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1.
Yankui Song 《Topology and its Applications》2012,159(5):1462-1466
2.
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.
3.
Tingxiu Wang 《Journal of Mathematical Analysis and Applications》2006,324(2):982-991
With the Lyapunov second method, we study the abstract functional differential equation, . We obtain inequalities of solutions and exponential stability with conditions like:
- (i)
- ,
- (ii)
- .
4.
Christopher Mouron 《Topology and its Applications》2009,156(3):558-576
Suppose that is a collection of disjoint subcontinua of continuum X such that limi→∞dH(Yi,X)=0 where dH is the Hausdorff metric. Then the following are true:
- (1)
- X is non-Suslinean.
- (2)
- If each Yi is chainable and X is finitely cyclic, then X is indecomposable or the union of 2 indecomposable subcontinua.
- (3)
- If X is G-like, then X is indecomposable.
- (4)
- If all lie in the same ray and X is finitely cyclic, then X is indecomposable.
5.
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
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7.
8.
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.
9.
Let G be a 2-dimensional connected, compact Abelian group and s be a positive integer. We prove that a classification of s-sheeted covering maps over G is reduced to a classification of s-index torsionfree supergroups of the Pontrjagin dual . Using group theoretic results from earlier paper we demonstrate its consequences. We also prove that for a connected compact group Y:
- (1)
- Every finite-sheeted covering map from a connected space over Y is equivalent to a covering homomorphism from a compact, connected group.
- (2)
- If two finite-sheeted covering homomorphisms over Y are equivalent, then they are equivalent as topological homomorphisms.
10.
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.
11.
Zongming Guo 《Journal of Differential Equations》2007,240(2):279-323
We consider the following Cauchy problem with a singular nonlinearity
- (P)
-
12.
Prem L. Sharma 《Discrete Mathematics》2008,308(24):6003-6008
Given a cubical box C2n+1 of side 2n+1 and a supply of 1×2×4 bricks, it is proved that if n≥2, then
- (A1)
- one can pack bricks for n odd, and bricks for n even,
- (A2)
- the capacity of C2n+1 is , and if n≡1 or 2 (mod4), this upper bound for the capacity can be reduced by 1.
13.
Zhi-Wei Sun 《Journal of Number Theory》2007,124(1):57-61
By some extremely simple arguments, we point out the following:
- (i)
- If n is the least positive kth power non-residue modulo a positive integer m, then the greatest number of consecutive kth power residues mod m is smaller than m/n.
- (ii)
- Let OK be the ring of algebraic integers in a quadratic field with d∈{−1,−2,−3,−7,−11}. Then, for any irreducible π∈OK and positive integer k not relatively prime to , there exists a kth power non-residue ω∈OK modulo π such that .
14.
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.
15.
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, .
16.
17.
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.
18.
Heybetkulu Mustafayev 《Journal of Functional Analysis》2007,248(2):428-447
A bounded linear operator T on a Banach space is said to be dissipative if ‖etT‖?1 for all t?0. We show that if T is a dissipative operator on a Banach space, then:
- (a)
- .
- (b)
- If σ(T)∩iR is contained in [−iπ/2,iπ/2], then
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20.
Linus Kramer 《Advances in Mathematics》2005,193(1):142-173
Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that and let Γ be a uniform lattice in G.
- (a)
- If CH holds, then Γ has a unique asymptotic cone up to homeomorphism.
- (b)
- If CH fails, then Γ has 22ω asymptotic cones up to homeomorphism.