralizing maps on triangular rings
X. F.
Qi
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
author
text
article
2016
eng
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 $x,\ y\in{\mathcal U}$ 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 $x\in{\mathcal U}$; (2) $[f(x),x^k]=0$ for all $x\in{\mathcal U}$; (3) $[f(x),x]=0$ for all $x\in{\mathcal U}$; (4) there exist a central element $z\in{\mathcal Z}({\mathcal U})$ and an additive modulo ${\mathcal Z}({\mathcal U})$ map $h:{\mathcal U}\rightarrow{\mathcal Z}({\mathcal U})$ such that $f(x)=zx+h(x)$ for all $x\in{\mathcal U}$. It is also shown that there is no nonzero additive $k$-skew-centralizing maps on triangular rings.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
539
554
http://bims.iranjournals.ir/article_776_5f93e5da86761d28483d66373943f57e.pdf
On radical formula and Prufer domains
R.
Nekooei
Department of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.
author
F.
Mirzaei
Department of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.
author
text
article
2016
eng
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 $R\bigoplus R$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
555
563
http://bims.iranjournals.ir/article_797_18ddba9d7a3f373b64964a1c3fa7e85c.pdf
On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature
M.
Zarei
Department of Pure Mathematics,
Faculty of Mathematical Sciences,
Tarbiat Modares University,
P.O. Box 14115-134,
Tehran, Iran.
author
S.M.B.
Kashani
Tarbiat Modares University
author
H.
Abedi
Mathematics Group, School of Sciences Bu-Ali Sina University, Hamedan, Iran.
author
text
article
2016
eng
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-topy groups of the orbits have been presented as well.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
565
584
http://bims.iranjournals.ir/article_798_57c6204c6001577ab8221c3c84ec415c.pdf
Complete characterization of the Mordell-Weil group of some families of elliptic curves
H.
Daghigh
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
author
S.
Didari
Faculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
585
594
http://bims.iranjournals.ir/article_799_3ad7f75a4be58868ac2adcc0d33b1d9f.pdf
Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix
X.
Liu
College of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.
author
J.
Benitez
Departamento de Matematica Aplicada, Instituto de Matematica Multidisciplinar,
Universidad Politecnica de Valencia, Valencia 46022, Spain.
author
M.
Zhang
College of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.
author
text
article
2016
eng
In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
595
610
http://bims.iranjournals.ir/article_800_4cbebc1a2c9731758eba450931c50d7d.pdf
Infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions
Y.
Jalilian
Department of Mathematics, Razi University,
Kermanshah, Iran.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
611
626
http://bims.iranjournals.ir/article_801_4e0cfaca570cffce5b5d67eec547dff4.pdf
T-dual Rickart modules
S.
Ebrahimi Atani
Department of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
author
M.
Khoramdel
Department of
Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
author
S.
Dolati Pish Hesari
Department of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.
author
text
article
2016
eng
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. Examplesillustrating the results are presented.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
611
642
http://bims.iranjournals.ir/article_802_ff60a17a6bbe853afe2fa8050110df8e.pdf
The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
H.
Tang
Department of Mathematics, Jilin University, Changchun 130012,
P.R. China
and
School of Science, Changchun University, Changchun 130022, P.R. China.
author
C.
Liu
Department of Mathematics, Jilin University, Changchun 130012,
P.R. China.
author
Z.
Zhao
Department of Mathematics, Changchun Normal University, Chang-chun
130032, P.R. China
and
Academy of Mathematics and Systems Science,
Chinese Academy of Sciences, Beijing, 100190, P.R. China.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
643
658
http://bims.iranjournals.ir/article_803_0b5005164973791b8218766a77550508.pdf
Nonlinear $*$-Lie higher derivations on factor von Neumann algebras
F.
Zhang
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, P. R. China.
author
X.
Qi
Department of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.
author
J.
Zhang
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R China.
author
text
article
2016
eng
Let $\mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation $D={\phi_{n}}_{n\in\mathbb{N}}$ on $\mathcal M$ is additive. In particular, if $\mathcal M$ is infinite type $I$ factor, a concrete characterization of $D$ is given.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
659
678
http://bims.iranjournals.ir/article_804_014d235291f660ccf7545720818e036c.pdf
Bounding cochordal cover number of graphs via vertex stretching
M. R.
Fander
Science and Research Branch, Islamic Azad University
(IAU), Tehran, Iran.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
679
685
http://bims.iranjournals.ir/article_805_81bd74ccf92af8a92a50edd4ec90271f.pdf
P-stability, TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation
A.
Shokri
Department of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.
author
H.
Saadat
Department of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.
author
text
article
2016
eng
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 ofphase-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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
687
706
http://bims.iranjournals.ir/article_806_30e8c4d6d6c54025669e5872bc7174c3.pdf
On subdifferential in Hadamard spaces
M.
Soleimani-damaneh
{School of Mathematics, Statistics and Computer Science, College of Science, University of
Tehran, Enghelab Avenue, Tehran, Iran.
author
M.
Movahedi
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
author
D.
Behmardi
Department of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
707
717
http://bims.iranjournals.ir/article_807_c964b05ed4b54e1642cbd753e007a371.pdf
Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
W.
Zhu
College of Management and Economics, Tianjin University,
Tianjin 300072, China.
author
S.
Ling
College of Management and Economics, Tianjin University,
Tianjin 300072, China.
author
text
article
2016
eng
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 $C$, $x_0\in C$ arbitrarily, ${\alpha_n}$ and ${\beta_n}$ are sequences in $[0,1]$. But in the case where $u\notin C$, 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 $0\in C$ or $0\notin C$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
719
730
http://bims.iranjournals.ir/article_808_2c7750cdcd7019d6e876e332881bea9f.pdf
On strongly dense submodules
E.
Ghashghaei
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
author
M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
author
text
article
2016
eng
The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $N\leq_{sd}M$, if for any index set $I$, $\prod _{I}N\leq_{d}\prod _{I}M$) 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 $M\leq_{sd} \tilde{E}(M)$, 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
731
747
http://bims.iranjournals.ir/article_809_9508d8b8a48f740c5b8f741a57040ea9.pdf
The power digraphs of safe primes
U.
Ahmad
Department of
Mathematics, University
of the Punjab, New Campus, Lahore, Pakistan.
author
S. M.
Husnine
Department of Humanities
and Sciences, National University
of Computer and Emerging Sciences(FAST), Lahore Campus, Lahore, Pakistan.
author
text
article
2016
eng
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 $L={(x,y):x^{k}\equiv y~(mod , n)}$ 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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
749
759
http://bims.iranjournals.ir/article_810_0df6b481f1fb0fa44a9e1d04a5d4fa1a.pdf
Applications of subordination theory to starlike functions
K.
Sharma
Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi 110021, India.
author
V.
Ravichandran
Department of Mathematics, University of Delhi, Delhi--110007, India.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
761
777
http://bims.iranjournals.ir/article_811_b56bdeb24d06f65b35a6ba3a70fd9fd6.pdf
Weak $F$-contractions and some fixed point results
N. A.
Secelean
Department of Mathematics and Informatics Faculty of Sciences,
Lucian Blaga University of Sibiu, Romania.
author
text
article
2016
eng
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.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
42
v.
3
no.
2016
779
798
http://bims.iranjournals.ir/article_812_f9360006c4cf94034e472005a0ef6475.pdf