Bulletin of the Iranian Mathematical Society
text
article
2014
eng
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
http://bims.iranjournals.ir/article_497_9cc7d666394b4cb7b0b14500de20ed08.pdf
Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
Mehdi
Dehghan
Prof.
author
Masoud
Hajarian
Department of Mathematics
Faculty of Mathematical Sciences
Shahid Beheshti University, G.C.,
Evin, Tehran 19839
Iran
author
text
article
2014
eng
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexive and anti-reflexive matrices. The convergence of the iterative methods is also proposed. Finally, a numerical example is given to show the efficiency of the presented results.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
295
323
http://bims.iranjournals.ir/article_498_e826f705a8bcdc93e8b4e86ef70af573.pdf
Bilateral composition operators on vector-valued Hardy spaces
Hamid
Rezaei
Yasouj University
author
text
article
2014
eng
Let $T$ be a bounded operator on the Banach space $X$ and $\ph$ be an analytic self-map of the unit disk $\Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{\ph, T}: f \ri T \circ f \circ \ph$ on the vector-valued Hardy space $H^p(X)$ for $1 \leq p \leq +\infty$. Compactness and weak compactness of $C_{\ph, T}$ on $H^p(X)$ are characterized and when $p=2$, a concrete formula for its adjoint is given.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
325
337
http://bims.iranjournals.ir/article_499_de6518007dfc715846c6f2e18e395a31.pdf
Periodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows
Afshin
Parvardeh
Academic Professor
author
Sareh
Goliforushani
Academic Professor
author
Ahmad Reza
Soltani
Academic Professor
author
text
article
2014
eng
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a periodic-cyclic flow.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
339
355
http://bims.iranjournals.ir/article_500_37ead49e70ddc70e5d343101a2a9cebe.pdf
Improvements of two preconditioned AOR iterative methods for Z-matrices
Mohsen
Hasani
Islamic Azad University
author
Davod
Khojasteh Salkuyeh
University of Guilan
author
text
article
2014
eng
In this paper, we propose two preconditioned AOR iterative methods to solve systems of linear equations whose coefficient matrices are Z-matrix. These methods can be considered as improvements of two previously presented ones in the literature. Finally some numerical experiments are given to show the effectiveness of the proposed preconditioners.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
357
371
http://bims.iranjournals.ir/article_501_8a1c873672368b347de367b050646428.pdf
Ostrowski type inequalities for functions whose derivatives are preinvex
Imdat
Işcan
Giresun University
author
text
article
2014
eng
In this paper, making use of a new identity, we establish new inequalities of Ostrowski type for the class of preinvex functions and gave some midpoint type inequalities.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
373
386
http://bims.iranjournals.ir/article_502_aa3a54cac93833e16043e4a243cffb1f.pdf
On the decomposable numerical range of operators
Yousef
Zamani
Sahand University of Technology
author
Sima
Ahsani
Sahand University of Technology
author
text
article
2014
eng
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $\chi :H\rightarrow \mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{\chi}(H)$ the symmetry class of tensors associated with $H$ and $\chi$. Let $K(T)\in
(V_{\chi}(H))$ be the operator induced by $T\in
\text{End}(V)$. The decomposable numerical range $W_{\chi}(T)$ of
$T$ is a subset of the classical numerical range $W(K(T))$ of $K(T)$ defined as:$$
W_{\chi}(T)=\{(K(T)x^{\ast }, x^{\ast}):x^{\ast }\ is a decomposable unit tensor\}.$$
In this paper, we study the interplay between the geometric properties of $W_{\chi}(T)$ and the algebraic properties of $T$. In fact, we extend some of the results of [C. K. Li and A. Zaharia, Decomposable numerical range on orthonormal decomposable tensors, Linear Algebra Appl. 308 (2000), no, 1-3, 139--152] and [C. K. Li and A. Zaharia, Induced operators on symmetry classes of tensors, Trans. Amer. Math. Soc. 354 (2002), no. 2, 807--836], to non-linear irreducible characters.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
387
398
http://bims.iranjournals.ir/article_503_b7e2e3cc8e6d67d8124fdf498d842b65.pdf
WZ factorization via Abay-Broyden-Spedicato algorithms
Effat
Golpar-Raboky
University of Qom
author
N.
Mahdavi-Amiri
Sharif University of Technology
author
text
article
2014
eng
Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as the $W^TW$ and $Z^TZ$ factorizations of a symmetric positives definite matrix. We also describe the QZ and the QW factorizations, with Q orthogonal, and show how to appropriate the parameters of the ABS algorithms to compute these factorizations.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
399
411
http://bims.iranjournals.ir/article_504_cc2f035a33cf3308b3f1d82d42cd6624.pdf
A graphical difference between the inverse and regular semigroups
Ayoub
Gharibkhajeh
Islamic Azad university North-Tehran Branch
author
Hossein
Doostie
Science and Research, Islamic Azad University Tehran- Iran
author
text
article
2014
eng
In this paper we investigate the Green graphs for the regular and inverse semigroups by considering the Green classes of them. And by using the properties of these semigroups, we prove that all of the five Green graphs for the inverse semigroups are isomorphic complete graphs, while this doesn't hold for the regular semigroups. In other words, we prove that in a regular semigroup $S$ two Green graph $\Gamma_{\mathcal{L}}(S)$ and $\Gamma_{\mathcal{H}}(S)$ are isomorphic, however, the other three Green graphs are non-isomorphic to them.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
413
421
http://bims.iranjournals.ir/article_505_8d4a7f029daec49b029448a7f5252b20.pdf
Gorenstein global dimensions for Hopf algebra actions
Qunxing
Pan
Department of Mathematics, Nanjing Agricultural University
author
Faqun
Cai
Department of Economic Management, Nanjing College of Chemical Technology
author
text
article
2014
eng
Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra. In this paper, we investigate Gorenstein global dimensions for Hopf algebras and twisted smash product algebras $A\star H$. Results from the literature are generalized.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
423
431
http://bims.iranjournals.ir/article_506_9440f67571725993f34bcd0d32f3296c.pdf
$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity
Mahmood
Behboodi
Isfahan University of Technology
author
Atefeh
Ghorbani
Isfahan University of Technology
author
Seyed Hossein
Shojaee
Isfahan university of technology
author
text
article
2014
eng
In this paper, we introduce the notion of $(m,n)$-algebraically compact modules as an analogue of algebraically compact modules and then we show that $(m,n)$-algebraically compactness and $(m,n)$-pure injectivity for modules coincide. Moreover, further characterizations of a $(m,n)$-pure injective module over a commutative ring are given.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
433
445
http://bims.iranjournals.ir/article_507_09d25bec7f5a7b3bdf5caa983c9d38ba.pdf
A Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind
Rahman
Farnoosh
School of Mathematics, Iran University of Science and Technology.
author
Mahboubeh
Aalaei
School of Mathematics, Iran University of Science and Technology.
author
text
article
2014
eng
In the present work, a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind. The solution of the integral equation is described by the Neumann series expansion. Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method. An algorithm is proposed to simulate a continuous Markov chain with probability density function arisen from an importance sampling technique. Theoretical results are established in a normed space to justify the convergence of the proposed method. The method has a simple structure and it is a good candidate for parallelization because of the fact that many independent sample paths are used to estimate the solution. Numerical results are performed in order to confirm the efficiency and accuracy of the present work.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
447
458
http://bims.iranjournals.ir/article_508_c94cabec98592f562c8a3e4567221f96.pdf
On $I$-statistical and $I$-lacunary statistical convergence of order $\alpha$
Pratulananda
Das
Jadavpour University
author
Ekrem
Savas
Istanbul Commerce University
author
text
article
2014
eng
In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, $I$-statistical convergence and $I$-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of $\mathbb{N}$) and introduce the notions of $I$-statistical convergence of order $\alpha$ and $I$-lacunary statistical convergence of order $\alpha$, where $0<\alpha< 1$. We mainly investigate their relationship and also make some observations about these classes and in the way try to give an answer to an open problem posed By Das, Savas and Ghosal in 2011. The study leaves a lot of interesting open problems.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
459
472
http://bims.iranjournals.ir/article_509_fe820582c3d031263737aa3b6e5a7007.pdf
A characterization of the symmetric group of prime degree
Qingliang
Zhang
School of Sciences, Nantong University, 226007, Nantong, P. R. China
author
Jinhua
Wang
School of Sciences, Nantong University, 226007, Nantong, P. R. China
author
Weijun
Liu
School of Sciences, Nantong University, 226007, Nantong, P. R. China
author
text
article
2014
eng
Let $G$ be a finite group and $\Gamma(G)$ the prime graph of $G$. Recently people have been using prime graphs to study simple groups. Naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? In this paper some results in this respect are obtained and as follows: $G\cong S_p$ if and only if $|G|=|S_p|$ and $\Gamma(G)=\Gamma(S_p)$, where $p$ is a prime.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
473
480
http://bims.iranjournals.ir/article_510_dee5dd7e5a3f35385b5ddbc71bf0cc1b.pdf
Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities
Hossein
Piri
Department of Mathematics,
University of Bonab, Bonab 5551761167, Iran
author
text
article
2014
eng
A new approximation method for the set of common fixed points of nonexpansive mappings and the set of solutions of systems of variational inequalities is introduced and studied. Moreover, we apply our main result to obtain strong convergence theorem to a common fixed point of a nonexpannsive mapping and solutions of a system of variational inequalities of an inverse strongly monotone mapping and strictly pseudo-contractive mapping of Browder-Petryshyn type.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
481
504
http://bims.iranjournals.ir/article_511_d0c5befcc72c8fd3470d89ccbd4d2ba3.pdf
Arens regularity of bilinear forms and unital Banach module spaces
kazem
Haghnejad Azar
Faculty member of Mohghegh Ardabili Universsity
author
text
article
2014
eng
Assume that $A$, $B$ are Banach algebras and that $m:Atimes Brightarrow B$, $m^prime:Atimes Arightarrow B$ are bounded bilinear mappings. We study the relationships between Arens regularity of $m$, $m^prime$ and the Banach algebras $A$, $B$. For a Banach $A$-bimodule $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}$-module. Let $Z_{e^{primeprime}}(B^{**})=B^{**}$ where $e^{primeprime}$ is a mixed unit of $A^{**}$. Then $B^*$ factors on both sides with respect to $A$ if and only if $B^{**}$ has a unit as $A^{**}$-module.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
505
520
http://bims.iranjournals.ir/article_512_7cc3f3725b7b3c1fe554083605917069.pdf
Weak Banach-Saks property in the space of compact operators
B. Khadijeh
Moosavi
Islamic Azad University, Bafgh Branch
author
S. Mohammad
Moshtaghioun
Yazd University
author
text
article
2014
eng
For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$, it is shown that the strong Banach-Saks-ness of all evaluation operators on ${mathcal M}$ is a sufficient condition for the weak Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in Y^*$, the evaluation operators on $mathcal{M}$ are defined by $phi_x(T)= Tx$ and $psi_{y^*}(T)= T^*y^*.$
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
521
530
http://bims.iranjournals.ir/article_513_d1178361f94ff0d658d4159f2e3bc59b.pdf
On generalisations of almost prime and weakly prime ideals
Mahdieh
Ebrahimpour
University of Vali-e-Asr
author
text
article
2014
eng
Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a<n> $(n-1,n)$-$\Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,\ldots,a_n\in R$, $a_1\cdots a_n\in P\backslash P^m$ ($a_1\cdots a_n\in P\backslash \{0\}$) implies $a_1\cdots a_{i-1}a_{i+1}\cdots a_n\in P$, for some $i\in\{1,\ldots,n\}$; ($m,n\geq 2$). In this paper several results concerning $(n-1,n)$-$\Phi_m$-prime and $(n-1,n)$-weakly prime ideals are proved. We show that in a Noetherian domain a $\Phi_m$-prime ideal is primary and we show that in some well known rings $(n-1,n)$-$\Phi_m$-prime ideals and $(n-1,n)$-prime ideals coincide.
Bulletin of the Iranian Mathematical Society
Iranian Mathematical Society (IMS)
1017-060X
40
v.
2
no.
2014
531
540
http://bims.iranjournals.ir/article_514_6d6ae9529874c4c6f84dc631664e5962.pdf