فهرست مطالب
Bulletin of Iranian Mathematical Society
Volume:40 Issue: 2, 2014
- تاریخ انتشار: 1393/02/23
- تعداد عناوین: 17
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Pages 295-323A 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.Keywords: Matrix equation, Reflexive matrix, Anti, reflexive matrix
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Pages 325-337Let $T$ 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.Keywords: vector, valued Hardy space, composition operator, linear fractional map, weak compactness
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Pages 339-355In 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.Keywords: multivariate stationary stable processes, flows, periodic, cyclic flows
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Pages 357-371In 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.Keywords: System of linear equations, Preconditioner, AOR iterative method, Z, matrix
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Pages 373-386In 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.Keywords: Ostrowski type inequalities, preinvex function, condition C
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Pages 387-398Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi: Hrightarrow 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 $Tin text{End}(V)$. 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.Keywords: symmetry class of tensors, decomposable numerical range, induced operator
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Pages 399-411Classes 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.Keywords: ABS algorithms, WZ factorization, ZW factorizatio, WTW factorization, ZTZ factorization, QZ factoriation, QW factorization
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Pages 413-421In 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.Keywords: Regular, inverse semigroup, Green relations, Green graphs
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Pages 423-431Let $H$ 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 $Astar H$. Results from the literature are generalized.Keywords: Hopf algebras, Gorenstein global dimensions, Morita equivalence, twisted smash products
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Pages 433-445In this paper, we introduce the notion of $(m,n)$- algebr aically 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.Keywords: (n, m), pure exact, m), pure injective, m), algebraically compact, pure injective, algebraically compac
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Pages 447-458In 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.Keywords: Fredholm integral equations, Monte Carlo method, Continuous Markov chain, Neumann series expansion, Importance sampling
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Pages 459-472In 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
Keywords: I, statistical convergence, I, lacunary statistical convergence, statistical convergence of order $alpha$
Pages 473-480
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: $Gcong S_p$ if and only if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$, where $p$ is a prime.
Keywords:
characterization, symmetric group, prime graph
Pages 481-504
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.
Keywords:
fixed point, $delta$, strongly monotone, $lambda$, strictly pseudo, contractive
Pages 505-520
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.
Keywords:
Arens regularity, bilinear mappings, Topological center, Unital A, module, Module action
Pages 521-530
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 $psi_{y^*}(T)= T^*y^*.$
Keywords:
weak Banach, Saks property, P, property, Schauder decomposition, compact operator, completely continuous operator
Pages 531-540
Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$, $a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). 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.
Keywords:
Quasi, local ringý, prime idealý, ýalmost prime idealý, ý$(n, 1, n)$, weakly prime idealý, n)$, $Phi, m$, prime idealý