BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2011 | Volume:37 | Issue:1|Papers Count:20

We study the relationships between the Baer, quasi-Baer and p.q.-Baer property of anR-module M and the polynomial extensions of moduleM. As a consequence of our results.

We first extend the Arens-Royden theorem to unital, commutative Frechet algebras under certain conditions. Then, we show that if A is a uniform Frechet algebra on X=MA, where MA is the continuous character space of A, then A does not have dense 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 in Banach algebras are extended to uniform Frechet 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 Î l1, lp, l ¥. Also, we review the behavior of these operators when the parameters are changing.Furthermore, we show that equivalent g-frames have equivalent multipliers and conversely. Finally, we specialize the results to fusion frames.

Let Qn(x)= Si=0n Aixi be a random algebraic polynomial where the coefficientsA0, A1,… form a sequence of centered Gaussian random variables. Moreover, assume that the increments Dj=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, of polynomial 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 j-factorable operators and Weyl-Heisenberg frames with respect to a function-valued inner product, the so called j-bracket product on L2 (G), where G is a locally compact abelian group and j is a topological isomorphism on G. We introduce j-factorable operators on L2 (G) and extend the Riesz Representation Theorems for these operators. Finally, as an application of the j-bracket product, we show that several well known theorems for Weyl-Heisenberg frames inL2 (R) remain valid in L2 (G), and they are unified within of group theory, in connection with the j-bracket product.

Let A= (a n,k)n, k³0 be a non-negative matrix. Denote by L w, p, q (A), the supremum of those L, satisfying the following inequality: (Sn=0¥ wn (S n=0¥ an,k xk)q)1/q ³ L ( S n=0¥  wk xkp)1/pwhere, x ³ 0 and xÎlp (w) and also w= (wn) is a decreasing, nonnegative sequence of real numbers. If p=q, then we use L w,p (A) inested of L w,p,p (A). Here, we focus on the evaluation of L w,p (At) for a lower triangular matrix A, where, 0<p<1. In particular, we apply our results to summability matrices, weighted mean matrices, Norlund matrices.

We provide an elementary proof of the fact that every bijective multiplicative map p: A® B of standard operator algebras on real normed spaces X and Y is respectively of the form p (A) =TAT-1 and AÎ 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 constant coefficients.

We introduce a new explicit composite iteration scheme with a viscosity iteration method for approximating a common fixed point of Lipschitzian semigroup on a compact convex subset of a smooth Banach space. We show that the iterative sequence converges strongly to a common fixed point under some parameter controlling conditions. Our results extend and improve the recent results by Saeidi.

The cyclicizer of an element x of a group G is defined as CycG (x) = {y Î G ½< x, y> is cyclic}. Here, we introduce an n-cyclicizer group and show that there is no finite n-cyclicizer group for n=2, 3. We prove that for any positive integer n ¹2, 3, there exists a finite n-cyclicizer group and determine the structure of finite 4 and 6-cyclicizer groups. Also, we characterize finite 5, 7 and 8-cyclicizer groups.

We present an effective algorithm for minimization of locally nonconvex Lipschitz functions based on mollifier functions approximating the Clarke generalized gradient. To this aim, first we approximate the Clarke generalized gradient by mollifier subgradients.To construct this approximation, we use a set of averaged functions gradients. Then, we show that the convex hull of this set serves as a good approximation for the Clarke generalized gradient.Using this approximation of the Clarke generalized gradient, we establish an algorithm for minimization of locally Lipschitz functions. Based on mollifier subgradient approximation, we propose a dynamic algorithm for finding a direction satisfying the Armijo condition without needing many subgradient evaluations. We prove that the search direction procedure terminates after finitely many iterations and show how to reduce the objective function value in the obtained search direction. We also prove that the first order optimality conditions are satisfied for any accumulation point of the sequence constructed by the algorithm. Finally, we implement our algorithm with MATLAB codes and approximate averaged functions gradients by the Monte-Carlo method. The numerical results show that our algorithm is effectively more efficient and also more robust than the GS algorithm, currently perceived to be a competitive algorithm for minimization of nonconvex Lipschitz functions.

Motivated by [B. Han and Q. Mo, Adv. Comp. Math. 18(2003) 211-245] and [B. Han and Z. Shen, Constr. Approx. 29 (2009) 369-406], we propose dual two-direction frames in dual Sobolev spaces (Hs (R), H-s (R)), with s>0. Based on the dual two-direction frames from a pair of two-direction refinable functions, dual multiwavelet frames with symmetry{ Y l(x): = (y1l(x), y2l(x)) T}l=1 d and {y~ l (x): = (y~l1(x), y~l2(x)) T} l=1d can be constructed very easily. The vanishing moment of the constructed multiwavelet frames is discussed. An example is given to illustrate our results.

Let M n,m be the vector space of all n×m real matrices. For A, B Î M n, m, it is said that B is gd-majorized by A (written A>gd B) if for every xÎ Rn there exists a g-doubly stochastic matrix Dx such that Bx=Dx (Ax). Here, we show that if A>gb B, then there exists a g-doubly stochastic matrix D (independent of x) such that B=DA. Also, the possible structures of linear preserving gd-majorization functions from M n, m to Mn, k are found. Finally, all linear strongly preserving gd-majorization functions from Mn, m to M n, k are characterized.

Let L (B(H)) be the algebra of all linear operators on B(H) and P be a property on B(H). For f1, f2 L (B(H)), we say that f1~ pf2, whenever f1(T) has property P, if and only if f2 (T) has this property. In particular, if I is the identity map on B (H), then-f~PI means that f preserves property P in both directions. Each property P produces an equivalence relation on L (B(H)). We study the relation between equivalence classes with respect to different properties such as being Fredholm, semi-Fredholm, compact, finite rank, generalized invertible, or having a specific semi-index.

Let C be a nonempty closed convex subset of a complete CAT (0) space and T: C®C be a generalized nonexpansive mapping with F (T)={x Î C: T (x)=x} ¹Æ. Suppose {xn} is generated iteratively by x1 Î C,xn+1=tnT[snTxn Å (1-sn) xn] Å (1-tn) xn,for all n ³ 1, where {tn} and {sn} are real sequences in [0, 1] such that one of the following two conditions is satisfied: (i)tn Î [a, b] and sn Î [0, 1], for some a, b with 0<a £ b<1, (ii)tn Î [a, 1] and sn Î [a, b], for some a, b with 0<a £ b<1.Then, the sequence{xn}, D-converges to a fixed point of T. Our results extend the ones in Laokul and Panyanak.

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 set of 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, we apply 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.