Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Forced oscillations of a damped‎ ‎Korteweg-de Vries equation on a periodic domain 1027 1038 EN M. Chen School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, ‎P‎. ‎R‎. ‎China. chenmochenmo.good@163.com ‎In this paper‎, ‎we investigate a damped Korteweg-de‎ ‎Vries equation with forcing on a periodic domain‎ ‎\$mathbb{T}=mathbb{R}/(2pimathbb{Z})\$‎. ‎We can obtain that if the‎ ‎forcing is periodic with small amplitude‎, ‎then the solution becomes‎ ‎eventually time-periodic. Forced oscillation‎,‎Korteweg-de Vries equation‎,‎stability‎,‎time-periodic solution‎ http://bims.iranjournals.ir/article_862.html http://bims.iranjournals.ir/article_862_ab038992016b1b175d32df688062e53c.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method 1039 1057 EN M‎. ‎ Garshasbi School of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran. m_garshasbi@iust.ac.ir F. ‎Hassani School of Mathematics‎, ‎Iran University of Science and Technology‎, ‎Tehran‎, ‎Iran. hasani_fh@yahoo.com ‎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. Inverse boundary problem,heat equation,boundary integral equation method,regularization.‎ http://bims.iranjournals.ir/article_863.html http://bims.iranjournals.ir/article_863_d469ccbf86a94e4c4831982ef32f13b6.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 On a generalization of condition (PWP) 1057 1076 EN X. Liang Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China.‎ ‎ lxl_119@126.com Y. Luo Department of Mathematics‎, ‎Lanzhou University‎, ‎Lanzhou‎, ‎Gansu 730000‎, ‎P.R. China. luoyf@lzu.edu.cn ‎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. \$S\$-act‎,‎Condition \$(PWP)\$‎,‎condition GP-\$(P)\$‎,‎generally left right ideal‎,‎quasi G-2-pure epimorphism‎ http://bims.iranjournals.ir/article_864.html http://bims.iranjournals.ir/article_864_6aca97cc012989be8545639bb27655ed.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Approximate solution of dual integral equations 1077 1086 EN S. ‎Ahdiaghdam Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. ahdi@marandiau.ac.ir K. ‎Ivaz Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. ivaz@tabrizu.ac.ir S. ‎Shahmorad Faculty of Mathematical Sciences‎, ‎University of Tabriz‎, ‎Tabriz‎, ‎Iran. shahmorad@tabrizu.ac.ir ‎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. Dual integral equation‎,‎Cauchy type integral‎ ‎equation‎,‎Fourier transform http://bims.iranjournals.ir/article_865.html http://bims.iranjournals.ir/article_865_36fdbd67705679576cbc4c02707cf62d.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 On the bounds in Poisson approximation for independent geometric distributed random variables 1087 1096 EN T. L. Hung University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7‎, ‎Ho Chi Minh city‎, ‎Vietnam. tlhung@ufm.edu.vn L. T. ‎Giang 0000-0001-7792-2191 University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7‎, ‎Ho Chi Minh city‎, ‎Vietnam. ltgiang@ufm.edu.vn ‎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. Poisson approximation‎,linear operator‎,geometric random variable‎,random sums‎ http://bims.iranjournals.ir/article_866.html http://bims.iranjournals.ir/article_866_5fccc709565917424a38a1fa4d5c23c3.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Which elements of a finite group are non-vanishing? 1097 1106 EN M. Arezoomand Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-83111, Isfahan‎, ‎Iran. arezoomand@math.iut.ac.ir B. Taeri Department of‎ ‎Mathematical Sciences, Isfahan University‎ ‎of Technology‎, ‎P‎.‎O‎. ‎Box 84156-838111, Isfahan‎, ‎Iran. b.taeri@cc.iut.ac.ir ‎Let \$G\$ be a finite group‎. ‎An element \$gin 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 \$Tsubseteq G\$‎, ‎is an undirected graph with‎ ‎vertex set \$Gtimes{1,2}\$ and edge set \${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}\$‎. ‎Let \${rm nv}(G)\$ be the set‎ ‎of all non-vanishing elements of a finite group \$G\$‎. ‎We show that \$gin 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) \$gin {rm nv}(G)\$ if and only if \$|Cl(g)|<p\$, <br />‎(2) if \$p\$ is the smallest prime divisor of \$|G|\$‎, ‎then \${rm nv}(G)=Z(G)\$‎. <br />‎‎Also we show that‎ <br />(a) if \${rm Cl}(g)={g,h}\$‎, ‎then \$gin {rm nv}(G)\$ if and only if \$gh^{-1}\$ has odd order‎, <br />(b) if \$|{rm Cl}(g)|in {2,3}\$ and \$({rm ord}(g),6)=1\$‎, ‎then \$gin {rm nv}(G)\$‎. Non-vanishing element‎,character‎,conjugacy class‎,‎Bi-Cayley graph‎ http://bims.iranjournals.ir/article_867.html http://bims.iranjournals.ir/article_867_e6b164bbe3a5bd8febacd1a5524efcc6.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Numerical approach for solving a class of nonlinear fractional differential equation 1107 1126 EN S. Irandoust-pakchin Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. s.irandoust@tabrizu.ac.ir M. Lakestani Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. lakestani@tabrizu.ac.ir H. ‎Kheiri Department of Applied Mathematics‎, ‎Faculty of Mathematical Sciences, University of Tabriz‎, ‎Tabriz‎, ‎Iran. h-kheiri@tabrizu.ac.ir ‎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. Fractional-order differential equation‎,‎operational matrix‎ ‎of fractional derivative‎,‎Caputo derivative‎,‎Chebyshev cardinal function‎,‎collocation method‎ http://bims.iranjournals.ir/article_868.html http://bims.iranjournals.ir/article_868_26827a7d21fe2b110ccd0dc9c647f92a.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 The use of inverse quadratic radial basis functions for the solution of an inverse heat problem 1127 1142 EN F. ‎Parzlivand Department of Mathematics‎, ‎Alzahra University‎, ‎Vanak‎, ‎Post Code 19834‎, ‎Tehran‎, ‎Iran. fparzlivand@gmail.com A. Shahrezaee Department of Mathematics‎, ‎Alzahra University‎, ‎Vanak‎, ‎Post Code 19834‎, ‎Tehran‎, ‎Iran. ashahrezaee@alzahra.ac.ir ‎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. Collocation‎,‎inverse parabolic problem‎,‎scattered data‎,‎RBFs‎ http://bims.iranjournals.ir/article_869.html http://bims.iranjournals.ir/article_869_56874af181e3b46e92db683c4c49a920.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Composition operators and natural metrics in meromorphic function classes \$Q_p\$ 1143 1154 EN A. Kamal Port Said University‎, ‎Faculty of Science‎, ‎Department of Mathematics, Port Said 42521‎, ‎Egypt. alaa_mohamed1@yahoo.com ‎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.\$ Meromorphic classes‎,composition operators‎,‎Lipschitz‎ ‎continuous http://bims.iranjournals.ir/article_870.html http://bims.iranjournals.ir/article_870_35e24f164aba15e6073c999fba0d70b5.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Multiplication operators on Banach modules over spectrally separable algebras 1155 1167 EN J. ‎Bračič Department of Materials and Metallurgy‎, ‎Faculty of Natural Sciences and Engineering‎, ‎University of Ljubljana‎, ‎Aškerčeva c‎. ‎12‎, ‎SI-1000 Ljubljana‎, ‎Slovenia. janko.bracic@fmf.uni-lj.si ‎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}\$‎.‎ Commutative Banach algebra‎,‎decomposable multiplication operator‎,‎spectrally separable algebra http://bims.iranjournals.ir/article_871.html http://bims.iranjournals.ir/article_871_9f5eadc32836600803a25c1fd5936d46.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 On a functional equation for symmetric linear operators on \$C^{*}\$ algebras 1169 1177 EN A. Taghavi Faculty of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎Iran. taghavi@du.ac.ir ‎Let \$A\$ be a \$C^{*}\$ algebra‎, ‎\$T‎: ‎Arightarrow 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}\$: ‎‎ <br />‎i) \$A\$ is a simple \$C^{*}\$-algebra‎. <br />‎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. <br />‎iii) \$A=B(H)\$ where \$H‎\$‎ is a separable Hilbert space‎.  <br />‎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 \$nin mathbb{N}\$ if and only if \$F\$ is a formally real field‎. "Functional Equations","\$C^{*}\$ algebras"," Formally real fields" http://bims.iranjournals.ir/article_872.html http://bims.iranjournals.ir/article_872_fd7287eb7f1365d9156e9da3ccb25196.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 The Fischer-Clifford matrices and character table of the maximal subgroup \$2^9{:}(L_3(4){:}S_3)\$ of \$U_6(2){:}S_3\$ 1179 1195 EN A. L. Prins Department of‎ ‎Mathematics‎, ‎Faculty of Military Science, Stellenbosch‎ University‎‎, ‎Private Bag X2, Saldanha‎, ‎7395‎, ‎South Africa. abraham.prins@ma2.sun.ac.za 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)\$. ‎Coset analysis‎,‎Fischer-Clifford matrices‎,‎permutation character‎,‎fusion map http://bims.iranjournals.ir/article_873.html http://bims.iranjournals.ir/article_873_6ec8116653a7fc6145c53dd9e3228b5f.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 11 01 Some commutativity theorems for \$*\$-prime rings with \$(sigma,tau)\$-derivation 1197 1206 EN M. Ashraf Department of Mathematics,‎ ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎202002, India. mashraf80@hotmail.com N. Parveen Department of Mathematics,‎ ‎Aligarh Muslim University‎, ‎Aligarh‎, ‎202002, ‎India. naziamath@gmail.com ‎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}={cin‎ ‎R~|~csigma(x)=tau(x)c~mbox{for~all}~xin 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}.\$ Prime-rings‎,‎derivations‎,‎ideal‎,involution map http://bims.iranjournals.ir/article_874.html http://bims.iranjournals.ir/article_874_0ec3eca69c4da52c1cf3357568f2b7fd.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 Common solutions to pseudomonotone equilibrium problems 1207 1219 EN D. V. ‎Hieu Department of Mathematics‎, ‎Ha Noi University of Science‎, ‎VNU‎. ‎334,‎ ‎Nguyen Trai Street, ‎‎‎Ha Noi‎, ‎Vietnam. dv.hieu83@gmail.com ‎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. Hybrid method‎,‎parallel algorithm‎,‎cyclic algorithm‎,‎extragradient method‎,‎equilibrium problem‎ http://bims.iranjournals.ir/article_875.html http://bims.iranjournals.ir/article_875_e39c67b7360a9dceda155977e3771762.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 \$mathcal{X}\$-injective and \$mathcal{X}\$-projective complexes 1221 1235 EN T. Özen Department of Mathematics‎, ‎Abant Izzet Baysal University‎, Gölköy Kampüsü Bolu, Turkey. ozen_t@ibu.edu.tr E. ‎Yıldırım Department of Mathematics‎, ‎Abant Izzet Baysal University‎, Gölköy Kampüsü Bolu, Turkey. emineyyildirim@gmail.com 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. Injective (Projective) complex‎,precover‎,preenvelope http://bims.iranjournals.ir/article_876.html http://bims.iranjournals.ir/article_876_bcc953321d1ed4f3a9c517d160fe4c40.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 Sufficient global optimality conditions for general mixed integer nonlinear programming problems 1237 1246 EN J. Quan Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China. quanjingcq@163.com Z. Y. Wu School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China. zhiyouwu@263.net G. Q. Li School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China. ligq@cqnu.edu.cn ‎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. Sufficient global optimality conditions‎,‎mixed‎ ‎integer nonlinear programming‎,‎mixed integer quadratic‎ ‎programming http://bims.iranjournals.ir/article_877.html http://bims.iranjournals.ir/article_877_e02f8f1f336deb5527f980f598eefbff.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 A note on Fouquet-Vanherpe’s question and Fulkerson conjecture 1247 1258 EN F. Chen Institute of Statistics and Applied Mathematics‎, ‎Anhui University of Finance and Economics‎, ‎Bengbu‎, ‎Anhui‎, ‎233030‎, ‎P‎. ‎R‎. ‎China. chenfuyuan19871010@163.com ‎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. Fulkerson-cover‎,excessive index‎,snark‎,‎hypohamiltonian graph‎ http://bims.iranjournals.ir/article_878.html http://bims.iranjournals.ir/article_878_1c321310c71687bcfea04de293b6da0f.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 Operator-valued tensors on manifolds 1259 1277 EN H. ‎Feizabadi Faculty of Mathematics & Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran. hassan_feiz1970@aut.ac.ir N. Boroojerdian Faculty of Mathematics \& Computer Science‎, ‎Amirkabir University of Technology‎, ‎Tehran‎, ‎Iran. broojerd@aut.ac.ir ‎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. Operator-valued tensors‎,operator-valued semi-Riemannian metrics‎,‎Levi-Civita connection‎,curvature‎,‎Hodge star operator http://bims.iranjournals.ir/article_879.html http://bims.iranjournals.ir/article_879_44f3202eefb900362bb1960d135193a5.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 Irreducible characters of Sylow \$p\$-subgroups of the Steinberg triality groups \${}^3D_4(p^{3m})\$ 1279 1291 EN T. Le Mathematics Department‎, ‎North-West University‎, ‎Mafikeng‎, ‎South Africa. lttung96@yahoo.com ‎‎Here we construct and count all ordinary irreducible characters of Sylow \$p\$-subgroups of the Steinberg triality groups \${}^3D_4(p^{3m})\$. Irreducible character‎,‎root system‎,‎Sylow subgroup‎,‎Steinberg triality http://bims.iranjournals.ir/article_880.html http://bims.iranjournals.ir/article_880_35a9b44674a8153d0f083d3be4621a0b.pdf
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 1735-8515 42 5 2016 10 01 On list vertex 2-arboricity of toroidal graphs without cycles of specific length 1293 1303 EN H. Zhang School of Mathematical Science‎, ‎Huaiyin Normal University‎, 111 Changjiang West Road‎, ‎Huaian‎, ‎Jiangsu‎, 223300‎, ‎P‎. ‎R‎. ‎China. hhzh@hytc.edu.cn 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. Vertex arboricity‎,‎toroidal graph‎,‎structure‎,‎cycle http://bims.iranjournals.ir/article_881.html http://bims.iranjournals.ir/article_881_1c2751a2e851f892b91c1fd5de3e21f4.pdf