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