Bulletin of Iranian Mathematical Society
Volume:37 Issue: 1, 2011

We study the relationships between the Baer, quasi- Baer and p.q.-Baer property of an R-module M and the polynomial extensions of module M. As a consequence of our results, we obtain some results of [C.Y. Hong, N.K. Kim and T.K. Kwak, J. Pure Appl. Algebra 151 (2000) 215-226.] and [E. Hashemi and A. Moussavi, Acta Math. Hungar. 107 (2005) 207-224.].

We first extend the Arens-Royden theorem to unital, commutative Fr´echet algebras under certain conditions. Then, we show that if A is a uniform Fr´echet algebra on X = MA, where MA is the continuous character space of A, then A does not havedense invertible group, if we impose some conditions on X. On the other hand, if A has dense invertible group, then it is shown that A = C(X), with certain conditions on X. Thus, the results of Dawson and Feinstein on denseness of the invertible group inBanach algebras are extended to uniform Fr´echet algebras.

We define algebras of triple semigroup and DeMorgan triple semigroup and by defining three Mann’s compositions and one unary operation on the set of 3-place(ternary) functions over some set, we construct a DeMorgan triple semigroup of 3-place (ternary) functions and so find an abstract characterization of this algebras.

We introduce a modified Noor iteration scheme generated by an infinite family of strict pseudo-contractive mappings and prove the strong convergence theorems of the scheme in the framework of q−uniformly smooth and strictly convex Banach space. Results shown here are extensions and refinements of previously known results.

In this paper, we introduce the concept of g-Bessel multipliers which generalizes Bessel multipliers for g-Bessel sequences and we study the properties of g-Bessel multipliers when the symbol m 2 `1, `p, `1. Also, we review the behavior of these operatorswhen the parameters are changing. Furthermore, we show that equivalent g-frames have equivalent multipliers and conversely. Finally, we specialize the results to fusionframes.

Let Qn(x) =Pni=0 Aixi be a random algebraic polynomialwhere the coefficients A0,A1, · · · form a sequence of centeredGaussian random variables. Moreover, assume that the increments
j = Aj −Aj−1, j = 0, 1, 2, · · ·, are independent, assuming A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We obtain the asymptotic behaviour of the expected number of u-sharp crossings, u > 0, ofpolynomial Qn(x). We refer to u-sharp crossings as those zero upcrossings with slope greater than u, or those down-crossings with slope smaller than −u. We consider the cases where u is unbounded and increasing with n, say u = o(n5/4), and u = o(n3/2).

We show that typical elements of the set of continuous functions from a compact differentiable manifold M to Rn are nowhere differentiable. Then, we study the box dimensions of typical elements in the set of images of M in Rn.

We investigate '-factorable operators and Weyl-Heisenberg frames with respect to a function-valued inner product, the so called '-bracket product on L2(G), where G is a locally compact abelian group and ' is a topological isomorphism on G. We introduce'-factorable operators on L2(G) and extend the Riesz Representation Theorems for these operators. Finally, as an application of the '-bracket product, we show that several well known theorems for Weyl-Heisenberg frames in L2(R) remain valid in L2(G), and they are unified within of group theory, in connection with the '-bracket product.

We provide an elementary proof of the fact that every bijective multiplicative map ': A! B of standard operator algebras on real normed spaces X and Y, is respectively of the form '(A) = TAT−1 and A 2 A, where T: X! Y is a bounded invertible linear operator.

In this paper, we discuss the existence of double Sumudu transform and study relationships between Laplace and Sumudu transforms. Further, we apply two transforms to solve linear ordinary differential equations with constant coefficients and non constantcoefficients.

We introduce an iterative algorithm for finding a common element of the set of fixed points for an infinite family of nonexpansive mappings, the set of solutions of the variational inequalities for a family of -inverse-strongly monotone mappings and the setof solutions of a system of equilibrium problems in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Moreover, weapply our result to the problem of finding a common fixed point of a family of strictly pseudocontractive mappings.

In [H. Mansouri and C. Roos, Numer. Algorithms 52 (2009) 225-255.], Mansouri and Ross presented a primal-dual infeasible interior-point algorithm with full-Newton steps whose iteration bound coincides with the best known bound for infeasible interior-point methods. Here, we introduce a slightly different algorithm with a different search direction and show that the same complexity result is obtained using a simpler analysis.