Bulletin of the Iranian Mathematical Society
text
article
2017
eng
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
http://bims.iranjournals.ir/article_989_5c1a0a5ede9dce9b4a8be03816801868.pdf
The associated measure on locally compact cocommutative KPC-hypergroups
S. M.
Tabatabaie
Department of Mathematics, The University of Qom, 3716146611, Iran.
author
F.
Haghighifar
Department of Mathematics, The University of Qom, 371614\newline 6611, Iran.
author
text
article
2017
eng
We study harmonic analysis on cocommutative KPC-hyper-groups, which is a generalization of DJS-hypergroups, introduced by Kalyuzhnyi, Podkolzin and Chapovsky. We prove that there is a relationship between the associated measures $\mu$ and $\gamma \mu$, where $\mu$ is a Radon measure on KPC-hypergroup $Q$ and $\gamma$ is a character on $Q$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
1
15
http://bims.iranjournals.ir/article_990_a23635573325622f485242df74978aa1.pdf
Modules of the toroidal Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$
N.
Jing
Department of Mathematics, Shanghai University, Shanghai 200444, China.
author
C.
Wang
School of Information and Mathematics, Yangtze University, Jingzhou 434023, China.
author
text
article
2017
eng
Highest weight modules of the double affine Lie algebra $\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal affine Lie subalgebras, and highest weight modules are described under the condition $c_1>0$ and $c_2=0$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
17
24
http://bims.iranjournals.ir/article_991_ec11bdd79102d5e774ba83e2d7387147.pdf
$\varphi$-Connes amenability of dual Banach algebras
A.
Ghaffari
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.
author
S.
Javadi
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran.
author
text
article
2017
eng
Generalizing the notion of character amenability for Banach algebras, we study the concept of $\varphi$-Connes amenability of a dual Banach algebra $\mathcal{A}$ with predual $\mathcal{A}_*$, where $\varphi$ is a homomorphism from $\mathcal{A}$ onto $\Bbb C$ that lies in $\mathcal{A}_*$. Several characterizations of $\varphi$-Connes amenability are given. We also prove that the following are equivalent for a unital weakly cancellative semigroup algebra $l^1(S)$: (i) $S$ is $\chi$-amenable. (ii) $l^1(S)$ is $\hat{\chi}$-Connes amenable. (iii) $l^1(S)$ has a $\hat{\chi}$-normal, virtual diagonal.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
25
39
http://bims.iranjournals.ir/article_992_6d8636f6087c3fdc1f05ec75a202eb7d.pdf
Clifford-Fischer theory applied to a group of the form $2_{-}^{1+6}{:}((3^{1+2}{:}8){:}2)$
A. B. M.
Basheer
School of Mathematical Sciences, North-West University (Mafikeng), P Bag X2046, Mmabatho 2735, South Africa.
author
J.
Moori
School of Mathematical Sciences, North-West University (Mafi-keng), P Bag X2046, Mmabatho 2735, South Africa.
author
text
article
2017
eng
In our paper [A. B. M. Basheer and J. Moori, On a group of the form $2^{10}{:}(U_{5}(2){:}2)$] we calculated the inertia factors, Fischer matrices and the ordinary character table of the split extension $ 2^{10}{:}(U_{5}(2){:}2)$ by means of Clifford-Fischer Theory. The second inertia factor group of $2^{10}{:}(U_{5}(2){:}2)$ is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{:}8){:}2).$ The purpose of this paper is the determination of the conjugacy classes of $\overline{G}$ using the coset analysis method, the determination of the inertia factors, the computations of the Fischer matrices and the ordinary character table of the split extension $\overline{G}=2_{-}^{1+6}{:}((3^{1+2}{:}8){:}2)$ by means of Clifford-Fischer Theory. Through various theoretical and computational aspects we were able to determine the structures of the inertia factor groups. These are the groups $H_{1} = H_{2} = (3^{1+2}{:}8){:}2,\ $ $H_{3} =QD_{16}$ and $H_{4} = D_{12}.$ The Fischer matrices $\mathcal{F}_{i}$ of $\overline{G},$ which are complex valued matrices, are all listed in this paper and their sizes range between 2 and 5. The full character table of $\overline{G},$ which is $41 \times 41$ complex valued matrix, is available in the PhD thesis of the first author, which could be accessed online.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
41
52
http://bims.iranjournals.ir/article_993_8b52bcdde77ab521f07a4dc12e8b2f9c.pdf
Construction of measures of noncompactness of $C^k(\Omega)$ and $C^k_0$ and their application to functional integral-differential equations
R.
Arab
Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
author
R.
Allahyari
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
author
A.
Shole Haghighi
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
author
text
article
2017
eng
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel\`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixed point theorem associated with these new measures of noncompactness. Further, some examples are presented to show the efficiency of our results.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
53
67
http://bims.iranjournals.ir/article_994_cd6cfba8a4671e144751135c1b54b0c3.pdf
Some lower bounds for the $L$-intersection number of graphs
B.
Omoomi
Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran.
author
Z.
Maleki
Department of Mathematical Sciences, Isfahan University of Technology,
84156-83111, Isfahan, Iran
author
text
article
2017
eng
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v \subseteq \{1,\dots, l\}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u \cap A_v|\in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the vertices in different parts. In this paper, some lower bounds for the (bipartite) $L$-intersection number of a graph for various types $L$ in terms of the minimum rank of graph are obtained. To achieve the main results we employ the inclusion matrices of set systems and show that how the linear algebra techniques give elegant proof and stronger results in some cases.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
69
78
http://bims.iranjournals.ir/article_995_9bdcf50ae5754e5585f6d9f15061a972.pdf
On dimension of a special subalgebra of derivations of nilpotent Lie algebras
S.
Sheikh-Mohseni
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
author
F.
Saeedi
Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
author
text
article
2017
eng
Let $L$ be a Lie algebra, $\mathrm{Der}(L)$ be the set of all derivations of $L$ and $\mathrm{Der}_c(L)$ denote the set of all derivations $\alpha\in\mathrm{Der}(L)$ for which $\alpha(x)\in [x,L]:=\{[x,y]\vert y\in L\}$ for all $x\in L$. We obtain an upper bound for dimension of $\mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classify all finite dimensional nilpotent Lie algebras $L$ over algebraically closed fields for which dim$\mathrm{Der}_c(L)$ attains its maximum value.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
79
93
http://bims.iranjournals.ir/article_996_759f8d9d27872918fa60879d5f1baaa4.pdf
Application of Hopf's lemma on contact CR-warped product submanifolds of a nearly Kenmotsu manifold
M. A.
Khan
Department of Mathematics, University of Tabuk, Kingdom of Saudi Arabia.
author
F. R.
Al-Solamy
Department of Mathematics, King Abdulaziz University, P.O. Box 80015, Jeddah 21589,
Kingdom of Saudi Arabia.
author
text
article
2017
eng
In this paper we consider contact CR-warped product submanifolds of the type $M = N_T\times_f N_\perp$, of a nearly Kenmotsu generalized Sasakian space form $\bar M(f_1, f_2, f_3)$ and by use of Hopf's Lemma we show that $M$ is simply contact CR-product under certain condition. Finally, we establish a sharp inequality for squared norm of the second fundamental form and equality case is discussed. The results in this paper generalize existing results in the literature.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
95
107
http://bims.iranjournals.ir/article_997_1702cd4c9ca4b5fd2b83f2047f8faeef.pdf
Structure of finite wavelet frames over prime fields
A.
Ghaani Farashahi
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria.
author
text
article
2017
eng
This article presents a systematic study for structure of finite wavelet frames over prime fields. Let $p$ be a positive prime integer and $\mathbb{W}_p$ be the finite wavelet group over the prime field $\mathbb{Z}_p$. We study theoretical frame aspects of finite wavelet systems generated by subgroups of the finite wavelet group $\mathbb{W}_p$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
109
120
http://bims.iranjournals.ir/article_998_dbe0ac2e91830adab113261e8b964e59.pdf
$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings
Y.
Kara
Hacettepe University, Faculty of Science, Department of Mathematics, 06532, Beytepe, Ankara, Turkey.
author
Adnan
Tercan
Hacettepe University Department of Mathematics
author
R.
Yaşar
Hacettepe University, Faculty of Science, Department of Mathematics, 06532, Beytepe, Ankara, Turkey.
author
text
article
2017
eng
A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper surfaces in projective spaces over complex numbers and obtain results when the $PI$-extending property is inherited by direct summands. Moreover, we show that under some module theoretical conditions $PI$-extending modules with Abelian endomorphism rings have indecomposable decompositions. Finally, we apply our former results, getting that, under suitable hypotheses, the finite exchange property implies the full exchange property.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
121
129
http://bims.iranjournals.ir/article_999_9307a1ce4337ba7bd09adbd5dc888465.pdf
Embedding normed linear spaces into $C(X)$
M.
Fakhar
Department of Mathematics, University of Isfahan, Isfahan 81745--163, Iran, and, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395--5746, Tehran, Iran.
author
M. R.
Koushesh
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156--83111, Iran, and, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395--5746, Tehran, Iran.
author
M.
Raoofi
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156--83111, Iran.
author
text
article
2017
eng
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can indeed be chosen to be the Stone--Cech compactification of $L^*\setminus\{0\}$, where $L^*\setminus\{0\}$ is endowed with the supremum norm topology.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
131
135
http://bims.iranjournals.ir/article_1000_77895c4a78751ae5a2b08a3a3f7d20d2.pdf
Local tracial C*-algebras
J.
Yang
Department of Mathematics,
Shanghai Maritime University, Shanghai 200135, China.
author
Q.
Fan
Department of Mathematics,
Shanghai Maritime University, Shanghai 200135, China.
author
text
article
2017
eng
Let $\Omega$ be a class of unital $C^*$-algebras. We introduce the notion of a local tracial $\Omega$-algebra. Let $A$ be an $\alpha$-simple unital local tracial $\Omega$-algebra. Suppose that $\alpha:G\to $Aut($A$) is an action of a finite group $G$ on $A$ which has a certain non-simple tracial Rokhlin property. Then the crossed product algebra $C^*(G,A,\alpha)$ is a unital local tracial $\Omega$-algebra.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
137
145
http://bims.iranjournals.ir/article_1001_a2d9d7e3dfb2e41c26c653faf93ba36b.pdf
Positive solutions for asymptotically periodic Kirchhoff-type equations with critical growth
H.
Shi
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.
author
H.
Chen
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.
author
text
article
2017
eng
In this paper, we consider the following Kirchhoff-type equations: $-\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)\Delta u+V(x) u=\lambda$ $f(x,u)+u^{5}, \quad \mbox{in }\mathbb{R}^{3},$ $u(x)>0, \quad \mbox{in }\mathbb{R}^{3},$ $u\in H^{1}(\mathbb{R}^{3}) ,$ where $a,b>0$ are constants and $\lambda$ is a positive parameter. The aim of this paper is to study the existence of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth under some suitable assumptions on $V(x)$ and $f(x,u)$. Recent results from the literature are improved and extended.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
147
161
http://bims.iranjournals.ir/article_1002_618460655d8d3715c47ad9fa384f957c.pdf
Some compact generalization of inequalities for polynomials with prescribed zeros
H. A.
Soliman Mezerji
Freelance Mathematics Researcher, Mashhad, Iran.
author
S.
Ahamadi
Department of Mathematics, Semnan University, Semnan, Iran.
author
M.
Bidkham
Department of Mathematics, Semnan University, Semnan, Iran.
author
text
article
2017
eng
Let $p(z)=z^s h(z)$ where $h(z)$ is a polynomial of degree at most $n-s$ having all its zeros in $|z|\geq k$ or in $|z|\leq k$. In this paper we obtain some new results about the dependence of $|p(Rz)|$ on $|p(rz)| $ for $r^2\leq rR\leq k^2$, $k^2 \leq rR\leq R^2$ and for $R\leq r \leq k$. Our results refine and generalize certain well-known polynomial inequalities.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
163
170
http://bims.iranjournals.ir/article_1003_d592347981a519ad897b7a527448ae58.pdf
Finite $p$-groups and centralizers of non-cyclic abelian subgroups
J.
Wang
Department of Mathematics, Shanghai University, Shanghai
200444, P.R. China.
author
X.
Guo
Department of Mathematics, Shanghai University, Shanghai
200444, P.R. China.
author
text
article
2017
eng
A $p$-group $G$ is called a $\mathcal{CAC}$-$p$-group if $C_G(H)/H$ is cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $H\nleq Z(G)$. In this paper, we give a complete classification of finite $\mathcal{CAC}$-$p$-groups.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
171
192
http://bims.iranjournals.ir/article_1004_cd9f50a94bd9ce4c81bc763dd8930a0a.pdf
On semi-$\Pi$-property of subgroups of finite group
A.
Liu
School of Applied Mathematics, Chengu Information Technology, Chengdu 610225, P. R. China.
author
B.
Li
School of Applied Mathematics, Chengu Information Technology, Chengdu 610225, P. R. China.
author
text
article
2017
eng
Let $G$ be a group and $H$ a subgroup of $G$. $H$ is said to have semi-$\Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T$ has $\Pi$-property in $T$. In this paper, investigating on semi-$\Pi$-property of subgroups, we shall obtain some new description of finite groups.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
193
204
http://bims.iranjournals.ir/article_1005_3c8c90d6c9f8d87acf96e66eeee1e5f2.pdf
Infinitely many solutions for a class of $p$-biharmonic equation in $\mathbb{R}^N$
Q.
Chen
College of Science, Hohai University, Nanjing 210098, P.R. China; Yancheng Institute of Technology, Yancheng 224051, P.R. China.
author
C.
Chen
College of Science, Hohai University, Nanjing 210098, P.R. China.
author
text
article
2017
eng
Using variational arguments, we prove the existence of infinitely many solutions to a class of $p$-biharmonic equation in $\mathbb{R}^N$. The existence of nontrivial solution is established under a new set of hypotheses on the potential $V(x)$ and the weight functions $h_1(x), h_2(x)$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
205
215
http://bims.iranjournals.ir/article_1006_5c370b44c312119124b4e2eccc8fbc13.pdf
On the diameter of the commuting graph of the full matrix ring over the real numbers
J. M.
Grau
Departamento de Matemáticas, Universidad de Oviedo. Avenida Calvo Sotelo s/n, 33007 Oviedo, Spain.
author
A.
Oller-Marcén
Centro Universitario de la Defensa de Zaragoza. Carretera de Huesca s/n, 50090 Zaragoza, Spain.
author
C.
Tasis
Departamento de Matemáticas, Universidad de Oviedo. Avenida Calvo Sotelo s/n, 33007 Oviedo, Spain.
author
text
article
2017
eng
In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring $\mathrm{M}_n(\mathbb{R})$ is equal to $4$ if either $n=3$ or $n\geq5$. But the case $n=4$ remained open, since the diameter could be $4$ or $5$. In this work we close the problem showing that also in this case the diameter is $4$.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
217
221
http://bims.iranjournals.ir/article_1007_ccedbbc0a55f567b52de49bd6484f998.pdf
Existence of solutions for a variational inequality on the half-line
O.
Frites
Laboratory of Fixed Point Theory and Applications, 'Ecole Normale Sup'erieure,
Kouba, Algiers, Algeria.
author
T.
Moussaoui
Laboratory of Fixed Point Theory and Applications, 'Ecole Normale Sup'erieure,
Kouba, Algiers, Algeria.
author
D.
O'Regan
School of Mathematics, Statistics and Applied Mathematics,
National University of Ireland, Galway, Ireland, NAAM Research
Group, King Abdulaziz University, Jeddah, Saudi Arabia.
author
text
article
2017
eng
In this paper we study the existence of nontrivial solutions for a variational inequality on the half-line. Our approach is based on the non-smooth critical point theory for Szulkin-type functionals.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
223
237
http://bims.iranjournals.ir/article_1008_f94700157329996cdf03d2c2f8b2241a.pdf
Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces
K.
Sitthithakerngkiet
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB),
1518, Pracharat 1 Road, Wongsawang, Bangsue, Bangkok, 10800, Thailand
author
P.
Sunthrayuth
KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand.
author
P.
Kumam
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.
author
text
article
2017
eng
The purpose of this paper is to introduce a new mapping for a finite family of accretive operators and introduce an iterative algorithm for finding a common zero of a finite family of accretive operators in a real reflexive strictly convex Banach space which has a uniformly G\^ateaux differentiable norm and admits the duality mapping $j_{\varphi}$, where $\varphi$ is a gauge function invariant on $[0,\infty)$. Furthermore, we prove the strong convergence under some certain conditions. The results obtained in this paper improve and extend the corresponding ones announced by many others.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
43
v.
1
no.
2017
239
258
http://bims.iranjournals.ir/article_1009_079258258926c9d4634783d3b9662fee.pdf