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1.
In this paper, we show that, for every locally compact abelian group G, the following statements are equivalent:
- (i)
- G contains no sequence such that {0}∪{±xn∣n∈N} is infinite and quasi-convex in G, and xn?0;
- (ii)
- one of the subgroups {g∈G∣2g=0} or {g∈G∣3g=0} is open in G;
- (iii)
- G contains an open compact subgroup of the form or for some cardinal κ.
2.
Puiman Ng 《Journal of Pure and Applied Algebra》2011,215(10):2378-2384
This paper studies the existence of Auslander-Reiten sequences in subcategories of mod(Λ), where Λ is a finite dimensional algebra over a field. The two main theorems give necessary and sufficient conditions for the existence of Auslander-Reiten sequences in subcategories.
Theorem.
LetMbe a subcategory ofmod(Λ)closed under extensions and direct summands, and letMbe an indecomposable module inMsuch thatfor someinM. Then the following are equivalent.
- (i)
- has an-precover in the stable category,
- (ii)
- There is an Auslander-Reiten sequence0→X→Y→M→0inM.
3.
Let M be a closed 5-manifold of pinched curvature 0<δ?secM?1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds:
- (i)
- The center of the fundamental group has index ?w(δ), a constant depending on δ;
- (ii)
- and the fundamental group is a non-cyclic group of order ?C, a constant;
- (iii)
- The volume is less than ?(δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ?w, a constant.
4.
5.
6.
We present a new construction of non-classical unitals from a classical unital U in . The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of with the following three properties:
- (i)
- points of Π are those of ;
- (ii)
- lines of Π are certain lines and conics of ;
- (iii)
- the points in U form a non-classical B-M unital in Π.
7.
M. Jahangiri 《Journal of Pure and Applied Algebra》2009,213(4):573-581
Let R=?n≥0Rn be a homogeneous Noetherian ring, let M be a finitely generated graded R-module and let R+=?n>0Rn. Let b?b0+R+, where b0 is an ideal of R0. In this paper, we first study the finiteness and vanishing of the n-th graded component of the i-th local cohomology module of M with respect to b. Then, among other things, we show that the set becomes ultimately constant, as n→−∞, in the following cases:
- (i)
- and (R0,m0) is a local ring;
- (ii)
- dim(R0)≤1 and R0 is either a finite integral extension of a domain or essentially of finite type over a field;
- (iii)
- i≤gb(M), where gb(M) denotes the cohomological finite length dimension of M with respect to b.
8.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
- (a)
- (b)
- for z in Ω;
- (c)
- ; and
- (d)
- for z in Ω.
9.
The level of a vertex in a rooted graph is one more than its distance from the root vertex. A generalized Bethe tree is a rooted tree in which vertices at the same level have the same degree. We characterize completely the eigenvalues of the Laplacian, signless Laplacian and adjacency matrices of a weighted rooted graph G obtained from a weighted generalized Bethe tree of k levels and weighted cliques in which
- (1)
- the edges connecting vertices at consecutive levels have the same weight,
- (2)
- each set of children, in one or more levels, defines a weighted clique, and
- (3)
- cliques at the same level are isomorphic.
10.
Mohamed Aziz Taoudi 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):478-3452
In this paper we prove the following Krasnosel’skii type fixed point theorem: Let M be a nonempty bounded closed convex subset of a Banach space X. Suppose that A:M→X and B:X→X are two weakly sequentially continuous mappings satisfying:
- (i)
- AM is relatively weakly compact;
- (ii)
- B is a strict contraction;
- (iii)
- .
11.
12.
Guangshi Lü 《Journal of Number Theory》2009,129(11):2790-2800
Let λ(n) be the nth normalized Fourier coefficient of a holomorphic Hecke eigencuspform f(z) of even integral weight k for the full modular group. In this paper we are able to prove the following results.
- (i)
- For any ε>0, we have
13.
Let C be a closed convex subset of a uniformly smooth Banach space E and let T:C→C be a nonexpansive mapping with a nonempty fixed points set. Given a point u∈C, the initial guess x0∈C is chosen arbitrarily and given sequences , and in (0,1), the following conditions are satisfied:
- (i)
- ;
- (ii)
- αn→0, βn→0 and 0<a?γn, for some a∈(0,1);
- (iii)
- , and . Let be a composite iteration process defined by
14.
Jochen Wengenroth 《Journal of Functional Analysis》2003,201(2):561-571
In 1971 Palamodov proved that in the category of locally convex spaces the derived functors Extk(E,X) of Hom(E,·) all vanish if E is a (DF)-space, X is a Fréchet space, and one of them is nuclear. He conjectured a “dual result”, namely that Extk(E,X)=0 for all if E is a metrizable locally convex space, X is a complete (DF)-space, and one of them is nuclear. Assuming the continuum hypothesis we give a complete answer to this conjecture: If X is an infinite-dimensional nuclear (DF)-space, then
- (1)
- There is a normed space E such that Ext1(E,X)≠0.
- (2)
- where is a countable product of lines.
- (3)
- Extk(E,X)=0 for all k?3 and all locally convex spaces E.
15.
Yankui Song 《Topology and its Applications》2012,159(5):1462-1466
16.
Daqing Yang 《Discrete Mathematics》2009,309(13):4614-4623
Let be a directed graph. A transitive fraternal augmentation of is a directed graph with the same vertex set, including all the arcs of and such that for any vertices x,y,z,
- 1.
- if and then or (fraternity);
- 2.
- if and then (transitivity).
17.
Let R be a commutative local noetherian ring, and let L and L′ be R-modules. We investigate the properties of the functors and . For instance, we show the following:
- (a)
- if L and L′ are artinian, then is artinian, and is noetherian over the completion ;
- (b)
- if L is artinian and L′ is Matlis reflexive, then , , and are Matlis reflexive.
18.
Su Gao 《Advances in Mathematics》2008,217(2):814-832
A group G?Sym(N) is cofinitary if g has finitely many fixed points for every g∈G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results:
- (1)
- Assuming V=L, there is a set of permutations on N which generates a maximal cofinitary group.
- (2)
- Assuming V=L, there is a mad permutation family in Sym(N).
19.
20.
Edith Hemaspaandra Lane A. Hemaspaandra Stanis?aw P. Radziszowski 《Discrete Applied Mathematics》2007,155(2):103-118
We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:
- (1)
- , , , and .
- (2)
- For all k?2, and .
- (3)
- For all k?2, .
- (4)
- .
- (5)
- For all k?2, .