Bulletin of the Iranian Mathematical Society text article 2016 eng Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 http://bims.iranjournals.ir/article_861_accfc01f02b7e1ec0a15b183341aeac2.pdf Forced oscillations of a damped‎ ‎Korteweg-de Vries equation on a periodic domain M. Chen School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, ‎P‎. ‎R‎. ‎China. author text article 2016 eng ‎In this paper‎, ‎we investigate a damped Korteweg-de‎ ‎Vries equation with forcing on a periodic domain‎ ‎$\mathbb{T}=\mathbb{R}/(2\pi\mathbb{Z})$‎. ‎We can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1027 1038 http://bims.iranjournals.ir/article_862_ab038992016b1b175d32df688062e53c.pdf Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method M‎. ‎ Garshasbi School of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran. author F. ‎Hassani School of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran. author text article 2016 eng ‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linear algebraic equations is ill-posed‎, ‎the Tikhonov first-order regularization procedure is employed to obtain a stable solution‎. ‎Determination of regularization parameter is based on L-curve technique‎. ‎Some numerical examples for the feasibility of the proposed method are presented‎. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1039 1057 http://bims.iranjournals.ir/article_863_d469ccbf86a94e4c4831982ef32f13b6.pdf On a generalization of condition (PWP) X. Liang Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China.‎ ‎ author Y. Luo Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China. author text article 2016 eng ‎There is a flatness property of acts over monoids called Condition $(PWP)$ which‎, ‎so far‎, ‎has received‎ ‎much attention‎. ‎In this paper‎, ‎we introduce Condition GP-$(P)$‎, ‎which is a generalization of Condition $(PWP)$‎. ‎Firstly‎, ‎some  characterizations of monoids by Condition GP-$(P)$ of their‎ ‎(cyclic‎, ‎Rees factor) acts are given‎, ‎and many known results are generalized‎. ‎Moreover‎, ‎some possible conditions on monoids that describe when their diagonal acts satisfy Condition GP-$(P)$ are found‎. ‎Finally‎, ‎using some new types of epimorphisms‎, ‎an alternative description of Condition GP-$(P)$ (resp.‎, ‎Condition $(PWP)$) is obtained‎, ‎and directed‎ ‎colimits of these new epimorphisms are investigated. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1057 1076 http://bims.iranjournals.ir/article_864_6aca97cc012989be8545639bb27655ed.pdf Approximate solution of dual integral equations S. ‎Ahdiaghdam Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. author K. ‎Ivaz Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. author S. ‎Shahmorad Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. author text article 2016 eng ‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will be‎ ‎used to approximate the solution of the main dual integral‎ ‎equations‎. ‎Numerical results demonstrate effectiveness of this method. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1077 1086 http://bims.iranjournals.ir/article_865_36fdbd67705679576cbc4c02707cf62d.pdf On the bounds in Poisson approximation for independent geometric distributed random variables T. L. Hung University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7‎, ‎Ho Chi Minh city‎, ‎Vietnam. author L. T. ‎Giang University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7‎, ‎Ho Chi Minh city‎, ‎Vietnam. author text article 2016 eng ‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1087 1096 http://bims.iranjournals.ir/article_866_5fccc709565917424a38a1fa4d5c23c3.pdf Which elements of a finite group are non-vanishing? M. Arezoomand Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-83111, Isfahan‎, ‎Iran. author B. Taeri Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-838111, Isfahan‎, ‎Iran. author text article 2016 eng ‎Let $G$ be a finite group‎. ‎An element $g\in G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $\chi$ of $G$‎, ‎$\chi(g)\neq 0$‎. ‎The bi-Cayley graph ${\rm BCay}(G,T)$ of $G$ with respect to a subset $T\subseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(tx,2)\}\mid x\in G‎, ‎\ t\in T\}$‎. ‎Let ${\rm nv}(G)$ be the set‎ ‎of all non-vanishing elements of a finite group $G$‎. ‎We show that $g\in nv(G)$ if and only if the adjacency matrix of ${\rm BCay}(G,T)$‎, ‎where $T={\rm Cl}(g)$ is the‎ ‎conjugacy class of $g$‎, ‎is non-singular‎. ‎We prove that ‎if the commutator subgroup of $G$ has prime order $p$‎, ‎then‎  ‎(1) $g\in {\rm nv}(G)$ if and only if $|Cl(g)|<p$, ‎(2) if $p$ is the smallest prime divisor of $|G|$‎, ‎then ${\rm nv}(G)=Z(G)$‎. ‎‎Also we show that‎ (a) if ${\rm Cl}(g)=\{g,h\}$‎, ‎then $g\in {\rm nv}(G)$ if and only if $gh^{-1}$ has odd order‎, (b) if $|{\rm Cl}(g)|\in \{2,3\}$ and $({\rm ord}(g),6)=1$‎, ‎then $g\in {\rm nv}(G)$‎. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1097 1106 http://bims.iranjournals.ir/article_867_e6b164bbe3a5bd8febacd1a5524efcc6.pdf Numerical approach for solving a class of nonlinear fractional differential equation S. Irandoust-pakchin Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. author M. Lakestani Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. author H. ‎Kheiri Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. author text article 2016 eng ‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described based on the‎ ‎Caputo sense‎. ‎Our main aim is to generalize the Chebyshev cardinal‎ ‎operational matrix to the fractional calculus‎. ‎In this work‎, ‎the‎ ‎Chebyshev cardinal functions together with the Chebyshev cardinal‎ ‎operational matrix of fractional derivatives are used for numerical‎ ‎solution of a class of fractional differential equations‎. ‎The main‎ ‎advantage of this approach is that it reduces fractional problems to‎ ‎a system of algebraic equations‎. ‎The method is applied to solve‎  ‎nonlinear fractional differential equations‎. ‎Illustrative examples‎ ‎are included to demonstrate the validity and applicability of the ‎presented technique‎. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1107 1126 http://bims.iranjournals.ir/article_868_26827a7d21fe2b110ccd0dc9c647f92a.pdf The use of inverse quadratic radial basis functions for the solution of an inverse heat problem F. ‎Parzlivand Department of Mathematics‎, ‎Alzahra University‎, ‎Vanak‎, ‎Post Code 19834‎, ‎Tehran‎, ‎Iran. author A. Shahrezaee Department of Mathematics‎, ‎Alzahra University‎, ‎Vanak‎, ‎Post Code 19834‎, ‎Tehran‎, ‎Iran. author text article 2016 eng ‎In this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎The method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadratic‎ ‎radial basis functions (IQ-RBFs)‎. ‎The operational matrix of‎ ‎derivative for IQ-RBFs is introduced and the new computational‎ ‎technique is used for this purpose‎. ‎The operational matrix of‎ ‎derivative is utilized to reduce the problem to a set of algebraic‎ ‎equations‎. ‎Some examples are given to demonstrate the validity and‎ ‎applicability of the new method and a comparison is made with the‎ ‎existing results. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1127 1142 http://bims.iranjournals.ir/article_869_56874af181e3b46e92db683c4c49a920.pdf Composition operators and natural metrics in meromorphic function classes $Q_p$ A. Kamal Port Said University‎, ‎Faculty of Science‎, ‎Department of Mathematics, Port Said 42521‎, ‎Egypt. author text article 2016 eng ‎In this paper‎, ‎we investigate some results on natural metrics on the $\mu$-normal functions and meromorphic $Q_p$-classes‎. ‎Also‎, ‎these classes are shown to be complete metric spaces with respect to the corresponding metrics‎. ‎Moreover‎, ‎compact composition operators $C_\phi$ and Lipschitz continuous operators acting from $\mu$-normal functions to the meromorphic $Q_p$-classes are characterized by conditions depending only on $\phi.$ Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1143 1154 http://bims.iranjournals.ir/article_870_35e24f164aba15e6073c999fba0d70b5.pdf Multiplication operators on Banach modules over spectrally separable algebras J. ‎Bračič Department of Materials and Metallurgy‎, ‎Faculty of Natural Sciences and Engineering‎, ‎University of Ljubljana‎, ‎Aškerčeva c‎. ‎12‎, ‎SI-1000 Ljubljana‎, ‎Slovenia. author text article 2016 eng ‎Let $\mathcal{A}$ be a commutative Banach algebra and $\mathscr{X}$ be a left Banach $\mathcal{A}$-module‎. ‎We study the set‎ ‎${\rm Dec}_{\mathcal{A}}(\mathscr{X})$ of all elements in $\mathcal{A}$ which induce a decomposable multiplication operator on $\mathscr{X}$‎. ‎In the case $\mathscr{X}=\mathcal{A}$‎, ‎${\rm Dec}_{\mathcal{A}}(\mathcal{A})$ is the well-known Apostol algebra of $\mathcal{A}$‎. ‎We show that ${\rm Dec}_{\mathcal{A}}(\mathscr{X})$ is intimately related with the largest spectrally separable subalgebra of $\mathcal{A}$ and in this context‎ ‎we give some results which are related to an open question if Apostol algebra is regular for any commutative algebra $\mathcal{A}$‎.‎ Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1155 1167 http://bims.iranjournals.ir/article_871_9f5eadc32836600803a25c1fd5936d46.pdf On a functional equation for symmetric linear operators on $C^{*}$ algebras A. Taghavi Faculty of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎Iran. author text article 2016 eng ‎Let $A$ be a $C^{*}$ algebra‎, ‎$T‎: ‎A\rightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),\;\;T(x^{*})=T(x)^{*}$‎. ‎We prove that under each of the following conditions‎, ‎$T$ must be the trivial map $T(x)=\lambda x$ for some $\lambda \in \mathbb{R}$: ‎‎ ‎i) $A$ is a simple $C^{*}$-algebra‎. ‎ii) $A$ is unital with trivial center and has a faithful trace such that each‎ ‎zero-trace element lies in the closure of the span of commutator elements‎. ‎iii) $A=B(H)$ where $H‎$‎ is a separable Hilbert space‎.  ‎For a given field $F$‎, ‎we consider a similar functional equation {$T(x)T(y) =T^{2}(xy), T(x^{tr})=T(x)^{tr},$} where $T$ is a linear map on $M_{n}(F)$ and‎ ‎"tr"‎ ‎is the transpose operator‎. ‎We prove that this functional equation has trivial solution for all $n\in \mathbb{N}$ if and only if $F$ is a formally real field‎. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1169 1177 http://bims.iranjournals.ir/article_872_fd7287eb7f1365d9156e9da3ccb25196.pdf The Fischer-Clifford matrices and character table of the maximal subgroup $2^9{:}(L_3(4){:}S_3)$ of $U_6(2){:}S_3$ A. L. Prins Department of‎ ‎Mathematics‎, ‎Faculty of Military Science, Stellenbosch‎ University‎‎, ‎Private Bag X2, Saldanha‎, ‎7395‎, ‎South Africa. author text article 2016 eng The full automorphism group of $U_6(2)$ is a group of the form $U_6(2){:}S_3$. The group $U_6(2){:}S_3$ has a maximal subgroup $2^9{:}(L_3(4){:}S_3)$ of order 61931520. In the present paper, we determine the Fischer-Clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(L_3(4){:}S_3)$. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1179 1195 http://bims.iranjournals.ir/article_873_6ec8116653a7fc6145c53dd9e3228b5f.pdf Some commutativity theorems for $*$-prime rings with $(\sigma,\tau)$-derivation M. Ashraf Department of Mathematics,‎ ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎202002, India. author N. Parveen Department of Mathematics,‎ ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎202002, ‎India. author text article 2016 eng ‎Let $R$ be a $*$-prime ring with center‎ ‎$Z(R)$‎, ‎$d$ a non-zero $(\sigma,\tau)$-derivation of $R$ with associated‎ ‎automorphisms $\sigma$ and $\tau$ of $R$‎, ‎such that $\sigma$‎, ‎$\tau$‎ ‎and $d$ commute with $'*'$‎. ‎Suppose that $U$ is an ideal of $R$ such that $U^*=U$‎, ‎and $C_{\sigma,\tau}=\{c\in‎ ‎R~|~c\sigma(x)=\tau(x)c~\mbox{for~all}~x\in R\}.$ In the present paper‎, ‎it is shown that if characteristic of $R$ is different from two and‎ ‎$[d(U),d(U)]_{\sigma,\tau}=\{0\},$ then $R$ is commutative‎. ‎Commutativity of $R$ has also been established in case if‎ ‎$[d(R),d(R)]_{\sigma,\tau}\subseteq C_{\sigma,\tau}.$ Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1197 1206 http://bims.iranjournals.ir/article_874_0ec3eca69c4da52c1cf3357568f2b7fd.pdf Common solutions to pseudomonotone equilibrium problems D. V. ‎Hieu Department of Mathematics‎, ‎Ha Noi University of Science‎, ‎VNU‎. ‎334,‎ ‎Nguyen Trai Street, ‎‎‎Ha Noi‎, ‎Vietnam. author text article 2016 eng ‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎. ‎In the cyclic algorithm‎, ‎using the known techniques‎, ‎we can perform and develop practical numerical experiments. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1207 1219 http://bims.iranjournals.ir/article_875_e39c67b7360a9dceda155977e3771762.pdf $\mathcal{X}$-injective and $\mathcal{X}$-projective complexes T. Özen Department of Mathematics‎, ‎Abant Izzet Baysal University‎, Gölköy Kampüsü Bolu, Turkey. author E. ‎Yıldırım Department of Mathematics‎, ‎Abant Izzet Baysal University‎, Gölköy Kampüsü Bolu, Turkey. author text article 2016 eng Let $\mathcal{X}$ be a class of $R$-modules‎. ‎In this paper‎, ‎we investigate \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and DG-injecti‎‎ve (projective) complexes‎. ‎We prove that some known results can be extended to the class of \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes for this general settings. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1221 1235 http://bims.iranjournals.ir/article_876_bcc953321d1ed4f3a9c517d160fe4c40.pdf Sufficient global optimality conditions for general mixed integer nonlinear programming problems J. Quan Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. author Z. Y. Wu School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China. author G. Q. Li School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China. author text article 2016 eng ‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are derived easily‎. ‎Numerical‎ ‎examples are also presented. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1237 1246 http://bims.iranjournals.ir/article_877_e02f8f1f336deb5527f980f598eefbff.pdf A note on Fouquet-Vanherpe’s question and Fulkerson conjecture F. Chen Institute of Statistics and Applied Mathematics‎, ‎Anhui University of Finance and Economics‎, ‎Bengbu‎, ‎Anhui‎, ‎233030‎, ‎P‎. ‎R‎. ‎China. author text article 2016 eng ‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe asked whether Petersen graph is the only one with that property‎. ‎H\"{a}gglund gave a negative answer to their question by constructing two graphs Blowup$(K_4‎, ‎C)$ and Blowup$(Prism‎, ‎C_4)$‎. ‎Based on the first graph‎, ‎Esperet et al‎. ‎constructed infinite families of cyclically 4-edge-connected snarks with excessive index at least five‎. ‎Based on these two graphs‎, ‎we construct infinite families of cyclically 4-edge-connected snarks $E_{0,1,2,\ldots‎, ‎(k-1)}$ in which $E_{0,1,2}$ is Esperet et al.'s construction‎. ‎In this note‎, ‎we prove that $E_{0,1,2,3}$ has excessive index at least five‎, ‎which gives a strongly negative answer to Fouquet and Vanherpe's question‎. ‎As a subcase of Fulkerson conjecture‎, ‎H\"{a}ggkvist conjectured that every cubic hypohamiltonian graph has a Fulkerson-cover‎. ‎Motivated by a related result due to Hou et al.'s‎, ‎in this note we prove that Fulkerson conjecture holds on some families of bridgeless cubic graphs. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1247 1258 http://bims.iranjournals.ir/article_878_1c321310c71687bcfea04de293b6da0f.pdf Operator-valued tensors on manifolds H. ‎Feizabadi Faculty of Mathematics & Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran. author N. Boroojerdian Faculty of Mathematics \& Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran. author text article 2016 eng ‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $\mathbb{R}$ by self-adjoint elements of a commutative $C^\star$-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian metrics to operator valued metrics‎. ‎Then‎, ‎in this new geometry‎, ‎some essential concepts of Riemannian geometry such as curvature tensor‎, ‎Levi-Civita connection‎, ‎Hodge star operator‎, ‎exterior derivative‎, ‎divergence,..‎. ‎will be considered. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1259 1277 http://bims.iranjournals.ir/article_879_44f3202eefb900362bb1960d135193a5.pdf Irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$ T. Le Mathematics Department‎, ‎North-West University‎, ‎Mafikeng‎, ‎South Africa. author text article 2016 eng ‎‎Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1279 1291 http://bims.iranjournals.ir/article_880_35a9b44674a8153d0f083d3be4621a0b.pdf On list vertex 2-arboricity of toroidal graphs without cycles of specific length H. Zhang School of Mathematical Science‎, ‎Huaiyin Normal University‎, 111 Changjiang West Road‎, ‎Huaian‎, ‎Jiangsu‎, 223300‎, ‎P‎. ‎R‎. ‎China. author text article 2016 eng The vertex arboricity $\rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph‎. ‎A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$‎, ‎one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by every color class is a forest‎. ‎The smallest $k$ for a graph to be list vertex $k$-arborable is denoted by $\rho_l(G)$‎. ‎Borodin‎, ‎Kostochka and Toft (Discrete Math‎. ‎214 (2000) 101-112) first introduced the list vertex arboricity of $G$‎. ‎In this paper‎, ‎we prove that $\rho_l(G)\leq 2$ for any toroidal graph without 5-cycles‎. ‎We also show that $\rho_l(G)\leq 2$ if $G$ contains neither adjacent 3-cycles nor cycles of lengths 6 and 7. Bulletin of the Iranian Mathematical Society Iranian Mathematical Society (IMS) 1017-060X 42 v. 5 no. 2016 1293 1303 http://bims.iranjournals.ir/article_881_1c2751a2e851f892b91c1fd5de3e21f4.pdf