Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Flag-transitive point-primitive $(v,k,4)$ symmetric designs with exceptional socle of Lie type259273929ENY. WangDepartment of Mathematics, South China University of Technology, 510640, Guangzhou, China.S. ZhouDepartment of Mathematics, South China University of Technology, 510640, Guangzhou, China.Journal Article20140425Let $G$ be an automorphism group of a $2$-$(v,k,4)$ symmetric design $mathcal D$. In this paper, we prove that if $G$ is flag-transitive point-primitive, then the socle of $G$ cannot be an exceptional group of Lie type.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Connections between labellings of trees275283930ENB. YaoCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China.X. LiuSchool of Mathematics and Statistics, Beijing Institute of Techology, Beijing 100081, China.M. YaoDepartment of Information Process and Control Engineering,
Lanzhou Petrochemical College of Vocational Technology, Lanzhou,
730060, China.Journal Article20131223There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Arens regularity of bilinear maps and Banach modules actions285289931ENA. SahlehFaculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.L. NajarpishehFaculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.Journal Article20150404Let $X$, $Y$ and $Z$ be Banach spaces and $f:Xtimes Y longrightarrow Z$ a bounded bilinear map. In this paper we study the relation between Arens regularity of $f$ and the reflexivity of $Y$. We also give some conditions under which the Arens regularity of a Banach algebra $A$ implies the Arens regularity of certain Banach right module action of $A$ .Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Multipliers of continuous $G$-frames in Hilbert spaces291305932ENM. R. AbdollahpourDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Y. AlizadehDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil 56199-11367, Iran.Journal Article20150607In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Study on multi-order fractional differential equations via operational matrix of hybrid basis functions307318933ENK. MaleknejadSchool of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16846 13114, Iran.K. NouriDepartment of Mathematics, Faculty of Mathematics, Statistics
and Computer Sciences, Semnan University, P.O. Box 35195-363,
Semnan, Iran.L. TorkzadehDepartment of Mathematics, Faculty of Mathematics, Statistics
and Computer Sciences, Semnan University, P.O. Box 35195-363,
Semnan, Iran.Journal Article20140228In this paper we apply hybrid functions of general block-pulse functions and Legendre polynomials for solving linear and nonlinear multi-order fractional differential equations (FDEs). Our approach is based on incorporating operational matrices of FDEs with hybrid functions that reduces the FDEs problems to the solution of algebraic systems. Error estimate that verifies a convergence of the approximate solutions is considered. The numerical results obtained by this scheme have been compared with the exact solution to show the efficiency of the method.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401A new result on chromaticity of K4-homoemorphs with girth 9319336934ENN.S.A. KarimDepartment of Mathematics, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris,
35900 Tanjong Malim, Perak, Malaysia.R. HasniSchool of Informatics and Applied Mathematics,
University Malaysia Terengganu,
21030 Kuala Terengganu, Terengganu, Malaysia.G.C. LauFaculty of Computer and Mathematical Sciences,
University Teknologi MARA (Segamat Campus)
85000 Segamat, Johor, Malaysia.Journal Article20150324For a graph $G$, let $P(G,lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if any graph chromatically equivalent to $G$ is isomorphic to $G$. A $K_4$-homeomorph is a subdivision of the complete graph $K_4$. In this paper, we determine a family of chromatically unique $K_4$-homeomorphs which have girth 9 and has exactly one path of length 1, and give sufficient and necessary condition for the graphs in this family to be chromatically unique.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Extrinsic sphere and totally umbilical submanifolds in Finsler spaces337347935ENB. BidabadFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914, Tehran, Iran.M. SedaghatFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914, Tehran, Iran.Journal Article20150118Based on a definition for circle in Finsler space, recently proposed by one of the present authors and Z. Shen, a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field, if and only if its circles coincide with circles of the ambient manifold.<br /> Finally, some examples of extrinsic sphere in Finsler geometry, particularly in Randers spaces are given.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Strong convergence theorem for solving split equality fixed point problem which does not involve the prior knowledge of operator norms349371936ENY. ShehuDepartment of Mathematics, University of Nigeria, Nsukka, Nigeria.F. U. OgbuisiSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa.O. S. IyiolaDepartment of Mathematical Sciences, University of Wisconsin-Milwaukee, Wisconsin, USAJournal Article20140716Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space. So many have used algorithms involving the operator norm for solving split equality fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, some researchers have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. To the best of our knowledge most of the works in literature that do not involve the calculation or estimation of the operator norm only obtained weak convergence results. In this paper, by appropriately modifying the simultaneous iterative algorithm introduced by Zhao, we state and prove a strong convergence result for solving split equality problem. We present some applications of our result and then give some numerical example to study its efficiency and implementation at the end of the paper.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian373384937ENA. DoganDepartment of Applied Mathematics, Faculty of Computer Sciences, Abdullah Gul University, Kayseri, 38039, Turkey.Journal Article20150611In this paper, we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401New classes of Lyapunov type inequalities of fractional $Delta$-difference Sturm-Liouville problems with applications385408938ENK. GhanbariDepartment of Applied Mathematics, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran.Y. GholamiDepartment of Applied Mathematics, Sahand University of Technology, P.O. Box 51335-1996, Tabriz, Iran.Journal Article20150829In this paper, we consider a new study about fractional $Delta$-difference equations. We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators. In couple of steps, the Lyapunov type inequalities for both classes will be obtained. As application, some qualitative behaviour of mentioned fractional problems such as stability, spectral, disconjugacy and some interesting results about zeros of (oscillatory) solutions will be concluded.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Some extended Simpson-type inequalities and applications409425939ENK. C. HsuDepartment of Business Administration, Aletheia University, Tamsui, New Taipei City 25103, Taiwan.S. R. HwangChina University of Science and Technology, Nankang, Taipei 11522, Taiwan.K. L. TsengDepartment of Applied Mathematics, Aletheia University, Tamsui, New Taipei City 25103, Taiwan.Journal Article20141125In this paper, we shall establish some extended Simpson-type inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Simpson formula are also given.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Left derivable or Jordan left derivable mappings on Banach algebras427437940ENY. DingDepartment of Mathematics, East China University of Science and Technology, Shanghai, China.J. LiDepartment of Mathematics, East China University of Science and Technology, Shanghai, China.Journal Article20150709Let $mathcal{A}$ be a unital Banach algebra, $mathcal{M}$ be a left $mathcal{A}$-module, and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$. We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$, then the following four conditions are equivalent: (i) $delta$ is a Jordan left derivation; (ii)$delta$ is left derivable at $W$; (iii) $delta$ is Jordan left derivable at $W$; (iv)$Adelta(B)+Bdelta(A)=delta(W)$ for each $A,B$ in $mathcal{A}$ with $AB=BA=W$.<br /> Let $mathcal{A}$ have property ($mathbb{B}$) (see Definition ref{Prop_B}), $mathcal{M}$ be a Banach left $mathcal{A}$-module, and $delta$ be a continuous linear operator from $mathcal{A}$ into $mathcal{M}$. Then $delta$ is a generalized Jordan left derivation if and only if $delta$ is Jordan left derivable at zero. In addition, if there exists an element $Cinmathcal{Z}(mathcal{A})$ which is a left separating point of $mathcal{M}$, and $Rann_{mathcal{M}}(mathcal{A})={0}$, then $delta$ is a generalized left derivation if and only if $delta$ is left derivable at zero.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401The Steiner diameter of a graph439454941ENY. MaoDepartment of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, China.Journal Article20140806The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the Steiner distance $d(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n,k$ be two integers with $2leq kleq n$. Then the Steiner $k$-eccentricity $e_k(v)$ of a vertex $v$ of $G$ is defined by $e_k(v)=max {d(S),|,Ssubseteq V(G), |S|=k, and vin S}$. Furthermore, the Steiner $k$-diameter of $G$ is $sdiam_k(G)=max {e_k(v),| vin V(G)}$. In 2011, Chartrand, Okamoto and Zhang showed that $k-1leq sdiam_k(G)leq n-1$. In this paper, graphs with $sdiam_3(G)=2,3,n-1$ are characterized, respectively. We also consider the Nordhaus-Gaddum-type results for the parameter $sdiam_k(G)$. We determine sharp upper and lower bounds of $sdiam_k(G)+sdiam_k(overline{G})$ and $sdiam_k(G)cdot sdiam_k(overline{G})$ for a graph $G$ of order $n$. Some graph classes attaining these bounds are also given. Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Module homomorphisms from Frechet algebras455466942ENH. ShayanpourDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Shahrekord, P.O. Box 88186-34141, Shahrekord, Iran.Journal Article20130724We first study some properties of $A$-module homomorphisms $theta:Xrightarrow Y$, where $X$ and $Y$ are Fréchet $A$-modules and $A$ is a unital Fréchet algebra. Then we show that if there exists a continued bisection of the identity for $A$, then $theta$ is automatically continuous under certain condition on $X$. In particular, every homomorphism from $A$ into certain Fréchet algebras (including Banach algebra) is automatically continuous. Finally, we show that every unital Fréchet algebra with a continued bisection of the identity, is functionally continuous.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401On convergence of sample and population Hilbertian functional principal components467475943ENA. R. SoltaniDepartment of Statistics, Shiraz University and Department of Statistics and Operations Research, Kuwait
University, State of Kuwait.A. R. NematollahiDepartment of Statistics, Shiraz University, Shiraz, Iran.R. NasirzadehDepartment of Statistics, Shiraz University, Shiraz, Iran.Journal Article20150704In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would imply the convergence of the corresponding sequences of the sample and<br />population eigenvalues and eigenvectors, and vice versa. In particular we prove that the principal component scores converge in distribution in certain family of Hilbertian elliptically contoured distributions.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Digital Borsuk-Ulam theorem477499944ENG. BurakDepartment of Mathematics, Pamukkale University, P.O. Box 20070, Denizli, Turkey.I. KaracaDepartment of Mathematics, Ege University, P.O .Box 35100, Izmir, Turkey.Journal Article20140603The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401A characterization of simple $K_4$-groups of type $L_2(q)$ and their automorphism groups501514945ENJ. LiDepartment of Mathematics and Chongqing Key Laboratory of GGTA,
Chongqing University of Arts and Sciences, Chongqing 402160, P.R.
China.D. YuDepartment of Mathematics and Chongqing Key Laboratory of GGTA,
Chongqing University of Arts and Sciences, Chongqing 402160, P.R.
China.G. ChenSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R. China.W. ShiDepartment of Mathematics and Chongqing Key Laboratory of GGTA,
Chongqing University of Arts and Sciences, Chongqing 402160, P.R.
China.Journal Article20150322In this paper, it is proved that all simple $K_4$-groups of type $L_2(q)$ can be characterized by their maximum element orders together with their orders. Furthermore, the automorphism groups of simple $K_4$-groups of type $L_2(q)$ are also considered.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains515534946ENX. LiSchool of Science, Hohai University, Nanjing, Jiangsu 210098, China.Journal Article20140906At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Comparative study on solving fractional differential equations via shifted Jacobi collocation method535560947ENM. BehroozifarDepartment of Mathematics, Faculty of Basic sciences, Babol Noshirvani University of Technology, Babol, Mazandaran, Iran.F. AhmadpourDepartment of Mathematics, Faculty of Basic sciences, Babol Noshirvani University of Technology, Babol, Mazandaran, Iran.Journal Article20150418In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equation are approximated by shifted Jacobi polynomials. Then, operational matrices and spectral collocation method are applied to obtain a linear or nonlinear system of algebraic equations. System of algebraic equations can be simultaneously solved (e.g. using Mathematica^{TM}). Main characteristic behind of the this technique is that only a small number of shifted Jacobi polynomials is needed to obtain a satisfactory result which demonstrates the validity and efficiency of the method. Comparison between this method and some other methods confirm the good performance of the presented method. Also, this method is generalized for the multi-point fractional differential equation.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43220170401Separating partial normality classes with weighted composition operators561574948ENH. EmamalipourFaculty of Mathematical Sciences, University of Tabriz, P.O. Box 5166615648,
Tabriz, Iran.M. R. JabbarzadehFaculty of Mathematical Sciences, University of Tabriz, P.O. Box 5166615648,
Tabriz, Iran.Z. MoayyerizadehFaculty of Mathematical Sciences, University of Tabriz, P.O. Box 5166615648,
Tabriz, Iran.Journal Article20140503In this article, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^{2}(Sigma)$ such as, $n$-power normal, $n$-power quasi-normal, $k$-quasi-paranormal and quasi-class$A$. Then we show that weighted composition operators can separate these classes.