BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2011 | Volume:37 | Issue:4|Papers Count:19

Here, a Finsler manifold (M, F) is considered with corresponding curvature tensor, regarded as 2-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of M determined by the curvature are introduced and called knullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Characterization of the k-nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of (M, F). The introduced k-nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and enlarged to Finsler setting by Akbar-Zadeh and contains it as a special case.

Relative to a hereditary torsion theory t we introduce a dimension for a module M, called t -rank of M, which coincides with the reduced rank of M whenever t is the Goldie torsion theory. It is shown that the t -rank of M is measured by the length of certain decompositions of the t -injective hull of M. Moreover, some relations between the t -rank of M and complements to t -torsionfree submodules of M are obtained.

A characteriation of continuity of the p-L-variation function is given and the Helly’s selection principle for LBV(p) functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class LBV(p) is found.

In this paper we introduce the notion of classical quasiprimary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same when Ris a domain with dim (R) £1.

Among the six classes of pro-2-groups of finite and fixed co-classes and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classesS5=<a, b ½ [b, a2] =1, a2= [b, a] 2, (b2) [b, a] b2=1>andS6=<a, t, b ½ a2=b2, [b, a]2=1, ta=t-1 [b, a], bt=aba>that have been conjectured to have deficiency zero presentations. In this paper we prove these conjectures. This completes the efficiency of all six classes of pro-2-groups of fixed co-classes.

Let A be a Banach algebra and M be a Banach A-bimodule. We say that a linear mapping d: A®M is a generalized s-derivation whenever there exists a s-derivation d: A ® M such that d(ab) =d(a) s(b) +s(a)d(b), for all a, bÎ A. Giving some facts concerning generalized s-derivations, we prove that if A is unital and if d: A®A is a generalized s-derivation and there exists an elementa 2 A such that d (a) is invertible, then d is continuous if and only if d is continuous. We also show that if M is unital, has no zero divisor and d: A® M is a generalized s-derivation such that d(1) ¹0, then ker (d) is a bi-ideal of A and ker(d) =ker (s) =ker (d), where 1 denotes the unit element of A.

Hardy and Littlewood conjectured that every large integer n that is not a square is the sum of a prime and a square. They believed that the number R (n) of such representations for n=p+m2 is asymptotically given byR(n) ~Ön/log n Õp=3¥ (1-1/p-1(n/p)),where p is a prime, m is an integer, and (n /p)denotes the Legendre symbol. Unfortunately, as we will later point out, this conjecture is difficult to prove and not all integers that are nonsquares can be represented as the sum of a prime and a square. Instead in this paper we prove two upper bounds for R (n) for n£N. The first upper bound applies to all n £ N. The second upper bound depends on the possible existence of the Siegel zero, and assumes its existence, and applies to all N/2<n £ N but at most <<N1−d1 of these integers, where N is a sufficiently large positive integer and 0<d1 £ 0.000025.

In this paper, we introduce a method by which we can find a close connection between the set of primez-ideals of C(X) and the same of C (Y), for some special subset Y of X. For instance, if Y=Coz (f) for some fÎC (X), then there exists a oneto-one correspondence between the set of primez-ideals of C (Y) and the set of primez-ideals of C (X) not containing f. Moreover, considering these relations, we obtain some new characterizations of classical concepts in the context of C (X). For example, X is an F-space if and only if the extension F: bY®bX of the identity map i: Y ® X is one-to-one, for each z-embedded subspace Y of X. Supposing p is a non-isolated Gd-point in X and Y=X \ {p}, we prove that Mp (X) contains no non-trivial maximal z-ideal if and only if pÎ bX is a quasi P-point if and only if each point of bY\ Y is a P-point with respect to Y.

For two algebras A and B, a linear map T: A® B is called separating, if x.y=0 implies Tx.Ty=0 for all x, yÎ A. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear separating map T: B®X, where B is a unital commutative semisimple regular Banach algebra satisfying the Ditkin’s condition and X is a left Banach module over a unital commutative Banach algebra. We also show that if X is hyper semisimple and T is bijective, then T is automatically continuous and T-1 is separating as well.

In this paper we introduce and study Besselian g-frames. We show that the kernel of associated synthesis operator for a Besselian g-frame is finite dimensional. We also introduce a-dual of a g-frame and we get some results when we use the Hilbert-Schmidt norm for the members of a g-frame in a finite dimensional Hilbert space.

Let S be an inverse semigroup and let E be its subsemigroup of idempotents. In this paper we define the n-th module co-homology group of Banach algebras and show that the first module co-homology group Hl1(E) 1 (l1 (S), l1(S) (n)) is zero, for every odd nÎN. Next, for a Clifford semigroupS we show that Hl1(E) 2 (l1(S), l1(S) (n)) is a Banach space, for every odd nÎN.

Let A be a Banach algebra and X be a Banach A-bimodule. Then S = AÅX, the l1-direct sum of A and X becomes a module extension Banach algebra when equipped with the algebra product (a, x).(a’, x’) = (aa’, ax’+xa’). In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on S = A Å A.

In this paper, several D and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results given by many authors.

A space Y is called an extension of a space X, if Y contains X as a dense subspace. Two extensions of X are said to be equivalent, if there is a homeomorphism between them which fixes X point-wise. For two (equivalence classes of) extensions Y and Y’ of X let Y£ Y’, if there is a continuous function of Y 0 intoY which fixes X point-wise. An extension Y of X is called a one-point extension, if Y \X is a singleton. An extension Y of X is called first-countable, if Y is first-countable at points of Y \X. Let P be a topological property. An extension Y of X is called a P-extension, if it has P.In this article, for a given locally compact paracompact space X, we consider the two classes of one-point Cech-complete, P extensions of X and one-point first-countable locally-P extensions of X, and we study their order-structures, by relating them to the topology of a certain subspace of the outgrowth bX\X. Here P is subject to some requirements and include s-compactness and the Lindelof property as special cases.

This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets A and B of a Hilbert space H and the set-valued maps F: A® 2B and G: A0®2A0, where A0= {xÎ A: ||x - y||=d (A, B) for some yÎ B}, best proximity pair theorems provide sufficient conditions that ensure the existence of anx0 2 A such thatd(G (x0), F (x0)) =d (A, B).

Let G be a p-group of nilpotency class k with finite exponent exp (G) and let m=|logp k|. We show that exp (M (c) (G)) divides exp (G) pm (k−1), for all c³1, where M (c) (G) denotes the c-nilpotent multiplier of G. This implies that exp (M (G)) divides exp (G), for all finite p-groups of class at most p − 1. Moreover, we show that our result is an improvement of some previous bounds for the exponent of M (c) (G) given by M. R. Jones, G. Ellis and P. Moravec in some cases.

In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to Z2. We also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

We observe some new characterizations of n-presented modules. Using the concepts of (n, 0)-injectivity and (n, 0)-flatness of modules, we also present some characterizations of right n-coherent rings, right n-hereditary rings, and right n-regular rings.

This paper considers the search problem, introduced by Srivastava [10]. This is a model discrimination problem. In the context of search linear models, discrimination ability of search de-signs has been studied by several researchers. Some criteria have been developed to measure this capability, however, they are re-stricted in a sense of being able to work for searching only one possible nonzero effect. In this paper, two criteria are proposed, based on Kullback-Leibler distance. These criteria are able to eval-uate the search ability of designs, without any restriction on the number of nonzero effects.