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1.
Wen-Chung Huang 《Discrete Mathematics》2006,306(13):1351-1357
Let {n;b2,b1} denote the class of extended directed triple systems of the order n in which the number of blocks of the form [a,b,a] is b2 and the number of blocks of the form [b,a,a] or [a,a,b] is b1. In this paper, we have shown that the necessary and sufficient condition for the existence of the class {n;b2,b1} is b1≠1, 0?b2+b1?n and
- (1)
- for ;
- (2)
- for .
2.
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.
3.
4.
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.
5.
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.
6.
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, .
7.
Emma D'Aniello 《Topology and its Applications》2010,157(5):954-960
Let M be the Cantor space or an n-dimensional manifold with C(M,M) the set of continuous self-maps of M, and . We prove the following:
- (1)
- If α≠∞, then Sα(M) is a nowhere dense subset of M×C(M,M) that contains no isolated points.
- (2)
- If α?β, then .
8.
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.
9.
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.
10.
Dejan Brcanov 《Discrete Mathematics》2010,310(19):2550-2554
Let and be two n-tuples of nonnegative integers. An all-4-kings n-partite tournament T(V1,V2,…Vn) is said to have a -property if there exists an n-partite tournament T1(W1,W2,…,Wn) such that for each i∈{1,…,n}:
- (1)
- Vi⊆Wi;
- (2)
- exactly ti 4-kings of Vi are not 4-kings in T1;
- (3)
- exactly ci 4-kings of Wi are not vertices of Vi.
11.
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.
12.
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.
13.
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.
14.
In this paper, we consider the initial-boundary value problem of a semilinear parabolic equation with local and non-local (localized) reactions in a ball: ut=Δu+up+uq(x*,t) in B(R) where p,q>0,B(R)={x∈RN:|x|<R} and x*≠0. If max(p,q)>1, there exist blow-up solutions of this problem for large initial data. We treat the radially symmetric and one peak non-negative solution of this problem. We give the complete classification of total blow-up phenomena and single point blow-up phenomena according to p and q.
- (i)
- If or p=q>2, then single point blow-up occurs whenever solutions blow up.
- (ii)
- If 1<p<q, both phenomena, total blow-up and single point blow-up, occur depending on the initial data.
- (iii)
- If p?1<q, total blow-up occurs whenever solutions blow up.
- (iv)
- If max(p,q)?1, every solution exists globally in time.
15.
Andrei C?ld?raru 《Advances in Mathematics》2005,194(1):34-66
We continue the study of the Hochschild structure of a smooth space that we began in our previous paper, examining implications of the Hochschild-Kostant-Rosenberg theorem. The main contributions of the present paper are:
- •
- we introduce a generalization of the usual notions of Mukai vector and Mukai pairing on differential forms that applies to arbitrary manifolds;
- •
- we give a proof of the fact that the natural Chern character map K0(X)→HH0(X) becomes, after the HKR isomorphism, the usual one ; and
- •
- we present a conjecture that relates the Hochschild and harmonic structures of a smooth space, similar in spirit to the Tsygan formality conjecture.
16.
Yankui Song 《Topology and its Applications》2012,159(5):1462-1466
17.
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)
- .
18.
19.
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).
20.
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).