Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Total perfect codes, OO-irredundant and total subdivision in graphs499506778ENH. HosseinzadehDepartment of Mathematics, Alzahra University, P.O. Box 19834, Tehran, Iran.N. SoltankhahDepartment of Mathematics, Alzahra University,
P.O. Box 19834, Tehran, Iran.Journal Article20140226Let $G=(V(G),E(G))$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601The theory of matrix-valued multiresolution analysis frames507519779ENP. ZhaoSchool of Science, Beijing Jiaotong University,
Beijing, 100044, China.C. ZhaoFaculty of Mathematics Science , Tianjin normal
University, Tianjin, 300074, ChinaJournal Article20160504A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Polynomially bounded solutions of the Loewner differential equation in several complex variables521537777ENA. EbadianDepartment of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.S. RahroviDepartment of Mathematics, Faculty of Basic Science, University of Bonab, P.O. Box 5551-761167, Bonab, Iran.S. ShamsDepartment of Mathematics, Urmia University, Urmia,
Iran.J. SokolDepartment of Mathematics, Rzesz'ow University of Technology, Poland.Journal Article20121029We 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601$k$-power centralizing and $k$-power skew-centralizing maps on triangular rings539554776ENX. F. QiDepartment of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.Journal Article20150105Let $mathcal A$ 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 /> Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601On radical formula and Prufer domains555563797ENR. NekooeiDepartment of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.F. MirzaeiDepartment of Pure
Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar
University
of Kerman, P.O. Box 76169133, Kerman, Iran.Journal Article20141129In 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 /> Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601On cohomogeneity one nonsimply connected 7-manifolds of constant positive curvature565584798ENM. ZareiDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
Tarbiat Modares University,
P.O. Box 14115-134,
Tehran, Iran.S.M.B. KashaniTarbiat Modares UniversityH. AbediMathematics Group, School of Sciences Bu-Ali Sina University, Hamedan, Iran.Journal Article20140816In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Complete characterization of the Mordell-Weil group of some families of elliptic curves585594799ENH. DaghighFaculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.S. DidariFaculty of Mathematical Sciences, University of Kashan, P.O. Box 8731751167, Kashan, Iran.Journal Article20140210 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Involutiveness of linear combinations of a quadratic or tripotent matrix and an arbitrary matrix595610800ENX. LiuCollege of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.J. BenitezDepartamento de Matematica Aplicada, Instituto de Matematica Multidisciplinar,
Universidad Politecnica de Valencia, Valencia 46022, Spain.M. ZhangCollege of Science, Guangxi
University for Nationalities, Nanning 530006, P. R. China.Journal Article20140930In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions611626801ENY. JalilianDepartment of Mathematics, Razi University,
Kermanshah, Iran.Journal Article20140707In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601T-dual Rickart modules611642802ENS. Ebrahimi AtaniDepartment of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.M. KhoramdelDepartment of
Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.S. Dolati Pish HesariDepartment of Mathematics, University
of Guilan, P.O. Box 1914, Rasht, Iran.Journal Article20130924We 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation643658803ENH. TangDepartment of Mathematics, Jilin University, Changchun 130012,
P.R. China
and
School of Science, Changchun University, Changchun 130022, P.R. China.C. LiuDepartment of Mathematics, Jilin University, Changchun 130012,
P.R. China.Z. ZhaoDepartment 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.Journal Article20140919In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Nonlinear $*$-Lie higher derivations on factor von Neumann algebras659678804ENF. ZhangSchool of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, P. R. China.X. QiDepartment of Mathematics, Shanxi University, Taiyuan 030006, P. R. China.J. ZhangCollege of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R China.Journal Article20140926Let $mathcal M$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Bounding cochordal cover number of graphs via vertex stretching679685805ENM. R. FanderScience and Research Branch, Islamic Azad University
(IAU), Tehran, Iran.Journal Article20140421It 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601P-stability, TF and VSDPL technique in Obrechkoff methods for the numerical solution of the Schrodinger equation687706806ENA. ShokriDepartment of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.H. SaadatDepartment of Mathematics, Faculty of Basic Science, University
of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.Journal Article20140923Many 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601On subdifferential in Hadamard spaces707717807ENM. Soleimani-damaneh{School of Mathematics, Statistics and Computer Science, College of Science, University of
Tehran, Enghelab Avenue, Tehran, Iran.M. MovahediDepartment of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.D. BehmardiDepartment of Mathematics, Faculty of Sciences, Alzahra University, Tehran, Iran.Journal Article20140913In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences719730808ENW. ZhuCollege of Management and Economics, Tianjin University,
Tianjin 300072, China.S. LingCollege of Management and Economics, Tianjin University,
Tianjin 300072, China.Journal Article20141212Let $C$ 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 $0notin C$.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601On strongly dense submodules731747809ENE. GhashghaeiDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.M. NamdariDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.Journal Article20140829The 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601The power digraphs of safe primes749759810ENU. AhmadDepartment of
Mathematics, University
of the Punjab, New Campus, Lahore, Pakistan.S. M. HusnineDepartment of Humanities
and Sciences, National University
of Computer and Emerging Sciences(FAST), Lahore Campus, Lahore, Pakistan.Journal Article20130913A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Applications of subordination theory to starlike functions761777811ENK. SharmaDepartment of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi 110021, India.V. RavichandranDepartment of Mathematics, University of Delhi, Delhi--110007, India.0000-0002-3632-7529Journal Article20150213Let $p$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42320160601Weak $F$-contractions and some fixed point results779798812ENN. A. SeceleanDepartment of Mathematics and Informatics Faculty of Sciences,
Lucian Blaga University of Sibiu, Romania.Journal Article20141024In 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.